Attribute (.DBF) API

+ + +class FGMatch { + +private: + + // nodes breakdown + Point3D sw_node, se_node, ne_node, nw_node; + point_list north_nodes, south_nodes, east_nodes, west_nodes; + point_list body_nodes; + + // normals breakdown + Point3D sw_normal, se_normal, ne_normal, nw_normal; + point_list north_normals, south_normals, east_normals, west_normals; + point_list body_normals; + + // flags + bool sw_flag, se_flag, ne_flag, nw_flag; + bool north_flag, south_flag, east_flag, west_flag; + + // segment breakdown + triseg_list north_segs, south_segs, east_segs, west_segs; + triseg_list body_segs; + +public: + + enum neighbor_type { + SW_Corner = 1, + SE_Corner = 2, + NE_Corner = 3, + NW_Corner = 4, + NORTH = 5, + SOUTH = 6, + EAST = 7, + WEST = 8 + }; + + // Constructor + FGMatch( void ); + + // Destructor + ~FGMatch( void ); + + // load any previously existing shared data from all neighbors (if + // shared data for a component exists set that components flag to + // true + void load_neighbor_shared( FGConstruct& c ); + + // scan the specified share file for the specified information + void scan_share_file( const string& dir, const FGBucket& b, + neighbor_type search, neighbor_type dest ); + + // try to find info for the specified shared component + void load_shared( const FGConstruct& c, neighbor_type n ); + + // split up the tile between the shared edge points, normals, and + // segments and the body. This must be done after calling + // load_neighbor_data() and will ignore any shared data from the + // current tile that already exists from a neighbor. + void split_tile( FGConstruct& c ); + + // write the new shared edge points, normals, and segments for + // this tile + void write_shared( FGConstruct& c ); + + // reassemble the tile pieces (combining the shared data and our + // own data) + void assemble_tile( FGConstruct& c ); +}; + + +#endif // _MATCH_HXX diff --git a/src/BuildTiles/Parallel/Makefile.am b/src/BuildTiles/Parallel/Makefile.am new file mode 100644 index 00000000..11779441 --- /dev/null +++ b/src/BuildTiles/Parallel/Makefile.am @@ -0,0 +1,14 @@ +bin_PROGRAMS = fgfs-tools-server fgfs-tools-client + +fgfs_tools_server_SOURCES = server.cxx + +fgfs_tools_server_LDADD = -lsgbucket -lsgmisc + +fgfs_tools_client_SOURCES = client.cxx + +fgfs_tools_client_LDADD = -lsgbucket -lsgmisc + +INCLUDES += \ + -I$(top_builddir) \ + -I$(top_builddir)/Lib \ + -I$(top_builddir)/Construct diff --git a/src/BuildTiles/Parallel/client.cxx b/src/BuildTiles/Parallel/client.cxx new file mode 100644 index 00000000..52c543e7 --- /dev/null +++ b/src/BuildTiles/Parallel/client.cxx @@ -0,0 +1,283 @@ +/* remote_exec.c -- Written by Curtis Olson */ +/* -- for CSci 5502 */ + + +#ifdef HAVE_CONFIG_H +# include +#endif + +#ifdef HAVE_SYS_PARAM_H +# include // BSD macro definitions +#endif + +#include // FD_ISSET(), etc. +#include +#include +#include +#include +#include +#include + +#include + +#include +#include // atoi() +#include // bcopy() + +#include +#include + +#include + + +#define MAXBUF 1024 +#define BUSY_WAIT_TIME 30 + + +string work_base = ""; +string output_base = ""; + + +// check if it is ok to run +void check_master_switch() { + string file = work_base + "/Status/MASTER_ON"; + + FILE *fp = fopen( file.c_str(), "r" ); + if ( fp == NULL ) { + cout << "MASTER_ON file, " << file << " not found ... exiting." << endl; + exit(0); + } + + fclose( fp ); +} + + +// check if the host system is free of interactive users +int system_free() { + +#ifndef BSD + struct utmp *uptr; + + setutent(); + + while ( (uptr = getutent()) != NULL ) { + // cout << "NULL = " << NULL << " uptr = " << uptr << endl; + // cout << "user = ut_user = " << uptr->ut_user << endl; + // cout << "user = ut_type = " << uptr->ut_type << endl; + if (uptr->ut_type == USER_PROCESS) { + // found someone + endutent(); + return 0; + } + } + + endutent(); +#else +# warning Port me +#endif + + return 1; +} + + +int make_socket (char *host, unsigned short int port) { + int sock; + struct sockaddr_in name; + struct hostent *hp; + + // Create the socket. + sock = socket (PF_INET, SOCK_STREAM, 0); + if (sock < 0) { + perror ("socket"); + exit (EXIT_FAILURE); + } + + // specify address family + name.sin_family = AF_INET; + + // get the hosts official name/info + hp = gethostbyname(host); + + // Connect this socket to the host and the port specified on the + // command line + bcopy(hp->h_addr, &(name.sin_addr.s_addr), hp->h_length); + name.sin_port = htons(port); + + if ( connect(sock, (struct sockaddr *) &name, + sizeof(struct sockaddr_in)) < 0 ) + { + close(sock); + perror("Cannot connect to stream socket"); + return -1; + } + + return sock; +} + + +// connect to the server and get the next task +long int get_next_task( const string& host, int port, long int last_tile ) { + long int tile; + int sock, len; + fd_set ready; + char message[256]; + + // loop till we get a socket connection + while ( (sock = make_socket( (char *)host.c_str(), port )) < 0 ) { + // check if the master switch is on + check_master_switch(); + + sleep(1); + } + + // build a command string from the argv[]'s + sprintf(message, "%ld", last_tile); + + // send command and arguments to remote server + if ( write(sock, message, sizeof(message)) < 0 ) { + perror("Cannot write to stream socket"); + } + + // loop until remote program finishes + cout << "querying server for next task ..." << endl; + + FD_ZERO(&ready); + FD_SET(sock, &ready); + + // block until input from sock + select(32, &ready, 0, 0, NULL); + cout << " received reply" << endl; + + if ( FD_ISSET(sock, &ready) ) { + /* input coming from socket */ + if ( (len = read(sock, message, 1024)) > 0 ) { + message[len] = '\0'; + tile = atoi(message); + cout << " tile to construct = " << tile << endl; + close(sock); + return tile; + } else { + close(sock); + return -1; + } + } + + close(sock); + return -1; +} + + +// build the specified tile, return true if contruction completed +// successfully +bool construct_tile( const FGBucket& b, const string& result_file ) { + double angle = 10.0; + bool still_trying = true; + + while ( still_trying ) { + still_trying = false; + char angle_str[256]; + sprintf(angle_str, "%.0f", angle); + string command = "fgfs-construct "; + command += angle_str; + command += " " + work_base + " " + output_base + " " + + b.gen_index_str() + " > " + result_file + " 2>&1"; + cout << command << endl; + + system( command.c_str() ); + + FILE *fp = fopen( result_file.c_str(), "r" ); + char line[256]; + while ( fgets( line, 256, fp ) != NULL ) { + string line_str = line; + line_str = line_str.substr(0, line_str.length() - 1); + // cout << line_str << endl; + if ( line_str == "[Finished successfully]" ) { + fclose(fp); + return true; + } else if + ( (line_str.substr(0, 31) == "Error: Ran out of precision at") + || (line_str.substr(0, 22) == "Error: Out of memory.") + || (line_str.substr(0, 23) == "Error: Too many nodes.") ) { + if ( angle > 9.0 ) { + angle = 5.0; + still_trying = true; + } else if ( angle > 4.0 ) { + angle = 0.0; + still_trying = true; + } + } + + } + fclose(fp); + + if ( !still_trying && ( angle > 0.0 ) ) { + // build died for some reason ... lets try one last time + // with an interior angle restriction of 0 + angle = 0.0; + still_trying = true; + } + } + return false; +} + + +main(int argc, char *argv[]) { + long int tile, last_tile; + bool rude = false; + bool result; + + // Check usage + if ( argc < 5 ) { + printf("Usage: %s remote_machine port work_base output_base [ -r ]\n", + argv[0]); + exit(1); + } + + string host = argv[1]; + int port = atoi( argv[2] ); + work_base = argv[3]; + output_base = argv[4]; + + if ( argc == 6 ) { + string option = argv[5]; + if ( option == "-r" ) { + cout << "Running in RUDE mode!" << endl; + rude = true; + } + } + // get hostname and pid + char hostname[MAXBUF]; + gethostname( hostname, MAXBUF ); + pid_t pid = getpid(); + + char tmp[MAXBUF]; + sprintf(tmp, "/tmp/result.%s.%d", hostname, pid); + string result_file = tmp; + + last_tile = 0; + + // check if the master switch is on + check_master_switch(); + + while ( (tile = get_next_task( host, port, last_tile )) >= 0 ) { + result = construct_tile( FGBucket(tile), result_file ); + if ( result ) { + last_tile = tile; + } else { + last_tile = -tile; + } + + // check if the master switch is on + check_master_switch(); + + // niceness policy: This whole process should run niced. But + // additionally, if there is interactive use, we will sleep + // for 60 seconds between each tile to stagger out the load + // and impose less of an impact on the machine. + if ( !system_free() && !rude) { + cout << "System has interactive use, sleeping for " + << BUSY_WAIT_TIME << " seconds..." << endl; + sleep( BUSY_WAIT_TIME ); + } + } +} diff --git a/src/BuildTiles/Parallel/server.cxx b/src/BuildTiles/Parallel/server.cxx new file mode 100644 index 00000000..872a772e --- /dev/null +++ b/src/BuildTiles/Parallel/server.cxx @@ -0,0 +1,406 @@ +// remote_server.c -- Written by Curtis Olson +// -- for CSci 5502 + + +#include +#include +#include // FD_ISSET(), etc. +#include // for stat() +#include // for time(); +#include + +#include // bind +#include + +#include +#include + +#include +#include + +#include + + +#if defined (sun) +# define WAIT_ANY (pid_t)-1 +#endif + +#define MAXBUF 1024 + + +static double start_lon, start_lat; +static double lat = 0.0; +static double lon = 0.0; +static double dy = 0.0; +static int pass = 0; + + +int make_socket (unsigned short int* port) { + int sock; + struct sockaddr_in name; + socklen_t length; + + // Create the socket. + sock = socket (PF_INET, SOCK_STREAM, 0); + if (sock < 0) { + perror ("socket"); + exit (EXIT_FAILURE); + } + + // Give the socket a name. + name.sin_family = AF_INET; + name.sin_addr.s_addr = INADDR_ANY; + name.sin_port = 0 /* htons (port) */; + name.sin_addr.s_addr = htonl (INADDR_ANY); + if (bind (sock, (struct sockaddr *) &name, sizeof (name)) < 0) { + perror ("bind"); + exit (EXIT_FAILURE); + } + + // Find the assigned port number + length = sizeof(struct sockaddr_in); + if ( getsockname(sock, (struct sockaddr *) &name, &length) ) { + perror("Cannot get socket's port number"); + } + *port = ntohs(name.sin_port); + + return sock; +} + + +#if 0 +// let's keep these two around for a while in case we need to revive +// them + +// return true if file exists +static bool file_exists( const string& file ) { + struct stat buf; + + if ( stat( file.c_str(), &buf ) == 0 ) { + return true; + } else { + return false; + } +} + + + +// check if the specified tile has data defined for it [ depricated ] +static bool has_data( const string& path, const FGBucket& b ) { + string dem_file = path + ".dem" + "/" + b.gen_base_path() + + "/" + b.gen_index_str() + ".dem"; + if ( file_exists( dem_file ) ) { + return true; + } + + dem_file += ".gz"; + if ( file_exists( dem_file ) ) { + return true; + } + + return false; +} +#endif + + +// initialize the tile counting system +void init_tile_count( const string& chunk ) { + // pre-pass + pass = 0; + + // initial bogus value + lat = 100; + + // determine tile height + FGBucket tmp1( 0.0, 0.0 ); + dy = tmp1.get_height(); + + string lons = chunk.substr(0, 4); + string lats = chunk.substr(4, 3); + cout << "lons = " << lons << " lats = " << lats << endl; + + string horz = lons.substr(0, 1); + start_lon = atof( lons.substr(1,3).c_str() ); + if ( horz == "w" ) { start_lon *= -1; } + + string vert = lats.substr(0, 1); + start_lat = atof( lats.substr(1,2).c_str() ); + if ( vert == "s" ) { start_lat *= -1; } + + cout << "start_lon = " << start_lon << " start_lat = " << start_lat + << endl; +} + + +// return the next tile +long int get_next_tile() { + FGBucket b; + static double shift_over = 0.0; + static double shift_up = 0.0; + static bool first_time = true; + static time_t start_seconds, seconds; + static int counter; + static int global_counter; + + // first time this routine is called, init counters + if ( first_time ) { + first_time = false; + start_seconds = seconds = time(NULL); + counter = global_counter = 0; + } + + // cout << "lon = " << lon << " lat = " << lat << endl; + // cout << "start_lat = " << start_lat << endl; + + if ( lon > start_lon + 10.0 ) { + // increment to next row + // skip every other row (to avoid two clients working on + // adjacent tiles) + lat += 2.0 * dy; + + FGBucket tmp( 0.0, lat ); + double dx = tmp.get_width(); + lon = start_lon + (shift_over*dx) + (dx*0.5); + } + + if ( lat > start_lat + 10.0 ) { + ++pass; + if ( pass == 1 ) { + shift_over = 0.0; + shift_up = 0.0; + } else if ( pass == 2 ) { + shift_over = 1.0; + shift_up = 0.0; + } else if ( pass == 3 ) { + shift_over = 0.0; + shift_up = 1.0; + } else if ( pass == 4 ) { + shift_over = 1.0; + shift_up = 1.0; + } else { + return -1; + } + + // reset lat + // lat = -89.0 + (shift_up*dy) - (dy*0.5); + // lat = 27.0 + (0*dy) + (dy*0.5); + lat = start_lat + (shift_up*dy) + (dy*0.5); + + // reset lon + FGBucket tmp( 0.0, lat ); + double dx = tmp.get_width(); + // lon = -82 + (shift_over*dx) + (dx*0.5); + lon = start_lon + (shift_over*dx) + (dx*0.5); + + cout << "starting pass = " << pass + << " with lat = " << lat << " lon = " << lon << endl; + } + + // if ( ! start_lon ) { + // lon = -180 + dx * 0.5; + // } else { + // start_lon = false; + // } + + b = FGBucket( lon, lat ); + + // increment to next tile + FGBucket tmp( 0.0, lat ); + double dx = tmp.get_width(); + + // skip every other column (to avoid two clients working on + // adjacent tiles) + lon += 2.0 * dx; + + ++global_counter; + ++counter; + + time_t tmp_time = time(NULL); + if ( tmp_time != seconds ) { + seconds = tmp_time; + cout << "Current tile per second rate = " << counter << endl; + cout << "Overall tile per second rate = " + << global_counter / ( seconds - start_seconds ) << endl; + counter = 0; + } + + return b.gen_index(); +} + + +// log a pending tile (has been given out as a taks for some client) +void log_pending_tile( const string& path, long int tile ) { + FGBucket b(tile); + + string pending_file = path + "/" + b.gen_index_str() + ".pending"; + + string command = "touch " + pending_file; + system( command.c_str() ); +} + + +// a tile is finished (removed the .pending file) +void log_finished_tile( const string& path, long int tile ) { + FGBucket b(tile); + + string finished_file = path + "/" + b.gen_index_str() + ".pending"; + // cout << "unlinking " << finished_file << endl; + unlink( finished_file.c_str() ); +} + + +// make note of a failed tile +void log_failed_tile( const string& path, long int tile ) { + FGBucket b(tile); + + string failed_file = path + "/" + b.gen_index_str() + ".failed"; + + string command = "touch " + failed_file; + system( command.c_str() ); + + cout << "logged bad tile = " << tile << endl; +} + + +// display usage and exit +void usage( const string name ) { + cout << "Usage: " << name << " chunk1 chunk2 ..." + << endl; + cout << "\twhere chunk represent the south west corner of a 10x10 degree" + << endl; + cout << "\tsquare and is of the form [we]xxx[ns]yy. For example:" + << endl; + cout << "\tw020n10 e150s70" << endl; + exit(-1); +} + + +int main( int argc, char **argv ) { + int arg_counter; + long int next_tile; + int sock, msgsock, length, pid; + fd_set ready; + short unsigned int port; + + // quick argument sanity check + if ( argc < 4 ) { + usage( argv[0] ); + } + + string work_base = argv[1]; + string output_base = argv[2]; + + arg_counter = 3; + + // initialize tile counter / incrementer + init_tile_count( argv[arg_counter++] ); + + // temp test + // while ( (next_tile = get_next_tile()) != -1 ) { + // cout << next_tile << " " << FGBucket(next_tile) << endl; + // } + // cout << "done" << endl; + // exit(0); + + // create the status directory + string status_dir = work_base + "/Status"; + string command = "mkdir -p " + status_dir; + system( command.c_str() ); + + // setup socket to listen on + sock = make_socket( &port ); + cout << "socket is connected to port = " << port << endl; + + // Specify the maximum length of the connection queue + listen(sock, 10); + + for ( ;; ) { + FD_ZERO(&ready); + FD_SET(sock, &ready); + + // block until we get some input on sock + select(32, &ready, 0, 0, NULL); + + if ( FD_ISSET(sock, &ready) ) { + // printf("%d %d Incomming message --> ", getpid(), pid); + + // get the next tile to work on + next_tile = get_next_tile(); + + if ( next_tile == -1 ) { + // end of chunk see if there are more chunks + if ( arg_counter < argc ) { + // still more chunks to process + init_tile_count( argv[arg_counter++] ); + next_tile = get_next_tile(); + } + } + + cout << "Bucket = " << FGBucket(next_tile) + << " (" << pass << ")" << endl; + + log_pending_tile( status_dir, next_tile ); + // cout << "next tile = " << next_tile << endl;; + + msgsock = accept(sock, 0, 0); + // cout << "msgsock = " << msgsock << endl; + + // spawn a child + pid = fork(); + + if ( pid < 0 ) { + // error + perror("Cannot fork child process"); + exit(-1); + } else if ( pid > 0 ) { + // This is the parent + close(msgsock); + + // clean up all of our zombie children + int status; + while ( (pid = waitpid( WAIT_ANY, &status, WNOHANG )) > 0 ) { + // cout << "waitpid(): pid = " << pid + // << " status = " << status << endl; + } + } else { + // This is the child + + // cout << "new process started to handle new connection for " + // << next_tile << endl; + + // Read client's message (which is the status of the + // last scenery creation task.) + char buf[MAXBUF]; + if ( (length = read(msgsock, buf, MAXBUF)) < 0) { + perror("Cannot read command"); + exit(-1); + } + buf[length] = '\0'; + long int returned_tile = atoi(buf); + cout << "client returned = " << returned_tile << endl; + + // record status + if ( returned_tile < 0 ) { + // failure + log_failed_tile( status_dir, -returned_tile ); + log_finished_tile( status_dir, -returned_tile ); + } else { + // success + log_finished_tile( status_dir, returned_tile ); + } + + // reply to the client + char message[MAXBUF]; + sprintf(message, "%ld", next_tile); + length = strlen(message); + if ( write(msgsock, message, length) < 0 ) { + perror("Cannot write to stream socket"); + } + close(msgsock); + // cout << "process for " << next_tile << " ended" << endl; + + exit(0); + } + } + } +} diff --git a/src/BuildTiles/Triangulate/Makefile.am b/src/BuildTiles/Triangulate/Makefile.am new file mode 100644 index 00000000..1a33eec0 --- /dev/null +++ b/src/BuildTiles/Triangulate/Makefile.am @@ -0,0 +1,10 @@ +noinst_LIBRARIES = libTriangulate.a + +libTriangulate_a_SOURCES = \ + triangle.cxx triangle.hxx \ + trieles.cxx trieles.hxx + +INCLUDES += \ + -I$(top_builddir) \ + -I$(top_builddir)/Lib \ + -I$(top_builddir)/Construct diff --git a/src/BuildTiles/Triangulate/triangle.cxx b/src/BuildTiles/Triangulate/triangle.cxx new file mode 100644 index 00000000..bd6cf566 --- /dev/null +++ b/src/BuildTiles/Triangulate/triangle.cxx @@ -0,0 +1,529 @@ +// triangle.cxx -- "Triangle" interface class +// +// Written by Curtis Olson, started March 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#include +#include + +#include "triangle.hxx" + + +// Constructor +FGTriangle::FGTriangle( void ) { +} + + +// Destructor +FGTriangle::~FGTriangle( void ) { +} + + +// populate this class based on the specified gpc_polys list +int +FGTriangle::build( const point_list& corner_list, + const point_list& fit_list, + const FGPolyList& gpc_polys ) +{ + int debug_counter = 0; + int index; + + in_nodes.clear(); + in_segs.clear(); + + // Point3D junkp; + // int junkc = 0; + // char junkn[256]; + // FILE *junkfp; + + // traverse the dem corner and fit lists and gpc_polys building a + // unified node list and converting the polygons so that they + // reference the node list by index (starting at zero) rather than + // listing the points explicitely + + // first the corners since these are important + const_point_list_iterator f_current, f_last; + f_current = corner_list.begin(); + f_last = corner_list.end(); + for ( ; f_current != f_last; ++f_current ) { + index = in_nodes.unique_add( *f_current ); + } + + // next process the polygons + FGPolygon gpc_poly; + const_poly_list_iterator current, last; + + // process polygons in priority order + cout << "prepairing node list and polygons" << endl; + + for ( int i = 0; i < FG_MAX_AREA_TYPES; ++i ) { + polylist[i].clear(); + + cout << "area type = " << i << endl; + debug_counter = 0; + current = gpc_polys.polys[i].begin(); + last = gpc_polys.polys[i].end(); + for ( ; current != last; ++current ) { + gpc_poly = *current; + + cout << "processing a polygon, contours = " + << gpc_poly.contours() << endl; + + if (gpc_poly.contours() <= 0 ) { + cout << "FATAL ERROR! no contours in this polygon" << endl; + exit(-1); + } + + int j; + for ( j = 0; j < gpc_poly.contours(); ++j ) { + cout << " processing contour = " << j << ", nodes = " + << gpc_poly.contour_size( j ) << ", hole = " + << gpc_poly.get_hole_flag( j ) << endl; + + // sprintf(junkn, "g.%d", junkc++); + // junkfp = fopen(junkn, "w"); + + for ( int k = 0; k < gpc_poly.contour_size( j ); k++ ) { + Point3D p = gpc_poly.get_pt( j, k ); + index = in_nodes.unique_add( p ); + // junkp = in_nodes.get_node( index ); + // fprintf(junkfp, "%.4f %.4f\n", junkp.x(), junkp.y()); + // cout << " - " << index << endl; + } + // fprintf(junkfp, "%.4f %.4f\n", + // gpc_poly->contour[j].vertex[0].x, + // gpc_poly->contour[j].vertex[0].y); + // fclose(junkfp); + } + + Point3D inside_pt; + for ( j = 0; j < gpc_poly.contours(); ++j ) { + inside_pt = calc_point_inside( gpc_poly, j, in_nodes ); + gpc_poly.set_point_inside( j, inside_pt ); + } + + polylist[i].push_back( gpc_poly ); + +#if 0 + // temporary ... write out hole/polygon info for debugging + for ( j = 0; j < (int)gpc_poly.contours(); ++j ) { + char pname[256]; + sprintf(pname, "poly%02d-%02d-%02d", i, debug_counter, j); + cout << "writing to " << pname << endl; + FILE *fp = fopen( pname, "w" ); + Point3D point; + for ( int k = 0; k < gpc_poly.contour_size( j ); ++k ) { + point = gpc_poly.get_pt( j, k ); + fprintf( fp, "%.6f %.6f\n", point.x(), point.y() ); + } + point = gpc_poly.get_pt( j, 0 ); + fprintf( fp, "%.6f %.6f\n", point.x(), point.y() ); + fclose(fp); + + char hname[256]; + sprintf(hname, "hole%02d-%02d-%02d", i, debug_counter, j); + FILE *fh = fopen( hname, "w" ); + point = gpc_poly.get_point_inside( j ); + fprintf( fh, "%.6f %.6f\n", point.x(), point.y() ); + fclose(fh); + } + + // cout << "type a letter + enter to continue: "; + // string input; + // cin >> input; +#endif + + ++debug_counter; + } + } + + // last, do the rest of the height nodes + f_current = fit_list.begin(); + f_last = fit_list.end(); + for ( ; f_current != f_last; ++f_current ) { + index = in_nodes.course_add( *f_current ); + } + + for ( int i = 0; i < FG_MAX_AREA_TYPES; ++i ) { + if ( polylist[i].size() ) { + cout << get_area_name((AreaType)i) << " = " + << polylist[i].size() << endl; + } + } + + // traverse the polygon lists and build the segment (edge) list + // that is used by the "Triangle" lib. + + cout << "building segment list" << endl; + int i1, i2; + Point3D p1, p2; + point_list node_list = in_nodes.get_node_list(); + FGPolygon poly; + + for ( int i = 0; i < FG_MAX_AREA_TYPES; ++i ) { + cout << "area type = " << i << endl; + poly_list_iterator tp_current, tp_last; + tp_current = polylist[i].begin(); + tp_last = polylist[i].end(); + + // process each polygon in list + for ( ; tp_current != tp_last; ++tp_current ) { + poly = *tp_current; + cout << " processing a polygon with contours = " + << poly.contours() << endl; + for ( int j = 0; j < (int)poly.contours(); ++j) { + for ( int k = 0; k < (int)(poly.contour_size(j) - 1); ++k ) { + p1 = poly.get_pt( j, k ); + p2 = poly.get_pt( j, k + 1 ); + i1 = in_nodes.find( p1 ); + i2 = in_nodes.find( p2 ); + // calc_line_params(i1, i2, &m, &b); + if ( i == (int)HoleArea ) { + // mark as a boundary + in_segs.unique_divide_and_add( node_list, + FGTriSeg(i1, i2, 1) ); + } else { + // non boundary + in_segs.unique_divide_and_add( node_list, + FGTriSeg(i1, i2, 0) ); + } + } + p1 = poly.get_pt( j, 0 ); + p2 = poly.get_pt( j, poly.contour_size(j) - 1 ); + i1 = in_nodes.find( p1 ); + i2 = in_nodes.find( p2 ); + // calc_line_params(i1, i2, &m, &b); + if ( i == (int)HoleArea ) { + // mark as a boundary + in_segs.unique_divide_and_add( node_list, + FGTriSeg(i1, i2, 1) ); + } else { + // non boundary + in_segs.unique_divide_and_add( node_list, + FGTriSeg(i1, i2, 0) ); + } + } + } + } + + return 0; +} + + +// populate this class based on the specified gpc_polys list +int FGTriangle::rebuild( FGConstruct& c ) { + in_nodes.clear(); + in_segs.clear(); + + in_nodes = c.get_tri_nodes(); + in_segs = c.get_tri_segs(); + + return 0; +} + + +static void write_out_data(struct triangulateio *out) { + FILE *node = fopen("tile.node", "w"); + fprintf(node, "%d 2 %d 0\n", + out->numberofpoints, out->numberofpointattributes); + for (int i = 0; i < out->numberofpoints; ++i) { + fprintf(node, "%d %.6f %.6f %.2f\n", + i, out->pointlist[2*i], out->pointlist[2*i + 1], 0.0); + } + fclose(node); + + FILE *ele = fopen("tile.ele", "w"); + fprintf(ele, "%d 3 0\n", out->numberoftriangles); + for (int i = 0; i < out->numberoftriangles; ++i) { + fprintf(ele, "%d ", i); + for (int j = 0; j < out->numberofcorners; ++j) { + fprintf(ele, "%d ", out->trianglelist[i * out->numberofcorners + j]); + } + for (int j = 0; j < out->numberoftriangleattributes; ++j) { + fprintf(ele, "%.6f ", + out->triangleattributelist[i + * out->numberoftriangleattributes + + j] + ); + } + fprintf(ele, "\n"); + } + fclose(ele); + + FILE *fp = fopen("tile.poly", "w"); + fprintf(fp, "0 2 1 0\n"); + fprintf(fp, "%d 1\n", out->numberofsegments); + for (int i = 0; i < out->numberofsegments; ++i) { + fprintf(fp, "%d %d %d %d\n", + i, out->segmentlist[2*i], out->segmentlist[2*i + 1], + out->segmentmarkerlist[i] ); + } + fprintf(fp, "%d\n", out->numberofholes); + for (int i = 0; i < out->numberofholes; ++i) { + fprintf(fp, "%d %.6f %.6f\n", + i, out->holelist[2*i], out->holelist[2*i + 1]); + } + fprintf(fp, "%d\n", out->numberofregions); + for (int i = 0; i < out->numberofregions; ++i) { + fprintf(fp, "%d %.6f %.6f %.6f\n", + i, out->regionlist[4*i], out->regionlist[4*i + 1], + out->regionlist[4*i + 2]); + } + fclose(fp); +} + + +// Front end triangulator for polygon list. Allocates and builds up +// all the needed structures for the triangulator, runs it, copies the +// results, and frees all the data structures used by the +// triangulator. "pass" can be 1 or 2. 1 = first pass which +// generates extra nodes for a better triangulation. 2 = second pass +// after split/reassem where we don't want any extra nodes generated. + +int FGTriangle::run_triangulate( const string& angle, const int pass ) { + FGPolygon poly; + Point3D p; + struct triangulateio in, out, vorout; + int counter; + + // point list + point_list node_list = in_nodes.get_node_list(); + in.numberofpoints = node_list.size(); + in.pointlist = (REAL *) malloc(in.numberofpoints * 2 * sizeof(REAL)); + + for ( int i = 0; i < in.numberofpoints; ++i ) { + in.pointlist[2*i] = node_list[i].x(); + in.pointlist[2*i + 1] = node_list[i].y(); + } + + in.numberofpointattributes = 1; + in.pointattributelist = (REAL *) malloc(in.numberofpoints * + in.numberofpointattributes * + sizeof(REAL)); + for ( int i = 0; i < in.numberofpoints * in.numberofpointattributes; ++i) { + in.pointattributelist[i] = node_list[i].z(); + } + + in.pointmarkerlist = (int *) malloc(in.numberofpoints * sizeof(int)); + for ( int i = 0; i < in.numberofpoints; ++i) { + in.pointmarkerlist[i] = 0; + } + + // triangle list + in.numberoftriangles = 0; + + // segment list + triseg_list seg_list = in_segs.get_seg_list(); + in.numberofsegments = seg_list.size(); + in.segmentlist = (int *) malloc(in.numberofsegments * 2 * sizeof(int)); + in.segmentmarkerlist = (int *) malloc(in.numberofsegments * sizeof(int)); + + triseg_list_iterator s_current, s_last; + s_current = seg_list.begin(); + s_last = seg_list.end(); + counter = 0; + for ( ; s_current != s_last; ++s_current ) { + in.segmentlist[counter++] = s_current->get_n1(); + in.segmentlist[counter++] = s_current->get_n2(); + } + s_current = seg_list.begin(); + s_last = seg_list.end(); + counter = 0; + for ( ; s_current != s_last; ++s_current ) { + in.segmentmarkerlist[counter++] = s_current->get_boundary_marker(); + } + + // hole list (make holes for airport ignore areas) + in.numberofholes = polylist[(int)HoleArea].size(); + in.holelist = (REAL *) malloc(in.numberofholes * 2 * sizeof(REAL)); + + poly_list_iterator h_current, h_last; + h_current = polylist[(int)HoleArea].begin(); + h_last = polylist[(int)HoleArea].end(); + counter = 0; + for ( ; h_current != h_last; ++h_current ) { + poly = *h_current; + for ( int j = 0; j < poly.contours(); ++j ) { + p = poly.get_point_inside( j ); + in.holelist[counter++] = p.x(); + in.holelist[counter++] = p.y(); + } + } + + // region list + in.numberofregions = 0; + for ( int i = 0; i < FG_MAX_AREA_TYPES; ++i ) { + poly_list_iterator h_current, h_last; + h_current = polylist[i].begin(); + h_last = polylist[i].end(); + for ( ; h_current != h_last; ++h_current ) { + poly = *h_current; + for ( int j = 0; j < poly.contours(); ++j ) { + if ( ! poly.get_hole_flag( j ) ) { + ++in.numberofregions; + } + } + } + } + + in.regionlist = (REAL *) malloc(in.numberofregions * 4 * sizeof(REAL)); + counter = 0; + for ( int i = 0; i < FG_MAX_AREA_TYPES; ++i ) { + poly_list_iterator h_current, h_last; + h_current = polylist[(int)i].begin(); + h_last = polylist[(int)i].end(); + for ( ; h_current != h_last; ++h_current ) { + poly = *h_current; + for ( int j = 0; j < poly.contours(); ++j ) { + if ( ! poly.get_hole_flag( j ) ) { + p = poly.get_point_inside( j ); + cout << "Region point = " << p << endl; + in.regionlist[counter++] = p.x(); // x coord + in.regionlist[counter++] = p.y(); // y coord + in.regionlist[counter++] = i; // region attribute + in.regionlist[counter++] = -1.0; // area constraint + // (unused) + } + } + } + } + + // prep the output structures + out.pointlist = (REAL *) NULL; // Not needed if -N switch used. + // Not needed if -N switch used or number of point attributes is zero: + out.pointattributelist = (REAL *) NULL; + out.pointmarkerlist = (int *) NULL; // Not needed if -N or -B switch used. + out.trianglelist = (int *) NULL; // Not needed if -E switch used. + // Not needed if -E switch used or number of triangle attributes is zero: + out.triangleattributelist = (REAL *) NULL; + out.neighborlist = (int *) NULL; // Needed only if -n switch used. + // Needed only if segments are output (-p or -c) and -P not used: + out.segmentlist = (int *) NULL; + // Needed only if segments are output (-p or -c) and -P and -B not used: + out.segmentmarkerlist = (int *) NULL; + out.edgelist = (int *) NULL; // Needed only if -e switch used. + out.edgemarkerlist = (int *) NULL; // Needed if -e used and -B not used. + + vorout.pointlist = (REAL *) NULL; // Needed only if -v switch used. + // Needed only if -v switch used and number of attributes is not zero: + vorout.pointattributelist = (REAL *) NULL; + vorout.edgelist = (int *) NULL; // Needed only if -v switch used. + vorout.normlist = (REAL *) NULL; // Needed only if -v switch used. + + // TEMPORARY + write_out_data(&in); + + // Triangulate the points. Switches are chosen to read and write + // a PSLG (p), preserve the convex hull (c), number everything + // from zero (z), assign a regional attribute to each element (A), + // and produce an edge list (e), and a triangle neighbor list (n). + + string tri_options; + if ( pass == 1 ) { + // use a quality value of 10 (q10) meaning no interior + // triangle angles less than 10 degrees + // tri_options = "pczAen"; + if ( angle == "0" ) { + tri_options = "pczAen"; + } else { + tri_options = "pczq" + angle + "Aen"; + } + // // string tri_options = "pzAen"; + // // string tri_options = "pczq15S400Aen"; + } else if ( pass == 2 ) { + // no new points on boundary (Y), no internal segment + // splitting (YY), no quality refinement (q) + tri_options = "pczYYAen"; + } else { + cout << "unknown pass number = " << pass + << " in FGTriangle::run_triangulate()" << endl; + exit(-1); + } + cout << "Triangulation with options = " << tri_options << endl; + + triangulate( (char *)tri_options.c_str(), &in, &out, &vorout ); + + // TEMPORARY + // write_out_data(&out); + + // now copy the results back into the corresponding FGTriangle + // structures + + // nodes + out_nodes.clear(); + for ( int i = 0; i < out.numberofpoints; ++i ) { + Point3D p( out.pointlist[2*i], out.pointlist[2*i + 1], + out.pointattributelist[i] ); + // cout << "point = " << p << endl; + out_nodes.simple_add( p ); + } + + // segments + out_segs.clear(); + for ( int i = 0; i < out.numberofsegments; ++i ) { + out_segs.unique_add( FGTriSeg( out.segmentlist[2*i], + out.segmentlist[2*i+1], + out.segmentmarkerlist[i] ) ); + } + + // triangles + elelist.clear(); + int n1, n2, n3; + double attribute; + for ( int i = 0; i < out.numberoftriangles; ++i ) { + n1 = out.trianglelist[i * 3]; + n2 = out.trianglelist[i * 3 + 1]; + n3 = out.trianglelist[i * 3 + 2]; + if ( out.numberoftriangleattributes > 0 ) { + attribute = out.triangleattributelist[i]; + } else { + attribute = 0.0; + } + // cout << "triangle = " << n1 << " " << n2 << " " << n3 << endl; + + elelist.push_back( FGTriEle( n1, n2, n3, attribute ) ); + } + + // free mem allocated to the "Triangle" structures + free(in.pointlist); + free(in.pointattributelist); + free(in.pointmarkerlist); + free(in.regionlist); + free(out.pointlist); + free(out.pointattributelist); + free(out.pointmarkerlist); + free(out.trianglelist); + free(out.triangleattributelist); + // free(out.trianglearealist); + free(out.neighborlist); + free(out.segmentlist); + free(out.segmentmarkerlist); + free(out.edgelist); + free(out.edgemarkerlist); + free(vorout.pointlist); + free(vorout.pointattributelist); + free(vorout.edgelist); + free(vorout.normlist); + + return 0; +} + + diff --git a/src/BuildTiles/Triangulate/triangle.hxx b/src/BuildTiles/Triangulate/triangle.hxx new file mode 100644 index 00000000..c998f505 --- /dev/null +++ b/src/BuildTiles/Triangulate/triangle.hxx @@ -0,0 +1,106 @@ +// triangle.hxx -- "Triangle" interface class +// +// Written by Curtis Olson, started March 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#ifndef _TRIANGLE_HXX +#define _TRIANGLE_HXX + + +#ifndef __cplusplus +# error This library requires C++ +#endif + + +#include +#include + +#include +#include +#include

+ +#include +#include +#include +#include + +#define REAL double +extern "C" { +#include +} + +#include "trieles.hxx" + + +class FGTriangle { + +private: + + // list of nodes + FGTriNodes in_nodes; + FGTriNodes out_nodes; + + // list of segments + FGTriSegments in_segs; + FGTriSegments out_segs; + + // polygon list + poly_list polylist[FG_MAX_AREA_TYPES]; + + // triangle list + triele_list elelist; + +public: + + // Constructor and destructor + FGTriangle( void ); + ~FGTriangle( void ); + + // add nodes from the dem fit + int add_nodes(); + + // populate this class based on the specified gpc_polys list + int build( const point_list& corner_list, + const point_list& fit_list, + const FGPolyList& gpc_polys ); + + // populate this class based on the specified gpc_polys list + int rebuild( FGConstruct& c ); + + // Front end triangulator for polygon list. Allocates and builds + // up all the needed structures for the triangulator, runs it, + // copies the results, and frees all the data structures used by + // the triangulator. "pass" can be 1 or 2. 1 = first pass which + // generates extra nodes for a better triangulation. 2 = second + // pass after split/reassem where we don't want any extra nodes + // generated. + int run_triangulate( const string& angle, const int pass ); + + inline FGTriNodes get_out_nodes() const { return out_nodes; } + inline size_t get_out_nodes_size() const { return out_nodes.size(); } + inline triele_list get_elelist() const { return elelist; } + inline FGTriSegments get_out_segs() const { return out_segs; } +}; + + +#endif // _TRIANGLE_HXX + + diff --git a/src/BuildTiles/Triangulate/trieles.cxx b/src/BuildTiles/Triangulate/trieles.cxx new file mode 100644 index 00000000..f3b66d6d --- /dev/null +++ b/src/BuildTiles/Triangulate/trieles.cxx @@ -0,0 +1,26 @@ +// trieles.cxx -- "Triangle" element management class +// +// Written by Curtis Olson, started March 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#include "trieles.hxx" + + diff --git a/src/BuildTiles/Triangulate/trieles.hxx b/src/BuildTiles/Triangulate/trieles.hxx new file mode 100644 index 00000000..29cb72e2 --- /dev/null +++ b/src/BuildTiles/Triangulate/trieles.hxx @@ -0,0 +1,75 @@ +// trieles.hxx -- "Triangle" element management class +// +// Written by Curtis Olson, started March 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#ifndef _TRIELES_HXX +#define _TRIELES_HXX + + +#ifndef __cplusplus +# error This library requires C++ +#endif + + +#include + +#include + +FG_USING_STD(vector); + + +// a segment is two integer pointers into the node list +class FGTriEle { + int n1, n2, n3; + + double attribute; + +public: + + // Constructor and destructor + inline FGTriEle( void ) { }; + inline FGTriEle( int i1, int i2, int i3, double a ) { + n1 = i1; n2 = i2; n3 = i3; attribute = a; + } + + inline ~FGTriEle( void ) { }; + + inline int get_n1() const { return n1; } + inline void set_n1( int i ) { n1 = i; } + inline int get_n2() const { return n2; } + inline void set_n2( int i ) { n2 = i; } + inline int get_n3() const { return n3; } + inline void set_n3( int i ) { n3 = i; } + + inline double get_attribute() const { return attribute; } + inline void set_attribute( double a ) { attribute = a; } +}; + + +typedef vector < FGTriEle > triele_list; +typedef triele_list::iterator triele_list_iterator; +typedef triele_list::const_iterator const_triele_list_iterator; + + +#endif // _TRIELES_HXX + + diff --git a/src/Include/config.h b/src/Include/config.h new file mode 100644 index 00000000..f71c69a2 --- /dev/null +++ b/src/Include/config.h @@ -0,0 +1,208 @@ +/* Include/config.h. Generated automatically by configure. */ +/* Include/config.h.in. Generated automatically from configure.in by autoheader. */ + +/* Define to empty if the keyword does not work. */ +/* #undef const */ + +/* Define if you don't have vprintf but do have _doprnt. */ +/* #undef HAVE_DOPRNT */ + +/* Define if you have the vprintf function. */ +#define HAVE_VPRINTF 1 + +/* Define as the return type of signal handlers (int or void). */ +#define RETSIGTYPE void + +/* Define to `unsigned' if doesn't define. */ +/* #undef size_t */ + +/* Define if you have the ANSI C header files. */ +#define STDC_HEADERS 1 + +/* Define if you can safely include both and . */ +#define TIME_WITH_SYS_TIME 1 + +/* Define if your declares struct tm. */ +/* #undef TM_IN_SYS_TIME */ + +/* Define if the X Window System is missing or not being used. */ +/* #undef X_DISPLAY_MISSING */ + +/* Define to empty if the keyword does not work. */ +/* #undef const */ + + +/* Define to eliminate all trace of debugging messages such as for a + release build */ +/* #undef FG_NDEBUG */ + + +/* Define to enable 3dfx/glide render in a window hack under unix. + This probably won't work under windows. */ +/* #undef XMESA */ +/* #undef FX */ + +/* Define if you don't have vprintf but do have _doprnt. */ +/* #undef HAVE_DOPRNT */ + +/* Define if you have the vprintf function. */ +#define HAVE_VPRINTF 1 + +/* Define to package name */ +#define PACKAGE "TerraGear" + +/* Define as the return type of signal handlers (int or void). */ +#define RETSIGTYPE void + +/* Define to `unsigned' if doesn't define. */ +/* #undef size_t */ + +/* Define if you have the ANSI C header files. */ +#define STDC_HEADERS 1 + +/* Define if you can safely include both and . */ +#define TIME_WITH_SYS_TIME 1 + +/* Define if your declares struct tm. */ +/* #undef TM_IN_SYS_TIME */ + +/* Define to version number */ +#define VERSION "0.0.0" + +/* Define if compiling on a Winbloze (95, NT, etc.) platform */ +/* #undef WIN32 */ + +/* Define if the X Window System is missing or not being used. */ +/* #undef X_DISPLAY_MISSING */ + +/* Define if you have the GetLocalTime function. */ +/* #undef HAVE_GETLOCALTIME */ + +/* Define if you have the bcopy function. */ +#define HAVE_BCOPY 1 + +/* Define if you have the ftime function. */ +#define HAVE_FTIME 1 + +/* Define if you have the getitimer function. */ +#define HAVE_GETITIMER 1 + +/* Define if you have the getrusage function. */ +#define HAVE_GETRUSAGE 1 + +/* Define if you have the gettimeofday function. */ +#define HAVE_GETTIMEOFDAY 1 + +/* Define if you have the memcpy function. */ +#define HAVE_MEMCPY 1 + +/* Define if you have the mktime function. */ +#define HAVE_MKTIME 1 + +/* Define if you have the rand function. */ +#define HAVE_RAND 1 + +/* Define if you have the random function. */ +#define HAVE_RANDOM 1 + +/* Define if you have the rint function. */ +#define HAVE_RINT 1 + +/* Define if you have the setitimer function. */ +#define HAVE_SETITIMER 1 + +/* Define if you have the signal function. */ +#define HAVE_SIGNAL 1 + +/* Define if you have the strstr function. */ +#define HAVE_STRSTR 1 + +/* Define if you have the timegm function. */ +#define HAVE_TIMEGM 1 + +/* Define if you have the header file. */ +#define HAVE_FCNTL_H 1 + +/* Define if you have the header file. */ +#define HAVE_GETOPT_H 1 + +/* Define if you have the header file. */ +#define HAVE_GPC_H 1 + +/* Define if you have the header file. */ +#define HAVE_MALLOC_H 1 + +/* Define if you have the header file. */ +#define HAVE_MEMORY_H 1 + +/* Define if you have the header file. */ +#define HAVE_STDLIB_H 1 + +/* Define if you have the header file. */ +#define HAVE_SYS_PARAM_H 1 + +/* Define if you have the header file. */ +#define HAVE_SYS_STAT_H 1 + +/* Define if you have the header file. */ +#define HAVE_SYS_TIME_H 1 + +/* Define if you have the header file. */ +#define HAVE_SYS_TIMEB_H 1 + +/* Define if you have the header file. */ +#define HAVE_UNISTD_H 1 + +/* Define if you have the header file. */ +#define HAVE_VALUES_H 1 + +/* Define if you have the header file. */ +/* #undef HAVE_WINBASE_H */ + +/* Define if you have the header file. */ +/* #undef HAVE_WINDOWS_H */ + +/* Define if you have the GL library (-lGL). */ +#define HAVE_LIBGL 1 + +/* Define if you have the GLU library (-lGLU). */ +/* #undef HAVE_LIBGLU */ + +/* Define if you have the GLcore library (-lGLcore). */ +/* #undef HAVE_LIBGLCORE */ + +/* Define if you have the ICE library (-lICE). */ +#define HAVE_LIBICE 1 + +/* Define if you have the MesaGL library (-lMesaGL). */ +/* #undef HAVE_LIBMESAGL */ + +/* Define if you have the MesaGLU library (-lMesaGLU). */ +#define HAVE_LIBMESAGLU 1 + +/* Define if you have the SM library (-lSM). */ +#define HAVE_LIBSM 1 + +/* Define if you have the X11 library (-lX11). */ +#define HAVE_LIBX11 1 + +/* Define if you have the Xext library (-lXext). */ +#define HAVE_LIBXEXT 1 + +/* Define if you have the Xi library (-lXi). */ +#define HAVE_LIBXI 1 + +/* Define if you have the Xmu library (-lXmu). */ +#define HAVE_LIBXMU 1 + +/* Define if you have the Xt library (-lXt). */ +#define HAVE_LIBXT 1 + +/* Define if you have the glut library (-lglut). */ +#define HAVE_LIBGLUT 1 + +/* Define if you have the m library (-lm). */ +#define HAVE_LIBM 1 + +/* Define if you have the socket library (-lsocket). */ +/* #undef HAVE_LIBSOCKET */ diff --git a/src/Include/config.h.in b/src/Include/config.h.in new file mode 100644 index 00000000..fa7ef654 --- /dev/null +++ b/src/Include/config.h.in @@ -0,0 +1,207 @@ +/* Include/config.h.in. Generated automatically from configure.in by autoheader. */ + +/* Define to empty if the keyword does not work. */ +#undef const + +/* Define if you don't have vprintf but do have _doprnt. */ +#undef HAVE_DOPRNT + +/* Define if you have the vprintf function. */ +#undef HAVE_VPRINTF + +/* Define as the return type of signal handlers (int or void). */ +#undef RETSIGTYPE + +/* Define to `unsigned' if doesn't define. */ +#undef size_t + +/* Define if you have the ANSI C header files. */ +#undef STDC_HEADERS + +/* Define if you can safely include both and . */ +#undef TIME_WITH_SYS_TIME + +/* Define if your declares struct tm. */ +#undef TM_IN_SYS_TIME + +/* Define if the X Window System is missing or not being used. */ +#undef X_DISPLAY_MISSING + +/* Define to empty if the keyword does not work. */ +#undef const + + +/* Define to eliminate all trace of debugging messages such as for a + release build */ +#undef FG_NDEBUG + + +/* Define to enable 3dfx/glide render in a window hack under unix. + This probably won't work under windows. */ +#undef XMESA +#undef FX + +/* Define if you don't have vprintf but do have _doprnt. */ +#undef HAVE_DOPRNT + +/* Define if you have the vprintf function. */ +#undef HAVE_VPRINTF + +/* Define to package name */ +#undef PACKAGE + +/* Define as the return type of signal handlers (int or void). */ +#undef RETSIGTYPE + +/* Define to `unsigned' if doesn't define. */ +#undef size_t + +/* Define if you have the ANSI C header files. */ +#undef STDC_HEADERS + +/* Define if you can safely include both and . */ +#undef TIME_WITH_SYS_TIME + +/* Define if your declares struct tm. */ +#undef TM_IN_SYS_TIME + +/* Define to version number */ +#undef VERSION + +/* Define if compiling on a Winbloze (95, NT, etc.) platform */ +#undef WIN32 + +/* Define if the X Window System is missing or not being used. */ +#undef X_DISPLAY_MISSING + +/* Define if you have the GetLocalTime function. */ +#undef HAVE_GETLOCALTIME + +/* Define if you have the bcopy function. */ +#undef HAVE_BCOPY + +/* Define if you have the ftime function. */ +#undef HAVE_FTIME + +/* Define if you have the getitimer function. */ +#undef HAVE_GETITIMER + +/* Define if you have the getrusage function. */ +#undef HAVE_GETRUSAGE + +/* Define if you have the gettimeofday function. */ +#undef HAVE_GETTIMEOFDAY + +/* Define if you have the memcpy function. */ +#undef HAVE_MEMCPY + +/* Define if you have the mktime function. */ +#undef HAVE_MKTIME + +/* Define if you have the rand function. */ +#undef HAVE_RAND + +/* Define if you have the random function. */ +#undef HAVE_RANDOM + +/* Define if you have the rint function. */ +#undef HAVE_RINT + +/* Define if you have the setitimer function. */ +#undef HAVE_SETITIMER + +/* Define if you have the signal function. */ +#undef HAVE_SIGNAL + +/* Define if you have the strstr function. */ +#undef HAVE_STRSTR + +/* Define if you have the timegm function. */ +#undef HAVE_TIMEGM + +/* Define if you have the header file. */ +#undef HAVE_FCNTL_H + +/* Define if you have the header file. */ +#undef HAVE_GETOPT_H + +/* Define if you have the header file. */ +#undef HAVE_GPC_H + +/* Define if you have the header file. */ +#undef HAVE_MALLOC_H + +/* Define if you have the header file. */ +#undef HAVE_MEMORY_H + +/* Define if you have the header file. */ +#undef HAVE_STDLIB_H + +/* Define if you have the header file. */ +#undef HAVE_SYS_PARAM_H + +/* Define if you have the header file. */ +#undef HAVE_SYS_STAT_H + +/* Define if you have the header file. */ +#undef HAVE_SYS_TIME_H + +/* Define if you have the header file. */ +#undef HAVE_SYS_TIMEB_H + +/* Define if you have the header file. */ +#undef HAVE_UNISTD_H + +/* Define if you have the header file. */ +#undef HAVE_VALUES_H + +/* Define if you have the header file. */ +#undef HAVE_WINBASE_H + +/* Define if you have the header file. */ +#undef HAVE_WINDOWS_H + +/* Define if you have the GL library (-lGL). */ +#undef HAVE_LIBGL + +/* Define if you have the GLU library (-lGLU). */ +#undef HAVE_LIBGLU + +/* Define if you have the GLcore library (-lGLcore). */ +#undef HAVE_LIBGLCORE + +/* Define if you have the ICE library (-lICE). */ +#undef HAVE_LIBICE + +/* Define if you have the MesaGL library (-lMesaGL). */ +#undef HAVE_LIBMESAGL + +/* Define if you have the MesaGLU library (-lMesaGLU). */ +#undef HAVE_LIBMESAGLU + +/* Define if you have the SM library (-lSM). */ +#undef HAVE_LIBSM + +/* Define if you have the X11 library (-lX11). */ +#undef HAVE_LIBX11 + +/* Define if you have the Xext library (-lXext). */ +#undef HAVE_LIBXEXT + +/* Define if you have the Xi library (-lXi). */ +#undef HAVE_LIBXI + +/* Define if you have the Xmu library (-lXmu). */ +#undef HAVE_LIBXMU + +/* Define if you have the Xt library (-lXt). */ +#undef HAVE_LIBXT + +/* Define if you have the glut library (-lglut). */ +#undef HAVE_LIBGLUT + +/* Define if you have the m library (-lm). */ +#undef HAVE_LIBM + +/* Define if you have the socket library (-lsocket). */ +#undef HAVE_LIBSOCKET diff --git a/src/Include/stamp-h b/src/Include/stamp-h new file mode 100644 index 00000000..9788f702 --- /dev/null +++ b/src/Include/stamp-h @@ -0,0 +1 @@ +timestamp diff --git a/src/Lib/Array/Makefile.am b/src/Lib/Array/Makefile.am new file mode 100644 index 00000000..02b49b02 --- /dev/null +++ b/src/Lib/Array/Makefile.am @@ -0,0 +1,17 @@ +noinst_LIBRARIES = libArray.a + +libArray_a_SOURCES = array.cxx array.hxx + +noinst_PROGRAMS = testarray + +testarray_SOURCES = testarray.cxx + +testarray_LDADD = \ + $(top_builddir)/Lib/Array/libArray.a \ + -lsgbucket -lsgmath -lsgmisc -lz + +INCLUDES += \ + -I$(top_builddir) \ + -I$(top_builddir)/Lib \ + -I$(top_builddir)/Tools/Lib \ + -I$(top_builddir)/Tools/Construct diff --git a/src/Lib/Array/array.cxx b/src/Lib/Array/array.cxx new file mode 100644 index 00000000..de6fb886 --- /dev/null +++ b/src/Lib/Array/array.cxx @@ -0,0 +1,577 @@ +// array.cxx -- Array management class +// +// Written by Curtis Olson, started March 1998. +// +// Copyright (C) 1998 - 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#ifdef HAVE_CONFIG_H +# include +#endif + +#include + +// #include // isspace() +// #include // atoi() +// #include // rint() +// #include +// #include +// #ifdef HAVE_SYS_STAT_H +// # include // stat() +// #endif +// #ifdef FG_HAVE_STD_INCLUDES +// # include +// #else +// # include +// #endif +// #ifdef HAVE_UNISTD_H +// # include // stat() +// #endif + +#include STL_STRING + +#include +#include +#include +#include + +#include "array.hxx" + +FG_USING_STD(string); + + +FGArray::FGArray( void ) { + // cout << "class FGArray CONstructor called." << endl; + in_data = new float[ARRAY_SIZE_1][ARRAY_SIZE_1]; + // out_data = new float[ARRAY_SIZE_1][ARRAY_SIZE_1]; +} + + +FGArray::FGArray( const string &file ) { + // cout << "class FGArray CONstructor called." << endl; + in_data = new float[ARRAY_SIZE_1][ARRAY_SIZE_1]; + // out_data = new float[ARRAY_SIZE_1][ARRAY_SIZE_1]; + + FGArray::open(file); +} + + +// open an Array file +int +FGArray::open( const string& file ) { + // open input file (or read from stdin) + if ( file == "-" ) { + cout << " Opening array data pipe from stdin" << endl; + // fd = stdin; + // fd = gzdopen(STDIN_FILENO, "r"); + cout << " Not yet ported ..." << endl; + return 0; + } else { + in = new fg_gzifstream( file ); + if ( ! in->is_open() ) { + cout << " Cannot open " << file << endl; + return 0; + } + cout << " Opening array data file: " << file << endl; + } + + return 1; +} + + +// close an Array file +int +FGArray::close() { + // the fg_gzifstream doesn't seem to have a close() + + delete in; + + return 1; +} + + +// parse Array file, pass in the bucket so we can make up values when +// the file wasn't found. +int +FGArray::parse( FGBucket& b ) { + if ( in->is_open() ) { + // file open, parse + *in >> originx >> originy; + *in >> cols >> col_step; + *in >> rows >> row_step; + + cout << " origin = " << originx << " " << originy << endl; + cout << " cols = " << cols << " rows = " << rows << endl; + cout << " col_step = " << col_step + << " row_step = " << row_step <> in_data[i][j]; + } + } + + cout << " Done parsing\n"; + } else { + // file not open (not found?), fill with zero'd data + + originx = ( b.get_center_lon() - 0.5 * b.get_width() ) * 3600.0; + originy = ( b.get_center_lat() - 0.5 * b.get_height() ) * 3600.0; + + double max_x = ( b.get_center_lon() + 0.5 * b.get_width() ) * 3600.0; + double max_y = ( b.get_center_lat() + 0.5 * b.get_height() ) * 3600.0; + + cols = 3; + col_step = (max_x - originx) / (cols - 1); + rows = 3; + row_step = (max_y - originy) / (rows - 1); + + cout << " origin = " << originx << " " << originy << endl; + cout << " cols = " << cols << " rows = " << rows << endl; + cout << " col_step = " << col_step + << " row_step = " << row_step < error_sq ) { + good_fit = false; + } + + end++; + } + + if ( !good_fit ) { + // error exceeded the threshold, back up + end -= 2; // back "end" up to the last good enough fit + n--; // back "n" up appropriately too + } else { + // we popped out of the above loop while still within + // the error threshold, so we must be at the end of + // the data set + end--; + } + + least_squares(x, y, n, &m, &b); + // ave_error = least_squares_error(x, y, n, m, b); + max_error = least_squares_max_error(x, y, n, m, b); + + /* + printf("\n"); + printf("%d - %d ave error = %.2f max error = %.2f y = %.2f*x + %.2f\n", + start, end, ave_error, max_error, m, b); + printf("\n"); + + fprintf(fit1, "%.2f %.2f\n", x[0], m * x[0] + b); + fprintf(fit1, "%.2f %.2f\n", x[end-start], m * x[end-start] + b); + */ + + if ( start > colmin ) { + // skip this for the first line segment + cury = m * x[0] + b; + add_fit_node( start, row, (lasty + cury) / 2 ); + // fprintf(fit, "%.2f %.2f\n", x[0], (lasty + cury) / 2); + } + + lasty = m * x[end-start] + b; + start = end; + } + + /* + fclose(fit); + fclose(fit1); + + dem = fopen("gnuplot.dat", "w"); + for ( j = 0; j < ARRAY_SIZE_1; j++) { + fprintf(dem, "%.2f %.2f\n", 0.0 + ( j * col_step ), + in_data[j][row]); + } + fclose(dem); + */ + + // NOTICE, this is for testing only. This instance of + // output_nodes should be removed. It should be called only + // once at the end once all the nodes have been generated. + // newmesh_output_nodes(&nm, "mesh.node"); + // printf("Please hit return: "); gets(junk); + } + + // outputmesh_output_nodes(fg_root, p); + + // return fit nodes + 4 corners + return node_list.size() + 4; +} + + +// return the current altitude based on grid data. We should rewrite +// this to interpolate exact values, but for now this is good enough +double FGArray::interpolate_altitude( double lon, double lat ) const { + // we expect incoming (lon,lat) to be in arcsec for now + + double xlocal, ylocal, dx, dy, zA, zB, elev; + int x1, x2, x3, y1, y2, y3; + float z1, z2, z3; + int xindex, yindex; + + /* determine if we are in the lower triangle or the upper triangle + ______ + | /| + | / | + | / | + |/ | + ------ + + then calculate our end points + */ + + xlocal = (lon - originx) / col_step; + ylocal = (lat - originy) / row_step; + + xindex = (int)(xlocal); + yindex = (int)(ylocal); + + // printf("xindex = %d yindex = %d\n", xindex, yindex); + + if ( xindex + 1 == cols ) { + xindex--; + } + + if ( yindex + 1 == rows ) { + yindex--; + } + + if ( (xindex < 0) || (xindex + 1 >= cols) || + (yindex < 0) || (yindex + 1 >= rows) ) { + cout << "WARNING: Attempt to interpolate value outside of array!!!" + << endl; + return -9999; + } + + dx = xlocal - xindex; + dy = ylocal - yindex; + + if ( dx > dy ) { + // lower triangle + // printf(" Lower triangle\n"); + + x1 = xindex; + y1 = yindex; + z1 = in_data[x1][y1]; + + x2 = xindex + 1; + y2 = yindex; + z2 = in_data[x2][y2]; + + x3 = xindex + 1; + y3 = yindex + 1; + z3 = in_data[x3][y3]; + + // printf(" dx = %.2f dy = %.2f\n", dx, dy); + // printf(" (x1,y1,z1) = (%d,%d,%d)\n", x1, y1, z1); + // printf(" (x2,y2,z2) = (%d,%d,%d)\n", x2, y2, z2); + // printf(" (x3,y3,z3) = (%d,%d,%d)\n", x3, y3, z3); + + zA = dx * (z2 - z1) + z1; + zB = dx * (z3 - z1) + z1; + + // printf(" zA = %.2f zB = %.2f\n", zA, zB); + + if ( dx > FG_EPSILON ) { + elev = dy * (zB - zA) / dx + zA; + } else { + elev = zA; + } + } else { + // upper triangle + // printf(" Upper triangle\n"); + + x1 = xindex; + y1 = yindex; + z1 = in_data[x1][y1]; + + x2 = xindex; + y2 = yindex + 1; + z2 = in_data[x2][y2]; + + x3 = xindex + 1; + y3 = yindex + 1; + z3 = in_data[x3][y3]; + + // printf(" dx = %.2f dy = %.2f\n", dx, dy); + // printf(" (x1,y1,z1) = (%d,%d,%d)\n", x1, y1, z1); + // printf(" (x2,y2,z2) = (%d,%d,%d)\n", x2, y2, z2); + // printf(" (x3,y3,z3) = (%d,%d,%d)\n", x3, y3, z3); + + zA = dy * (z2 - z1) + z1; + zB = dy * (z3 - z1) + z1; + + // printf(" zA = %.2f zB = %.2f\n", zA, zB ); + // printf(" xB - xA = %.2f\n", col_step * dy / row_step); + + if ( dy > FG_EPSILON ) { + elev = dx * (zB - zA) / dy + zA; + } else { + elev = zA; + } + } + + return(elev); +} + + +#if 0 +// Write out a node file that can be used by the "triangle" program. +// Check for an optional "index.node.ex" file in case there is a .poly +// file to go along with this node file. Include these nodes first +// since they are referenced by position from the .poly file. +void FGArray::outputmesh_output_nodes( const string& fg_root, FGBucket& p ) +{ + double exnodes[MAX_EX_NODES][3]; + struct stat stat_buf; + string dir, file; + char exfile[256]; +#ifdef WIN32 + char tmp_path[256]; +#endif + string command; + FILE *fd; + int colmin, colmax, rowmin, rowmax; + int i, j, count, excount, result; + + // determine dimensions + colmin = p.get_x() * ( (cols - 1) / 8); + colmax = colmin + ( (cols - 1) / 8); + rowmin = p.get_y() * ( (rows - 1) / 8); + rowmax = rowmin + ( (rows - 1) / 8); + cout << " dumping region = " << colmin << "," << rowmin << " to " << + colmax << "," << rowmax << "\n"; + + // generate the base directory + string base_path = p.gen_base_path(); + cout << " fg_root = " << fg_root << " Base Path = " << base_path << endl; + dir = fg_root + "/" + base_path; + cout << " Dir = " << dir << endl; + + // stat() directory and create if needed + errno = 0; + result = stat(dir.c_str(), &stat_buf); + if ( result != 0 && errno == ENOENT ) { + cout << " Creating directory\n"; + + command = "mkdir -p " + dir + "\n"; + system( command.c_str() ); + } else { + // assume directory exists + } + + // get index and generate output file name + file = dir + "/" + p.gen_index_str() + ".node"; + + // get (optional) extra node file name (in case there is matching + // .poly file. + exfile = file + ".ex"; + + // load extra nodes if they exist + excount = 0; + if ( (fd = fopen(exfile, "r")) != NULL ) { + int junki; + fscanf(fd, "%d %d %d %d", &excount, &junki, &junki, &junki); + + if ( excount > MAX_EX_NODES - 1 ) { + printf("Error, too many 'extra' nodes, increase array size\n"); + exit(-1); + } else { + printf(" Expecting %d 'extra' nodes\n", excount); + } + + for ( i = 1; i <= excount; i++ ) { + fscanf(fd, "%d %lf %lf %lf\n", &junki, + &exnodes[i][0], &exnodes[i][1], &exnodes[i][2]); + printf("(extra) %d %.2f %.2f %.2f\n", + i, exnodes[i][0], exnodes[i][1], exnodes[i][2]); + } + fclose(fd); + } + + printf("Creating node file: %s\n", file); + fd = fopen(file, "w"); + + // first count regular nodes to generate header + count = 0; + for ( j = rowmin; j <= rowmax; j++ ) { + for ( i = colmin; i <= colmax; i++ ) { + if ( out_data[i][j] > -9000.0 ) { + count++; + } + } + // printf(" count = %d\n", count); + } + fprintf(fd, "%d 2 1 0\n", count + excount); + + // now write out extra node data + for ( i = 1; i <= excount; i++ ) { + fprintf(fd, "%d %.2f %.2f %.2f\n", + i, exnodes[i][0], exnodes[i][1], exnodes[i][2]); + } + + // write out actual node data + count = excount + 1; + for ( j = rowmin; j <= rowmax; j++ ) { + for ( i = colmin; i <= colmax; i++ ) { + if ( out_data[i][j] > -9000.0 ) { + fprintf(fd, "%d %.2f %.2f %.2f\n", + count++, + originx + (double)i * col_step, + originy + (double)j * row_step, + out_data[i][j]); + } + } + // printf(" count = %d\n", count); + } + + fclose(fd); +} +#endif + + +FGArray::~FGArray( void ) { + // printf("class FGArray DEstructor called.\n"); + delete [] in_data; + // delete [] out_data; +} + + diff --git a/src/Lib/Array/array.hxx b/src/Lib/Array/array.hxx new file mode 100644 index 00000000..38d5e3b1 --- /dev/null +++ b/src/Lib/Array/array.hxx @@ -0,0 +1,124 @@ +// array.hxx -- Array management class +// +// Written by Curtis Olson, started March 1998. +// +// Copyright (C) 1998 - 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#ifndef _ARRAY_HXX +#define _ARRAY_HXX + + +#ifndef __cplusplus +# error This library requires C++ +#endif + + +#include + +#include + +#include + +#include +#include +#include + + +FG_USING_STD(vector); + + +#define ARRAY_SIZE 1200 +#define ARRAY_SIZE_1 1201 + + +class FGArray { + +private: + + // file pointer for input + // gzFile fd; + fg_gzifstream *in; + + // coordinates (in arc seconds) of south west corner + double originx, originy; + + // number of columns and rows + int cols, rows; + + // Distance between column and row data points (in arc seconds) + double col_step, row_step; + + // pointers to the actual grid data allocated here + float (*in_data)[ARRAY_SIZE_1]; + // float (*out_data)[ARRAY_SIZE_1]; + + // output nodes + point_list corner_list; + point_list node_list; + +public: + + // Constructor + FGArray( void ); + FGArray( const string& file ); + + // Destructor + ~FGArray( void ); + + // open an Array file (use "-" if input is coming from stdin) + int open ( const string& file ); + + // close a Array file + int close(); + + // parse a Array file + int parse( FGBucket& b ); + + // Use least squares to fit a simpler data set to dem data. + // Return the number of fitted nodes + int fit( double error ); + + // add a node to the output corner node list + void add_corner_node( int i, int j, double val ); + + // add a node to the output fitted node list + void add_fit_node( int i, int j, double val ); + + // return the current altitude based on grid data. We should + // rewrite this to interpolate exact values, but for now this is + // good enough + double interpolate_altitude( double lon, double lat ) const; + + // Informational methods + inline double get_originx() const { return originx; } + inline double get_originy() const { return originy; } + inline int get_cols() const { return cols; } + inline int get_rows() const { return rows; } + inline double get_col_step() const { return col_step; } + inline double get_row_step() const { return row_step; } + + inline point_list get_corner_node_list() const { return corner_list; } + inline point_list get_fit_node_list() const { return node_list; } +}; + + +#endif // _ARRAY_HXX + + diff --git a/src/Lib/Array/testarray.cxx b/src/Lib/Array/testarray.cxx new file mode 100644 index 00000000..b3781881 --- /dev/null +++ b/src/Lib/Array/testarray.cxx @@ -0,0 +1,33 @@ +#include + +#include "array.hxx" + +main(int argc, char **argv) { + double lon, lat; + + if ( argc != 2 ) { + cout << "Usage: " << argv[0] << " work_dir" << endl; + exit(-1); + } + + string work_dir = argv[1]; + + lon = -146.248360; lat = 61.133950; // PAVD (Valdez, AK) + lon = -110.664244; lat = 33.352890; // P13 + + FGBucket b( lon, lat ); + string base = b.gen_base_path(); + string path = work_dir + "/" + base; + + string arrayfile = path + "/" + b.gen_index_str() + ".dem"; + cout << "arrayfile = " << arrayfile << endl; + + FGArray a(arrayfile); + a.parse( b ); + + lon *= 3600; + lat *= 3600; + cout << " " << a.interpolate_altitude(lon, lat) << endl; + + a.fit( 100 ); +} diff --git a/src/Lib/DEM/Makefile.am b/src/Lib/DEM/Makefile.am new file mode 100644 index 00000000..91bfd90d --- /dev/null +++ b/src/Lib/DEM/Makefile.am @@ -0,0 +1,11 @@ +noinst_LIBRARIES = libDEM.a + +libDEM_a_SOURCES = dem.cxx dem.hxx + +INCLUDES += -I$(top_builddir) -I$(top_builddir)/Lib + +# We can't build this with "-O2" (optimization) since this causes a seg fault +# I haven't found a way to strip this out of the CXXFLAGS, so I'm just +# setting it to "-g" +# CXXFLAGS = -g + diff --git a/src/Lib/DEM/dem.cxx b/src/Lib/DEM/dem.cxx new file mode 100644 index 00000000..22d74f5a --- /dev/null +++ b/src/Lib/DEM/dem.cxx @@ -0,0 +1,871 @@ +// dem.cxx -- DEM management class +// +// Written by Curtis Olson, started March 1998. +// +// Copyright (C) 1998 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#ifdef HAVE_CONFIG_H +# include +#endif + +#include + +#include // isspace() +#include // atoi() +#include // rint() +#include +#include + +#ifdef HAVE_SYS_STAT_H +# include // stat() +#endif + +#ifdef FG_HAVE_STD_INCLUDES +# include +#else +# include +#endif + +#ifdef HAVE_UNISTD_H +# include // stat() +#endif + +#include +#include +#include + +#include "dem.hxx" + + +#define MAX_EX_NODES 10000 + +#if 0 +#ifdef WIN32 +# ifdef __BORLANDC__ +# include +# define MKDIR(a) mkdir(a) +# else +# define MKDIR(a) mkdir(a,S_IRWXU) // I am just guessing at this flag (NHV) +# endif // __BORLANDC__ +#endif // WIN32 +#endif //0 + + +FGDem::FGDem( void ) { + // cout << "class FGDem CONstructor called." << endl; + dem_data = new float[DEM_SIZE_1][DEM_SIZE_1]; + output_data = new float[DEM_SIZE_1][DEM_SIZE_1]; +} + + +FGDem::FGDem( const string &file ) { + // cout << "class FGDem CONstructor called." << endl; + dem_data = new float[DEM_SIZE_1][DEM_SIZE_1]; + output_data = new float[DEM_SIZE_1][DEM_SIZE_1]; + + FGDem::open(file); +} + + +// open a DEM file +int +FGDem::open ( const string& file ) { + // open input file (or read from stdin) + if ( file == "-" ) { + printf("Loading DEM data file: stdin\n"); + // fd = stdin; + // fd = gzdopen(STDIN_FILENO, "r"); + printf("Not yet ported ...\n"); + return 0; + } else { + in = new fg_gzifstream( file ); + if ( !(*in) ) { + cout << "Cannot open " << file << endl; + return 0; + } + cout << "Loading DEM data file: " << file << endl; + } + + return 1; +} + + +// close a DEM file +int +FGDem::close () { + // the fg_gzifstream doesn't seem to have a close() + + delete in; + + return 1; +} + + +// return next token from input stream +string +FGDem::next_token() { + string token; + + *in >> token; + + // cout << " returning " + token + "\n"; + + return token; +} + + +// return next integer from input stream +int +FGDem::next_int() { + int result; + + *in >> result; + + return result; +} + + +// return next double from input stream +double +FGDem::next_double() { + double result; + + *in >> result; + + return result; +} + + +// return next exponential num from input stream +double +FGDem::next_exp() { + string token; + + token = next_token(); + + const char* p = token.c_str(); + char buf[64]; + char* bp = buf; + + for ( ; *p != 0; ++p ) + { + if ( *p == 'D' ) + *bp++ = 'E'; + else + *bp++ = *p; + } + *bp = 0; + return ::atof( buf ); +} + + +// read and parse DEM "A" record +int +FGDem::read_a_record() { + int i, inum; + double dnum; + string name, token; + char c; + + // get the name field (144 characters) + for ( i = 0; i < 144; i++ ) { + in->get(c); + name += c; + } + + // clean off the trailing whitespace + name = trim(name); + cout << " Quad name field: " << name << endl; + + // DEM level code, 3 reflects processing by DMA + inum = next_int(); + cout << " DEM level code = " << inum << "\n"; + + if ( inum > 3 ) { + return 0; + } + + // Pattern code, 1 indicates a regular elevation pattern + inum = next_int(); + cout << " Pattern code = " << inum << "\n"; + + // Planimetric reference system code, 0 indicates geographic + // coordinate system. + inum = next_int(); + cout << " Planimetric reference code = " << inum << "\n"; + + // Zone code + inum = next_int(); + cout << " Zone code = " << inum << "\n"; + + // Map projection parameters (ignored) + for ( i = 0; i < 15; i++ ) { + dnum = next_exp(); + // printf("%d: %f\n",i,dnum); + } + + // Units code, 3 represents arc-seconds as the unit of measure for + // ground planimetric coordinates throughout the file. + inum = next_int(); + if ( inum != 3 ) { + cout << " Unknown (X,Y) units code = " << inum << "!\n"; + exit(-1); + } + + // Units code; 2 represents meters as the unit of measure for + // elevation coordinates throughout the file. + inum = next_int(); + if ( inum != 2 ) { + cout << " Unknown (Z) units code = " << inum << "!\n"; + exit(-1); + } + + // Number (n) of sides in the polygon which defines the coverage of + // the DEM file (usually equal to 4). + inum = next_int(); + if ( inum != 4 ) { + cout << " Unknown polygon dimension = " << inum << "!\n"; + exit(-1); + } + + // Ground coordinates of bounding box in arc-seconds + dem_x1 = originx = next_exp(); + dem_y1 = originy = next_exp(); + cout << " Origin = (" << originx << "," << originy << ")\n"; + + dem_x2 = next_exp(); + dem_y2 = next_exp(); + + dem_x3 = next_exp(); + dem_y3 = next_exp(); + + dem_x4 = next_exp(); + dem_y4 = next_exp(); + + // Minimum/maximum elevations in meters + dem_z1 = next_exp(); + dem_z2 = next_exp(); + cout << " Elevation range " << dem_z1 << " to " << dem_z2 << "\n"; + + // Counterclockwise angle from the primary axis of ground + // planimetric referenced to the primary axis of the DEM local + // reference system. + token = next_token(); + + // Accuracy code; 0 indicates that a record of accuracy does not + // exist and that no record type C will follow. + + // DEM spacial resolution. Usually (3,3,1) (3,6,1) or (3,9,1) + // depending on latitude + + // I will eventually have to do something with this for data at + // higher latitudes */ + token = next_token(); + cout << " accuracy & spacial resolution string = " << token << endl; + i = token.length(); + cout << " length = " << i << "\n"; + + inum = atoi( token.substr( 0, i - 36 ) ); + row_step = atof( token.substr( i - 24, 12 ) ); + col_step = atof( token.substr( i - 36, 12 ) ); + cout << " Accuracy code = " << inum << "\n"; + cout << " column step = " << col_step << + " row step = " << row_step << "\n"; + + // dimension of arrays to follow (1) + token = next_token(); + + // number of profiles + dem_num_profiles = cols = next_int(); + cout << " Expecting " << dem_num_profiles << " profiles\n"; + + return 1; +} + + +// read and parse DEM "B" record +void +FGDem::read_b_record( ) { + string token; + int i; + int last; + + // row / column id of this profile + prof_row = next_int(); + prof_col = next_int(); + // printf("col id = %d row id = %d\n", prof_col, prof_row); + + // Number of columns and rows (elevations) in this profile + prof_num_rows = rows = next_int(); + prof_num_cols = next_int(); + // printf(" profile num rows = %d\n", prof_num_rows); + + // Ground planimetric coordinates (arc-seconds) of the first + // elevation in the profile + prof_x1 = next_exp(); + prof_y1 = next_exp(); + // printf(" Starting at %.2f %.2f\n", prof_x1, prof_y1); + + // Elevation of local datum for the profile. Always zero for + // 1-degree DEM, the reference is mean sea level. + token = next_token(); + + // Minimum and maximum elevations for the profile. + token = next_token(); + token = next_token(); + + // One (usually) dimensional array (prof_num_cols,1) of elevations + last = 0; + for ( i = 0; i < prof_num_rows; i++ ) { + prof_data = next_int(); + + // a bit of sanity checking that is unfortunately necessary + if ( prof_data > 10000 ) { // meters + prof_data = last; + } + + dem_data[cur_col][i] = (float)prof_data; + last = prof_data; + } +} + + +// parse dem file +int +FGDem::parse( ) { + int i; + + cur_col = 0; + + if ( !read_a_record() ) { + return(0); + } + + for ( i = 0; i < dem_num_profiles; i++ ) { + // printf("Ready to read next b record\n"); + read_b_record(); + cur_col++; + + if ( cur_col % 100 == 0 ) { + cout << " loaded " << cur_col << " profiles of data\n"; + } + } + + cout << " Done parsing\n"; + + return 1; +} + + +// write out the area of data covered by the specified bucket. Data +// is written out column by column starting at the lower left hand +// corner. +int +FGDem::write_area( const string& root, FGBucket& b, bool compress ) { + // calculate some boundaries + double min_x = ( b.get_center_lon() - 0.5 * b.get_width() ) * 3600.0; + double max_x = ( b.get_center_lon() + 0.5 * b.get_width() ) * 3600.0; + + double min_y = ( b.get_center_lat() - 0.5 * b.get_height() ) * 3600.0; + double max_y = ( b.get_center_lat() + 0.5 * b.get_height() ) * 3600.0; + + cout << b << endl; + cout << "width = " << b.get_width() << " height = " << b.get_height() + << endl; + + int start_x = (int)((min_x - originx) / col_step); + int span_x = (int)(b.get_width() * 3600.0 / col_step); + + int start_y = (int)((min_y - originy) / row_step); + int span_y = (int)(b.get_height() * 3600.0 / row_step); + + cout << "start_x = " << start_x << " span_x = " << span_x << endl; + cout << "start_y = " << start_y << " span_y = " << span_y << endl; + + // Do a simple sanity checking. But, please, please be nice to + // this write_area() routine and feed it buckets that coincide + // well with the underlying grid structure and spacing. + + if ( ( min_x < originx ) + || ( max_x > originx + cols * col_step ) + || ( min_y < originy ) + || ( max_y > originy + rows * row_step ) ) { + cout << " ERROR: bucket at least partially outside DEM data range!" << + endl; + return 0; + } + + // generate output file name + string base = b.gen_base_path(); + string path = root + "/" + base; + string command = "mkdir -p " + path; + system( command.c_str() ); + + string demfile = path + "/" + b.gen_index_str() + ".dem"; + cout << "demfile = " << demfile << endl; + + // write the file + FILE *fp; + if ( (fp = fopen(demfile.c_str(), "w")) == NULL ) { + cout << "cannot open " << demfile << " for writing!" << endl; + exit(-1); + } + + fprintf( fp, "%d %d\n", (int)min_x, (int)min_y ); + fprintf( fp, "%d %d %d %d\n", span_x + 1, (int)col_step, + span_y + 1, (int)row_step ); + for ( int i = start_x; i <= start_x + span_x; ++i ) { + for ( int j = start_y; j <= start_y + span_y; ++j ) { + fprintf( fp, "%d ", (int)dem_data[i][j] ); + } + fprintf( fp, "\n" ); + } + fclose(fp); + + if ( compress ) { + string command = "gzip --best -f " + demfile; + system( command.c_str() ); + } + + return 1; +} + + +#if 0 + +// return the current altitude based on grid data. We should rewrite +// this to interpolate exact values, but for now this is good enough +double FGDem::interpolate_altitude( double lon, double lat ) { + // we expect incoming (lon,lat) to be in arcsec for now + + double xlocal, ylocal, dx, dy, zA, zB, elev; + int x1, x2, x3, y1, y2, y3; + float z1, z2, z3; + int xindex, yindex; + + /* determine if we are in the lower triangle or the upper triangle + ______ + | /| + | / | + | / | + |/ | + ------ + + then calculate our end points + */ + + xlocal = (lon - originx) / col_step; + ylocal = (lat - originy) / row_step; + + xindex = (int)(xlocal); + yindex = (int)(ylocal); + + // printf("xindex = %d yindex = %d\n", xindex, yindex); + + if ( xindex + 1 == cols ) { + xindex--; + } + + if ( yindex + 1 == rows ) { + yindex--; + } + + if ( (xindex < 0) || (xindex + 1 >= cols) || + (yindex < 0) || (yindex + 1 >= rows) ) { + return(-9999); + } + + dx = xlocal - xindex; + dy = ylocal - yindex; + + if ( dx > dy ) { + // lower triangle + // printf(" Lower triangle\n"); + + x1 = xindex; + y1 = yindex; + z1 = dem_data[x1][y1]; + + x2 = xindex + 1; + y2 = yindex; + z2 = dem_data[x2][y2]; + + x3 = xindex + 1; + y3 = yindex + 1; + z3 = dem_data[x3][y3]; + + // printf(" dx = %.2f dy = %.2f\n", dx, dy); + // printf(" (x1,y1,z1) = (%d,%d,%d)\n", x1, y1, z1); + // printf(" (x2,y2,z2) = (%d,%d,%d)\n", x2, y2, z2); + // printf(" (x3,y3,z3) = (%d,%d,%d)\n", x3, y3, z3); + + zA = dx * (z2 - z1) + z1; + zB = dx * (z3 - z1) + z1; + + // printf(" zA = %.2f zB = %.2f\n", zA, zB); + + if ( dx > FG_EPSILON ) { + elev = dy * (zB - zA) / dx + zA; + } else { + elev = zA; + } + } else { + // upper triangle + // printf(" Upper triangle\n"); + + x1 = xindex; + y1 = yindex; + z1 = dem_data[x1][y1]; + + x2 = xindex; + y2 = yindex + 1; + z2 = dem_data[x2][y2]; + + x3 = xindex + 1; + y3 = yindex + 1; + z3 = dem_data[x3][y3]; + + // printf(" dx = %.2f dy = %.2f\n", dx, dy); + // printf(" (x1,y1,z1) = (%d,%d,%d)\n", x1, y1, z1); + // printf(" (x2,y2,z2) = (%d,%d,%d)\n", x2, y2, z2); + // printf(" (x3,y3,z3) = (%d,%d,%d)\n", x3, y3, z3); + + zA = dy * (z2 - z1) + z1; + zB = dy * (z3 - z1) + z1; + + // printf(" zA = %.2f zB = %.2f\n", zA, zB ); + // printf(" xB - xA = %.2f\n", col_step * dy / row_step); + + if ( dy > FG_EPSILON ) { + elev = dx * (zB - zA) / dy + zA; + } else { + elev = zA; + } + } + + return(elev); +} + + +// Use least squares to fit a simpler data set to dem data +void FGDem::fit( double error, FGBucket& p ) { + double x[DEM_SIZE_1], y[DEM_SIZE_1]; + double m, b, ave_error, max_error; + double cury, lasty; + int n, row, start, end; + int colmin, colmax, rowmin, rowmax; + bool good_fit; + // FILE *dem, *fit, *fit1; + + printf("Initializing output mesh structure\n"); + outputmesh_init(); + + // determine dimensions + colmin = p.get_x() * ( (cols - 1) / 8); + colmax = colmin + ( (cols - 1) / 8); + rowmin = p.get_y() * ( (rows - 1) / 8); + rowmax = rowmin + ( (rows - 1) / 8); + printf("Fitting region = %d,%d to %d,%d\n", colmin, rowmin, colmax, rowmax); + + // include the corners explicitly + outputmesh_set_pt(colmin, rowmin, dem_data[colmin][rowmin]); + outputmesh_set_pt(colmin, rowmax, dem_data[colmin][rowmax]); + outputmesh_set_pt(colmax, rowmax, dem_data[colmax][rowmax]); + outputmesh_set_pt(colmax, rowmin, dem_data[colmax][rowmin]); + + printf("Beginning best fit procedure\n"); + + for ( row = rowmin; row <= rowmax; row++ ) { + // fit = fopen("fit.dat", "w"); + // fit1 = fopen("fit1.dat", "w"); + + start = colmin; + + // printf(" fitting row = %d\n", row); + + while ( start < colmax ) { + end = start + 1; + good_fit = true; + + x[(end - start) - 1] = 0.0 + ( start * col_step ); + y[(end - start) - 1] = dem_data[start][row]; + + while ( (end <= colmax) && good_fit ) { + n = (end - start) + 1; + // printf("Least square of first %d points\n", n); + x[end - start] = 0.0 + ( end * col_step ); + y[end - start] = dem_data[end][row]; + least_squares(x, y, n, &m, &b); + ave_error = least_squares_error(x, y, n, m, b); + max_error = least_squares_max_error(x, y, n, m, b); + + /* + printf("%d - %d ave error = %.2f max error = %.2f y = %.2f*x + %.2f\n", + start, end, ave_error, max_error, m, b); + + f = fopen("gnuplot.dat", "w"); + for ( j = 0; j <= end; j++) { + fprintf(f, "%.2f %.2f\n", 0.0 + ( j * col_step ), + dem_data[row][j]); + } + for ( j = start; j <= end; j++) { + fprintf(f, "%.2f %.2f\n", 0.0 + ( j * col_step ), + dem_data[row][j]); + } + fclose(f); + + printf("Please hit return: "); gets(junk); + */ + + if ( max_error > error ) { + good_fit = false; + } + + end++; + } + + if ( !good_fit ) { + // error exceeded the threshold, back up + end -= 2; // back "end" up to the last good enough fit + n--; // back "n" up appropriately too + } else { + // we popped out of the above loop while still within + // the error threshold, so we must be at the end of + // the data set + end--; + } + + least_squares(x, y, n, &m, &b); + ave_error = least_squares_error(x, y, n, m, b); + max_error = least_squares_max_error(x, y, n, m, b); + + /* + printf("\n"); + printf("%d - %d ave error = %.2f max error = %.2f y = %.2f*x + %.2f\n", + start, end, ave_error, max_error, m, b); + printf("\n"); + + fprintf(fit1, "%.2f %.2f\n", x[0], m * x[0] + b); + fprintf(fit1, "%.2f %.2f\n", x[end-start], m * x[end-start] + b); + */ + + if ( start > colmin ) { + // skip this for the first line segment + cury = m * x[0] + b; + outputmesh_set_pt(start, row, (lasty + cury) / 2); + // fprintf(fit, "%.2f %.2f\n", x[0], (lasty + cury) / 2); + } + + lasty = m * x[end-start] + b; + start = end; + } + + /* + fclose(fit); + fclose(fit1); + + dem = fopen("gnuplot.dat", "w"); + for ( j = 0; j < DEM_SIZE_1; j++) { + fprintf(dem, "%.2f %.2f\n", 0.0 + ( j * col_step ), + dem_data[j][row]); + } + fclose(dem); + */ + + // NOTICE, this is for testing only. This instance of + // output_nodes should be removed. It should be called only + // once at the end once all the nodes have been generated. + // newmesh_output_nodes(&nm, "mesh.node"); + // printf("Please hit return: "); gets(junk); + } + + // outputmesh_output_nodes(fg_root, p); +} + + +// Initialize output mesh structure +void FGDem::outputmesh_init( void ) { + int i, j; + + for ( j = 0; j < DEM_SIZE_1; j++ ) { + for ( i = 0; i < DEM_SIZE_1; i++ ) { + output_data[i][j] = -9999.0; + } + } +} + + +// Get the value of a mesh node +double FGDem::outputmesh_get_pt( int i, int j ) { + return ( output_data[i][j] ); +} + + +// Set the value of a mesh node +void FGDem::outputmesh_set_pt( int i, int j, double value ) { + // printf("Setting data[%d][%d] = %.2f\n", i, j, value); + output_data[i][j] = value; +} + + +// Write out a node file that can be used by the "triangle" program. +// Check for an optional "index.node.ex" file in case there is a .poly +// file to go along with this node file. Include these nodes first +// since they are referenced by position from the .poly file. +void FGDem::outputmesh_output_nodes( const string& fg_root, FGBucket& p ) +{ + double exnodes[MAX_EX_NODES][3]; + struct stat stat_buf; + string dir; + char file[256], exfile[256]; +#ifdef WIN32 + char tmp_path[256]; +#endif + string command; + FILE *fd; + long int index; + int colmin, colmax, rowmin, rowmax; + int i, j, count, excount, result; + + // determine dimensions + colmin = p.get_x() * ( (cols - 1) / 8); + colmax = colmin + ( (cols - 1) / 8); + rowmin = p.get_y() * ( (rows - 1) / 8); + rowmax = rowmin + ( (rows - 1) / 8); + cout << " dumping region = " << colmin << "," << rowmin << " to " << + colmax << "," << rowmax << "\n"; + + // generate the base directory + string base_path = p.gen_base_path(); + cout << "fg_root = " << fg_root << " Base Path = " << base_path << endl; + dir = fg_root + "/" + base_path; + cout << "Dir = " << dir << endl; + + // stat() directory and create if needed + errno = 0; + result = stat(dir.c_str(), &stat_buf); + if ( result != 0 && errno == ENOENT ) { + cout << "Creating directory\n"; + +// #ifndef WIN32 + + command = "mkdir -p " + dir + "\n"; + system( command.c_str() ); + +#if 0 +// #else // WIN32 + + // Cygwin crashes when trying to output to node file + // explicitly making directory structure seems OK on Win95 + + extract_path (base_path, tmp_path); + + dir = fg_root + "/" + tmp_path; + if (my_mkdir ( dir.c_str() )) { exit (-1); } + + dir = fg_root + "/" + base_path; + if (my_mkdir ( dir.c_str() )) { exit (-1); } + +// #endif // WIN32 +#endif //0 + + } else { + // assume directory exists + } + + // get index and generate output file name + index = p.gen_index(); + sprintf(file, "%s/%ld.node", dir.c_str(), index); + + // get (optional) extra node file name (in case there is matching + // .poly file. + strcpy(exfile, file); + strcat(exfile, ".ex"); + + // load extra nodes if they exist + excount = 0; + if ( (fd = fopen(exfile, "r")) != NULL ) { + int junki; + fscanf(fd, "%d %d %d %d", &excount, &junki, &junki, &junki); + + if ( excount > MAX_EX_NODES - 1 ) { + printf("Error, too many 'extra' nodes, increase array size\n"); + exit(-1); + } else { + printf(" Expecting %d 'extra' nodes\n", excount); + } + + for ( i = 1; i <= excount; i++ ) { + fscanf(fd, "%d %lf %lf %lf\n", &junki, + &exnodes[i][0], &exnodes[i][1], &exnodes[i][2]); + printf("(extra) %d %.2f %.2f %.2f\n", + i, exnodes[i][0], exnodes[i][1], exnodes[i][2]); + } + fclose(fd); + } + + printf("Creating node file: %s\n", file); + fd = fopen(file, "w"); + + // first count regular nodes to generate header + count = 0; + for ( j = rowmin; j <= rowmax; j++ ) { + for ( i = colmin; i <= colmax; i++ ) { + if ( output_data[i][j] > -9000.0 ) { + count++; + } + } + // printf(" count = %d\n", count); + } + fprintf(fd, "%d 2 1 0\n", count + excount); + + // now write out extra node data + for ( i = 1; i <= excount; i++ ) { + fprintf(fd, "%d %.2f %.2f %.2f\n", + i, exnodes[i][0], exnodes[i][1], exnodes[i][2]); + } + + // write out actual node data + count = excount + 1; + for ( j = rowmin; j <= rowmax; j++ ) { + for ( i = colmin; i <= colmax; i++ ) { + if ( output_data[i][j] > -9000.0 ) { + fprintf(fd, "%d %.2f %.2f %.2f\n", + count++, + originx + (double)i * col_step, + originy + (double)j * row_step, + output_data[i][j]); + } + } + // printf(" count = %d\n", count); + } + + fclose(fd); +} +#endif + + +FGDem::~FGDem( void ) { + // printf("class FGDem DEstructor called.\n"); + delete [] dem_data; + delete [] output_data; +} + + diff --git a/src/Lib/DEM/dem.hxx b/src/Lib/DEM/dem.hxx new file mode 100644 index 00000000..eb23738c --- /dev/null +++ b/src/Lib/DEM/dem.hxx @@ -0,0 +1,154 @@ +// dem.hxx -- DEM management class +// +// Written by Curtis Olson, started March 1998. +// +// Copyright (C) 1998 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#ifndef _DEM_HXX +#define _DEM_HXX + + +#ifndef __cplusplus +# error This library requires C++ +#endif + + +#include +#include + + +#define DEM_SIZE 1200 +#define DEM_SIZE_1 1201 + + +class FGDem { + +private: + + // file pointer for input + // gzFile fd; + fg_gzifstream *in; + + // coordinates (in arc seconds) of south west corner + double originx, originy; + + // number of columns and rows + int cols, rows; + + // Distance between column and row data points (in arc seconds) + double col_step, row_step; + + // pointers to the actual grid data allocated here + float (*dem_data)[DEM_SIZE_1]; + float (*output_data)[DEM_SIZE_1]; + + // Current "A" Record Information + char dem_description[80], dem_quadrangle[80]; + double dem_x1, dem_y1, dem_x2, dem_y2, dem_x3, dem_y3, dem_x4, dem_y4; + double dem_z1, dem_z2; + int dem_resolution, dem_num_profiles; + + // Current "B" Record Information + int prof_col, prof_row; + int prof_num_cols, prof_num_rows; + double prof_x1, prof_y1; + int prof_data; + + // temporary values for the class to use + char option_name[32]; + int do_data; + int cur_col, cur_row; + + // return next token from input stream + string next_token(); + + // return next integer from input stream + int next_int(); + + // return next double from input stream + double next_double(); + + // return next exponential num from input stream + double next_exp(); + +public: + + // Constructor + FGDem( void ); + FGDem( const string& file ); + + // Destructor + ~FGDem( void ); + + // open a DEM file (use "-" if input is coming from stdin) + int open ( const string& file ); + + // close a DEM file + int close(); + + // parse a DEM file + int parse(); + + // read and parse DEM "A" record + int read_a_record(); + + // read and parse DEM "B" record + void read_b_record(); + + // write out the area of data covered by the specified bucket. + // Data is written out column by column starting at the lower left + // hand corner. + int write_area( const string& root, FGBucket& b, bool compress ); + +#if 0 + // return the current altitude based on grid data. We should + // rewrite this to interpolate exact values, but for now this is + // good enough + double interpolate_altitude( double lon, double lat ); + + // Use least squares to fit a simpler data set to dem data + void fit( double error, FGBucket& p ); + + // Initialize output mesh structure + void outputmesh_init( void ); + + // Get the value of a mesh node + double outputmesh_get_pt( int i, int j ); + + // Set the value of a mesh node + void outputmesh_set_pt( int i, int j, double value ); + + // Write out a node file that can be used by the "triangle" program + void outputmesh_output_nodes( const string& fg_root, FGBucket& p ); +#endif + + // Informational methods + inline double get_originx() const { return originx; } + inline double get_originy() const { return originy; } + inline int get_cols() const { return cols; } + inline int get_rows() const { return rows; } + inline double get_col_step() const { return col_step; } + inline double get_row_step() const { return row_step; } +}; + + +#endif // _DEM_HXX + + diff --git a/src/Lib/Geometry/Makefile.am b/src/Lib/Geometry/Makefile.am new file mode 100644 index 00000000..c7266c5a --- /dev/null +++ b/src/Lib/Geometry/Makefile.am @@ -0,0 +1,8 @@ +noinst_LIBRARIES = libBuild.a + +libBuild_a_SOURCES = \ + poly_support.cxx poly_support.hxx \ + trinodes.cxx trinodes.hxx \ + trisegs.cxx trisegs.hxx + +INCLUDES += -I$(top_builddir) -I$(top_builddir)/Lib -I$(top_builddir)/Tools/Lib diff --git a/src/Lib/Geometry/poly_support.cxx b/src/Lib/Geometry/poly_support.cxx new file mode 100644 index 00000000..1ac847d5 --- /dev/null +++ b/src/Lib/Geometry/poly_support.cxx @@ -0,0 +1,229 @@ +// poly_support.cxx -- additional supporting routines for the FGPolygon class +// specific to the object building process. +// +// Written by Curtis Olson, started October 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#include +#include + +#include + +#include "trinodes.hxx" + + +// calculate some "arbitrary" point inside the specified contour for +// assigning attribute areas. This requires data structures outside +// of "FGPolygon" which is why it is living over here in "Lib/Build" + +void calc_point_inside( const int contour, const FGTriNodes& trinodes ); + + +#include +#include + +#include + + +// Given a line segment specified by two endpoints p1 and p2, return +// the slope of the line. +static double slope( const Point3D& p0, const Point3D& p1 ) { + if ( fabs(p0.x() - p1.x()) > FG_EPSILON ) { + return (p0.y() - p1.y()) / (p0.x() - p1.x()); + } else { + return 1.0e+999; // really big number + } +} + + +// Given a line segment specified by two endpoints p1 and p2, return +// the y value of a point on the line that intersects with the +// verticle line through x. Return true if an intersection is found, +// false otherwise. +static bool intersects( Point3D p0, Point3D p1, double x, Point3D *result ) { + // sort the end points + if ( p0.x() > p1.x() ) { + Point3D tmp = p0; + p0 = p1; + p1 = tmp; + } + + if ( (x < p0.x()) || (x > p1.x()) ) { + // out of range of line segment, bail right away + return false; + } + + // equation of a line through (x0,y0) and (x1,y1): + // + // y = y1 + (x - x1) * (y0 - y1) / (x0 - x1) + + double y; + + if ( fabs(p0.x() - p1.x()) > FG_EPSILON ) { + y = p1.y() + (x - p1.x()) * (p0.y() - p1.y()) / (p0.x() - p1.x()); + } else { + return false; + } + result->setx(x); + result->sety(y); + + if ( p0.y() <= p1.y() ) { + if ( (p0.y() <= y) && (y <= p1.y()) ) { + return true; + } + } else { + if ( (p0.y() >= y) && (y >= p1.y()) ) { + return true; + } + } + + return false; +} + + +// calculate some "arbitrary" point inside the specified contour for +// assigning attribute areas +Point3D calc_point_inside( const FGPolygon& p, const int contour, + const FGTriNodes& trinodes ) { + Point3D tmp, min, ln, p1, p2, p3, m, result, inside_pt; + int min_node_index = 0; + int min_index = 0; + int p1_index = 0; + int p2_index = 0; + int ln_index = 0; + + // 1. find a point on the specified contour, min, with smallest y + + // min.y() starts greater than the biggest possible lat (degrees) + min.sety( 100.0 ); + + point_list c = p.get_contour(contour); + point_list_iterator current, last; + current = c.begin(); + last = c.end(); + + for ( int i = 0; i < p.contour_size( contour ); ++i ) { + tmp = p.get_pt( contour, i ); + if ( tmp.y() < min.y() ) { + min = tmp; + min_index = trinodes.find( min ); + min_node_index = i; + + // cout << "min index = " << *current + // << " value = " << min_y << endl; + } else { + // cout << " index = " << *current << endl; + } + } + + cout << "min node index = " << min_node_index << endl; + cout << "min index = " << min_index + << " value = " << trinodes.get_node( min_index ) + << " == " << min << endl; + + // 2. take midpoint, m, of min with neighbor having lowest + // fabs(slope) + + if ( min_node_index == 0 ) { + p1 = c[1]; + p2 = c[c.size() - 1]; + } else if ( min_node_index == (int)(c.size()) - 1 ) { + p1 = c[0]; + p2 = c[c.size() - 2]; + } else { + p1 = c[min_node_index - 1]; + p2 = c[min_node_index + 1]; + } + p1_index = trinodes.find( p1 ); + p2_index = trinodes.find( p2 ); + + double s1 = fabs( slope(min, p1) ); + double s2 = fabs( slope(min, p2) ); + if ( s1 < s2 ) { + ln_index = p1_index; + ln = p1; + } else { + ln_index = p2_index; + ln = p2; + } + + FGTriSeg base_leg( min_index, ln_index, 0 ); + + m.setx( (min.x() + ln.x()) / 2.0 ); + m.sety( (min.y() + ln.y()) / 2.0 ); + cout << "low mid point = " << m << endl; + + // 3. intersect vertical line through m and all other segments of + // all other contours of this polygon. save point, p3, with + // smallest y > m.y + + p3.sety(100); + + for ( int i = 0; i < (int)p.contours(); ++i ) { + cout << "contour = " << i << " size = " << p.contour_size( i ) << endl; + for ( int j = 0; j < (int)(p.contour_size( i ) - 1); ++j ) { + // cout << " p1 = " << poly[i][j] << " p2 = " + // << poly[i][j+1] << endl; + p1 = p.get_pt( i, j ); + p2 = p.get_pt( i, j+1 ); + p1_index = trinodes.find( p1 ); + p2_index = trinodes.find( p2 ); + + if ( intersects(p1, p2, m.x(), &result) ) { + cout << "intersection = " << result << endl; + if ( ( result.y() < p3.y() ) && + ( result.y() > m.y() ) && + ( base_leg != FGTriSeg(p1_index, p2_index, 0) ) ) { + p3 = result; + } + } + } + // cout << " p1 = " << poly[i][0] << " p2 = " + // << poly[i][poly[i].size() - 1] << endl; + p1 = p.get_pt( i, 0 ); + p2 = p.get_pt( i, p.contour_size( i ) - 1 ); + p1_index = trinodes.find( p1 ); + p2_index = trinodes.find( p2 ); + if ( intersects(p1, p2, m.x(), &result) ) { + cout << "intersection = " << result << endl; + if ( ( result.y() < p3.y() ) && + ( result.y() > m.y() ) && + ( base_leg != FGTriSeg(p1_index, p2_index, 0) ) ) { + p3 = result; + } + } + } + if ( p3.y() < 100 ) { + cout << "low intersection of other segment = " << p3 << endl; + inside_pt = Point3D( (m.x() + p3.x()) / 2.0, + (m.y() + p3.y()) / 2.0, + 0.0 ); + } else { + cout << "Error: Failed to find a point inside :-(" << endl; + inside_pt = p3; + } + + // 4. take midpoint of p2 && m as an arbitrary point inside polygon + + cout << "inside point = " << inside_pt << endl; + + return inside_pt; +} diff --git a/src/Lib/Geometry/poly_support.hxx b/src/Lib/Geometry/poly_support.hxx new file mode 100644 index 00000000..d6fd40d3 --- /dev/null +++ b/src/Lib/Geometry/poly_support.hxx @@ -0,0 +1,52 @@ +// poly_support.hxx -- additional supporting routines for the FGPolygon class +// specific to the object building process. +// +// Written by Curtis Olson, started October 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#ifndef _POLY_SUPPORT_HXX +#define _POLY_SUPPORT_HXX + + +#ifndef __cplusplus +# error This library requires C++ +#endif + + +#include +#include + +#include + +#include "trinodes.hxx" + + +// calculate some "arbitrary" point inside the specified contour for +// assigning attribute areas. This requires data structures outside +// of "FGPolygon" which is why it is living over here in "Lib/Build" + +Point3D calc_point_inside( const FGPolygon& p, const int contour, + const FGTriNodes& trinodes ); + + +#endif // _POLY_SUPPORT_HXX + + diff --git a/src/Lib/Geometry/trinodes.cxx b/src/Lib/Geometry/trinodes.cxx new file mode 100644 index 00000000..42258451 --- /dev/null +++ b/src/Lib/Geometry/trinodes.cxx @@ -0,0 +1,123 @@ +// trinodes.cxx -- "Triangle" nodes management class +// +// Written by Curtis Olson, started March 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#include "trinodes.hxx" + + +// Constructor +FGTriNodes::FGTriNodes( void ) { +} + + +// Destructor +FGTriNodes::~FGTriNodes( void ) { +} + + +// Add a point to the point list if it doesn't already exist. Returns +// the index (starting at zero) of the point in the list. +int FGTriNodes::unique_add( const Point3D& p ) { + point_list_iterator current, last; + int counter = 0; + + // cout << p.x() << "," << p.y() << endl; + + // see if point already exists + current = node_list.begin(); + last = node_list.end(); + for ( ; current != last; ++current ) { + if ( close_enough(p, *current) ) { + // cout << "found an existing match!" << endl; + return counter; + } + + ++counter; + } + + // add to list + node_list.push_back( p ); + + return counter; +} + + +// Add the point with no uniqueness checking +int FGTriNodes::simple_add( const Point3D& p ) { + node_list.push_back( p ); + + return node_list.size() - 1; +} + + +// Add a point to the point list if it doesn't already exist. Returns +// the index (starting at zero) of the point in the list. Use a +// course proximity check +int FGTriNodes::course_add( const Point3D& p ) { + point_list_iterator current, last; + int counter = 0; + + // cout << p.x() << "," << p.y() << endl; + + // see if point already exists + current = node_list.begin(); + last = node_list.end(); + for ( ; current != last; ++current ) { + if ( course_close_enough(p, *current) ) { + // cout << "found an existing match!" << endl; + return counter; + } + + ++counter; + } + + // add to list + node_list.push_back( p ); + + return counter; +} + + +// Find the index of the specified point (compair to the same +// tolerance as unique_add(). Returns -1 if not found. +int FGTriNodes::find( const Point3D& p ) const { + const_point_list_iterator current, last; + int counter = 0; + + // cout << p.x() << "," << p.y() << endl; + + // see if point already exists + current = node_list.begin(); + last = node_list.end(); + for ( ; current != last; ++current ) { + if ( close_enough(p, *current) ) { + // cout << "found an existing match!" << endl; + return counter; + } + + ++counter; + } + + return -1; +} + + diff --git a/src/Lib/Geometry/trinodes.hxx b/src/Lib/Geometry/trinodes.hxx new file mode 100644 index 00000000..8259a63e --- /dev/null +++ b/src/Lib/Geometry/trinodes.hxx @@ -0,0 +1,124 @@ +// trinodes.hxx -- "Triangle" nodes management class +// +// Written by Curtis Olson, started March 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#ifndef _TRINODES_HXX +#define _TRINODES_HXX + + +#ifndef __cplusplus +# error This library requires C++ +#endif + + +#include +#include +#include + + + +#define FG_PROXIMITY_EPSILON 0.000001 +#define FG_COURSE_EPSILON 0.0003 + + +class FGTriNodes { + +private: + + point_list node_list; + + // return true of the two points are "close enough" as defined by + // FG_PROXIMITY_EPSILON + bool close_enough( const Point3D& p, const Point3D& p ) const; + + // return true of the two points are "close enough" as defined by + // FG_COURSE_EPSILON + bool course_close_enough( const Point3D& p1, const Point3D& p2 ); + +public: + + // Constructor and destructor + FGTriNodes( void ); + ~FGTriNodes( void ); + + // delete all the data out of node_list + inline void clear() { node_list.clear(); } + + // Add a point to the point list if it doesn't already exist. + // Returns the index (starting at zero) of the point in the list. + int unique_add( const Point3D& p ); + + // Add the point with no uniqueness checking + int simple_add( const Point3D& p ); + + // Add a point to the point list if it doesn't already exist. + // Returns the index (starting at zero) of the point in the list. + // Use a course proximity check + int course_add( const Point3D& p ); + + // Find the index of the specified point (compair to the same + // tolerance as unique_add(). Returns -1 if not found. + int find( const Point3D& p ) const; + + // return the master node list + inline point_list get_node_list() const { return node_list; } + inline void set_node_list( point_list pl ) { node_list = pl; } + + // return the ith point + inline Point3D get_node( int i ) const { return node_list[i]; } + + // return the size of the node list + inline size_t size() const { return node_list.size(); } +}; + + +// return true of the two points are "close enough" as defined by +// FG_PROXIMITY_EPSILON +inline bool FGTriNodes::close_enough( const Point3D& p1, const Point3D& p2 ) + const +{ + if ( ( fabs(p1.x() - p2.x()) < FG_PROXIMITY_EPSILON ) && + ( fabs(p1.y() - p2.y()) < FG_PROXIMITY_EPSILON ) ) { + return true; + } else { + return false; + } +} + + +// return true of the two points are "close enough" as defined by +// FG_COURSE_EPSILON +inline bool FGTriNodes::course_close_enough( const Point3D& p1, + const Point3D& p2 ) +{ + if ( ( fabs(p1.x() - p2.x()) < FG_COURSE_EPSILON ) && + ( fabs(p1.y() - p2.y()) < FG_COURSE_EPSILON ) ) { + return true; + } else { + return false; + } +} + + +#endif // _TRINODES_HXX + + diff --git a/src/Lib/Geometry/trisegs.cxx b/src/Lib/Geometry/trisegs.cxx new file mode 100644 index 00000000..9828c284 --- /dev/null +++ b/src/Lib/Geometry/trisegs.cxx @@ -0,0 +1,210 @@ +// trisegs.cxx -- "Triangle" segment management class +// +// Written by Curtis Olson, started March 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#include +#include + +#include "trinodes.hxx" + +#include "trisegs.hxx" + + +// Constructor +FGTriSegments::FGTriSegments( void ) { +} + + +// Destructor +FGTriSegments::~FGTriSegments( void ) { +} + + +// Add a segment to the segment list if it doesn't already exist. +// Returns the index (starting at zero) of the segment in the list. +int FGTriSegments::unique_add( const FGTriSeg& s ) +{ + triseg_list_iterator current, last; + int counter = 0; + + // cout << s.get_n1() << "," << s.get_n2() << endl; + + // check if segment has duplicated endpoints + if ( s.get_n1() == s.get_n2() ) { + cout << "WARNING: ignoring null segment with the same " + << "point for both endpoints" << endl; + return -1; + } + + // check if segment already exists + current = seg_list.begin(); + last = seg_list.end(); + for ( ; current != last; ++current ) { + if ( s == *current ) { + // cout << "found an existing segment match" << endl; + return counter; + } + + ++counter; + } + + // add to list + seg_list.push_back( s ); + + return counter; +} + + +// Divide segment if there are other points on it, return the divided +// list of segments +void FGTriSegments::unique_divide_and_add( const point_list& nodes, + const FGTriSeg& s ) +{ + Point3D p0 = nodes[ s.get_n1() ]; + Point3D p1 = nodes[ s.get_n2() ]; + + bool found_extra = false; + int extra_index = 0; + int counter; + double m, m1, b, b1, y_err, x_err, y_err_min, x_err_min; + const_point_list_iterator current, last; + + // bool temp = false; + // if ( s == FGTriSeg( 170, 206 ) ) { + // cout << "this is it!" << endl; + // temp = true; + // } + + double xdist = fabs(p0.x() - p1.x()); + double ydist = fabs(p0.y() - p1.y()); + x_err_min = xdist + 1.0; + y_err_min = ydist + 1.0; + + if ( xdist > ydist ) { + // use y = mx + b + + // sort these in a sensible order + if ( p0.x() > p1.x() ) { + Point3D tmp = p0; + p0 = p1; + p1 = tmp; + } + + m = (p0.y() - p1.y()) / (p0.x() - p1.x()); + b = p1.y() - m * p1.x(); + + // if ( temp ) { + // cout << "m = " << m << " b = " <x() > (p0.x() + FG_EPSILON)) + && (current->x() < (p1.x() - FG_EPSILON)) ) { + + // if ( temp ) { + // cout << counter << endl; + // } + + y_err = fabs(current->y() - (m * current->x() + b)); + + if ( y_err < FG_PROXIMITY_EPSILON ) { + cout << "FOUND EXTRA SEGMENT NODE (Y)" << endl; + cout << p0 << " < " << *current << " < " + << p1 << endl; + found_extra = true; + if ( y_err < y_err_min ) { + extra_index = counter; + y_err_min = y_err; + } + } + } + ++counter; + } + } else { + // use x = m1 * y + b1 + + // sort these in a sensible order + if ( p0.y() > p1.y() ) { + Point3D tmp = p0; + p0 = p1; + p1 = tmp; + } + + m1 = (p0.x() - p1.x()) / (p0.y() - p1.y()); + b1 = p1.x() - m1 * p1.y(); + + // bool temp = true; + // if ( temp ) { + // cout << "xdist = " << xdist << " ydist = " << ydist << endl; + // cout << " p0 = " << p0 << " p1 = " << p1 << endl; + // cout << " m1 = " << m1 << " b1 = " << b1 << endl; + // } + + // cout << " should = 0 = " << fabs(p0.x() - (m1 * p0.y() + b1)) << endl;; + // cout << " should = 0 = " << fabs(p1.x() - (m1 * p1.y() + b1)) << endl;; + + current = nodes.begin(); + last = nodes.end(); + counter = 0; + for ( ; current != last; ++current ) { + if ( (current->y() > (p0.y() + FG_EPSILON)) + && (current->y() < (p1.y() - FG_EPSILON)) ) { + + x_err = fabs(current->x() - (m1 * current->y() + b1)); + + // if ( temp ) { + // cout << " (" << counter << ") x_err = " << x_err << endl; + // } + + if ( x_err < FG_PROXIMITY_EPSILON ) { + cout << "FOUND EXTRA SEGMENT NODE (X)" << endl; + cout << p0 << " < " << *current << " < " + << p1 << endl; + found_extra = true; + if ( x_err < x_err_min ) { + extra_index = counter; + x_err_min = x_err; + } + } + } + ++counter; + } + } + + if ( found_extra ) { + // recurse with two sub segments + cout << "dividing " << s.get_n1() << " " << extra_index + << " " << s.get_n2() << endl; + unique_divide_and_add( nodes, FGTriSeg( s.get_n1(), extra_index, + s.get_boundary_marker() ) ); + unique_divide_and_add( nodes, FGTriSeg( extra_index, s.get_n2(), + s.get_boundary_marker() ) ); + } else { + // this segment does not need to be divided, lets add it + unique_add( s ); + } +} + + diff --git a/src/Lib/Geometry/trisegs.hxx b/src/Lib/Geometry/trisegs.hxx new file mode 100644 index 00000000..4f2c59cc --- /dev/null +++ b/src/Lib/Geometry/trisegs.hxx @@ -0,0 +1,123 @@ +// trisegs.hxx -- "Triangle" segment management class +// +// Written by Curtis Olson, started March 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#ifndef _TRISEGS_HXX +#define _TRISEGS_HXX + + +#ifndef __cplusplus +# error This library requires C++ +#endif + + +#include + +#include + +#include "trinodes.hxx" + +FG_USING_STD(vector); + + +// a segment is two integer pointers into the node list +class FGTriSeg { + int n1, n2; // indices into point list + int boundary_marker; // flag if segment is a boundary + // (i.e. shouldn't get split) + +public: + + // Constructor and destructor + inline FGTriSeg( void ) { }; + inline FGTriSeg( int i1, int i2, int b ) { + n1 = i1; + n2 = i2; + boundary_marker = b; + } + + inline ~FGTriSeg( void ) { }; + + inline int get_n1() const { return n1; } + inline void set_n1( int i ) { n1 = i; } + inline int get_n2() const { return n2; } + inline void set_n2( int i ) { n2 = i; } + inline int get_boundary_marker() const { return boundary_marker; } + inline void set_boundary_marker( int b ) { boundary_marker = b; } + + friend bool operator == (const FGTriSeg& a, const FGTriSeg& b); + +}; + +inline bool operator == (const FGTriSeg& a, const FGTriSeg& b) +{ + return ((a.n1 == b.n1) && (a.n2 == b.n2)) + || ((a.n1 == b.n2) && (a.n2 == b.n1)); +} + + +typedef vector < FGTriSeg > triseg_list; +typedef triseg_list::iterator triseg_list_iterator; +typedef triseg_list::const_iterator const_triseg_list_iterator; + + +class FGTriSegments { + +private: + + triseg_list seg_list; + + // Divide segment if there are other points on it, return the + // divided list of segments + triseg_list divide_segment( const point_list& nodes, + const FGTriSeg& s ); + +public: + + // Constructor and destructor + FGTriSegments( void ); + ~FGTriSegments( void ); + + // delete all the data out of seg_list + inline void clear() { seg_list.clear(); } + + // Add a segment to the segment list if it doesn't already exist. + // Returns the index (starting at zero) of the segment in the + // list. + int unique_add( const FGTriSeg& s ); + + // Add a segment to the segment list if it doesn't already exist. + // Returns the index (starting at zero) of the segment in the list. + void unique_divide_and_add( const point_list& node_list, + const FGTriSeg& s ); + + // return the master segment list + inline triseg_list get_seg_list() const { return seg_list; } + + // return the ith segment + inline FGTriSeg get_seg( int i ) const { return seg_list[i]; } +}; + + +#endif // _TRISEGS_HXX + + diff --git a/src/Lib/Makefile.am b/src/Lib/Makefile.am new file mode 100644 index 00000000..385d126a --- /dev/null +++ b/src/Lib/Makefile.am @@ -0,0 +1,8 @@ +SUBDIRS = \ + Array \ + Build \ + DEM \ + Polygon \ + poly2tri \ + shapelib \ + Triangle diff --git a/src/Lib/Optimize/Makefile.am b/src/Lib/Optimize/Makefile.am new file mode 100644 index 00000000..e039449c --- /dev/null +++ b/src/Lib/Optimize/Makefile.am @@ -0,0 +1,8 @@ +noinst_LIBRARIES = libCombine.a + +libCombine_a_SOURCES = genfans.cxx genfans.hxx + +INCLUDES += \ + -I$(top_builddir) \ + -I$(top_builddir)/Lib \ + -I$(top_builddir)/Construct diff --git a/src/Lib/Optimize/genfans.cxx b/src/Lib/Optimize/genfans.cxx new file mode 100644 index 00000000..78f0e707 --- /dev/null +++ b/src/Lib/Optimize/genfans.cxx @@ -0,0 +1,244 @@ +// genfans.cxx -- Combine individual triangles into more optimal fans. +// +// Written by Curtis Olson, started March 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#include "genfans.hxx" + + +// make sure the list is expanded at least to hold "n" and then push +// "i" onto the back of the "n" list. +void FGGenFans::add_and_expand( reverse_list& by_node, int n, int i ) { + int_list empty; + + int size = (int)by_node.size(); + if ( size > n ) { + // ok + } else { + // cout << "capacity = " << by_node.capacity() << endl; + // cout << "size = " << size << " n = " << n + // << " need to push = " << n - size + 1 << endl; + for ( int i = 0; i < n - size + 1; ++i ) { + by_node.push_back(empty); + } + } + + by_node[n].push_back(i); +} + + +// given an input triangle, shuffle nodes so that "center" is the +// first node, but maintain winding order. +static FGTriEle canonify( const FGTriEle& t, int center ) { + if ( t.get_n1() == center ) { + // already ok + return t; + } else if ( t.get_n2() == center ) { + return FGTriEle( t.get_n2(), t.get_n3(), t.get_n1(), 0.0 ); + } else if ( t.get_n3() == center ) { + return FGTriEle( t.get_n3(), t.get_n1(), t.get_n2(), 0.0 ); + } else { + cout << "ERROR, index doesn't refer to this triangle!!!" << endl; + exit(-1); + } +} + +// returns a list of triangle indices +static int_list make_best_fan( const triele_list& master_tris, + const int center, const int_list& local_tris ) +{ + int_list best_result; + + // try starting with each of local_tris to find the best fan + // arrangement + for ( int start = 0; start < (int)local_tris.size(); ++start ) { + // cout << "trying with first triangle = " << local_tris[start] << endl; + + int_list tmp_result; + tmp_result.clear(); + + FGTriEle current_tri; + FGTriEle test; + current_tri = canonify( master_tris[local_tris[start]], center ); + tmp_result.push_back( local_tris[start] ); + + // follow the ring + int next = -1; + bool matches = true; + while ( (next != start) && matches ) { + // find next triangle in ring + matches = false; + for ( int i = 0; i < (int)local_tris.size(); ++i ) { + test = canonify( master_tris[local_tris[i]], center ); + if ( current_tri.get_n3() == test.get_n2() ) { + if ( i != start ) { + // cout << " next triangle = " << local_tris[i] << endl; + current_tri = test; + tmp_result.push_back( local_tris[i] ); + matches = true; + next = i; + break; + } + } + } + } + + if ( tmp_result.size() == local_tris.size() ) { + // we found a complete usage, no need to go on + // cout << "we found a complete usage, no need to go on" << endl; + best_result = tmp_result; + break; + } else if ( tmp_result.size() > best_result.size() ) { + // we found a better way to fan + // cout << "we found a better fan arrangement" << endl; + best_result = tmp_result; + } + } + + return best_result; +} + + +static bool in_fan(int index, const int_list& fan ) { + const_int_list_iterator current = fan.begin(); + const_int_list_iterator last = fan.end(); + + for ( ; current != last; ++current ) { + if ( index == *current ) { + return true; + } + } + + return false; +} + + +// recursive build fans from triangle list +fan_list FGGenFans::greedy_build( triele_list tris ) { + cout << "starting greedy build of fans" << endl; + + fans.clear(); + + while ( ! tris.empty() ) { + // cout << "building reverse_list" << endl; + reverse_list by_node; + by_node.clear(); + + // traverse the triangle list and for each node, build a list of + // triangles that attach to it. + + for ( int i = 0; i < (int)tris.size(); ++i ) { + int n1 = tris[i].get_n1(); + int n2 = tris[i].get_n2(); + int n3 = tris[i].get_n3(); + + add_and_expand( by_node, n1, i ); + add_and_expand( by_node, n2, i ); + add_and_expand( by_node, n3, i ); + } + + // find the node in the tris list that attaches to the most + // triangles + + // cout << "find most connected node" << endl; + + int_list biggest_group; + reverse_list_iterator r_current = by_node.begin(); + reverse_list_iterator r_last = by_node.end(); + int index = 0; + int counter = 0; + for ( ; r_current != r_last; ++r_current ) { + if ( r_current->size() > biggest_group.size() ) { + biggest_group = *r_current; + index = counter; + } + ++counter; + } + // cout << "triangle pool = " << tris.size() << endl; + // cout << "biggest_group = " << biggest_group.size() << endl; + // cout << "center node = " << index << endl; + + // make the best fan we can out of this group + // cout << "before make_best_fan()" << endl; + int_list best_fan = make_best_fan( tris, index, biggest_group ); + // cout << "after make_best_fan()" << endl; + + // generate point form of best_fan + int_list node_list; + node_list.clear(); + + int_list_iterator i_start = best_fan.begin(); + int_list_iterator i_current = i_start; + int_list_iterator i_last = best_fan.end(); + for ( ; i_current != i_last; ++i_current ) { + FGTriEle t = canonify( tris[*i_current], index ); + if ( i_start == i_current ) { + node_list.push_back( t.get_n1() ); + node_list.push_back( t.get_n2() ); + } + node_list.push_back( t.get_n3() ); + } + // cout << "best list size = " << node_list.size() << endl; + + // add this fan to the fan list + fans.push_back( node_list ); + + // delete the triangles in best_fan out of tris and repeat + triele_list_iterator t_current = tris.begin(); + triele_list_iterator t_last = tris.end(); + counter = 0; + while ( t_current != t_last ) { + if ( in_fan(counter, best_fan) ) { + // cout << "erasing " + // << t_current->get_n1() << "," + // << t_current->get_n2() << "," + // << t_current->get_n3() + // << " from master tri pool" + // << endl; + tris.erase( t_current ); + } else { + ++t_current; + } + ++counter; + } + } + + cout << "end of greedy build of fans" << endl; + cout << "average fan size = " << ave_size() << endl; + + return fans; +} + + +// report average fan size +double FGGenFans::ave_size() { + double sum = 0.0; + + fan_list_iterator current = fans.begin(); + fan_list_iterator last = fans.end(); + for ( ; current != last; ++current ) { + sum += current->size(); + } + + return sum / (double)fans.size(); +} + + diff --git a/src/Lib/Optimize/genfans.hxx b/src/Lib/Optimize/genfans.hxx new file mode 100644 index 00000000..c56af87a --- /dev/null +++ b/src/Lib/Optimize/genfans.hxx @@ -0,0 +1,81 @@ +// genfans.hxx -- Combine individual triangles into more optimal fans. +// +// Written by Curtis Olson, started March 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#ifndef _GENFANS_HXX +#define _GENFANS_HXX + + +#ifndef __cplusplus +# error This library requires C++ +#endif + + +#include + +#include + +#include + +#include + +FG_USING_STD(vector); + + +typedef vector < int_list > fan_list; +typedef fan_list::iterator fan_list_iterator; +typedef fan_list::const_iterator const_fan_list_iterator; + +typedef vector < int_list > reverse_list; +typedef reverse_list::iterator reverse_list_iterator; +typedef reverse_list::const_iterator const_reverse_list_iterator; + + + +class FGGenFans { + +private: + + fan_list fans; + + // make sure the list is expanded at least to hold "n" and then + // push "i" onto the back of the "n" list. + void add_and_expand( reverse_list& by_node, int n, int i ); + +public: + + // Constructor && Destructor + inline FGGenFans() { } + inline ~FGGenFans() { } + + // recursive build fans from triangle list + // fan_list greedy_build( triele_list tris ); + fan_list greedy_build( triele_list tris ); + + // report average fan size + double ave_size(); +}; + + +#endif // _GENFANS_HXX + + diff --git a/src/Lib/Polygon/Makefile.am b/src/Lib/Polygon/Makefile.am new file mode 100644 index 00000000..e6bc3a04 --- /dev/null +++ b/src/Lib/Polygon/Makefile.am @@ -0,0 +1,9 @@ +noinst_LIBRARIES = libPolygon.a + +libPolygon_a_SOURCES = \ + index.cxx index.hxx \ + names.cxx names.hxx \ + polygon.cxx polygon.hxx \ + split.cxx split.hxx + +INCLUDES += -I$(top_builddir) -I$(top_builddir)/Lib -I$(top_builddir)/Tools/Lib diff --git a/src/Lib/Polygon/index.cxx b/src/Lib/Polygon/index.cxx new file mode 100644 index 00000000..a37db140 --- /dev/null +++ b/src/Lib/Polygon/index.cxx @@ -0,0 +1,71 @@ +// index.cxx -- routines to handle a unique/persistant integer polygon index +// +// Written by Curtis Olson, started February 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or modify +// it under the terms of the GNU General Public License as published by +// the Free Software Foundation; either version 2 of the License, or +// (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + +#include + +#include STL_STRING + +#include + +#include "index.hxx" + + +static long int poly_index; +static string poly_path; + + +// initialize the unique polygon index counter stored in path +bool poly_index_init( string path ) { + poly_path = path; + + FILE *fp = fopen( poly_path.c_str(), "r" ); + + if ( fp == NULL ) { + cout << "Error cannot open " << poly_path << endl; + poly_index = 0; + return false; + } + + fscanf( fp, "%ld", &poly_index ); + + fclose( fp ); +} + + +// increment the persistant counter and return the next poly_index +long int poly_index_next() { + ++poly_index; + + FILE *fp = fopen( poly_path.c_str(), "w" ); + + if ( fp == NULL ) { + cout << "Error cannot open " << poly_path << " for writing" << endl; + } + + fprintf( fp, "%ld\n", poly_index ); + + fclose( fp ); + + return poly_index; +} + + diff --git a/src/Lib/Polygon/index.hxx b/src/Lib/Polygon/index.hxx new file mode 100644 index 00000000..c2336cd0 --- /dev/null +++ b/src/Lib/Polygon/index.hxx @@ -0,0 +1,43 @@ +// index.cxx -- routines to handle a unique/persistant integer polygon index +// +// Written by Curtis Olson, started February 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or modify +// it under the terms of the GNU General Public License as published by +// the Free Software Foundation; either version 2 of the License, or +// (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#ifndef _INDEX_HXX +#define _INDEX_HXX + + +#include + +#include STL_STRING + + +// initialize the unique polygon index counter stored in path +bool poly_index_init( string path ); + +// increment the persistant counter and return the next poly_index +long int poly_index_next(); + + + +#endif // _INDEX_HXX + + diff --git a/src/Lib/Polygon/names.cxx b/src/Lib/Polygon/names.cxx new file mode 100644 index 00000000..b631c791 --- /dev/null +++ b/src/Lib/Polygon/names.cxx @@ -0,0 +1,118 @@ +// names.cxx -- process shapefiles names +// +// Written by Curtis Olson, started February 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or modify +// it under the terms of the GNU General Public License as published by +// the Free Software Foundation; either version 2 of the License, or +// (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + +#include + +#include STL_STRING + +#include "names.hxx" + + +// return area type from text name +AreaType get_area_type( string area ) { + if ( area == "SomeSort" ) { + return SomeSortOfArea; + } else if ( area == "Hole" ) { + return HoleArea; + } else if ( (area == "Swamp or Marsh") + || (area == "Marsh") ) { + return MarshArea; + } else if ( area == "Lake" ) { + return LakeArea; + } else if ( (area == "Lake Dry") + || (area == "DryLake") ) { + return DryLakeArea; + } else if ( (area == "Lake Intermittent") + || (area == "IntermittentLake") ) { + return IntLakeArea; + } else if ( area == "Reservoir" ) { + return ReservoirArea; + } else if ( (area == "Reservoir Intermittent") + || (area == "IntermittentReservoir") ) { + return IntReservoirArea; + } else if ( area == "Stream" ) { + return StreamArea; + } else if ( area == "Canal" ) { + return CanalArea; + } else if ( area == "Glacier" ) { + return GlacierArea; + } else if ( area == "Urban" ) { + return UrbanArea; + } else if ( area == "Default" ) { + return DefaultArea; + } else if ( (area == "Bay Estuary or Ocean") + || (area == "Ocean") ) { + return OceanArea; + } else if ( area == "Void Area" ) { + return VoidArea; + } else if ( area == "Null" ) { + return NullArea; + } else { + cout << "unknown area = '" << area << "'" << endl; + // cout << "area = " << area << endl; + // for ( int i = 0; i < area.length(); i++ ) { + // cout << i << ") " << (int)area[i] << endl; + // } + return UnknownArea; + } +} + + +// return text from of area name +string get_area_name( AreaType area ) { + if ( area == DefaultArea ) { + return "Default"; + } else if ( area == HoleArea ) { + return "Hole"; + } else if ( area == MarshArea ) { + return "Marsh"; + } else if ( area == LakeArea ) { + return "Lake"; + } else if ( area == DryLakeArea ) { + return "DryLake"; + } else if ( area == IntLakeArea ) { + return "IntermittentLake"; + } else if ( area == ReservoirArea ) { + return "Reservoir"; + } else if ( area == IntReservoirArea ) { + return "IntermittentReservoir"; + } else if ( area == StreamArea ) { + return "Stream"; + } else if ( area == CanalArea ) { + return "Canal"; + } else if ( area == GlacierArea ) { + return "Glacier"; + } else if ( area == UrbanArea ) { + return "Urban"; + } else if ( area == OceanArea ) { + return "Ocean"; + } else if ( area == VoidArea ) { + return "VoidArea"; + } else if ( area == NullArea ) { + return "Null"; + } else { + cout << "unknown area code = " << (int)area << endl; + return "Unknown"; + } +} + + diff --git a/src/Lib/Polygon/names.hxx b/src/Lib/Polygon/names.hxx new file mode 100644 index 00000000..9b3d86fd --- /dev/null +++ b/src/Lib/Polygon/names.hxx @@ -0,0 +1,68 @@ +// names.hxx -- process shapefiles names +// +// Written by Curtis Olson, started February 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or modify +// it under the terms of the GNU General Public License as published by +// the Free Software Foundation; either version 2 of the License, or +// (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#ifndef _NAMES_HXX +#define _NAMES_HXX + + +#include + +#include STL_STRING + +FG_USING_STD(string); + + +// Posible shape file types. Note the order of these is important and +// defines the priority of these shapes if they should intersect. The +// smaller the number, the higher the priority. +enum AreaType { + SomeSortOfArea = 0, + HoleArea = 1, + LakeArea = 2, + DryLakeArea = 3, + IntLakeArea = 4, + ReservoirArea = 5, + IntReservoirArea = 6, + StreamArea = 7, + CanalArea = 8, + GlacierArea = 9, + OceanArea = 10, + UrbanArea = 11, + MarshArea = 12, + DefaultArea = 13, + VoidArea = 9997, + NullArea = 9998, + UnknownArea = 9999 +}; + + +// return area type from text name +AreaType get_area_type( string area ); + +// return text form of area name +string get_area_name( AreaType area ); + + +#endif // _NAMES_HXX + + diff --git a/src/Lib/Polygon/polygon.cxx b/src/Lib/Polygon/polygon.cxx new file mode 100644 index 00000000..1b340865 --- /dev/null +++ b/src/Lib/Polygon/polygon.cxx @@ -0,0 +1,493 @@ +// polygon.cxx -- polygon (with holes) management class +// +// Written by Curtis Olson, started March 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +// include Generic Polygon Clipping Library +// +// http://www.cs.man.ac.uk/aig/staff/alan/software/ +// +extern "C" { +#include +} + +#include +#include + +#include + +#include "polygon.hxx" + + +// Constructor +FGPolygon::FGPolygon( void ) { +} + + +// Destructor +FGPolygon::~FGPolygon( void ) { +} + + +// Calculate theta of angle (a, b, c) +static double calc_angle(point2d a, point2d b, point2d c) { + point2d u, v; + double udist, vdist, uv_dot, tmp; + + // u . v = ||u|| * ||v|| * cos(theta) + + u.x = b.x - a.x; + u.y = b.y - a.y; + udist = sqrt( u.x * u.x + u.y * u.y ); + // printf("udist = %.6f\n", udist); + + v.x = b.x - c.x; + v.y = b.y - c.y; + vdist = sqrt( v.x * v.x + v.y * v.y ); + // printf("vdist = %.6f\n", vdist); + + uv_dot = u.x * v.x + u.y * v.y; + // printf("uv_dot = %.6f\n", uv_dot); + + tmp = uv_dot / (udist * vdist); + // printf("tmp = %.6f\n", tmp); + + return acos(tmp); +} + + +// return the perimeter of a contour (assumes simple polygons, +// i.e. non-self intersecting.) +// +// negative areas indicate counter clockwise winding +// postitive areas indicate clockwise winding. + +double FGPolygon::area_contour( const int contour ) const { + // area = 1/2 * sum[i = 0 to k-1][x(i)*y(i+1) - x(i+1)*y(i)] + // where k is defined as 0 + + point_list c = poly[contour]; + int size = c.size(); + double sum = 0.0; + + for ( int i = 0; i < size; ++i ) { + sum += c[(i+1)%size].x() * c[i].y() - c[i].x() * c[(i+1)%size].y(); + } + + // area can be negative or positive depending on the polygon + // winding order + return fabs(sum / 2.0); +} + + +// return the smallest interior angle of the polygon +double FGPolygon::minangle_contour( const int contour ) { + point_list c = poly[contour]; + int size = c.size(); + int p1_index, p2_index, p3_index; + point2d p1, p2, p3; + double angle; + double min_angle = 2.0 * FG_PI; + + for ( int i = 0; i < size; ++i ) { + p1_index = i - 1; + if ( p1_index < 0 ) { + p1_index += size; + } + + p2_index = i; + + p3_index = i + 1; + if ( p3_index >= size ) { + p3_index -= size; + } + + p1.x = c[p1_index].x(); + p1.y = c[p1_index].y(); + + p2.x = c[p2_index].x(); + p2.y = c[p2_index].y(); + + p3.x = c[p3_index].x(); + p3.y = c[p3_index].y(); + + angle = calc_angle( p1, p2, p3 ); + + if ( angle < min_angle ) { + min_angle = angle; + } + } + + return min_angle; +} + + +// shift every point in the polygon by lon, lat +void FGPolygon::shift( double lon, double lat ) { + for ( int i = 0; i < (int)poly.size(); ++i ) { + for ( int j = 0; j < (int)poly[i].size(); ++j ) { + poly[i][j].setx( poly[i][j].x() + lon ); + poly[i][j].sety( poly[i][j].y() + lat ); + } + } +} + + +// output +void FGPolygon::write( const string& file ) { + FILE *fp = fopen( file.c_str(), "w" ); + + for ( int i = 0; i < (int)poly.size(); ++i ) { + for ( int j = 0; j < (int)poly[i].size(); ++j ) { + fprintf(fp, "%.6f %.6f\n", poly[i][j].x(), poly[i][j].y()); + } + fprintf(fp, "%.6f %.6f\n", poly[i][0].x(), poly[i][0].y()); + } + + fclose(fp); +} + + +// +// wrapper functions for gpc polygon clip routines +// + +// Make a gpc_poly from an FGPolygon +void make_gpc_poly( const FGPolygon& in, gpc_polygon *out ) { + gpc_vertex_list v_list; + v_list.num_vertices = 0; + v_list.vertex = new gpc_vertex[FG_MAX_VERTICES]; + + // cout << "making a gpc_poly" << endl; + // cout << " input contours = " << in.contours() << endl; + + Point3D p; + // build the gpc_polygon structures + for ( int i = 0; i < in.contours(); ++i ) { + // cout << " contour " < FG_MAX_VERTICES ) { + cout << "Polygon too large, need to increase FG_MAX_VERTICES to at " + << "least " << in.contour_size( i ) << endl; + exit(-1); + } + + for ( int j = 0; j < in.contour_size( i ); ++j ) { + p = in.get_pt( i, j ); + v_list.vertex[j].x = p.x(); + v_list.vertex[j].y = p.y(); + } + v_list.num_vertices = in.contour_size( i ); + gpc_add_contour( out, &v_list, in.get_hole_flag( i ) ); + } + + // free alocated memory + delete v_list.vertex; +} + + +// Set operation type +typedef enum { + POLY_DIFF, // Difference + POLY_INT, // Intersection + POLY_XOR, // Exclusive or + POLY_UNION // Union +} clip_op; + + +// Generic clipping routine +FGPolygon polygon_clip( clip_op poly_op, const FGPolygon& subject, + const FGPolygon& clip ) +{ + FGPolygon result; + + gpc_polygon *gpc_subject = new gpc_polygon; + gpc_subject->num_contours = 0; + gpc_subject->contour = NULL; + gpc_subject->hole = NULL; + make_gpc_poly( subject, gpc_subject ); + + gpc_polygon *gpc_clip = new gpc_polygon; + gpc_clip->num_contours = 0; + gpc_clip->contour = NULL; + gpc_clip->hole = NULL; + make_gpc_poly( clip, gpc_clip ); + + gpc_polygon *gpc_result = new gpc_polygon; + gpc_result->num_contours = 0; + gpc_result->contour = NULL; + gpc_result->hole = NULL; + + gpc_op op; + if ( poly_op == POLY_DIFF ) { + op = GPC_DIFF; + } else if ( poly_op == POLY_INT ) { + op = GPC_INT; + } else if ( poly_op == POLY_XOR ) { + op = GPC_XOR; + } else if ( poly_op == POLY_UNION ) { + op = GPC_UNION; + } else { + cout << "Unknown polygon op, exiting." << endl; + exit(-1); + } + + gpc_polygon_clip( op, gpc_subject, gpc_clip, gpc_result ); + + for ( int i = 0; i < gpc_result->num_contours; ++i ) { + // cout << " processing contour = " <contour[i].num_vertices << ", hole = " + // << gpc_result->hole[i] << endl; + + // sprintf(junkn, "g.%d", junkc++); + // junkfp = fopen(junkn, "w"); + + for ( int j = 0; j < gpc_result->contour[i].num_vertices; j++ ) { + Point3D p( gpc_result->contour[i].vertex[j].x, + gpc_result->contour[i].vertex[j].y, + 0 ); + // junkp = in_nodes.get_node( index ); + // fprintf(junkfp, "%.4f %.4f\n", junkp.x(), junkp.y()); + result.add_node(i, p); + // cout << " - " << index << endl; + } + // fprintf(junkfp, "%.4f %.4f\n", + // gpc_result->contour[i].vertex[0].x, + // gpc_result->contour[i].vertex[0].y); + // fclose(junkfp); + + result.set_hole_flag( i, gpc_result->hole[i] ); + } + + // free allocated memory + gpc_free_polygon( gpc_subject ); + gpc_free_polygon( gpc_clip ); + gpc_free_polygon( gpc_result ); + + return result; +} + + +// Difference +FGPolygon polygon_diff( const FGPolygon& subject, const FGPolygon& clip ) { + return polygon_clip( POLY_DIFF, subject, clip ); +} + +// Intersection +FGPolygon polygon_int( const FGPolygon& subject, const FGPolygon& clip ) { + return polygon_clip( POLY_INT, subject, clip ); +} + + +// Exclusive or +FGPolygon polygon_xor( const FGPolygon& subject, const FGPolygon& clip ) { + return polygon_clip( POLY_XOR, subject, clip ); +} + + +// Union +FGPolygon polygon_union( const FGPolygon& subject, const FGPolygon& clip ) { + return polygon_clip( POLY_UNION, subject, clip ); +} + + +// canonify the polygon winding, outer contour must be anti-clockwise, +// all inner contours must be clockwise. +FGPolygon polygon_canonify( const FGPolygon& in_poly ) { + FGPolygon result; + result.erase(); + + // Negative areas indicate counter clockwise winding. Postitive + // areas indicate clockwise winding. + + int non_hole_count = 0; + + for ( int i = 0; i < in_poly.contours(); ++i ) { + point_list contour = in_poly.get_contour( i ); + int hole_flag = in_poly.get_hole_flag( i ); + if ( !hole_flag ) { + non_hole_count++; + if ( non_hole_count > 1 ) { + cout << "ERROR: polygon with more than one enclosing" << endl; + cout << " contour. I bet you don't handle that!" << endl; + cout << " dying!!!" << endl; + } + } + double area = in_poly.area_contour( i ); + if ( hole_flag && (area < 0) ) { + // reverse contour + point_list rcontour; + rcontour.clear(); + for ( int j = (int)contour.size() - 1; j >= 0; --j ) { + rcontour.push_back( contour[j] ); + } + result.add_contour( rcontour, hole_flag ); + } else if ( !hole_flag && (area > 0) ) { + // reverse contour + point_list rcontour; + rcontour.clear(); + for ( int j = (int)contour.size() - 1; j >= 0; --j ) { + rcontour.push_back( contour[j] ); + } + result.add_contour( rcontour, hole_flag ); + } else { + result.add_contour( contour, hole_flag ); + } + } + + return result; +} + + +// Wrapper for the fast Polygon Triangulation based on Seidel's +// Algorithm by Atul Narkhede and Dinesh Manocha +// http://www.cs.unc.edu/~dm/CODE/GEM/chapter.html + +// I make this oversize because given an n sided concave polygon with +// m, n, o, ... sided holes, I have no idea how many triangles would +// result and I don't have time right now to see if an upper bound can +// be determined easily. +#define FG_MAX_TRIANGLES 100000 + +FGPolygon polygon_to_tristrip( const FGPolygon& in_poly ) { + + // canonify the polygon winding, outer contour must be + // anti-clockwise, all inner contours must be clockwise. + FGPolygon canon_poly = polygon_canonify( in_poly ); + + // create and fill in the required structures + int ncontours = canon_poly.contours(); + int cntr[ncontours]; + int vsize = 1; + for ( int i = 0; i < canon_poly.contours(); ++i ) { + cntr[i] = canon_poly.contour_size( i ); + vsize += cntr[i]; + } + double vertices[vsize][2]; + int counter = 1; + Point3D p; + for ( int i = 0; i < canon_poly.contours(); ++i ) { + for ( int j = 0; j < canon_poly.contour_size( i ); ++j ) { + p = canon_poly.get_pt( i, j ); + vertices[counter][0] = p.x(); + vertices[counter][1] = p.y(); + counter++; + } + } + int triangles[FG_MAX_TRIANGLES][3]; + + // do the triangulation + int ntriangles = triangulate_polygon(ncontours, cntr, vertices, triangles); + + /* + gpc_polygon *tmp_poly = new gpc_polygon; + tmp_poly->num_contours = 0; + tmp_poly->contour = NULL; + tmp_poly->hole = NULL; + make_gpc_poly( in_poly, tmp_poly ); + + gpc_tristrip *tmp_tristrip = new gpc_tristrip; + tmp_tristrip->num_strips = 0; + tmp_tristrip->strip = NULL; + + gpc_polygon_to_tristrip( tmp_poly, tmp_tristrip ); + + FGPolygon result; + + for ( int i = 0; i < tmp_tristrip->num_strips; ++i ) { + cout << " processing strip = " <strip[i].num_vertices << endl; + + // sprintf(junkn, "g.%d", junkc++); + // junkfp = fopen(junkn, "w"); + + for ( int j = 0; j < tmp_tristrip->strip[i].num_vertices; j++ ) { + Point3D p( tmp_tristrip->strip[i].vertex[j].x, + tmp_tristrip->strip[i].vertex[j].y, + 0 ); + // junkp = in_nodes.get_node( index ); + // fprintf(junkfp, "%.4f %.4f\n", junkp.x(), junkp.y()); + result.add_node(i, p); + // cout << " - " << index << endl; + } + // fprintf(junkfp, "%.4f %.4f\n", + // gpc_result->contour[i].vertex[0].x, + // gpc_result->contour[i].vertex[0].y); + // fclose(junkfp); + } + + // free allocated memory + gpc_free_polygon( tmp_poly ); + gpc_free_tristrip( tmp_tristrip ); + */ + + // return result; +} + + +#if 0 +// +// wrapper functions for gpc polygon to tristrip routine +// + +FGPolygon polygon_to_tristrip_old( const FGPolygon& in_poly ) { + gpc_polygon *tmp_poly = new gpc_polygon; + tmp_poly->num_contours = 0; + tmp_poly->contour = NULL; + tmp_poly->hole = NULL; + make_gpc_poly( in_poly, tmp_poly ); + + gpc_tristrip *tmp_tristrip = new gpc_tristrip; + tmp_tristrip->num_strips = 0; + tmp_tristrip->strip = NULL; + + gpc_polygon_to_tristrip( tmp_poly, tmp_tristrip ); + + FGPolygon result; + + for ( int i = 0; i < tmp_tristrip->num_strips; ++i ) { + cout << " processing strip = " <strip[i].num_vertices << endl; + + // sprintf(junkn, "g.%d", junkc++); + // junkfp = fopen(junkn, "w"); + + for ( int j = 0; j < tmp_tristrip->strip[i].num_vertices; j++ ) { + Point3D p( tmp_tristrip->strip[i].vertex[j].x, + tmp_tristrip->strip[i].vertex[j].y, + 0 ); + // junkp = in_nodes.get_node( index ); + // fprintf(junkfp, "%.4f %.4f\n", junkp.x(), junkp.y()); + result.add_node(i, p); + // cout << " - " << index << endl; + } + // fprintf(junkfp, "%.4f %.4f\n", + // gpc_result->contour[i].vertex[0].x, + // gpc_result->contour[i].vertex[0].y); + // fclose(junkfp); + } + + // free allocated memory + gpc_free_polygon( tmp_poly ); + gpc_free_tristrip( tmp_tristrip ); + + return result; +} +#endif diff --git a/src/Lib/Polygon/polygon.hxx b/src/Lib/Polygon/polygon.hxx new file mode 100644 index 00000000..d3f39eea --- /dev/null +++ b/src/Lib/Polygon/polygon.hxx @@ -0,0 +1,189 @@ +// polygon.hxx -- polygon (with holes) management class +// +// Written by Curtis Olson, started March 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of the +// License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, but +// WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#ifndef _POLYGON_HXX +#define _POLYGON_HXX + + +#ifndef __cplusplus +# error This library requires C++ +#endif + + +#include +#include + +#include +#include + +FG_USING_STD(string); +FG_USING_STD(vector); + + +#define FG_MAX_VERTICES 1500000 + + +typedef vector < point_list > polytype; +typedef polytype::iterator polytype_iterator; +typedef polytype::const_iterator const_polytype_iterator; + + +class FGPolygon { + +private: + + polytype poly; // polygons + point_list inside_list; // point inside list + int_list hole_list; // hole flag list + +public: + + // Constructor and destructor + FGPolygon( void ); + ~FGPolygon( void ); + + // Add a contour + inline void add_contour( const point_list contour, const int hole_flag ) { + poly.push_back( contour ); + hole_list.push_back( hole_flag ); + } + + // Get a contour + inline point_list get_contour( const int i ) const { + return poly[i]; + } + + // Delete a contour + inline void delete_contour( const int i ) { + polytype_iterator start_poly = poly.begin(); + poly.erase( start_poly + i ); + + int_list_iterator start_hole = hole_list.begin(); + hole_list.erase( start_hole + i ); + } + + // Add the specified node (index) to the polygon + inline void add_node( int contour, Point3D p ) { + if ( contour >= (int)poly.size() ) { + // extend polygon + point_list empty_contour; + empty_contour.clear(); + for ( int i = 0; i < contour - (int)poly.size() + 1; ++i ) { + poly.push_back( empty_contour ); + inside_list.push_back( Point3D(0.0) ); + hole_list.push_back( 0 ); + } + } + poly[contour].push_back( p ); + } + + // return size + inline int contours() const { return poly.size(); } + inline int contour_size( int contour ) const { + return poly[contour].size(); + } + + // return the ith polygon point index from the specified contour + inline Point3D get_pt( int contour, int i ) const { + return poly[contour][i]; + } + + // update the value of a point + inline void set_pt( int contour, int i, const Point3D& p ) { + poly[contour][i] = p; + } + + // get and set an arbitrary point inside the specified polygon contour + inline Point3D get_point_inside( const int contour ) const { + return inside_list[contour]; + } + inline void set_point_inside( int contour, const Point3D& p ) { + inside_list[contour] = p; + } + + // get and set hole flag + inline int get_hole_flag( const int contour ) const { + return hole_list[contour]; + } + inline void set_hole_flag( const int contour, const int flag ) { + hole_list[contour] = flag; + } + + // shift every point in the polygon by lon, lat + void shift( double lon, double lat ); + + // erase + inline void erase() { poly.clear(); } + + // informational + + // return the area of a contour (assumes simple polygons, + // i.e. non-self intersecting.) + // + // negative areas indicate counter clockwise winding + // postitive areas indicate clockwise winding. + double area_contour( const int contour ) const; + + // return the smallest interior angle of the polygon + double minangle_contour( const int contour ); + + // output + void write( const string& file ); +}; + + +typedef vector < FGPolygon > poly_list; +typedef poly_list::iterator poly_list_iterator; +typedef poly_list::const_iterator const_poly_list_iterator; + + +// canonify the polygon winding, outer contour must be anti-clockwise, +// all inner contours must be clockwise. +FGPolygon polygon_canonify( const FGPolygon& in_poly ); + + +// Wrapper for the fast Polygon Triangulation based on Seidel's +// Algorithm by Atul Narkhede and Dinesh Manocha +// http://www.cs.unc.edu/~dm/CODE/GEM/chapter.html + +FGPolygon polygon_to_tristrip( const FGPolygon& poly ); + + +// wrapper functions for gpc polygon clip routines + +// Difference +FGPolygon polygon_diff( const FGPolygon& subject, const FGPolygon& clip ); + +// Intersection +FGPolygon polygon_int( const FGPolygon& subject, const FGPolygon& clip ); + +// Exclusive or +FGPolygon polygon_xor( const FGPolygon& subject, const FGPolygon& clip ); + +// Union +FGPolygon polygon_union( const FGPolygon& subject, const FGPolygon& clip ); + + +#endif // _POLYGON_HXX + + diff --git a/src/Lib/Polygon/split.cxx b/src/Lib/Polygon/split.cxx new file mode 100644 index 00000000..1c1a0bc2 --- /dev/null +++ b/src/Lib/Polygon/split.cxx @@ -0,0 +1,233 @@ +// split.cxx -- polygon splitting utils +// +// Written by Curtis Olson, started February 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or modify +// it under the terms of the GNU General Public License as published by +// the Free Software Foundation; either version 2 of the License, or +// (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#include + +#include STL_STRING + +#include +#include + +#include "index.hxx" +#include "names.hxx" +#include "split.hxx" + + +static void clip_and_write_poly( string root, long int p_index, AreaType area, + FGBucket b, const FGPolygon& shape ) { + Point3D c, min, max, p; + c = Point3D( b.get_center_lon(), b.get_center_lat(), 0 ); + double span = bucket_span( c.y() ); + FGPolygon base, result; + char tile_name[256], poly_index[256]; + + // calculate bucket dimensions + if ( (c.y() >= -89.0) && (c.y() < 89.0) ) { + min.setx( c.x() - span / 2.0 ); + max.setx( c.x() + span / 2.0 ); + min.sety( c.y() - FG_HALF_BUCKET_SPAN ); + max.sety( c.y() + FG_HALF_BUCKET_SPAN ); + } else if ( c.y() < -89.0) { + min.setx( -90.0 ); + max.setx( -89.0 ); + min.sety( -180.0 ); + max.sety( 180.0 ); + } else if ( c.y() >= 89.0) { + min.setx( 89.0 ); + max.setx( 90.0 ); + min.sety( -180.0 ); + max.sety( 180.0 ); + } else { + FG_LOG ( FG_GENERAL, FG_ALERT, + "Out of range latitude in clip_and_write_poly() = " << c.y() ); + } + + FG_LOG( FG_GENERAL, FG_DEBUG, " (" << min << ") (" << max << ")" ); + + // set up clipping tile + base.add_node( 0, Point3D(min.x(), min.y(), 0) ); + base.add_node( 0, Point3D(max.x(), min.y(), 0) ); + base.add_node( 0, Point3D(max.x(), max.y(), 0) ); + base.add_node( 0, Point3D(min.x(), max.y(), 0) ); + + // FG_LOG( FG_GENERAL, FG_DEBUG, "base = 4 vertices" ); + + /* + FILE *bfp= fopen("base", "w"); + gpc_write_polygon(bfp, &base); + fclose(bfp); + */ + + result = polygon_int( base, shape ); + + if ( result.contours() > 0 ) { + long int t_index = b.gen_index(); + string path = root + "/" + b.gen_base_path(); + string command = "mkdir -p " + path; + system( command.c_str() ); + + sprintf( tile_name, "%ld", t_index ); + string polyfile = path + "/" + tile_name; + + sprintf( poly_index, "%ld", p_index ); + polyfile += "."; + polyfile += poly_index; + + string poly_type = get_area_name( area ); + if ( poly_type == "Unknown" ) { + cout << "unknown area type in clip_and_write_poly()!" << endl; + exit(-1); + } + + FILE *rfp= fopen( polyfile.c_str(), "w" ); + fprintf( rfp, "%s\n", poly_type.c_str() ); + + fprintf( rfp, "%d\n", result.contours() ); + for ( int i = 0; i < result.contours(); ++i ) { + fprintf( rfp, "%d\n", result.contour_size(i) ); + fprintf( rfp, "%d\n", result.get_hole_flag(i) ); + for ( int j = 0; j < result.contour_size(i); ++j ) { + p = result.get_pt( i, j ); + fprintf( rfp, "%.15f %.15f\n", p.x(), p.y() ); + } + } + fclose( rfp ); + } +} + + +// process shape (write polygon to all intersecting tiles) +void split_polygon(const string& path, AreaType area, const FGPolygon& shape) { + Point3D min, max, p; + // point2d min, max; + long int index; + int i, j; + + // bail out immediately if polygon is empty + if ( shape.contours() == 0 ) { + return; + } + + min = Point3D( 200.0 ); + max = Point3D( -200.0 ); + + // find min/max of polygon + for ( i = 0; i < shape.contours(); i++ ) { + for ( j = 0; j < shape.contour_size(i); j++ ) { + p = shape.get_pt( i, j ); + + if ( p.x() < min.x() ) { min.setx( p.x() ); } + if ( p.y() < min.y() ) { min.sety( p.y() ); } + if ( p.x() > max.x() ) { max.setx( p.x() ); } + if ( p.y() > max.y() ) { max.sety( p.y() ); } + } + } + + // get next polygon index + index = poly_index_next(); + + FG_LOG( FG_GENERAL, FG_INFO, " min = " << min << " max = " << max ); + + // find buckets for min, and max points of convex hull. + // note to self: self, you should think about checking for + // polygons that span the date line + FGBucket b_min( min.x(), min.y() ); + FGBucket b_max( max.x(), max.y() ); + FG_LOG( FG_GENERAL, FG_INFO, " Bucket min = " << b_min ); + FG_LOG( FG_GENERAL, FG_INFO, " Bucket max = " << b_max ); + + if ( b_min == b_max ) { + clip_and_write_poly( path, index, area, b_min, shape ); + } else { + FGBucket b_cur; + int dx, dy, i, j; + + fgBucketDiff(b_min, b_max, &dx, &dy); + FG_LOG( FG_GENERAL, FG_INFO, + " polygon spans tile boundaries" ); + FG_LOG( FG_GENERAL, FG_INFO, " dx = " << dx + << " dy = " << dy ); + + if ( (dx > 2880) || (dy > 1440) ) { + FG_LOG( FG_GENERAL, FG_ALERT, + "somethings really wrong!!!!" ); + exit(-1); + } + + for ( j = 0; j <= dy; j++ ) { + // for performance reasons, we'll clip out just this + // horizontal row, and clip all the tiles in this row + // against the smaller shape + + FG_LOG ( FG_GENERAL, FG_INFO, + "Generating clip row " << j << " of " << dy ); + + FGBucket b_clip = fgBucketOffset(min.x(), min.y(), 0, j); + FGPolygon row, clip_row; + Point3D c, clip_max, clip_min; + c = Point3D( b_clip.get_center_lon(), b_clip.get_center_lat(), 0 ); + + row.erase(); + clip_row.erase(); + + // calculate bucket clip_min.y and clip_max.y + if ( (c.y() >= -89.0) && (c.y() < 89.0) ) { + clip_min.sety( c.y() - FG_HALF_BUCKET_SPAN ); + clip_max.sety( c.y() + FG_HALF_BUCKET_SPAN ); + } else if ( c.y() < -89.0) { + clip_min.sety( -90.0 ); + clip_max.sety( -89.0 ); + } else if ( c.y() >= 89.0) { + clip_min.sety( 89.0 ); + clip_max.sety( 90.0 ); + } else { + FG_LOG ( FG_GENERAL, FG_ALERT, + "Out of range latitude in clip_and_write_poly() = " + << c.y() ); + } + clip_min.setx( -180.0 ); + clip_max.setx( 180.0 ); + + // set up clipping tile + row.add_node( 0, Point3D(clip_min.x(), clip_min.y(), 0) ); + row.add_node( 0, Point3D(clip_max.x(), clip_min.y(), 0) ); + row.add_node( 0, Point3D(clip_max.x(), clip_max.y(), 0) ); + row.add_node( 0, Point3D(clip_min.x(), clip_max.y(), 0) ); + + clip_row = polygon_int( row, shape ); + + /* FILE *sfp = fopen("shape", "w"); + gpc_write_polygon(sfp, 0, shape); + fclose(sfp); + sfp = fopen("clip_row", "w"); + gpc_write_polygon(sfp, 0, &clip_row); + fclose(sfp); */ + + for ( i = 0; i <= dx; i++ ) { + b_cur = fgBucketOffset(min.x(), min.y(), i, j); + clip_and_write_poly( path, index, area, b_cur, clip_row ); + } + } + // string answer; cin >> answer; + } +} diff --git a/src/Lib/Polygon/split.hxx b/src/Lib/Polygon/split.hxx new file mode 100644 index 00000000..55ab2af4 --- /dev/null +++ b/src/Lib/Polygon/split.hxx @@ -0,0 +1,38 @@ +// split.hxx -- polygon splitting utils +// +// Written by Curtis Olson, started February 1999. +// +// Copyright (C) 1999 Curtis L. Olson - curt@flightgear.org +// +// This program is free software; you can redistribute it and/or modify +// it under the terms of the GNU General Public License as published by +// the Free Software Foundation; either version 2 of the License, or +// (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +// +// $Id$ + + +#ifndef _SPLIT_HXX +#define _SPLIT_HXX + + +#include "names.hxx" +#include "polygon.hxx" + + +// process shape (write polygon to all intersecting tiles) +void split_polygon(const string& path, AreaType area, const FGPolygon& shape); + + +#endif // _SPLIT_HXX + + diff --git a/src/Lib/TriangleJRS/Makefile.am b/src/Lib/TriangleJRS/Makefile.am new file mode 100644 index 00000000..7788c150 --- /dev/null +++ b/src/Lib/TriangleJRS/Makefile.am @@ -0,0 +1,24 @@ +# CPPFLAGS is a list of definitions used to compile an object code version +# of Triangle (triangle.o) to be called by another program. The file +# "triangle.h" contains detailed information on how to call triangle.o. +# +# The -DTRILIBRARY should always be used when compiling Triangle into an +# object file. +# +# An example DEFS line is: +# +# CPPFLAGS = -DTRILIBRARY -DREDUCED -DCDT_ONLY + +CPPFLAGS += -DTRILIBRARY + +noinst_LIBRARIES = libTriangle.a + +libTriangle_a_SOURCES = triangle.c triangle.h + +if HAVE_XWINDOWS + +bin_PROGRAMS = showme +showme_SOURCES = showme.c +showme_LDADD = -lX11 + +endif \ No newline at end of file diff --git a/src/Lib/TriangleJRS/README b/src/Lib/TriangleJRS/README new file mode 100644 index 00000000..571d5689 --- /dev/null +++ b/src/Lib/TriangleJRS/README @@ -0,0 +1,181 @@ +Triangle +A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. +Version 1.3 + +Show Me +A Display Program for Meshes and More. +Version 1.3 + +Copyright 1996 Jonathan Richard Shewchuk +School of Computer Science +Carnegie Mellon University +5000 Forbes Avenue +Pittsburgh, Pennsylvania 15213-3891 +Please send bugs and comments to jrs@cs.cmu.edu + +Created as part of the Archimedes project (tools for parallel FEM). +Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship. +There is no warranty whatsoever. Use at your own risk. + + +Triangle generates exact Delaunay triangulations, constrained Delaunay +triangulations, and quality conforming Delaunay triangulations. The +latter can be generated with no small angles, and are thus suitable for +finite element analysis. Show Me graphically displays the contents of +the geometric files used by Triangle. Show Me can also write images in +PostScript form. + +Information on the algorithms used by Triangle, including complete +references, can be found in the comments at the beginning of the triangle.c +source file. Another listing of these references, with PostScript copies +of some of the papers, is available from the Web page + + http://www.cs.cmu.edu/~quake/triangle.research.html + +------------------------------------------------------------------------------ + +These programs may be freely redistributed under the condition that the +copyright notices (including the copy of this notice in the code comments +and the copyright notice printed when the `-h' switch is selected) are +not removed, and no compensation is received. Private, research, and +institutional use is free. You may distribute modified versions of this +code UNDER THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT +IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH +SOURCE AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND +CLEAR NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as +part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT +WITH THE AUTHOR. (If you are not directly supplying this code to a +customer, and you are instead telling them how they can obtain it for +free, then you are not required to make any arrangement with me.) + +------------------------------------------------------------------------------ + +The files included in this distribution are: + + README The file you're reading now. + triangle.c Complete C source code for Triangle. + showme.c Complete C source code for Show Me. + triangle.h Include file for calling Triangle from another program. + tricall.c Sample program that calls Triangle. + makefile Makefile for compiling Triangle and Show Me. + A.poly A sample data file. + +Triangle and Show Me are each a single portable C file. The easiest way to +compile them is to edit and use the included makefile. Before compiling, +read the makefile, which describes your options, and edit it accordingly. +You should specify: + + The source and binary directories. + + The C compiler and level of optimization. + + Do you want single precision or double? Do you want to leave out some of + Triangle's features to reduce the size of the executable file? + + The "correct" directories for include files (especially X include files), + if necessary. + +Once you've done this, type "make" to compile the programs. Alternatively, +the files are usually easy to compile without a makefile: + + cc -O -o triangle triangle.c -lm + cc -O -o showme showme.c -lX11 + +On some systems, the C compiler won't be able to find the X include files +or libraries, and you'll need to specify an include path or library path: + + cc -O -I/usr/local/include -o showme showme.c -L/usr/local/lib -lX11 + +However, on other systems (like my workstation), the latter incantation +will cause the wrong files to be read, and the Show Me mouse buttons won't +work properly in the main window. Hence, try the "-I" and "-L" switches +ONLY if the compiler fails without it. (If you're using the makefile, you +may edit it to add this switch.) + +Some processors, possibly including Intel x86 family and Motorola 68xxx +family chips, are IEEE conformant but have extended length internal +floating-point registers that may defeat Triangle's exact arithmetic +routines by failing to cause enough roundoff error! Typically, there is +a way to set these internal registers so that they are rounded off to +IEEE single or double precision format. If you have such a processor, +you should check your C compiler or system manuals to find out how to +configure these internal registers to the precision you are using. +Otherwise, the exact arithmetic routines won't be exact at all. +Unfortunately, I don't have access to any such systems, and can't give +advice on how to configure them. These problems don't occur on any +workstations I am aware of. However, Triangle's exact arithmetic hasn't +a hope of working on machines like the Cray C90 or Y-MP, which are not +IEEE conformant and have inaccurate rounding. + +Triangle and Show Me both produce their own documentation. Complete +instructions are printed by invoking each program with the `-h' switch: + + triangle -h + showme -h + +The instructions are long; you'll probably want to pipe the output to +`more' or `lpr' or redirect it to a file. Both programs give a short list +of command line options if they are invoked without arguments (that is, +just type `triangle' or `showme'). Alternatively, you may want to read +the instructions on the World Wide Web. The appropriate URLs are: + + http://www.cs.cmu.edu/~quake/triangle.html + http://www.cs.cmu.edu/~quake/showme.html + +Try out Triangle on the enclosed sample file, A.poly: + + triangle -p A + showme A.poly & + +Triangle will read the Planar Straight Line Graph defined by A.poly, and +write its constrained Delaunay triangulation to A.1.node and A.1.ele. +Show Me will display the figure defined by A.poly. There are two buttons +marked "ele" in the Show Me window; click on the top one. This will cause +Show Me to load and display the triangulation. + +For contrast, try running + + triangle -pq A + +Now, click on the same "ele" button. A new triangulation will be loaded; +this one having no angles smaller than 20 degrees. + +To see a Voronoi diagram, try this: + + cp A.poly A.node + triangle -v A + +Click the "ele" button again. You will see the Delaunay triangulation of +the points in A.poly, without the segments. Now click the top "voro" button. +You will see the Voronoi diagram corresponding to that Delaunay triangulation. +Click the "Reset" button to see the full extent of the diagram. + +------------------------------------------------------------------------------ + +If you wish to call Triangle from another program, instructions for doing +so are contained in the file `triangle.h' (but read Triangle's regular +instructions first!). Also look at `tricall.c', which provides an example. + +Type "make trilibrary" to create triangle.o, a callable object file. +Alternatively, the object file is usually easy to compile without a +makefile: + + cc -DTRILIBRARY -O -c triangle.c + +------------------------------------------------------------------------------ + +If you use Triangle, and especially if you use it to accomplish real +work, I would like very much to hear from you. A short letter or email +(to jrs@cs.cmu.edu) describing how you use Triangle will mean a lot to +me. The more people I know are using this program, the more easily I can +justify spending time on improvements and on the three-dimensional +successor to Triangle, which in turn will benefit you. Also, I can put +you on a list to receive email whenever a new version of Triangle is +available. + +If you use a mesh generated by Triangle or plotted by Show Me in a +publication, please include an acknowledgment as well. + + +Jonathan Richard Shewchuk +July 20, 1996 diff --git a/src/Lib/TriangleJRS/showme.c b/src/Lib/TriangleJRS/showme.c new file mode 100644 index 00000000..722cba8a --- /dev/null +++ b/src/Lib/TriangleJRS/showme.c @@ -0,0 +1,3384 @@ +/*****************************************************************************/ +/* */ +/* ,d88^^o 888 o o */ +/* 8888 888o^88, o88^^o Y88b o / d8b d8b o88^^8o */ +/* "Y88b 888 888 d888 b Y88b d8b / d888bdY88b d888 88b */ +/* "Y88b, 888 888 8888 8 Y888/Y88b/ / Y88Y Y888b 8888oo888 */ +/* o 8888 888 888 q888 p Y8/ Y8/ / YY Y888b q888 */ +/* "oo88P" 888 888 "88oo" Y Y / Y888b "88oooo" */ +/* */ +/* A Display Program for Meshes and More. */ +/* (showme.c) */ +/* */ +/* Version 1.3 */ +/* July 20, 1996 */ +/* */ +/* Copyright 1996 */ +/* Jonathan Richard Shewchuk */ +/* School of Computer Science */ +/* Carnegie Mellon University */ +/* 5000 Forbes Avenue */ +/* Pittsburgh, Pennsylvania 15213-3891 */ +/* jrs@cs.cmu.edu */ +/* */ +/* This program may be freely redistributed under the condition that the */ +/* copyright notices (including this entire header and the copyright */ +/* notice printed when the `-h' switch is selected) are not removed, and */ +/* no compensation is received. Private, research, and institutional */ +/* use is free. You may distribute modified versions of this code UNDER */ +/* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */ +/* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE */ +/* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR */ +/* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as */ +/* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */ +/* WITH THE AUTHOR. (If you are not directly supplying this code to a */ +/* customer, and you are instead telling them how they can obtain it for */ +/* free, then you are not required to make any arrangement with me.) */ +/* */ +/* Hypertext instructions for Triangle are available on the Web at */ +/* */ +/* http://www.cs.cmu.edu/~quake/showme.html */ +/* */ +/* Show Me was created as part of the Archimedes project in the School of */ +/* Computer Science at Carnegie Mellon University. Archimedes is a */ +/* system for compiling parallel finite element solvers. For further */ +/* information, see Anja Feldmann, Omar Ghattas, John R. Gilbert, Gary L. */ +/* Miller, David R. O'Hallaron, Eric J. Schwabe, Jonathan R. Shewchuk, */ +/* and Shang-Hua Teng. "Automated Parallel Solution of Unstructured PDE */ +/* Problems." To appear in Communications of the ACM, we hope. */ +/* */ +/* If you make any improvements to this code, please please please let me */ +/* know, so that I may obtain the improvements. Even if you don't change */ +/* the code, I'd still love to hear what it's being used for. */ +/* */ +/* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */ +/* whatsoever. Use at your own risk. */ +/* */ +/*****************************************************************************/ + +/* For single precision (which will save some memory and reduce paging), */ +/* write "#define SINGLE" below. */ +/* */ +/* For double precision (which will allow you to display triangulations of */ +/* a finer resolution), leave SINGLE undefined. */ + +/* #define SINGLE */ + +#ifdef SINGLE +#define REAL float +#else +#define REAL double +#endif + +/* Maximum number of characters in a file name (including the null). */ + +#define FILENAMESIZE 1024 + +/* Maximum number of characters in a line read from a file (including the */ +/* null). */ + +#define INPUTLINESIZE 512 + +#define STARTWIDTH 414 +#define STARTHEIGHT 414 +#define MINWIDTH 50 +#define MINHEIGHT 50 +#define BUTTONHEIGHT 21 +#define BUTTONROWS 3 +#define PANELHEIGHT (BUTTONHEIGHT * BUTTONROWS) +#define MAXCOLORS 64 + +#define IMAGE_TYPES 7 +#define NOTHING -1 +#define NODE 0 +#define POLY 1 +#define ELE 2 +#define EDGE 3 +#define PART 4 +#define ADJ 5 +#define VORO 6 + +#define STARTEXPLOSION 0.5 + +#include +#include +#include +#include +#include + +/* The following obscenity seems to be necessary to ensure that this program */ +/* will port to Dec Alphas running OSF/1, because their stdio.h file commits */ +/* the unpardonable sin of including stdlib.h. Hence, malloc(), free(), and */ +/* exit() may or may not already be defined at this point. I declare these */ +/* functions explicitly because some non-ANSI C compilers lack stdlib.h. */ + +#ifndef _STDLIB_H_ +extern char *malloc(); +extern void free(); +extern void exit(); +extern double strtod(); +extern long strtol(); +#endif + +/* A necessary forward declaration. */ + +int load_image(); + +Display *display; +int screen; +Window rootwindow; +Window mainwindow; +Window quitwin; +Window leftwin; +Window rightwin; +Window upwin; +Window downwin; +Window resetwin; +Window pswin; +Window epswin; +Window expwin; +Window exppluswin; +Window expminuswin; +Window widthpluswin; +Window widthminuswin; +Window versionpluswin; +Window versionminuswin; +Window fillwin; +Window nodewin[2]; +Window polywin[2]; +Window elewin[2]; +Window edgewin[2]; +Window partwin[2]; +Window adjwin[2]; +Window voronoiwin[2]; + +int windowdepth; +XEvent event; +Colormap rootmap; +XFontStruct *font; +int width, height; +int black, white; +int showme_foreground; +GC fontgc; +GC blackfontgc; +GC linegc; +GC trianglegc; +int colors[MAXCOLORS]; +XColor rgb[MAXCOLORS]; +int color; + +int start_image, current_image; +int start_inc, current_inc; +int loweriteration; +int line_width; +int loaded[2][IMAGE_TYPES]; +REAL xlo[2][IMAGE_TYPES], ylo[2][IMAGE_TYPES]; +REAL xhi[2][IMAGE_TYPES], yhi[2][IMAGE_TYPES]; +REAL xscale, yscale; +REAL xoffset, yoffset; +int zoom; + +int nodes[2], node_dim[2]; +REAL *nodeptr[2]; +int polynodes[2], poly_dim[2], polyedges[2], polyholes[2]; +REAL *polynodeptr[2], *polyholeptr[2]; +int *polyedgeptr[2]; +int elems[2], ele_corners[2]; +int *eleptr[2]; +int edges[2]; +int *edgeptr[2]; +REAL *normptr[2]; +int subdomains[2]; +int *partpart[2]; +REAL *partcenter[2], *partshift[2]; +int adjsubdomains[2]; +int *adjptr[2]; +int vnodes[2], vnode_dim[2]; +REAL *vnodeptr[2]; +int vedges[2]; +int *vedgeptr[2]; +REAL *vnormptr[2]; +int firstnumber[2]; + +int quiet, fillelem, bw_ps, explode; +REAL explosion; + +char filename[FILENAMESIZE]; +char nodefilename[2][FILENAMESIZE]; +char polyfilename[2][FILENAMESIZE]; +char elefilename[2][FILENAMESIZE]; +char edgefilename[2][FILENAMESIZE]; +char partfilename[2][FILENAMESIZE]; +char adjfilename[2][FILENAMESIZE]; +char vnodefilename[2][FILENAMESIZE]; +char vedgefilename[2][FILENAMESIZE]; + +char *colorname[] = {"aquamarine", "red", "green yellow", "magenta", + "yellow", "green", "orange", "blue", + "white", "sandy brown", "cyan", "moccasin", + "cadet blue", "coral", "cornflower blue", "sky blue", + "firebrick", "forest green", "gold", "goldenrod", + "gray", "hot pink", "chartreuse", "pale violet red", + "indian red", "khaki", "lavender", "light blue", + "light gray", "light steel blue", "lime green", "azure", + "maroon", "medium aquamarine", "dodger blue", "honeydew", + "medium orchid", "medium sea green", "moccasin", + "medium slate blue", "medium spring green", + "medium turquoise", "medium violet red", + "orange red", "chocolate", "light goldenrod", + "orchid", "pale green", "pink", "plum", + "purple", "salmon", "sea green", + "sienna", "slate blue", "spring green", + "steel blue", "tan", "thistle", "turquoise", + "violet", "violet red", "wheat", + "yellow green"}; + +void syntax() +{ + printf("showme [-bfw_Qh] input_file\n"); + printf(" -b Black and white PostScript (default is color).\n"); + printf(" -f Fill triangles of partitioned mesh with color.\n"); + printf(" -w Set line width to some specified number.\n"); + printf(" -Q Quiet: No terminal output except errors.\n"); + printf(" -h Help: Detailed instructions for Show Me.\n"); + exit(0); +} + +void info() +{ + printf("Show Me\n"); + printf("A Display Program for Meshes and More.\n"); + printf("Version 1.3\n\n"); + printf( +"Copyright 1996 Jonathan Richard Shewchuk (bugs/comments to jrs@cs.cmu.edu)\n" +); + printf("School of Computer Science / Carnegie Mellon University\n"); + printf("5000 Forbes Avenue / Pittsburgh, Pennsylvania 15213-3891\n"); + printf( +"Created as part of the Archimedes project (tools for parallel FEM).\n"); + printf( +"Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n"); + printf("There is no warranty whatsoever. Use at your own risk.\n"); +#ifdef SINGLE + printf("This executable is compiled for single precision arithmetic.\n\n\n"); +#else + printf("This executable is compiled for double precision arithmetic.\n\n\n"); +#endif + printf( +"Show Me graphically displays the contents of geometric files, especially\n"); + printf( +"those generated by Triangle, my two-dimensional quality mesh generator and\n" +); + printf( +"Delaunay triangulator. Show Me can also write images in PostScript form.\n"); + printf( +"Show Me is also useful for checking the consistency of the files you create\n" +); + printf( +"as input to Triangle; Show Me does these checks more thoroughly than\n"); + printf("Triangle does. The command syntax is:\n\n"); + printf("showme [-bfw_Qh] input_file\n\n"); + printf( +"The underscore indicates that a number should follow the -w switch.\n"); + printf( +"input_file may be one of several types of file. It must have extension\n"); + printf( +".node, .poly, .ele, .edge, .part, or .adj. If no extension is provided,\n"); + printf( +"Show Me will assume the extension .ele. A .node file represents a set of\n"); + printf( +"points; a .poly file represents a Planar Straight Line Graph; an .ele file\n" +); + printf( +"(coupled with a .node file) represents the elements of a mesh or the\n"); + printf( +"triangles of a triangulation; an .edge file (coupled with a .node file)\n"); + printf( +"represents a set of edges; a .part file specifies a partition of a mesh;\n"); + printf( +"and a .adj file represents the adjacency graph defined by a partition.\n"); + printf("\n"); + printf("Command Line Switches:\n"); + printf("\n"); + printf( +" -b Makes all PostScript output black and white. If this switch is not\n" +); + printf( +" selected, color PostScript is used for partitioned meshes and\n"); + printf(" adjacency graphs (.part and .adj files).\n"); + printf( +" -f On color displays and in color PostScript, displays partitioned\n"); + printf( +" meshes by filling triangles with color, rather than by coloring the\n" +); + printf( +" edges. This switch will result in a clearer picture if all\n"); + printf( +" triangles are reasonably large, and a less clear picture if small\n"); + printf( +" triangles are present. (There is also a button to toggle this\n"); + printf(" behavior.)\n"); + printf( +" -w Followed by an integer, specifies the line width used in all\n"); + printf( +" images. (There are also buttons to change the line width.)\n"); + printf( +" -Q Quiet: Suppresses all explanation of what Show Me is doing, unless\n" +); + printf(" an error occurs.\n"); + printf(" -h Help: Displays these instructions.\n"); + printf("\n"); + printf("Controls:\n"); + printf("\n"); + printf( +" To zoom in on an image, point at the location where you want a closer\n"); + printf( +" look, and click the left mouse button. To zoom out, click the right\n"); + printf( +" mouse button. In either case, the point you click on will be centered in\n" +); + printf( +" the window. If you want to know the coordinates of a point, click the\n"); + printf( +" middle mouse button; the coordinates will be printed on the terminal you\n" +); + printf(" invoked Show Me from.\n\n"); + printf( +" If you resize the window, the image will grow or shrink to match.\n"); + printf("\n"); + printf( +" There is a panel of control buttons at the bottom of the Show Me window:\n" +); + printf("\n"); + printf(" Quit: Shuts down Show Me.\n"); + printf(" <, >, ^, v: Moves the image in the indicated direction.\n"); + printf( +" Reset: Unzooms and centers the image in the window. When you switch from\n" +); + printf( +" one image to another, the viewing region does not change, so you may\n"); + printf( +" need to reset the new image to make it fully visible. This often is\n"); + printf( +" the case when switching between Delaunay triangulations and their\n"); + printf( +" corresponding Voronoi diagrams, as Voronoi vertices can be far from the\n" +); + printf(" initial point set.\n"); + printf( +" Width+, -: Increases or decreases the width of all lines and points.\n"); + printf( +" Exp, +, -: These buttons appear only when you are viewing a partitioned\n" +); + printf( +" mesh (.part file). `Exp' toggles between an exploded and non-exploded\n" +); + printf( +" image of the mesh. The non-exploded image will not show the partition\n" +); + printf( +" on a black and white monitor. `+' and `-' allow you to adjust the\n"); + printf( +" spacing between pieces of the mesh to better distinguish them.\n"); + printf( +" Fill: This button appears only when you are viewing a partitioned mesh\n"); + printf( +" (.part file). It toggles between color-filled triangles and colored\n"); + printf( +" edges (as the -f switch does). Filled triangles look better when all\n"); + printf( +" triangles are reasonably large; colored edges look better when there\n"); + printf(" are very small triangles present.\n"); + printf( +" PS: Creates a PostScript file containing the image you are viewing. If\n" +); + printf( +" the -b switch is selected, all PostScript output will be black and\n"); + printf( +" white; otherwise, .part.ps and .adj.ps files will be color, independent\n" +); + printf( +" of whether you are using a color monitor. Normally the output will\n"); + printf( +" preserve the properties of the image you see on the screen, including\n"); + printf( +" zoom and line width; however, if black and white output is selected (-b\n" +); + printf( +" switch), partitioned meshes will always be drawn exploded. The output\n" +); + printf( +" file name depends on the image being viewed. If you want several\n"); + printf( +" different snapshots (zooming in on different parts) of the same object,\n" +); + printf( +" you'll have to rename each file after Show Me creates it so that it\n"); + printf(" isn't overwritten by the next snapshot.\n"); + printf( +" EPS: Creates an encapsulated PostScript file, suitable for inclusion in\n" +); + printf( +" documents. Otherwise, this button is just like the PS button. (The\n"); + printf( +" main difference is that .eps files lack a `showpage' command at the\n"); + printf(" end.)\n\n"); + printf( +" There are two nearly-identical rows of buttons that load different images\n" +); + printf(" from disk. Each row contains the following buttons:\n\n"); + printf(" node: Loads a .node file.\n"); + printf( +" poly: Loads a .poly file (and possibly an associated .node file).\n"); + printf(" ele: Loads an .ele file (and associated .node file).\n"); + printf(" edge: Loads an .edge file (and associated .node file).\n"); + printf( +" part: Loads a .part file (and associated .node and .ele files).\n"); + printf( +" adj: Loads an .adj file (and associated .node, .ele, and .part files).\n"); + printf(" voro: Loads a .v.node and .v.edge file for a Voronoi diagram.\n"); + printf("\n"); + printf( +" Each row represents a different iteration number of the geometry files.\n"); + printf( +" For a full explanation of iteration numbers, read the instructions for\n"); + printf( +" Triangle. Briefly, iteration numbers are used to allow a user to easily\n" +); + printf( +" represent a sequence of related triangulations. Iteration numbers are\n"); + printf( +" used in the names of geometry files; for instance, mymesh.3.ele is a\n"); + printf( +" triangle file with iteration number three, and mymesh.ele has an implicit\n" +); + printf(" iteration number of zero.\n\n"); + printf( +" The control buttons at the right end of each row display the two\n"); + printf( +" iterations currently under view. These buttons can be clicked to\n"); + printf( +" increase or decrease the iteration numbers, and thus conveniently view\n"); + printf(" a sequence of meshes.\n\n"); + printf( +" Show Me keeps each file in memory after loading it, but you can force\n"); + printf( +" Show Me to reread a set of files (for one iteration number) by reclicking\n" +); + printf( +" the button that corresponds to the current image. This is convenient if\n" +); + printf(" you have changed a geometry file.\n\n"); + printf("File Formats:\n\n"); + printf( +" All files may contain comments prefixed by the character '#'. Points,\n"); + printf( +" segments, holes, triangles, edges, and subdomains must be numbered\n"); + printf( +" consecutively, starting from either 1 or 0. Whichever you choose, all\n"); + printf( +" input files must be consistent (for any single iteration number); if the\n" +); + printf( +" nodes are numbered from 1, so must be all other objects. Show Me\n"); + printf( +" automatically detects your choice while reading a .node (or .poly) file.\n" +); + printf(" Examples of these file formats are given below.\n\n"); + printf(" .node files:\n"); + printf( +" First line: <# of points> <# of attributes>\n"); + printf( +" <# of boundary markers (0 or 1)>\n" +); + printf( +" Remaining lines: [attributes] [boundary marker]\n"); + printf("\n"); + printf( +" The attributes, which are typically floating-point values of physical\n"); + printf( +" quantities (such as mass or conductivity) associated with the nodes of\n" +); + printf( +" a finite element mesh, are ignored by Show Me. Show Me also ignores\n"); + printf( +" boundary markers. See the instructions for Triangle to find out what\n"); + printf(" attributes and boundary markers are.\n\n"); + printf(" .poly files:\n"); + printf( +" First line: <# of points> <# of attributes>\n"); + printf( +" <# of boundary markers (0 or 1)>\n" +); + printf( +" Following lines: [attributes] [boundary marker]\n"); + printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n"); + printf( +" Following lines: [boundary marker]\n"); + printf(" One line: <# of holes>\n"); + printf(" Following lines: \n"); + printf(" [Optional additional lines that are ignored]\n\n"); + printf( +" A .poly file represents a Planar Straight Line Graph (PSLG), an idea\n"); + printf( +" familiar to computational geometers. By definition, a PSLG is just a\n"); + printf( +" list of points and edges. A .poly file also contains some additional\n"); + printf(" information.\n\n"); + printf( +" The first section lists all the points, and is identical to the format\n" +); + printf( +" of .node files. <# of points> may be set to zero to indicate that the\n" +); + printf( +" points are listed in a separate .node file; .poly files produced by\n"); + printf( +" Triangle always have this format. When Show Me reads such a file, it\n"); + printf(" also reads the corresponding .node file.\n\n"); + printf( +" The second section lists the segments. Segments are edges whose\n"); + printf( +" presence in a triangulation produced from the PSLG is enforced. Each\n"); + printf( +" segment is specified by listing the indices of its two endpoints. This\n" +); + printf( +" means that its endpoints must be included in the point list. Each\n"); + printf( +" segment, like each point, may have a boundary marker, which is ignored\n" +); + printf(" by Show Me.\n\n"); + printf( +" The third section lists holes and concavities that are desired in any\n"); + printf( +" triangulation generated from the PSLG. Holes are specified by\n"); + printf(" identifying a point inside each hole.\n\n"); + printf(" .ele files:\n"); + printf( +" First line: <# of triangles> <# of attributes>\n"); + printf( +" Remaining lines: ... [attributes]\n" +); + printf("\n"); + printf( +" Points are indices into the corresponding .node file. Show Me ignores\n" +); + printf( +" all but the first three points of each triangle; these should be the\n"); + printf( +" corners listed in counterclockwise order around the triangle. The\n"); + printf(" attributes are ignored by Show Me.\n\n"); + printf(" .edge files:\n"); + printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n"); + printf( +" Following lines: [boundary marker]\n"); + printf("\n"); + printf( +" Endpoints are indices into the corresponding .node file. The boundary\n" +); + printf(" markers are ignored by Show Me.\n\n"); + printf( +" In Voronoi diagrams, one also finds a special kind of edge that is an\n"); + printf( +" infinite ray with only one endpoint. For these edges, a different\n"); + printf(" format is used:\n\n"); + printf(" -1 \n\n"); + printf( +" The `direction' is a floating-point vector that indicates the direction\n" +); + printf(" of the infinite ray.\n\n"); + printf(" .part files:\n"); + printf(" First line: <# of triangles> <# of subdomains>\n"); + printf(" Remaining lines: \n\n"); + printf( +" The set of triangles is partitioned by a .part file; each triangle is\n"); + printf(" mapped to a subdomain.\n\n"); + printf(" .adj files:\n"); + printf(" First line: <# of subdomains>\n"); + printf(" Remaining lines: \n\n"); + printf( +" An .adj file represents adjacencies between subdomains (presumably\n"); + printf(" computed by a partitioner). The first line is followed by\n"); + printf( +" (subdomains X subdomains) lines, each containing one entry of the\n"); + printf( +" adjacency matrix. A nonzero entry indicates that two subdomains are\n"); + printf(" adjacent (share a point).\n\n"); + printf("Example:\n\n"); + printf( +" Here is a sample file `box.poly' describing a square with a square hole:\n" +); + printf("\n"); + printf( +" # A box with eight points in 2D, no attributes, no boundary marker.\n"); + printf(" 8 2 0 0\n"); + printf(" # Outer box has these vertices:\n"); + printf(" 1 0 0\n"); + printf(" 2 0 3\n"); + printf(" 3 3 0\n"); + printf(" 4 3 3\n"); + printf(" # Inner square has these vertices:\n"); + printf(" 5 1 1\n"); + printf(" 6 1 2\n"); + printf(" 7 2 1\n"); + printf(" 8 2 2\n"); + printf(" # Five segments without boundary markers.\n"); + printf(" 5 0\n"); + printf(" 1 1 2 # Left side of outer box.\n"); + printf(" 2 5 7 # Segments 2 through 5 enclose the hole.\n"); + printf(" 3 7 8\n"); + printf(" 4 8 6\n"); + printf(" 5 6 5\n"); + printf(" # One hole in the middle of the inner square.\n"); + printf(" 1\n"); + printf(" 1 1.5 1.5\n\n"); + printf( +" After this PSLG is triangulated by Triangle, the resulting triangulation\n" +); + printf( +" consists of a .node and .ele file. Here is the former, `box.1.node',\n"); + printf(" which duplicates the points of the PSLG:\n\n"); + printf(" 8 2 0 0\n"); + printf(" 1 0 0\n"); + printf(" 2 0 3\n"); + printf(" 3 3 0\n"); + printf(" 4 3 3\n"); + printf(" 5 1 1\n"); + printf(" 6 1 2\n"); + printf(" 7 2 1\n"); + printf(" 8 2 2\n"); + printf(" # Generated by triangle -pcBev box\n"); + printf("\n"); + printf(" Here is the triangulation file, `box.1.ele'.\n"); + printf("\n"); + printf(" 8 3 0\n"); + printf(" 1 1 5 6\n"); + printf(" 2 5 1 3\n"); + printf(" 3 2 6 8\n"); + printf(" 4 6 2 1\n"); + printf(" 5 7 3 4\n"); + printf(" 6 3 7 5\n"); + printf(" 7 8 4 2\n"); + printf(" 8 4 8 7\n"); + printf(" # Generated by triangle -pcBev box\n\n"); + printf(" Here is the edge file for the triangulation, `box.1.edge'.\n\n"); + printf(" 16 0\n"); + printf(" 1 1 5\n"); + printf(" 2 5 6\n"); + printf(" 3 6 1\n"); + printf(" 4 1 3\n"); + printf(" 5 3 5\n"); + printf(" 6 2 6\n"); + printf(" 7 6 8\n"); + printf(" 8 8 2\n"); + printf(" 9 2 1\n"); + printf(" 10 7 3\n"); + printf(" 11 3 4\n"); + printf(" 12 4 7\n"); + printf(" 13 7 5\n"); + printf(" 14 8 4\n"); + printf(" 15 4 2\n"); + printf(" 16 8 7\n"); + printf(" # Generated by triangle -pcBev box\n"); + printf("\n"); + printf( +" Here's a file `box.1.part' that partitions the mesh into four subdomains.\n" +); + printf("\n"); + printf(" 8 4\n"); + printf(" 1 3\n"); + printf(" 2 3\n"); + printf(" 3 4\n"); + printf(" 4 4\n"); + printf(" 5 1\n"); + printf(" 6 1\n"); + printf(" 7 2\n"); + printf(" 8 2\n"); + printf(" # Generated by slice -s4 box.1\n\n"); + printf( +" Here's a file `box.1.adj' that represents the resulting adjacencies.\n"); + printf("\n"); + printf(" 4\n"); + printf(" 9\n"); + printf(" 2\n"); + printf(" 2\n"); + printf(" 0\n"); + printf(" 2\n"); + printf(" 9\n"); + printf(" 0\n"); + printf(" 2\n"); + printf(" 2\n"); + printf(" 0\n"); + printf(" 9\n"); + printf(" 2\n"); + printf(" 0\n"); + printf(" 2\n"); + printf(" 2\n"); + printf(" 9\n"); + printf("\n"); + printf("Display Speed:\n"); + printf("\n"); + printf( +" It is worthwhile to note that .edge files typically plot and print twice\n" +); + printf( +" as quickly as .ele files, because .ele files cause each internal edge to\n" +); + printf( +" be drawn twice. For the same reason, PostScript files created from edge\n" +); + printf(" sets are smaller than those created from triangulations.\n\n"); + printf("Show Me on the Web:\n\n"); + printf( +" To see an illustrated, updated version of these instructions, check out\n"); + printf("\n"); + printf(" http://www.cs.cmu.edu/~quake/showme.html\n"); + printf("\n"); + printf("A Brief Plea:\n"); + printf("\n"); + printf( +" If you use Show Me (or Triangle), and especially if you use it to\n"); + printf( +" accomplish real work, I would like very much to hear from you. A short\n"); + printf( +" letter or email (to jrs@cs.cmu.edu) describing how you use Show Me (and\n"); + printf( +" its sister programs) will mean a lot to me. The more people I know\n"); + printf( +" are using my programs, the more easily I can justify spending time on\n"); + printf( +" improvements, which in turn will benefit you. Also, I can put you\n"); + printf( +" on a list to receive email whenever new versions are available.\n"); + printf("\n"); + printf( +" If you use a PostScript file generated by Show Me in a publication,\n"); + printf(" please include an acknowledgment as well.\n\n"); + exit(0); +} + +void set_filenames(filename, lowermeshnumber) +char *filename; +int lowermeshnumber; +{ + char numberstring[100]; + int i; + + for (i = 0; i < 2; i++) { + strcpy(nodefilename[i], filename); + strcpy(polyfilename[i], filename); + strcpy(elefilename[i], filename); + strcpy(edgefilename[i], filename); + strcpy(partfilename[i], filename); + strcpy(adjfilename[i], filename); + strcpy(vnodefilename[i], filename); + strcpy(vedgefilename[i], filename); + + if (lowermeshnumber + i > 0) { + sprintf(numberstring, ".%d", lowermeshnumber + i); + strcat(nodefilename[i], numberstring); + strcat(polyfilename[i], numberstring); + strcat(elefilename[i], numberstring); + strcat(edgefilename[i], numberstring); + strcat(partfilename[i], numberstring); + strcat(adjfilename[i], numberstring); + strcat(vnodefilename[i], numberstring); + strcat(vedgefilename[i], numberstring); + } + + strcat(nodefilename[i], ".node"); + strcat(polyfilename[i], ".poly"); + strcat(elefilename[i], ".ele"); + strcat(edgefilename[i], ".edge"); + strcat(partfilename[i], ".part"); + strcat(adjfilename[i], ".adj"); + strcat(vnodefilename[i], ".v.node"); + strcat(vedgefilename[i], ".v.edge"); + } +} + +void parsecommandline(argc, argv) +int argc; +char **argv; +{ + int increment; + int meshnumber; + int i, j; + + quiet = 0; + fillelem = 0; + line_width = 1; + bw_ps = 0; + start_image = ELE; + filename[0] = '\0'; + for (i = 1; i < argc; i++) { + if (argv[i][0] == '-') { + for (j = 1; argv[i][j] != '\0'; j++) { + if (argv[i][j] == 'f') { + fillelem = 1; + } + if (argv[i][j] == 'w') { + if ((argv[i][j + 1] >= '1') && (argv[i][j + 1] <= '9')) { + line_width = 0; + while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) { + j++; + line_width = line_width * 10 + (int) (argv[i][j] - '0'); + } + if (line_width > 100) { + printf("Error: Line width cannot exceed 100.\n"); + line_width = 1; + } + } + } + if (argv[i][j] == 'b') { + bw_ps = 1; + } + if (argv[i][j] == 'Q') { + quiet = 1; + } + if ((argv[i][j] == 'h') || (argv[i][j] == 'H') || + (argv[i][j] == '?')) { + info(); + } + } + } else { + strcpy(filename, argv[i]); + } + } + if (filename[0] == '\0') { + syntax(); + } + if (!strcmp(&filename[strlen(filename) - 5], ".node")) { + filename[strlen(filename) - 5] = '\0'; + start_image = NODE; + } + if (!strcmp(&filename[strlen(filename) - 5], ".poly")) { + filename[strlen(filename) - 5] = '\0'; + start_image = POLY; + } + if (!strcmp(&filename[strlen(filename) - 4], ".ele")) { + filename[strlen(filename) - 4] = '\0'; + start_image = ELE; + } + if (!strcmp(&filename[strlen(filename) - 5], ".edge")) { + filename[strlen(filename) - 5] = '\0'; + start_image = EDGE; + } + if (!strcmp(&filename[strlen(filename) - 5], ".part")) { + filename[strlen(filename) - 5] = '\0'; + start_image = PART; + } + if (!strcmp(&filename[strlen(filename) - 4], ".adj")) { + filename[strlen(filename) - 4] = '\0'; + start_image = ADJ; + } + + increment = 0; + j = 1; + while (filename[j] != '\0') { + if ((filename[j] == '.') && (filename[j + 1] != '\0')) { + increment = j + 1; + } + j++; + } + meshnumber = 0; + if (increment > 0) { + j = increment; + do { + if ((filename[j] >= '0') && (filename[j] <= '9')) { + meshnumber = meshnumber * 10 + (int) (filename[j] - '0'); + } else { + increment = 0; + } + j++; + } while (filename[j] != '\0'); + } + if (increment > 0) { + filename[increment - 1] = '\0'; + } + + if (meshnumber == 0) { + start_inc = 0; + loweriteration = 0; + } else { + start_inc = 1; + loweriteration = meshnumber - 1; + } + set_filenames(filename, loweriteration); +} + +void free_inc(inc) +int inc; +{ + if (loaded[inc][NODE]) { + free(nodeptr[inc]); + } + if (loaded[inc][POLY]) { + if (polynodes[inc] > 0) { + free(polynodeptr[inc]); + } + free(polyedgeptr[inc]); + free(polyholeptr[inc]); + } + if (loaded[inc][ELE]) { + free(eleptr[inc]); + } + if (loaded[inc][PART]) { + free(partpart[inc]); + free(partcenter[inc]); + free(partshift[inc]); + } + if (loaded[inc][EDGE]) { + free(edgeptr[inc]); + free(normptr[inc]); + } + if (loaded[inc][ADJ]) { + free(adjptr[inc]); + } + if (loaded[inc][VORO]) { + free(vnodeptr[inc]); + free(vedgeptr[inc]); + free(vnormptr[inc]); + } +} + +void move_inc(inc) +int inc; +{ + int i; + + free_inc(1 - inc); + for (i = 0; i < IMAGE_TYPES; i++) { + loaded[1 - inc][i] = loaded[inc][i]; + loaded[inc][i] = 0; + xlo[1 - inc][i] = xlo[inc][i]; + ylo[1 - inc][i] = ylo[inc][i]; + xhi[1 - inc][i] = xhi[inc][i]; + yhi[1 - inc][i] = yhi[inc][i]; + } + nodes[1 - inc] = nodes[inc]; + node_dim[1 - inc] = node_dim[inc]; + nodeptr[1 - inc] = nodeptr[inc]; + polynodes[1 - inc] = polynodes[inc]; + poly_dim[1 - inc] = poly_dim[inc]; + polyedges[1 - inc] = polyedges[inc]; + polyholes[1 - inc] = polyholes[inc]; + polynodeptr[1 - inc] = polynodeptr[inc]; + polyedgeptr[1 - inc] = polyedgeptr[inc]; + polyholeptr[1 - inc] = polyholeptr[inc]; + elems[1 - inc] = elems[inc]; + ele_corners[1 - inc] = ele_corners[inc]; + eleptr[1 - inc] = eleptr[inc]; + edges[1 - inc] = edges[inc]; + edgeptr[1 - inc] = edgeptr[inc]; + normptr[1 - inc] = normptr[inc]; + subdomains[1 - inc] = subdomains[inc]; + partpart[1 - inc] = partpart[inc]; + partcenter[1 - inc] = partcenter[inc]; + partshift[1 - inc] = partshift[inc]; + adjsubdomains[1 - inc] = adjsubdomains[inc]; + adjptr[1 - inc] = adjptr[inc]; + vnodes[1 - inc] = vnodes[inc]; + vnode_dim[1 - inc] = vnode_dim[inc]; + vnodeptr[1 - inc] = vnodeptr[inc]; + vedges[1 - inc] = vedges[inc]; + vedgeptr[1 - inc] = vedgeptr[inc]; + vnormptr[1 - inc] = vnormptr[inc]; + firstnumber[1 - inc] = firstnumber[inc]; + firstnumber[inc] = -1; +} + +void unload_inc(inc) +int inc; +{ + int i; + + current_image = NOTHING; + for (i = 0; i < IMAGE_TYPES; i++) { + loaded[inc][i] = 0; + firstnumber[inc] = -1; + } +} + +void showme_init() +{ + current_image = NOTHING; + current_inc = 0; + explosion = STARTEXPLOSION; + unload_inc(0); + unload_inc(1); +} + +char *readline(string, infile, infilename) +char *string; +FILE *infile; +char *infilename; +{ + char *result; + + do { + result = fgets(string, INPUTLINESIZE, infile); + if (result == (char *) NULL) { + printf(" Error: Unexpected end of file in %s.\n", + infilename); + exit(1); + } + while ((*result != '\0') && (*result != '#') + && (*result != '.') && (*result != '+') && (*result != '-') + && ((*result < '0') || (*result > '9'))) { + result++; + } + } while ((*result == '#') || (*result == '\0')); + return result; +} + +char *findfield(string) +char *string; +{ + char *result; + + result = string; + while ((*result != '\0') && (*result != '#') + && (*result != ' ') && (*result != '\t')) { + result++; + } + while ((*result != '\0') && (*result != '#') + && (*result != '.') && (*result != '+') && (*result != '-') + && ((*result < '0') || (*result > '9'))) { + result++; + } + if (*result == '#') { + *result = '\0'; + } + return result; +} + +int load_node(fname, firstnumber, nodes, dim, ptr, xmin, ymin, xmax, ymax) +char *fname; +int *firstnumber; +int *nodes; +int *dim; +REAL **ptr; +REAL *xmin; +REAL *ymin; +REAL *xmax; +REAL *ymax; +{ + FILE *infile; + char inputline[INPUTLINESIZE]; + char *stringptr; + int extras; + int nodemarks; + int index; + int nodenumber; + int i, j; + int smallerr; + REAL x, y; + + *xmin = *ymin = 0.0; + *xmax = *ymax = 1.0; + if (!quiet) { + printf("Opening %s.\n", fname); + } + infile = fopen(fname, "r"); + if (infile == (FILE *) NULL) { + printf(" Error: Cannot access file %s.\n", fname); + return 1; + } + stringptr = readline(inputline, infile, fname); + *nodes = (int) strtol (stringptr, &stringptr, 0); + if (*nodes < 3) { + printf(" Error: %s contains %d points.\n", fname, *nodes); + return 1; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + *dim = 2; + } else { + *dim = (int) strtol (stringptr, &stringptr, 0); + } + if (*dim < 1) { + printf(" Error: %s has dimensionality %d.\n", fname, *dim); + return 1; + } + if (*dim != 2) { + printf(" I only understand two-dimensional meshes.\n"); + return 1; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + extras = 0; + } else { + extras = (int) strtol (stringptr, &stringptr, 0); + } + if (extras < 0) { + printf(" Error: %s has negative value for number of attributes.\n", + fname); + return 1; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + nodemarks = 0; + } else { + nodemarks = (int) strtol (stringptr, &stringptr, 0); + } + if (nodemarks < 0) { + printf(" Warning: %s has negative value for number of point markers.\n", + fname); + } + if (nodemarks > 1) { + printf( + " Warning: %s has value greater than one for number of point markers.\n", + fname); + } + *ptr = (REAL *) malloc((*nodes + 1) * *dim * sizeof(REAL)); + if (*ptr == (REAL *) NULL) { + printf(" Out of memory.\n"); + return 1; + } + index = *dim; + smallerr = 1; + for (i = 0; i < *nodes; i++) { + stringptr = readline(inputline, infile, fname); + nodenumber = (int) strtol (stringptr, &stringptr, 0); + if ((i == 0) && (*firstnumber == -1)) { + if (nodenumber == 0) { + *firstnumber = 0; + } else { + *firstnumber = 1; + } + } + if ((nodenumber != *firstnumber + i) && (smallerr)) { + printf(" Warning: Points in %s are not numbered correctly\n", fname); + printf(" (starting with point %d).\n", *firstnumber + i); + smallerr = 0; + } + for (j = 0; j < *dim; j++) { + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Point %d is missing a coordinate in %s.\n", + *firstnumber + i, fname); + free(*ptr); + return 1; + } + (*ptr)[index++] = (REAL) strtod(stringptr, &stringptr); + } + } + fclose(infile); + index = *dim; + *xmin = *xmax = (*ptr)[index]; + *ymin = *ymax = (*ptr)[index + 1]; + for (i = 2; i <= *nodes; i++) { + index += *dim; + x = (*ptr)[index]; + y = (*ptr)[index + 1]; + if (x < *xmin) { + *xmin = x; + } + if (y < *ymin) { + *ymin = y; + } + if (x > *xmax) { + *xmax = x; + } + if (y > *ymax) { + *ymax = y; + } + } + if (*xmin == *xmax) { + *xmin -= 0.5; + *xmax += 0.5; + } + if (*ymin == *ymax) { + *ymin -= 0.5; + *ymax += 0.5; + } + return 0; +} + +int load_poly(inc, fname, firstnumber, pnodes, dim, edges, holes, nodeptr, + edgeptr, holeptr, xmin, ymin, xmax, ymax) +int inc; +char *fname; +int *firstnumber; +int *pnodes; +int *dim; +int *edges; +int *holes; +REAL **nodeptr; +int **edgeptr; +REAL **holeptr; +REAL *xmin; +REAL *ymin; +REAL *xmax; +REAL *ymax; +{ + FILE *infile; + char inputline[INPUTLINESIZE]; + char *stringptr; + int extras; + int nodemarks; + int segmentmarks; + int index; + int nodenumber, edgenumber, holenumber; + int maxnode; + int i, j; + int smallerr; + REAL x, y; + + if (!quiet) { + printf("Opening %s.\n", fname); + } + infile = fopen(fname, "r"); + if (infile == (FILE *) NULL) { + printf(" Error: Cannot access file %s.\n", fname); + return 1; + } + stringptr = readline(inputline, infile, fname); + *pnodes = (int) strtol (stringptr, &stringptr, 0); + if (*pnodes == 0) { + if (!loaded[inc][NODE]) { + if (load_image(inc, NODE)) { + return 1; + } + } + maxnode = nodes[inc]; + *xmin = xlo[inc][NODE]; + *ymin = ylo[inc][NODE]; + *xmax = xhi[inc][NODE]; + *ymax = yhi[inc][NODE]; + } else { + if (*pnodes < 1) { + printf(" Error: %s contains %d points.\n", fname, *pnodes); + return 1; + } + maxnode = *pnodes; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + *dim = 2; + } else { + *dim = (int) strtol (stringptr, &stringptr, 0); + } + if (*dim < 1) { + printf(" Error: %s has dimensionality %d.\n", fname, *dim); + return 1; + } + if (*dim != 2) { + printf(" I only understand two-dimensional meshes.\n"); + return 1; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + extras = 0; + } else { + extras = (int) strtol (stringptr, &stringptr, 0); + } + if (extras < 0) { + printf(" Error: %s has negative value for number of attributes.\n", + fname); + return 1; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + nodemarks = 0; + } else { + nodemarks = (int) strtol (stringptr, &stringptr, 0); + } + if (nodemarks < 0) { + printf(" Warning: %s has negative value for number of point markers.\n", + fname); + } + if (nodemarks > 1) { + printf( + " Warning: %s has value greater than one for number of point markers.\n", + fname); + } + if (*pnodes > 0) { + *nodeptr = (REAL *) malloc((*pnodes + 1) * *dim * sizeof(REAL)); + if (*nodeptr == (REAL *) NULL) { + printf(" Out of memory.\n"); + return 1; + } + index = *dim; + smallerr = 1; + for (i = 0; i < *pnodes; i++) { + stringptr = readline(inputline, infile, fname); + nodenumber = (int) strtol (stringptr, &stringptr, 0); + if ((i == 0) && (*firstnumber == -1)) { + if (nodenumber == 0) { + *firstnumber = 0; + } else { + *firstnumber = 1; + } + } + if ((nodenumber != *firstnumber + i) && (smallerr)) { + printf(" Warning: Points in %s are not numbered correctly.\n", + fname); + printf(" (starting with point %d).\n", *firstnumber + i); + smallerr = 0; + } + for (j = 0; j < *dim; j++) { + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Point %d is missing a coordinate in %s.\n", + *firstnumber + i, fname); + free(*nodeptr); + return 1; + } + (*nodeptr)[index++] = (REAL) strtod(stringptr, &stringptr); + } + } + } + stringptr = readline(inputline, infile, fname); + *edges = (int) strtol (stringptr, &stringptr, 0); + if (*edges < 0) { + printf(" Error: %s contains %d segments.\n", fname, *edges); + free(*nodeptr); + return 1; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + segmentmarks = 0; + } else { + segmentmarks = (int) strtol (stringptr, &stringptr, 0); + } + if (segmentmarks < 0) { + printf(" Error: %s has negative value for number of segment markers.\n", + fname); + free(*nodeptr); + return 1; + } + if (segmentmarks > 1) { + printf( + " Error: %s has value greater than one for number of segment markers.\n", + fname); + free(*nodeptr); + return 1; + } + *edgeptr = (int *) malloc(((*edges + 1) << 1) * sizeof(int)); + if (*edgeptr == (int *) NULL) { + printf(" Out of memory.\n"); + free(*nodeptr); + return 1; + } + index = 2; + smallerr = 1; + for (i = *firstnumber; i < *firstnumber + *edges; i++) { + stringptr = readline(inputline, infile, fname); + edgenumber = (int) strtol (stringptr, &stringptr, 0); + if ((edgenumber != i) && (smallerr)) { + printf(" Warning: Segments in %s are not numbered correctly.\n", + fname); + printf(" (starting with segment %d).\n", i); + smallerr = 0; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Segment %d is missing its endpoints in %s.\n", i, fname); + free(*nodeptr); + free(*edgeptr); + return 1; + } + (*edgeptr)[index] = (int) strtol (stringptr, &stringptr, 0) + 1 - + *firstnumber; + if (((*edgeptr)[index] < 1) || ((*edgeptr)[index] > maxnode)) { + printf("Error: Segment %d has invalid endpoint in %s.\n", i, fname); + return 1; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Segment %d is missing an endpoint in %s.\n", i, fname); + free(*nodeptr); + free(*edgeptr); + return 1; + } + (*edgeptr)[index + 1] = (int) strtol (stringptr, &stringptr, 0) + 1 - + *firstnumber; + if (((*edgeptr)[index + 1] < 1) || ((*edgeptr)[index + 1] > maxnode)) { + printf("Error: Segment %d has invalid endpoint in %s.\n", i, fname); + return 1; + } + index += 2; + } + stringptr = readline(inputline, infile, fname); + *holes = (int) strtol (stringptr, &stringptr, 0); + if (*holes < 0) { + printf(" Error: %s contains %d holes.\n", fname, *holes); + free(*nodeptr); + free(*edgeptr); + return 1; + } + *holeptr = (REAL *) malloc((*holes + 1) * *dim * sizeof(REAL)); + if (*holeptr == (REAL *) NULL) { + printf(" Out of memory.\n"); + free(*nodeptr); + free(*edgeptr); + return 1; + } + index = *dim; + smallerr = 1; + for (i = *firstnumber; i < *firstnumber + *holes; i++) { + stringptr = readline(inputline, infile, fname); + holenumber = (int) strtol (stringptr, &stringptr, 0); + if ((holenumber != i) && (smallerr)) { + printf(" Warning: Holes in %s are not numbered correctly.\n", fname); + printf(" (starting with hole %d).\n", i); + smallerr = 0; + } + for (j = 0; j < *dim; j++) { + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Hole %d is missing a coordinate in %s.\n", i, + fname); + free(*nodeptr); + free(*edgeptr); + free(*holeptr); + return 1; + } + (*holeptr)[index++] = (REAL) strtod(stringptr, &stringptr); + } + } + fclose(infile); + if (*pnodes > 0) { + index = *dim; + *xmin = *xmax = (*nodeptr)[index]; + *ymin = *ymax = (*nodeptr)[index + 1]; + for (i = 2; i <= *pnodes; i++) { + index += *dim; + x = (*nodeptr)[index]; + y = (*nodeptr)[index + 1]; + if (x < *xmin) { + *xmin = x; + } + if (y < *ymin) { + *ymin = y; + } + if (x > *xmax) { + *xmax = x; + } + if (y > *ymax) { + *ymax = y; + } + } + } + index = *dim; + for (i = 1; i <= *holes; i++) { + x = (*holeptr)[index]; + y = (*holeptr)[index + 1]; + if (x < *xmin) { + *xmin = x; + } + if (y < *ymin) { + *ymin = y; + } + if (x > *xmax) { + *xmax = x; + } + if (y > *ymax) { + *ymax = y; + } + index += *dim; + } + return 0; +} + +int load_ele(fname, firstnumber, nodes, elems, corners, ptr) +char *fname; +int firstnumber; +int nodes; +int *elems; +int *corners; +int **ptr; +{ + FILE *infile; + char inputline[INPUTLINESIZE]; + char *stringptr; + int extras; + int index; + int elemnumber; + int i, j; + int smallerr; + + if (!quiet) { + printf("Opening %s.\n", fname); + } + infile = fopen(fname, "r"); + if (infile == (FILE *) NULL) { + printf(" Error: Cannot access file %s.\n", fname); + return 1; + } + stringptr = readline(inputline, infile, fname); + *elems = (int) strtol (stringptr, &stringptr, 0); + if (*elems < 1) { + printf(" Error: %s contains %d triangles.\n", fname, *elems); + return 1; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + *corners = 3; + } else { + *corners = (int) strtol (stringptr, &stringptr, 0); + } + if (*corners < 3) { + printf(" Error: Triangles in %s have only %d corners.\n", fname, + *corners); + return 1; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + extras = 0; + } else { + extras = (int) strtol (stringptr, &stringptr, 0); + } + if (extras < 0) { + printf(" Error: %s has negative value for extra fields.\n", fname); + return 1; + } + *ptr = (int *) malloc((*elems + 1) * 3 * sizeof(int)); + if (*ptr == (int *) NULL) { + printf(" Out of memory.\n"); + return 1; + } + index = 3; + smallerr = 1; + for (i = firstnumber; i < firstnumber + *elems; i++) { + stringptr = readline(inputline, infile, fname); + elemnumber = (int) strtol (stringptr, &stringptr, 0); + if ((elemnumber != i) && (smallerr)) { + printf(" Warning: Triangles in %s are not numbered correctly.\n", + fname); + printf(" (starting with triangle %d).\n", i); + smallerr = 0; + } + for (j = 0; j < 3; j++) { + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Triangle %d is missing a corner in %s.\n", i, fname); + free(*ptr); + return 1; + } + (*ptr)[index] = (int) strtol (stringptr, &stringptr, 0) + 1 - + firstnumber; + if (((*ptr)[index] < 1) || ((*ptr)[index] > nodes)) { + printf("Error: Triangle %d has invalid corner in %s.\n", i, fname); + return 1; + } + index++; + } + } + fclose(infile); + return 0; +} + +int load_edge(fname, firstnumber, nodes, edges, edgeptr, normptr) +char *fname; +int firstnumber; +int nodes; +int *edges; +int **edgeptr; +REAL **normptr; +{ + FILE *infile; + char inputline[INPUTLINESIZE]; + char *stringptr; + int index; + int edgenumber; + int edgemarks; + int i; + int smallerr; + + if (!quiet) { + printf("Opening %s.\n", fname); + } + infile = fopen(fname, "r"); + if (infile == (FILE *) NULL) { + printf(" Error: Cannot access file %s.\n", fname); + return 1; + } + stringptr = readline(inputline, infile, fname); + *edges = (int) strtol (stringptr, &stringptr, 0); + if (*edges < 1) { + printf(" Error: %s contains %d edges.\n", fname, *edges); + return 1; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + edgemarks = 0; + } else { + edgemarks = (int) strtol (stringptr, &stringptr, 0); + } + if (edgemarks < 0) { + printf(" Error: %s has negative value for number of edge markers.\n", + fname); + return 1; + } + if (edgemarks > 1) { + printf( + " Error: %s has value greater than one for number of edge markers.\n", + fname); + return 1; + } + *edgeptr = (int *) malloc(((*edges + 1) << 1) * sizeof(int)); + if (*edgeptr == (int *) NULL) { + printf(" Out of memory.\n"); + return 1; + } + *normptr = (REAL *) malloc(((*edges + 1) << 1) * sizeof(REAL)); + if (*normptr == (REAL *) NULL) { + printf(" Out of memory.\n"); + free(*edgeptr); + return 1; + } + index = 2; + smallerr = 1; + for (i = firstnumber; i < firstnumber + *edges; i++) { + stringptr = readline(inputline, infile, fname); + edgenumber = (int) strtol (stringptr, &stringptr, 0); + if ((edgenumber != i) && (smallerr)) { + printf(" Warning: Edges in %s are not numbered correctly.\n", fname); + printf(" (starting with edge %d).\n", i); + smallerr = 0; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Edge %d is missing its endpoints in %s.\n", i, fname); + free(*edgeptr); + free(*normptr); + return 1; + } + (*edgeptr)[index] = (int) strtol (stringptr, &stringptr, 0) + 1 - + firstnumber; + if (((*edgeptr)[index] < 1) || ((*edgeptr)[index] > nodes)) { + printf("Error: Edge %d has invalid endpoint in %s.\n", i, fname); + return 1; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Edge %d is missing an endpoint in %s.\n", i, fname); + free(*edgeptr); + free(*normptr); + return 1; + } + (*edgeptr)[index + 1] = (int) strtol (stringptr, &stringptr, 0); + if ((*edgeptr)[index + 1] == -1) { + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Edge %d is missing its direction in %s.\n", i, fname); + free(*edgeptr); + free(*normptr); + return 1; + } + (*normptr)[index] = (REAL) strtod(stringptr, &stringptr); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Edge %d is missing a direction coordinate in %s.\n", + i, fname); + free(*edgeptr); + free(*normptr); + return 1; + } + (*normptr)[index + 1] = (REAL) strtod(stringptr, &stringptr); + } else { + (*edgeptr)[index + 1] += 1 - firstnumber; + if (((*edgeptr)[index + 1] < 1) || ((*edgeptr)[index + 1] > nodes)) { + printf("Error: Edge %d has invalid endpoint in %s.\n", i, fname); + return 1; + } + } + index += 2; + } + fclose(infile); + return 0; +} + +int load_part(fname, dim, firstnumber, elems, nodeptr, eleptr, parts, + partition, partcenter, partshift) +char *fname; +int dim; +int firstnumber; +int elems; +REAL *nodeptr; +int *eleptr; +int *parts; +int **partition; +REAL **partcenter; +REAL **partshift; +{ + FILE *infile; + char inputline[INPUTLINESIZE]; + char *stringptr; + int partelems; + int index; + int elemnumber; + int i, j; + int smallerr; + int *partsize; + + if (!quiet) { + printf("Opening %s.\n", fname); + } + infile = fopen(fname, "r"); + if (infile == (FILE *) NULL) { + printf(" Error: Cannot access file %s.\n", fname); + return 1; + } + stringptr = readline(inputline, infile, fname); + partelems = (int) strtol (stringptr, &stringptr, 0); + if (partelems != elems) { + printf( + " Error: .ele and .part files do not agree on number of triangles.\n"); + return 1; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + *parts = 1; + } else { + *parts = (int) strtol (stringptr, &stringptr, 0); + } + if (*parts < 1) { + printf(" Error: %s specifies %d subdomains.\n", fname, *parts); + return 1; + } + *partition = (int *) malloc((elems + 1) * sizeof(int)); + if (*partition == (int *) NULL) { + printf(" Out of memory.\n"); + return 1; + } + smallerr = 1; + for (i = firstnumber; i < firstnumber + partelems; i++) { + stringptr = readline(inputline, infile, fname); + elemnumber = (int) strtol (stringptr, &stringptr, 0); + if ((elemnumber != i) && (smallerr)) { + printf(" Warning: Triangles in %s are not numbered correctly.\n", + fname); + printf(" (starting with triangle %d).\n", i); + smallerr = 0; + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Triangle %d has no subdomain in %s.\n", i, fname); + free(*partition); + return 1; + } + (*partition)[i] = (int) strtol (stringptr, &stringptr, 0) - firstnumber; + if (((*partition)[i] >= *parts) || ((*partition)[i] < 0)) { + printf(" Error: Triangle %d of %s has an invalid subdomain.\n", + i, fname); + free(*partition); + return 1; + } + } + fclose(infile); + *partcenter = (REAL *) malloc(((*parts + 1) << 1) * sizeof(REAL)); + if (*partcenter == (REAL *) NULL) { + printf("Error: Out of memory.\n"); + free(*partition); + return 1; + } + *partshift = (REAL *) malloc((*parts << 1) * sizeof(REAL)); + if (*partshift == (REAL *) NULL) { + printf("Error: Out of memory.\n"); + free(*partition); + free(*partcenter); + return 1; + } + partsize = (int *) malloc((*parts + 1) * sizeof(int)); + if (partsize == (int *) NULL) { + printf("Error: Out of memory.\n"); + free(*partition); + free(*partcenter); + free(*partshift); + return 1; + } + index = 3; + for (i = 0; i <= *parts; i++) { + partsize[i] = 0; + (*partcenter)[i << 1] = 0.0; + (*partcenter)[(i << 1) + 1] = 0.0; + } + for (i = 1; i <= elems; i++) { + partsize[(*partition)[i]] += 3; + for (j = 0; j < 3; j++) { + (*partcenter)[(*partition)[i] << 1] += + nodeptr[eleptr[index] * dim]; + (*partcenter)[((*partition)[i] << 1) + 1] += + nodeptr[eleptr[index++] * dim + 1]; + } + } + for (i = 0; i < *parts; i++) { + (*partcenter)[i << 1] /= (REAL) partsize[i]; + (*partcenter)[(i << 1) + 1] /= (REAL) partsize[i]; + (*partcenter)[*parts << 1] += (*partcenter)[i << 1]; + (*partcenter)[(*parts << 1) + 1] += (*partcenter)[(i << 1) + 1]; + } + (*partcenter)[*parts << 1] /= (REAL) *parts; + (*partcenter)[(*parts << 1) + 1] /= (REAL) *parts; + free(partsize); + return 0; +} + +int load_adj(fname, subdomains, ptr) +char *fname; +int *subdomains; +int **ptr; +{ + FILE *infile; + char inputline[INPUTLINESIZE]; + char *stringptr; + int i, j; + + if (!quiet) { + printf("Opening %s.\n", fname); + } + infile = fopen(fname, "r"); + if (infile == (FILE *) NULL) { + printf(" Error: Cannot access file %s.\n", fname); + return 1; + } + stringptr = readline(inputline, infile, fname); + *subdomains = (int) strtol (stringptr, &stringptr, 0); + if (*subdomains < 1) { + printf(" Error: %s contains %d subdomains.\n", fname, *subdomains); + return 1; + } + *ptr = (int *) malloc(*subdomains * *subdomains * sizeof(int)); + if (*ptr == (int *) NULL) { + printf(" Out of memory.\n"); + return 1; + } + for (i = 0; i < *subdomains; i++) { + for (j = 0; j < *subdomains; j++) { + stringptr = readline(inputline, infile, fname); + (*ptr)[i * *subdomains + j] = (int) strtol (stringptr, &stringptr, 0); + } + } + return 0; +} + +void findpartshift(parts, explosion, partcenter, partshift) +int parts; +REAL explosion; +REAL *partcenter; +REAL *partshift; +{ + int i; + + for (i = 0; i < parts; i++) { + partshift[i << 1] = explosion * + (partcenter[i << 1] - partcenter[parts << 1]); + partshift[(i << 1) + 1] = explosion * + (partcenter[(i << 1) + 1] - partcenter[(parts << 1) + 1]); + } +} + +int load_image(inc, image) +int inc; +int image; +{ + int error; + + switch (image) { + case NODE: + error = load_node(nodefilename[inc], &firstnumber[inc], &nodes[inc], + &node_dim[inc], &nodeptr[inc], &xlo[inc][NODE], + &ylo[inc][NODE], &xhi[inc][NODE], &yhi[inc][NODE]); + break; + case POLY: + error = load_poly(inc, polyfilename[inc], &firstnumber[inc], + &polynodes[inc], &poly_dim[inc], &polyedges[inc], + &polyholes[inc], &polynodeptr[inc], &polyedgeptr[inc], + &polyholeptr[inc], + &xlo[inc][POLY], &ylo[inc][POLY], + &xhi[inc][POLY], &yhi[inc][POLY]); + break; + case ELE: + error = load_ele(elefilename[inc], firstnumber[inc], nodes[inc], + &elems[inc], &ele_corners[inc], &eleptr[inc]); + xlo[inc][ELE] = xlo[inc][NODE]; + ylo[inc][ELE] = ylo[inc][NODE]; + xhi[inc][ELE] = xhi[inc][NODE]; + yhi[inc][ELE] = yhi[inc][NODE]; + break; + case EDGE: + error = load_edge(edgefilename[inc], firstnumber[inc], nodes[inc], + &edges[inc], &edgeptr[inc], &normptr[inc]); + xlo[inc][EDGE] = xlo[inc][NODE]; + ylo[inc][EDGE] = ylo[inc][NODE]; + xhi[inc][EDGE] = xhi[inc][NODE]; + yhi[inc][EDGE] = yhi[inc][NODE]; + break; + case PART: + error = load_part(partfilename[inc], node_dim[inc], firstnumber[inc], + elems[inc], nodeptr[inc], eleptr[inc], + &subdomains[inc], &partpart[inc], &partcenter[inc], + &partshift[inc]); + if (!error) { + findpartshift(subdomains[inc], explosion, partcenter[inc], + partshift[inc]); + } + xlo[inc][PART] = xlo[inc][NODE]; + ylo[inc][PART] = ylo[inc][NODE]; + xhi[inc][PART] = xhi[inc][NODE]; + yhi[inc][PART] = yhi[inc][NODE]; + break; + case ADJ: + error = load_adj(adjfilename[inc], &adjsubdomains[inc], &adjptr[inc]); + xlo[inc][ADJ] = xlo[inc][NODE]; + ylo[inc][ADJ] = ylo[inc][NODE]; + xhi[inc][ADJ] = xhi[inc][NODE]; + yhi[inc][ADJ] = yhi[inc][NODE]; + break; + case VORO: + error = load_node(vnodefilename[inc], &firstnumber[inc], &vnodes[inc], + &vnode_dim[inc], &vnodeptr[inc], &xlo[inc][VORO], + &ylo[inc][VORO], &xhi[inc][VORO], &yhi[inc][VORO]); + if (!error) { + error = load_edge(vedgefilename[inc], firstnumber[inc], vnodes[inc], + &vedges[inc], &vedgeptr[inc], &vnormptr[inc]); + } + break; + default: + error = 1; + } + if (!error) { + loaded[inc][image] = 1; + } + return error; +} + +void choose_image(inc, image) +int inc; +int image; +{ + if (!loaded[inc][image]) { + if ((image == ELE) || (image == EDGE) || (image == PART) + || (image == ADJ)) { + if (!loaded[inc][NODE]) { + if (load_image(inc, NODE)) { + return; + } + } + } + if ((image == PART) || (image == ADJ)) { + if (!loaded[inc][ELE]) { + if (load_image(inc, ELE)) { + return; + } + } + } + if (image == ADJ) { + if (!loaded[inc][PART]) { + if (load_image(inc, PART)) { + return; + } + } + } + if (load_image(inc, image)) { + return; + } + } + current_inc = inc; + current_image = image; +} + +Window make_button(name, x, y, width) +char *name; +int x; +int y; +int width; +{ + XSetWindowAttributes attr; + XSizeHints hints; + Window button; + + attr.background_pixel = black; + attr.border_pixel = white; + attr.backing_store = NotUseful; + attr.event_mask = ExposureMask | ButtonReleaseMask | ButtonPressMask; + attr.bit_gravity = SouthWestGravity; + attr.win_gravity = SouthWestGravity; + attr.save_under = False; + button = XCreateWindow(display, mainwindow, x, y, width, BUTTONHEIGHT - 4, + 2, 0, InputOutput, CopyFromParent, + CWBackPixel | CWBorderPixel | CWEventMask | + CWBitGravity | CWWinGravity | CWBackingStore | + CWSaveUnder, &attr); + hints.width = width; + hints.height = BUTTONHEIGHT - 4; + hints.min_width = 0; + hints.min_height = BUTTONHEIGHT - 4; + hints.max_width = width; + hints.max_height = BUTTONHEIGHT - 4; + hints.width_inc = 1; + hints.height_inc = 1; + hints.flags = PMinSize | PMaxSize | PSize | PResizeInc; + XSetStandardProperties(display, button, name, "showme", None, (char **) NULL, + 0, &hints); + return button; +} + +void make_buttons(y) +int y; +{ + int i; + + for (i = 1; i >= 0; i--) { + nodewin[i] = make_button("node", 0, y + (1 - i) * BUTTONHEIGHT, 42); + XMapWindow(display, nodewin[i]); + polywin[i] = make_button("poly", 44, y + (1 - i) * BUTTONHEIGHT, 42); + XMapWindow(display, polywin[i]); + elewin[i] = make_button("ele", 88, y + (1 - i) * BUTTONHEIGHT, 33); + XMapWindow(display, elewin[i]); + edgewin[i] = make_button("edge", 123, y + (1 - i) * BUTTONHEIGHT, 42); + XMapWindow(display, edgewin[i]); + partwin[i] = make_button("part", 167, y + (1 - i) * BUTTONHEIGHT, 42); + XMapWindow(display, partwin[i]); + adjwin[i] = make_button("adj", 211, y + (1 - i) * BUTTONHEIGHT, 33); + XMapWindow(display, adjwin[i]); + voronoiwin[i] = make_button("voro", 246, y + (1 - i) * BUTTONHEIGHT, 42); + XMapWindow(display, voronoiwin[i]); + } + versionpluswin = make_button(" +", 290, y, 52); + XMapWindow(display, versionpluswin); + versionminuswin = make_button(" -", 290, y + BUTTONHEIGHT, 52); + XMapWindow(display, versionminuswin); + + quitwin = make_button("Quit", 0, y + 2 * BUTTONHEIGHT, 42); + XMapWindow(display, quitwin); + leftwin = make_button("<", 44, y + 2 * BUTTONHEIGHT, 14); + XMapWindow(display, leftwin); + rightwin = make_button(">", 60, y + 2 * BUTTONHEIGHT, 14); + XMapWindow(display, rightwin); + upwin = make_button("^", 76, y + 2 * BUTTONHEIGHT, 14); + XMapWindow(display, upwin); + downwin = make_button("v", 92, y + 2 * BUTTONHEIGHT, 14); + XMapWindow(display, downwin); + resetwin = make_button("Reset", 108, y + 2 * BUTTONHEIGHT, 52); + XMapWindow(display, resetwin); + widthpluswin = make_button("Width+", 162, y + 2 * BUTTONHEIGHT, 61); + XMapWindow(display, widthpluswin); + widthminuswin = make_button("-", 225, y + 2 * BUTTONHEIGHT, 14); + XMapWindow(display, widthminuswin); + expwin = make_button("Exp", 241, y + 2 * BUTTONHEIGHT, 33); + XMapWindow(display, expwin); + exppluswin = make_button("+", 276, y + 2 * BUTTONHEIGHT, 14); + XMapWindow(display, exppluswin); + expminuswin = make_button("-", 292, y + 2 * BUTTONHEIGHT, 14); + XMapWindow(display, expminuswin); + fillwin = make_button("Fill", 308, y + 2 * BUTTONHEIGHT, 41); + XMapWindow(display, fillwin); + pswin = make_button("PS", 351, y + 2 * BUTTONHEIGHT, 24); + XMapWindow(display, pswin); + epswin = make_button("EPS", 377, y + 2 * BUTTONHEIGHT, 33); + XMapWindow(display, epswin); +} + +void fill_button(button) +Window button; +{ + int x, y; + unsigned int w, h, d, b; + Window rootw; + + XGetGeometry(display, button, &rootw, &x, &y, &w, &h, &d, &b); + XFillRectangle(display, button, fontgc, 0, 0, w, h); +} + +void draw_buttons() +{ + char numberstring[32]; + char buttonstring[6]; + int i; + + for (i = 1; i >= 0; i--) { + if ((current_image == NODE) && (current_inc == i)) { + fill_button(nodewin[i]); + XDrawString(display, nodewin[i], blackfontgc, 2, 13, "node", 4); + } else { + XClearWindow(display, nodewin[i]); + XDrawString(display, nodewin[i], fontgc, 2, 13, "node", 4); + } + if ((current_image == POLY) && (current_inc == i)) { + fill_button(polywin[i]); + XDrawString(display, polywin[i], blackfontgc, 2, 13, "poly", 4); + } else { + XClearWindow(display, polywin[i]); + XDrawString(display, polywin[i], fontgc, 2, 13, "poly", 4); + } + if ((current_image == ELE) && (current_inc == i)) { + fill_button(elewin[i]); + XDrawString(display, elewin[i], blackfontgc, 2, 13, "ele", 3); + } else { + XClearWindow(display, elewin[i]); + XDrawString(display, elewin[i], fontgc, 2, 13, "ele", 3); + } + if ((current_image == EDGE) && (current_inc == i)) { + fill_button(edgewin[i]); + XDrawString(display, edgewin[i], blackfontgc, 2, 13, "edge", 4); + } else { + XClearWindow(display, edgewin[i]); + XDrawString(display, edgewin[i], fontgc, 2, 13, "edge", 4); + } + if ((current_image == PART) && (current_inc == i)) { + fill_button(partwin[i]); + XDrawString(display, partwin[i], blackfontgc, 2, 13, "part", 4); + } else { + XClearWindow(display, partwin[i]); + XDrawString(display, partwin[i], fontgc, 2, 13, "part", 4); + } + if ((current_image == ADJ) && (current_inc == i)) { + fill_button(adjwin[i]); + XDrawString(display, adjwin[i], blackfontgc, 2, 13, "adj", 3); + } else { + XClearWindow(display, adjwin[i]); + XDrawString(display, adjwin[i], fontgc, 2, 13, "adj", 3); + } + if ((current_image == VORO) && (current_inc == i)) { + fill_button(voronoiwin[i]); + XDrawString(display, voronoiwin[i], blackfontgc, 2, 13, "voro", 4); + } else { + XClearWindow(display, voronoiwin[i]); + XDrawString(display, voronoiwin[i], fontgc, 2, 13, "voro", 4); + } + } + + XClearWindow(display, versionpluswin); + sprintf(numberstring, "%d", loweriteration + 1); + sprintf(buttonstring, "%-4.4s+", numberstring); + XDrawString(display, versionpluswin, fontgc, 2, 13, buttonstring, 5); + XClearWindow(display, versionminuswin); + sprintf(numberstring, "%d", loweriteration); + if (loweriteration == 0) { + sprintf(buttonstring, "%-4.4s", numberstring); + } else { + sprintf(buttonstring, "%-4.4s-", numberstring); + } + XDrawString(display, versionminuswin, fontgc, 2, 13, buttonstring, 5); + + XClearWindow(display, quitwin); + XDrawString(display, quitwin, fontgc, 2, 13, "Quit", 4); + XClearWindow(display, leftwin); + XDrawString(display, leftwin, fontgc, 2, 13, "<", 1); + XClearWindow(display, rightwin); + XDrawString(display, rightwin, fontgc, 2, 13, ">", 1); + XClearWindow(display, upwin); + XDrawString(display, upwin, fontgc, 2, 13, "^", 1); + XClearWindow(display, downwin); + XDrawString(display, downwin, fontgc, 2, 13, "v", 1); + XClearWindow(display, resetwin); + XDrawString(display, resetwin, fontgc, 2, 13, "Reset", 6); + XClearWindow(display, widthpluswin); + if (line_width < 100) { + XDrawString(display, widthpluswin, fontgc, 2, 13, "Width+", 6); + } else { + XDrawString(display, widthpluswin, fontgc, 2, 13, "Width ", 6); + } + XClearWindow(display, widthminuswin); + if (line_width > 1) { + XDrawString(display, widthminuswin, fontgc, 2, 13, "-", 1); + } + XClearWindow(display, expwin); + XClearWindow(display, exppluswin); + XClearWindow(display, expminuswin); + XClearWindow(display, fillwin); + if (current_image == PART) { + if (explode) { + fill_button(expwin); + XDrawString(display, expwin, blackfontgc, 2, 13, "Exp", 3); + } else { + XDrawString(display, expwin, fontgc, 2, 13, "Exp", 3); + } + XDrawString(display, exppluswin, fontgc, 2, 13, "+", 1); + XDrawString(display, expminuswin, fontgc, 2, 13, "-", 1); + if (fillelem) { + fill_button(fillwin); + XDrawString(display, fillwin, blackfontgc, 2, 13, "Fill", 4); + } else { + XDrawString(display, fillwin, fontgc, 2, 13, "Fill", 4); + } + } + XClearWindow(display, pswin); + XDrawString(display, pswin, fontgc, 2, 13, "PS", 2); + XClearWindow(display, epswin); + XDrawString(display, epswin, fontgc, 2, 13, "EPS", 3); +} + +void showme_window(argc, argv) +int argc; +char **argv; +{ + XSetWindowAttributes attr; + XSizeHints hints; + XGCValues fontvalues, linevalues; + XColor alloc_color, exact_color; + int i; + + display = XOpenDisplay((char *) NULL); + if (!display) { + printf("Error: Cannot open display.\n"); + exit(1); + } + screen = DefaultScreen(display); + rootwindow = DefaultRootWindow(display); + black = BlackPixel(display, screen); + white = WhitePixel(display, screen); + windowdepth = DefaultDepth(display, screen); + rootmap = DefaultColormap(display, screen); + width = STARTWIDTH; + height = STARTHEIGHT; + attr.background_pixel = black; + attr.border_pixel = white; + attr.backing_store = NotUseful; + attr.event_mask = ExposureMask | ButtonReleaseMask | ButtonPressMask | + StructureNotifyMask; + attr.bit_gravity = NorthWestGravity; + attr.win_gravity = NorthWestGravity; + attr.save_under = False; + mainwindow = XCreateWindow(display, rootwindow, 0, 0, width, + height + PANELHEIGHT, 3, 0, + InputOutput, CopyFromParent, + CWBackPixel | CWBorderPixel | CWEventMask | + CWBitGravity | CWWinGravity | CWBackingStore | + CWSaveUnder, &attr); + hints.width = width; + hints.height = height + PANELHEIGHT; + hints.min_width = MINWIDTH; + hints.min_height = MINHEIGHT + PANELHEIGHT; + hints.width_inc = 1; + hints.height_inc = 1; + hints.flags = PMinSize | PSize | PResizeInc; + XSetStandardProperties(display, mainwindow, "Show Me", "showme", None, + argv, argc, &hints); + XChangeProperty(display, mainwindow, XA_WM_CLASS, XA_STRING, 8, + PropModeReplace, "showme\0Archimedes", 18); + XClearWindow(display, mainwindow); + XMapWindow(display, mainwindow); + if ((windowdepth > 1) && + XAllocNamedColor(display, rootmap, "yellow", &alloc_color, + &exact_color)) { + color = 1; + explode = bw_ps; + fontvalues.foreground = alloc_color.pixel; + linevalues.foreground = alloc_color.pixel; + showme_foreground = alloc_color.pixel; + for (i = 0; i < 64; i++) { + if (XAllocNamedColor(display, rootmap, colorname[i], &alloc_color, + &rgb[i])) { + colors[i] = alloc_color.pixel; + } else { + colors[i] = white; + rgb[i].red = alloc_color.red; + rgb[i].green = alloc_color.green; + rgb[i].blue = alloc_color.blue; + if (!quiet) { + printf("Warning: I could not allocate %s.\n", colorname[i]); + } + } + } + } else { + color = 0; + fillelem = 0; + explode = 1; + fontvalues.foreground = white; + linevalues.foreground = white; + showme_foreground = white; + } + font = XLoadQueryFont(display, "9x15"); + fontvalues.background = black; + fontvalues.font = font->fid; + fontvalues.fill_style = FillSolid; + fontvalues.line_width = 2; + fontgc = XCreateGC(display, rootwindow, GCForeground | GCBackground | + GCFont | GCLineWidth | GCFillStyle, &fontvalues); + fontvalues.foreground = black; + blackfontgc = XCreateGC(display, rootwindow, GCForeground | GCBackground | + GCFont | GCLineWidth | GCFillStyle, &fontvalues); + linevalues.background = black; + linevalues.line_width = line_width; + linevalues.cap_style = CapRound; + linevalues.join_style = JoinRound; + linevalues.fill_style = FillSolid; + linegc = XCreateGC(display, rootwindow, GCForeground | GCBackground | + GCLineWidth | GCCapStyle | GCJoinStyle | GCFillStyle, + &linevalues); + trianglegc = XCreateGC(display, rootwindow, GCForeground | GCBackground | + GCLineWidth | GCCapStyle | GCJoinStyle | GCFillStyle, + &linevalues); + make_buttons(height); + XFlush(display); +} + +void draw_node(nodes, dim, ptr, xscale, yscale, xoffset, yoffset) +int nodes; +int dim; +REAL *ptr; +REAL xscale; +REAL yscale; +REAL xoffset; +REAL yoffset; +{ + int i; + int index; + + index = dim; + for (i = 1; i <= nodes; i++) { + XFillRectangle(display, mainwindow, linegc, + (int) (ptr[index] * xscale + xoffset) - (line_width >> 1), + (int) (ptr[index + 1] * yscale + yoffset) - + (line_width >> 1), line_width, line_width); + index += dim; + } +} + +void draw_poly(nodes, dim, edges, holes, nodeptr, edgeptr, holeptr, + xscale, yscale, xoffset, yoffset) +int nodes; +int dim; +int edges; +int holes; +REAL *nodeptr; +int *edgeptr; +REAL *holeptr; +REAL xscale; +REAL yscale; +REAL xoffset; +REAL yoffset; +{ + int i; + int index; + REAL *point1, *point2; + int x1, y1, x2, y2; + + index = dim; + for (i = 1; i <= nodes; i++) { + XFillRectangle(display, mainwindow, linegc, + (int) (nodeptr[index] * xscale + xoffset) - + (line_width >> 1), + (int) (nodeptr[index + 1] * yscale + yoffset) - + (line_width >> 1), line_width, line_width); + index += dim; + } + index = 2; + for (i = 1; i <= edges; i++) { + point1 = &nodeptr[edgeptr[index++] * dim]; + point2 = &nodeptr[edgeptr[index++] * dim]; + XDrawLine(display, mainwindow, linegc, + (int) (point1[0] * xscale + xoffset), + (int) (point1[1] * yscale + yoffset), + (int) (point2[0] * xscale + xoffset), + (int) (point2[1] * yscale + yoffset)); + } + index = dim; + if (color) { + XSetForeground(display, linegc, colors[0]); + } + for (i = 1; i <= holes; i++) { + x1 = (int) (holeptr[index] * xscale + xoffset) - 3; + y1 = (int) (holeptr[index + 1] * yscale + yoffset) - 3; + x2 = x1 + 6; + y2 = y1 + 6; + XDrawLine(display, mainwindow, linegc, x1, y1, x2, y2); + XDrawLine(display, mainwindow, linegc, x1, y2, x2, y1); + index += dim; + } + XSetForeground(display, linegc, showme_foreground); +} + +void draw_ele(inc, elems, corners, ptr, partition, shift, + xscale, yscale, xoffset, yoffset) +int inc; +int elems; +int corners; +int *ptr; +int *partition; +REAL *shift; +REAL xscale; +REAL yscale; +REAL xoffset; +REAL yoffset; +{ + int i, j; + int index; + REAL shiftx, shifty; + REAL *prevpoint, *nowpoint; + XPoint *vertices; + + if (color && fillelem && (partition != (int *) NULL)) { + vertices = (XPoint *) malloc(3 * sizeof(XPoint)); + if (vertices == (XPoint *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + index = 3; + for (i = 1; i <= elems; i++) { + if ((partition != (int *) NULL) && explode) { + shiftx = shift[partition[i] << 1]; + shifty = shift[(partition[i] << 1) + 1]; + } + if (color && (partition != (int *) NULL)) { + if (fillelem) { + XSetForeground(display, trianglegc, colors[partition[i] & 63]); + } else { + XSetForeground(display, linegc, colors[partition[i] & 63]); + } + } + if (color && fillelem && (partition != (int *) NULL)) { + if ((partition != (int *) NULL) && explode) { + for (j = 0; j < 3; j++) { + nowpoint = &nodeptr[inc][ptr[index + j] * node_dim[inc]]; + vertices[j].x = (nowpoint[0] + shiftx) * xscale + xoffset; + vertices[j].y = (nowpoint[1] + shifty) * yscale + yoffset; + } + } else { + for (j = 0; j < 3; j++) { + nowpoint = &nodeptr[inc][ptr[index + j] * node_dim[inc]]; + vertices[j].x = nowpoint[0] * xscale + xoffset; + vertices[j].y = nowpoint[1] * yscale + yoffset; + } + } + XFillPolygon(display, mainwindow, trianglegc, vertices, 3, + Convex, CoordModeOrigin); + } + prevpoint = &nodeptr[inc][ptr[index + 2] * node_dim[inc]]; + if ((partition != (int *) NULL) && explode) { + for (j = 0; j < 3; j++) { + nowpoint = &nodeptr[inc][ptr[index++] * node_dim[inc]]; + XDrawLine(display, mainwindow, linegc, + (int) ((prevpoint[0] + shiftx) * xscale + xoffset), + (int) ((prevpoint[1] + shifty) * yscale + yoffset), + (int) ((nowpoint[0] + shiftx) * xscale + xoffset), + (int) ((nowpoint[1] + shifty) * yscale + yoffset)); + prevpoint = nowpoint; + } + } else { + for (j = 0; j < 3; j++) { + nowpoint = &nodeptr[inc][ptr[index++] * node_dim[inc]]; + XDrawLine(display, mainwindow, linegc, + (int) (prevpoint[0] * xscale + xoffset), + (int) (prevpoint[1] * yscale + yoffset), + (int) (nowpoint[0] * xscale + xoffset), + (int) (nowpoint[1] * yscale + yoffset)); + prevpoint = nowpoint; + } + } + } + if (color && fillelem && (partition != (int *) NULL)) { + free(vertices); + } + XSetForeground(display, linegc, showme_foreground); +} + +void draw_edge(nodes, dim, edges, nodeptr, edgeptr, normptr, + xscale, yscale, xoffset, yoffset) +int nodes; +int dim; +int edges; +REAL *nodeptr; +int *edgeptr; +REAL *normptr; +REAL xscale; +REAL yscale; +REAL xoffset; +REAL yoffset; +{ + int i; + int index; + REAL *point1, *point2; + REAL normx, normy; + REAL normmult, normmultx, normmulty; + REAL windowxmin, windowymin, windowxmax, windowymax; + + index = 2; + for (i = 1; i <= edges; i++) { + point1 = &nodeptr[edgeptr[index++] * dim]; + if (edgeptr[index] == -1) { + normx = normptr[index - 1]; + normy = normptr[index++]; + normmultx = 0.0; + if (normx > 0) { + windowxmax = (width - 1 - xoffset) / xscale; + normmultx = (windowxmax - point1[0]) / normx; + } else if (normx < 0) { + windowxmin = -xoffset / xscale; + normmultx = (windowxmin - point1[0]) / normx; + } + normmulty = 0.0; + if (normy > 0) { + windowymax = -yoffset / yscale; + normmulty = (windowymax - point1[1]) / normy; + } else if (normy < 0) { + windowymin = (height - 1 - yoffset) / yscale; + normmulty = (windowymin - point1[1]) / normy; + } + if (normmultx == 0.0) { + normmult = normmulty; + } else if (normmulty == 0.0) { + normmult = normmultx; + } else if (normmultx < normmulty) { + normmult = normmultx; + } else { + normmult = normmulty; + } + if (normmult > 0.0) { + XDrawLine(display, mainwindow, linegc, + (int) (point1[0] * xscale + xoffset), + (int) (point1[1] * yscale + yoffset), + (int) ((point1[0] + normmult * normx) * xscale + xoffset), + (int) ((point1[1] + normmult * normy) * yscale + yoffset)); + } + } else { + point2 = &nodeptr[edgeptr[index++] * dim]; + XDrawLine(display, mainwindow, linegc, + (int) (point1[0] * xscale + xoffset), + (int) (point1[1] * yscale + yoffset), + (int) (point2[0] * xscale + xoffset), + (int) (point2[1] * yscale + yoffset)); + } + } +} + +void draw_adj(dim, subdomains, ptr, center, xscale, yscale, + xoffset, yoffset) +int dim; +int subdomains; +int *ptr; +REAL *center; +REAL xscale; +REAL yscale; +REAL xoffset; +REAL yoffset; +{ + int i, j; + REAL *point1, *point2; + + for (i = 0; i < subdomains; i++) { + for (j = i + 1; j < subdomains; j++) { + if (ptr[i * subdomains + j]) { + point1 = ¢er[i * dim]; + point2 = ¢er[j * dim]; + XDrawLine(display, mainwindow, linegc, + (int) (point1[0] * xscale + xoffset), + (int) (point1[1] * yscale + yoffset), + (int) (point2[0] * xscale + xoffset), + (int) (point2[1] * yscale + yoffset)); + } + } + } + for (i = 0; i < subdomains; i++) { + point1 = ¢er[i * dim]; + if (color) { + XSetForeground(display, linegc, colors[i & 63]); + } + XFillArc(display, mainwindow, linegc, + (int) (point1[0] * xscale + xoffset) - 5 - (line_width >> 1), + (int) (point1[1] * yscale + yoffset) - 5 - (line_width >> 1), + line_width + 10, line_width + 10, 0, 23040); + } + XSetForeground(display, linegc, showme_foreground); +} + +void draw(inc, image, xmin, ymin, xmax, ymax) +int inc; +int image; +REAL xmin; +REAL ymin; +REAL xmax; +REAL ymax; +{ + draw_buttons(); + XClearWindow(display, mainwindow); + if (image == NOTHING) { + return; + } + if (!loaded[inc][image]) { + return; + } + if ((image == PART) && explode) { + xmin += (xmin - partcenter[inc][subdomains[inc] << 1]) * explosion; + xmax += (xmax - partcenter[inc][subdomains[inc] << 1]) * explosion; + ymin += (ymin - partcenter[inc][(subdomains[inc] << 1) + 1]) * explosion; + ymax += (ymax - partcenter[inc][(subdomains[inc] << 1) + 1]) * explosion; + } + xscale = (REAL) (width - line_width - 4) / (xmax - xmin); + yscale = (REAL) (height - line_width - 4) / (ymax - ymin); + if (xscale > yscale) { + xscale = yscale; + } else { + yscale = xscale; + } + xoffset = 0.5 * ((REAL) width - xscale * (xmax - xmin)) - + xscale * xmin; + yoffset = (REAL) height - 0.5 * ((REAL) height - yscale * (ymax - ymin)) + + yscale * ymin; + yscale = - yscale; + switch(image) { + case NODE: + draw_node(nodes[inc], node_dim[inc], nodeptr[inc], + xscale, yscale, xoffset, yoffset); + break; + case POLY: + if (polynodes[inc] > 0) { + draw_poly(polynodes[inc], poly_dim[inc], polyedges[inc], + polyholes[inc], polynodeptr[inc], polyedgeptr[inc], + polyholeptr[inc], + xscale, yscale, xoffset, yoffset); + } else { + draw_poly(nodes[inc], node_dim[inc], polyedges[inc], + polyholes[inc], nodeptr[inc], polyedgeptr[inc], + polyholeptr[inc], + xscale, yscale, xoffset, yoffset); + } + break; + case ELE: + draw_ele(inc, elems[inc], ele_corners[inc], eleptr[inc], + (int *) NULL, (REAL *) NULL, + xscale, yscale, xoffset, yoffset); + break; + case EDGE: + draw_edge(nodes[inc], node_dim[inc], edges[inc], + nodeptr[inc], edgeptr[inc], normptr[inc], + xscale, yscale, xoffset, yoffset); + break; + case PART: + draw_ele(inc, elems[inc], ele_corners[inc], eleptr[inc], + partpart[inc], partshift[inc], + xscale, yscale, xoffset, yoffset); + break; + case ADJ: + draw_adj(node_dim[inc], adjsubdomains[inc], adjptr[inc], partcenter[inc], + xscale, yscale, xoffset, yoffset); + break; + case VORO: + if (loaded[inc][NODE]) { + draw_node(nodes[inc], node_dim[inc], nodeptr[inc], + xscale, yscale, xoffset, yoffset); + } + draw_edge(vnodes[inc], vnode_dim[inc], vedges[inc], + vnodeptr[inc], vedgeptr[inc], vnormptr[inc], + xscale, yscale, xoffset, yoffset); + break; + default: + break; + } +} + +void addps(instring, outstring, eps) +char *instring; +char *outstring; +int eps; +{ + strcpy(outstring, instring); + if (eps) { + strcat(outstring, ".eps"); + } else { + strcat(outstring, ".ps"); + } +} + +int print_head(fname, file, llcornerx, llcornery, eps) +char *fname; +FILE **file; +int llcornerx; +int llcornery; +int eps; +{ + if (!quiet) { + printf("Writing %s\n", fname); + } + *file = fopen(fname, "w"); + if (*file == (FILE *) NULL) { + printf(" Error: Could not open %s\n", fname); + return 1; + } + if (eps) { + fprintf(*file, "%%!PS-Adobe-2.0 EPSF-2.0\n"); + } else { + fprintf(*file, "%%!PS-Adobe-2.0\n"); + } + fprintf(*file, "%%%%BoundingBox: %d %d %d %d\n", llcornerx, llcornery, + 612 - llcornerx, 792 - llcornery); + fprintf(*file, "%%%%Creator: Show Me\n"); + fprintf(*file, "%%%%EndComments\n\n"); + fprintf(*file, "1 setlinecap\n"); + fprintf(*file, "1 setlinejoin\n"); + fprintf(*file, "%d setlinewidth\n", line_width); + fprintf(*file, "%d %d moveto\n", llcornerx, llcornery); + fprintf(*file, "%d %d lineto\n", 612 - llcornerx, llcornery); + fprintf(*file, "%d %d lineto\n", 612 - llcornerx, 792 - llcornery); + fprintf(*file, "%d %d lineto\n", llcornerx, 792 - llcornery); + fprintf(*file, "closepath\nclip\nnewpath\n"); + return 0; +} + +void print_node(nodefile, nodes, dim, ptr, xscale, yscale, + xoffset, yoffset) +FILE *nodefile; +int nodes; +int dim; +REAL *ptr; +REAL xscale; +REAL yscale; +REAL xoffset; +REAL yoffset; +{ + int i; + int index; + + index = dim; + for (i = 1; i <= nodes; i++) { + fprintf(nodefile, "%d %d %d 0 360 arc\nfill\n", + (int) (ptr[index] * xscale + xoffset), + (int) (ptr[index + 1] * yscale + yoffset), + 1 + (line_width >> 1)); + index += dim; + } +} + +void print_poly(polyfile, nodes, dim, edges, holes, nodeptr, edgeptr, holeptr, + xscale, yscale, xoffset, yoffset) +FILE *polyfile; +int nodes; +int dim; +int edges; +int holes; +REAL *nodeptr; +int *edgeptr; +REAL *holeptr; +REAL xscale; +REAL yscale; +REAL xoffset; +REAL yoffset; +{ + int i; + int index; + REAL *point1, *point2; + + index = dim; + for (i = 1; i <= nodes; i++) { + fprintf(polyfile, "%d %d %d 0 360 arc\nfill\n", + (int) (nodeptr[index] * xscale + xoffset), + (int) (nodeptr[index + 1] * yscale + yoffset), + 1 + (line_width >> 1)); + index += dim; + } + index = 2; + for (i = 1; i <= edges; i++) { + point1 = &nodeptr[edgeptr[index++] * dim]; + point2 = &nodeptr[edgeptr[index++] * dim]; + fprintf(polyfile, "%d %d moveto\n", + (int) (point1[0] * xscale + xoffset), + (int) (point1[1] * yscale + yoffset)); + fprintf(polyfile, "%d %d lineto\nstroke\n", + (int) (point2[0] * xscale + xoffset), + (int) (point2[1] * yscale + yoffset)); + } +} + +void print_ele(elefile, nodes, dim, elems, corners, nodeptr, eleptr, + partition, shift, + xscale, yscale, xoffset, yoffset, llcornerx, llcornery) +FILE *elefile; +int nodes; +int dim; +int elems; +int corners; +REAL *nodeptr; +int *eleptr; +int *partition; +REAL *shift; +REAL xscale; +REAL yscale; +REAL xoffset; +REAL yoffset; +int llcornerx; +int llcornery; +{ + int i, j; + int index, colorindex; + REAL shiftx, shifty; + REAL *nowpoint; + + index = 3; + if ((partition != (int *) NULL) && !bw_ps) { + fprintf(elefile, "0 0 0 setrgbcolor\n"); + fprintf(elefile, "%d %d moveto\n", llcornerx, llcornery); + fprintf(elefile, "%d %d lineto\n", 612 - llcornerx, llcornery); + fprintf(elefile, "%d %d lineto\n", 612 - llcornerx, 792 - llcornery); + fprintf(elefile, "%d %d lineto\n", llcornerx, 792 - llcornery); + fprintf(elefile, "fill\n"); + } + for (i = 1; i <= elems; i++) { + if ((partition != (int *) NULL) && !bw_ps) { + colorindex = partition[i] & 63; + fprintf(elefile, "%6.3f %6.3f %6.3f setrgbcolor\n", + (REAL) rgb[colorindex].red / 65535.0, + (REAL) rgb[colorindex].green / 65535.0, + (REAL) rgb[colorindex].blue / 65535.0); + } + nowpoint = &nodeptr[eleptr[index + 2] * dim]; + if ((partition != (int *) NULL) && (explode || bw_ps)) { + shiftx = shift[partition[i] << 1]; + shifty = shift[(partition[i] << 1) + 1]; + fprintf(elefile, "%d %d moveto\n", + (int) ((nowpoint[0] + shiftx) * xscale + xoffset), + (int) ((nowpoint[1] + shifty) * yscale + yoffset)); + for (j = 0; j < 3; j++) { + nowpoint = &nodeptr[eleptr[index++] * dim]; + fprintf(elefile, "%d %d lineto\n", + (int) ((nowpoint[0] + shiftx) * xscale + xoffset), + (int) ((nowpoint[1] + shifty) * yscale + yoffset)); + } + } else { + fprintf(elefile, "%d %d moveto\n", + (int) (nowpoint[0] * xscale + xoffset), + (int) (nowpoint[1] * yscale + yoffset)); + for (j = 0; j < 3; j++) { + nowpoint = &nodeptr[eleptr[index++] * dim]; + fprintf(elefile, "%d %d lineto\n", + (int) (nowpoint[0] * xscale + xoffset), + (int) (nowpoint[1] * yscale + yoffset)); + } + } + if (fillelem && !bw_ps) { + fprintf(elefile, "gsave\nfill\ngrestore\n1 1 0 setrgbcolor\n"); + } + fprintf(elefile, "stroke\n"); + } +} + +void print_edge(edgefile, nodes, dim, edges, nodeptr, edgeptr, normptr, + xscale, yscale, xoffset, yoffset, llcornerx, llcornery) +FILE *edgefile; +int nodes; +int dim; +int edges; +REAL *nodeptr; +int *edgeptr; +REAL *normptr; +REAL xscale; +REAL yscale; +REAL xoffset; +REAL yoffset; +int llcornerx; +int llcornery; +{ + int i; + int index; + REAL *point1, *point2; + REAL normx, normy; + REAL normmult, normmultx, normmulty; + REAL windowxmin, windowymin, windowxmax, windowymax; + + index = 2; + for (i = 1; i <= edges; i++) { + point1 = &nodeptr[edgeptr[index++] * dim]; + if (edgeptr[index] == -1) { + normx = normptr[index - 1]; + normy = normptr[index++]; + normmultx = 0.0; + if (normx > 0) { + windowxmax = ((REAL) (612 - llcornerx) - xoffset) / xscale; + normmultx = (windowxmax - point1[0]) / normx; + } else if (normx < 0) { + windowxmin = ((REAL) llcornerx - xoffset) / xscale; + normmultx = (windowxmin - point1[0]) / normx; + } + normmulty = 0.0; + if (normy > 0) { + windowymax = ((REAL) (792 - llcornery) - yoffset) / yscale; + normmulty = (windowymax - point1[1]) / normy; + } else if (normy < 0) { + windowymin = ((REAL) llcornery - yoffset) / yscale; + normmulty = (windowymin - point1[1]) / normy; + } + if (normmultx == 0.0) { + normmult = normmulty; + } else if (normmulty == 0.0) { + normmult = normmultx; + } else if (normmultx < normmulty) { + normmult = normmultx; + } else { + normmult = normmulty; + } + if (normmult > 0.0) { + fprintf(edgefile, "%d %d moveto\n", + (int) (point1[0] * xscale + xoffset), + (int) (point1[1] * yscale + yoffset)); + fprintf(edgefile, "%d %d lineto\nstroke\n", + (int) ((point1[0] + normmult * normx) * xscale + xoffset), + (int) ((point1[1] + normmult * normy) * yscale + yoffset)); + } + } else { + point2 = &nodeptr[edgeptr[index++] * dim]; + fprintf(edgefile, "%d %d moveto\n", + (int) (point1[0] * xscale + xoffset), + (int) (point1[1] * yscale + yoffset)); + fprintf(edgefile, "%d %d lineto\nstroke\n", + (int) (point2[0] * xscale + xoffset), + (int) (point2[1] * yscale + yoffset)); + } + } +} + +void print_adj(adjfile, dim, subdomains, ptr, center, xscale, yscale, + xoffset, yoffset, llcornerx, llcornery) +FILE *adjfile; +int dim; +int subdomains; +int *ptr; +REAL *center; +REAL xscale; +REAL yscale; +REAL xoffset; +REAL yoffset; +int llcornerx; +int llcornery; +{ + int i, j; + REAL *point1, *point2; + int colorindex; + + if (!bw_ps) { + fprintf(adjfile, "0 0 0 setrgbcolor\n"); + fprintf(adjfile, "%d %d moveto\n", llcornerx, llcornery); + fprintf(adjfile, "%d %d lineto\n", 612 - llcornerx, llcornery); + fprintf(adjfile, "%d %d lineto\n", 612 - llcornerx, 792 - llcornery); + fprintf(adjfile, "%d %d lineto\n", llcornerx, 792 - llcornery); + fprintf(adjfile, "fill\n"); + fprintf(adjfile, "1 1 0 setrgbcolor\n"); + } + for (i = 0; i < subdomains; i++) { + for (j = i + 1; j < subdomains; j++) { + if (ptr[i * subdomains + j]) { + point1 = ¢er[i * dim]; + point2 = ¢er[j * dim]; + fprintf(adjfile, "%d %d moveto\n", + (int) (point1[0] * xscale + xoffset), + (int) (point1[1] * yscale + yoffset)); + fprintf(adjfile, "%d %d lineto\nstroke\n", + (int) (point2[0] * xscale + xoffset), + (int) (point2[1] * yscale + yoffset)); + } + } + } + for (i = 0; i < subdomains; i++) { + point1 = ¢er[i * dim]; + if (!bw_ps) { + colorindex = i & 63; + fprintf(adjfile, "%6.3f %6.3f %6.3f setrgbcolor\n", + (REAL) rgb[colorindex].red / 65535.0, + (REAL) rgb[colorindex].green / 65535.0, + (REAL) rgb[colorindex].blue / 65535.0); + fprintf(adjfile, "%d %d %d 0 360 arc\nfill\n", + (int) (point1[0] * xscale + xoffset), + (int) (point1[1] * yscale + yoffset), + 5 + (line_width >> 1)); + } else { + fprintf(adjfile, "%d %d %d 0 360 arc\nfill\n", + (int) (point1[0] * xscale + xoffset), + (int) (point1[1] * yscale + yoffset), + 3 + (line_width >> 1)); + } + } +} + +void print(inc, image, xmin, ymin, xmax, ymax, eps) +int inc; +int image; +REAL xmin; +REAL ymin; +REAL xmax; +REAL ymax; +int eps; +{ + REAL xxscale, yyscale, xxoffset, yyoffset; + char psfilename[FILENAMESIZE]; + int llcornerx, llcornery; + FILE *psfile; + + if (image == NOTHING) { + return; + } + if (!loaded[inc][image]) { + return; + } + if ((image == PART) && (explode || bw_ps)) { + xmin += (xmin - partcenter[inc][subdomains[inc] << 1]) * explosion; + xmax += (xmax - partcenter[inc][subdomains[inc] << 1]) * explosion; + ymin += (ymin - partcenter[inc][(subdomains[inc] << 1) + 1]) * explosion; + ymax += (ymax - partcenter[inc][(subdomains[inc] << 1) + 1]) * explosion; + } + xxscale = (460.0 - (REAL) line_width) / (xmax - xmin); + yyscale = (640.0 - (REAL) line_width) / (ymax - ymin); + if (xxscale > yyscale) { + xxscale = yyscale; + llcornerx = (604 - (int) (yyscale * (xmax - xmin)) - line_width) >> 1; + llcornery = 72; + } else { + yyscale = xxscale; + llcornerx = 72; + llcornery = (784 - (int) (xxscale * (ymax - ymin)) - line_width) >> 1; + } + xxoffset = 0.5 * (612.0 - xxscale * (xmax - xmin)) - xxscale * xmin + + (line_width >> 1); + yyoffset = 0.5 * (792.0 - yyscale * (ymax - ymin)) - yyscale * ymin + + (line_width >> 1); + switch(image) { + case NODE: + addps(nodefilename[inc], psfilename, eps); + break; + case POLY: + addps(polyfilename[inc], psfilename, eps); + break; + case ELE: + addps(elefilename[inc], psfilename, eps); + break; + case EDGE: + addps(edgefilename[inc], psfilename, eps); + break; + case PART: + addps(partfilename[inc], psfilename, eps); + break; + case ADJ: + addps(adjfilename[inc], psfilename, eps); + break; + case VORO: + addps(vedgefilename[inc], psfilename, eps); + break; + default: + break; + } + if (print_head(psfilename, &psfile, llcornerx, llcornery, eps)) { + return; + } + switch(image) { + case NODE: + print_node(psfile, nodes[inc], node_dim[inc], nodeptr[inc], + xxscale, yyscale, xxoffset, yyoffset); + break; + case POLY: + if (polynodes[inc] > 0) { + print_poly(psfile, polynodes[inc], poly_dim[inc], polyedges[inc], + polyholes[inc], polynodeptr[inc], polyedgeptr[inc], + polyholeptr[inc], xxscale, yyscale, xxoffset, yyoffset); + } else { + print_poly(psfile, nodes[inc], node_dim[inc], polyedges[inc], + polyholes[inc], nodeptr[inc], polyedgeptr[inc], + polyholeptr[inc], xxscale, yyscale, xxoffset, yyoffset); + } + break; + case ELE: + print_ele(psfile, nodes[inc], node_dim[inc], elems[inc], + ele_corners[inc], nodeptr[inc], eleptr[inc], + (int *) NULL, (REAL *) NULL, + xxscale, yyscale, xxoffset, yyoffset, llcornerx, llcornery); + break; + case EDGE: + print_edge(psfile, nodes[inc], node_dim[inc], edges[inc], + nodeptr[inc], edgeptr[inc], normptr[inc], + xxscale, yyscale, xxoffset, yyoffset, llcornerx, llcornery); + break; + case PART: + print_ele(psfile, nodes[inc], node_dim[inc], elems[inc], + ele_corners[inc], nodeptr[inc], eleptr[inc], + partpart[inc], partshift[inc], + xxscale, yyscale, xxoffset, yyoffset, llcornerx, llcornery); + break; + case ADJ: + print_adj(psfile, node_dim[inc], adjsubdomains[inc], adjptr[inc], + partcenter[inc], + xxscale, yyscale, xxoffset, yyoffset, llcornerx, llcornery); + break; + case VORO: + print_edge(psfile, vnodes[inc], vnode_dim[inc], vedges[inc], + vnodeptr[inc], vedgeptr[inc], vnormptr[inc], + xxscale, yyscale, xxoffset, yyoffset, llcornerx, llcornery); + break; + default: + break; + } + if (!eps) { + fprintf(psfile, "showpage\n"); + } + fclose(psfile); +} + +int main(argc, argv) +int argc; +char **argv; +{ + REAL xmin, ymin, xmax, ymax; + REAL xptr, yptr, xspan, yspan; + int past_image; + int new_image; + int new_inc; + + parsecommandline(argc, argv); + showme_init(); + choose_image(start_inc, start_image); + showme_window(argc, argv); + + if (current_image != NOTHING) { + xmin = xlo[current_inc][current_image]; + ymin = ylo[current_inc][current_image]; + xmax = xhi[current_inc][current_image]; + ymax = yhi[current_inc][current_image]; + zoom = 0; + } + + XMaskEvent(display, ExposureMask, &event); + while (1) { + switch (event.type) { + case ButtonRelease: + if (event.xany.window == quitwin) { + XDestroyWindow(display, mainwindow); + XCloseDisplay(display); + return 0; + } else if (event.xany.window == leftwin) { + xspan = 0.25 * (xmax - xmin); + xmin += xspan; + xmax += xspan; + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + } else if (event.xany.window == rightwin) { + xspan = 0.25 * (xmax - xmin); + xmin -= xspan; + xmax -= xspan; + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + } else if (event.xany.window == upwin) { + yspan = 0.25 * (ymax - ymin); + ymin -= yspan; + ymax -= yspan; + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + } else if (event.xany.window == downwin) { + yspan = 0.25 * (ymax - ymin); + ymin += yspan; + ymax += yspan; + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + } else if (event.xany.window == resetwin) { + xmin = xlo[current_inc][current_image]; + ymin = ylo[current_inc][current_image]; + xmax = xhi[current_inc][current_image]; + ymax = yhi[current_inc][current_image]; + zoom = 0; + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + } else if (event.xany.window == widthpluswin) { + if (line_width < 100) { + line_width++; + XSetLineAttributes(display, linegc, line_width, LineSolid, + CapRound, JoinRound); + XSetLineAttributes(display, trianglegc, line_width, LineSolid, + CapRound, JoinRound); + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + } + } else if (event.xany.window == widthminuswin) { + if (line_width > 1) { + line_width--; + XSetLineAttributes(display, linegc, line_width, LineSolid, + CapRound, JoinRound); + XSetLineAttributes(display, trianglegc, line_width, LineSolid, + CapRound, JoinRound); + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + } + } else if (event.xany.window == expwin) { + if ((current_image == PART) && loaded[current_inc][PART]) { + explode = !explode; + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + } + } else if (event.xany.window == exppluswin) { + if ((current_image == PART) && loaded[PART] && explode) { + explosion += 0.125; + findpartshift(subdomains[current_inc], explosion, + partcenter[current_inc], partshift[current_inc]); + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + } + } else if (event.xany.window == expminuswin) { + if ((current_image == PART) && loaded[PART] && explode && + (explosion >= 0.125)) { + explosion -= 0.125; + findpartshift(subdomains[current_inc], explosion, + partcenter[current_inc], partshift[current_inc]); + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + } + } else if (event.xany.window == fillwin) { + if ((current_image == PART) && loaded[PART]) { + fillelem = !fillelem; + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + } + } else if (event.xany.window == pswin) { + fill_button(pswin); + XFlush(display); + print(current_inc, current_image, xmin, ymin, xmax, ymax, 0); + XClearWindow(display, pswin); + XDrawString(display, pswin, fontgc, 2, 13, "PS", 2); + } else if (event.xany.window == epswin) { + fill_button(epswin); + XFlush(display); + print(current_inc, current_image, xmin, ymin, xmax, ymax, 1); + XClearWindow(display, epswin); + XDrawString(display, epswin, fontgc, 2, 13, "EPS", 3); + } else if (event.xany.window == versionpluswin) { + move_inc(1); + loweriteration++; + set_filenames(filename, loweriteration); + if (current_inc == 1) { + current_inc = 0; + } else { + current_image = NOTHING; + XClearWindow(display, mainwindow); + } + draw_buttons(); + } else if (event.xany.window == versionminuswin) { + if (loweriteration > 0) { + move_inc(0); + loweriteration--; + set_filenames(filename, loweriteration); + if (current_inc == 0) { + current_inc = 1; + } else { + current_image = NOTHING; + XClearWindow(display, mainwindow); + } + draw_buttons(); + } + } else if ((event.xany.window == nodewin[0]) || + (event.xany.window == polywin[0]) || + (event.xany.window == elewin[0]) || + (event.xany.window == edgewin[0]) || + (event.xany.window == partwin[0]) || + (event.xany.window == adjwin[0]) || + (event.xany.window == voronoiwin[0]) || + (event.xany.window == nodewin[1]) || + (event.xany.window == polywin[1]) || + (event.xany.window == elewin[1]) || + (event.xany.window == edgewin[1]) || + (event.xany.window == partwin[1]) || + (event.xany.window == adjwin[1]) || + (event.xany.window == voronoiwin[1])) { + if (event.xany.window == nodewin[0]) { + new_inc = 0; + new_image = NODE; + } + if (event.xany.window == polywin[0]) { + new_inc = 0; + new_image = POLY; + } + if (event.xany.window == elewin[0]) { + new_inc = 0; + new_image = ELE; + } + if (event.xany.window == edgewin[0]) { + new_inc = 0; + new_image = EDGE; + } + if (event.xany.window == partwin[0]) { + new_inc = 0; + new_image = PART; + } + if (event.xany.window == adjwin[0]) { + new_inc = 0; + new_image = ADJ; + } + if (event.xany.window == voronoiwin[0]) { + new_inc = 0; + new_image = VORO; + } + if (event.xany.window == nodewin[1]) { + new_inc = 1; + new_image = NODE; + } + if (event.xany.window == polywin[1]) { + new_inc = 1; + new_image = POLY; + } + if (event.xany.window == elewin[1]) { + new_inc = 1; + new_image = ELE; + } + if (event.xany.window == edgewin[1]) { + new_inc = 1; + new_image = EDGE; + } + if (event.xany.window == partwin[1]) { + new_inc = 1; + new_image = PART; + } + if (event.xany.window == adjwin[1]) { + new_inc = 1; + new_image = ADJ; + } + if (event.xany.window == voronoiwin[1]) { + new_inc = 1; + new_image = VORO; + } + past_image = current_image; + if ((current_inc == new_inc) && (current_image == new_image)) { + free_inc(new_inc); + unload_inc(new_inc); + } + choose_image(new_inc, new_image); + if ((past_image == NOTHING) && (current_image != NOTHING)) { + xmin = xlo[current_inc][current_image]; + ymin = ylo[current_inc][current_image]; + xmax = xhi[current_inc][current_image]; + ymax = yhi[current_inc][current_image]; + zoom = 0; + } + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + } else { + xptr = ((REAL) event.xbutton.x - xoffset) / xscale; + yptr = ((REAL) event.xbutton.y - yoffset) / yscale; + if ((current_image == PART) && loaded[PART] && explode) { + xptr = (xptr + partcenter[current_inc] + [subdomains[current_inc] << 1] + * explosion) / (1.0 + explosion); + yptr = (yptr + partcenter[current_inc] + [(subdomains[current_inc] << 1) + 1] + * explosion) / (1.0 + explosion); + } + if ((event.xbutton.button == Button1) + || (event.xbutton.button == Button3)) { + if (event.xbutton.button == Button1) { + xspan = 0.25 * (xmax - xmin); + yspan = 0.25 * (ymax - ymin); + zoom++; + } else { + xspan = xmax - xmin; + yspan = ymax - ymin; + zoom--; + } + xmin = xptr - xspan; + ymin = yptr - yspan; + xmax = xptr + xspan; + ymax = yptr + yspan; + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + } else if (event.xbutton.button == Button2) { + printf("x = %.9f, y = %.9f\n", xptr, yptr); + } + } + break; + case DestroyNotify: + XDestroyWindow(display, mainwindow); + XCloseDisplay(display); + return 0; + case ConfigureNotify: + if ((width != event.xconfigure.width) || + (height != event.xconfigure.height - PANELHEIGHT)) { + width = event.xconfigure.width; + height = event.xconfigure.height - PANELHEIGHT; + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + while (XCheckMaskEvent(display, ExposureMask, &event)); + } + break; + case Expose: + draw(current_inc, current_image, xmin, ymin, xmax, ymax); + while (XCheckMaskEvent(display, ExposureMask, &event)); + break; + default: + break; + } + XNextEvent(display, &event); + } +} diff --git a/src/Lib/TriangleJRS/triangle.c b/src/Lib/TriangleJRS/triangle.c new file mode 100644 index 00000000..9af47a49 --- /dev/null +++ b/src/Lib/TriangleJRS/triangle.c @@ -0,0 +1,13241 @@ +/*****************************************************************************/ +/* */ +/* 888888888 ,o, / 888 */ +/* 888 88o88o " o8888o 88o8888o o88888o 888 o88888o */ +/* 888 888 888 88b 888 888 888 888 888 d888 88b */ +/* 888 888 888 o88^o888 888 888 "88888" 888 8888oo888 */ +/* 888 888 888 C888 888 888 888 / 888 q888 */ +/* 888 888 888 "88o^888 888 888 Cb 888 "88oooo" */ +/* "8oo8D */ +/* */ +/* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */ +/* (triangle.c) */ +/* */ +/* Version 1.3 */ +/* July 19, 1996 */ +/* */ +/* Copyright 1996 */ +/* Jonathan Richard Shewchuk */ +/* School of Computer Science */ +/* Carnegie Mellon University */ +/* 5000 Forbes Avenue */ +/* Pittsburgh, Pennsylvania 15213-3891 */ +/* jrs@cs.cmu.edu */ +/* */ +/* This program may be freely redistributed under the condition that the */ +/* copyright notices (including this entire header and the copyright */ +/* notice printed when the `-h' switch is selected) are not removed, and */ +/* no compensation is received. Private, research, and institutional */ +/* use is free. You may distribute modified versions of this code UNDER */ +/* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */ +/* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE */ +/* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR */ +/* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as */ +/* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */ +/* WITH THE AUTHOR. (If you are not directly supplying this code to a */ +/* customer, and you are instead telling them how they can obtain it for */ +/* free, then you are not required to make any arrangement with me.) */ +/* */ +/* Hypertext instructions for Triangle are available on the Web at */ +/* */ +/* http://www.cs.cmu.edu/~quake/triangle.html */ +/* */ +/* Some of the references listed below are marked [*]. These are available */ +/* for downloading from the Web page */ +/* */ +/* http://www.cs.cmu.edu/~quake/triangle.research.html */ +/* */ +/* A paper discussing some aspects of Triangle is available. See Jonathan */ +/* Richard Shewchuk, "Triangle: Engineering a 2D Quality Mesh Generator */ +/* and Delaunay Triangulator," First Workshop on Applied Computational */ +/* Geometry, ACM, May 1996. [*] */ +/* */ +/* Triangle was created as part of the Archimedes project in the School of */ +/* Computer Science at Carnegie Mellon University. Archimedes is a */ +/* system for compiling parallel finite element solvers. For further */ +/* information, see Anja Feldmann, Omar Ghattas, John R. Gilbert, Gary L. */ +/* Miller, David R. O'Hallaron, Eric J. Schwabe, Jonathan R. Shewchuk, */ +/* and Shang-Hua Teng, "Automated Parallel Solution of Unstructured PDE */ +/* Problems." To appear in Communications of the ACM, we hope. */ +/* */ +/* The quality mesh generation algorithm is due to Jim Ruppert, "A */ +/* Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh */ +/* Generation," Journal of Algorithms 18(3):548-585, May 1995. [*] */ +/* */ +/* My implementation of the divide-and-conquer and incremental Delaunay */ +/* triangulation algorithms follows closely the presentation of Guibas */ +/* and Stolfi, even though I use a triangle-based data structure instead */ +/* of their quad-edge data structure. (In fact, I originally implemented */ +/* Triangle using the quad-edge data structure, but switching to a */ +/* triangle-based data structure sped Triangle by a factor of two.) The */ +/* mesh manipulation primitives and the two aforementioned Delaunay */ +/* triangulation algorithms are described by Leonidas J. Guibas and Jorge */ +/* Stolfi, "Primitives for the Manipulation of General Subdivisions and */ +/* the Computation of Voronoi Diagrams," ACM Transactions on Graphics */ +/* 4(2):74-123, April 1985. */ +/* */ +/* Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai */ +/* Lee and Bruce J. Schachter, "Two Algorithms for Constructing the */ +/* Delaunay Triangulation," International Journal of Computer and */ +/* Information Science 9(3):219-242, 1980. The idea to improve the */ +/* divide-and-conquer algorithm by alternating between vertical and */ +/* horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and- */ +/* Conquer Algorithm for Constructing Delaunay Triangulations," */ +/* Algorithmica 2(2):137-151, 1987. */ +/* */ +/* The incremental insertion algorithm was first proposed by C. L. Lawson, */ +/* "Software for C1 Surface Interpolation," in Mathematical Software III, */ +/* John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977. */ +/* For point location, I use the algorithm of Ernst P. Mucke, Isaac */ +/* Saias, and Binhai Zhu, "Fast Randomized Point Location Without */ +/* Preprocessing in Two- and Three-dimensional Delaunay Triangulations," */ +/* Proceedings of the Twelfth Annual Symposium on Computational Geometry, */ +/* ACM, May 1996. [*] If I were to randomize the order of point */ +/* insertion (I currently don't bother), their result combined with the */ +/* result of Leonidas J. Guibas, Donald E. Knuth, and Micha Sharir, */ +/* "Randomized Incremental Construction of Delaunay and Voronoi */ +/* Diagrams," Algorithmica 7(4):381-413, 1992, would yield an expected */ +/* O(n^{4/3}) bound on running time. */ +/* */ +/* The O(n log n) sweepline Delaunay triangulation algorithm is taken from */ +/* Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams", */ +/* Algorithmica 2(2):153-174, 1987. A random sample of edges on the */ +/* boundary of the triangulation are maintained in a splay tree for the */ +/* purpose of point location. Splay trees are described by Daniel */ +/* Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */ +/* Trees," Journal of the ACM 32(3):652-686, July 1985. */ +/* */ +/* The algorithms for exact computation of the signs of determinants are */ +/* described in Jonathan Richard Shewchuk, "Adaptive Precision Floating- */ +/* Point Arithmetic and Fast Robust Geometric Predicates," Technical */ +/* Report CMU-CS-96-140, School of Computer Science, Carnegie Mellon */ +/* University, Pittsburgh, Pennsylvania, May 1996. [*] (Submitted to */ +/* Discrete & Computational Geometry.) An abbreviated version appears as */ +/* Jonathan Richard Shewchuk, "Robust Adaptive Floating-Point Geometric */ +/* Predicates," Proceedings of the Twelfth Annual Symposium on Computa- */ +/* tional Geometry, ACM, May 1996. [*] Many of the ideas for my exact */ +/* arithmetic routines originate with Douglas M. Priest, "Algorithms for */ +/* Arbitrary Precision Floating Point Arithmetic," Tenth Symposium on */ +/* Computer Arithmetic, 132-143, IEEE Computer Society Press, 1991. [*] */ +/* Many of the ideas for the correct evaluation of the signs of */ +/* determinants are taken from Steven Fortune and Christopher J. Van Wyk, */ +/* "Efficient Exact Arithmetic for Computational Geometry," Proceedings */ +/* of the Ninth Annual Symposium on Computational Geometry, ACM, */ +/* pp. 163-172, May 1993, and from Steven Fortune, "Numerical Stability */ +/* of Algorithms for 2D Delaunay Triangulations," International Journal */ +/* of Computational Geometry & Applications 5(1-2):193-213, March-June */ +/* 1995. */ +/* */ +/* For definitions of and results involving Delaunay triangulations, */ +/* constrained and conforming versions thereof, and other aspects of */ +/* triangular mesh generation, see the excellent survey by Marshall Bern */ +/* and David Eppstein, "Mesh Generation and Optimal Triangulation," in */ +/* Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang, */ +/* editors, World Scientific, Singapore, pp. 23-90, 1992. */ +/* */ +/* The time for incrementally adding PSLG (planar straight line graph) */ +/* segments to create a constrained Delaunay triangulation is probably */ +/* O(n^2) per segment in the worst case and O(n) per edge in the common */ +/* case, where n is the number of triangles that intersect the segment */ +/* before it is inserted. This doesn't count point location, which can */ +/* be much more expensive. (This note does not apply to conforming */ +/* Delaunay triangulations, for which a different method is used to */ +/* insert segments.) */ +/* */ +/* The time for adding segments to a conforming Delaunay triangulation is */ +/* not clear, but does not depend upon n alone. In some cases, very */ +/* small features (like a point lying next to a segment) can cause a */ +/* single segment to be split an arbitrary number of times. Of course, */ +/* floating-point precision is a practical barrier to how much this can */ +/* happen. */ +/* */ +/* The time for deleting a point from a Delaunay triangulation is O(n^2) in */ +/* the worst case and O(n) in the common case, where n is the degree of */ +/* the point being deleted. I could improve this to expected O(n) time */ +/* by "inserting" the neighboring vertices in random order, but n is */ +/* usually quite small, so it's not worth the bother. (The O(n) time */ +/* for random insertion follows from L. Paul Chew, "Building Voronoi */ +/* Diagrams for Convex Polygons in Linear Expected Time," Technical */ +/* Report PCS-TR90-147, Department of Mathematics and Computer Science, */ +/* Dartmouth College, 1990. */ +/* */ +/* Ruppert's Delaunay refinement algorithm typically generates triangles */ +/* at a linear rate (constant time per triangle) after the initial */ +/* triangulation is formed. There may be pathological cases where more */ +/* time is required, but these never arise in practice. */ +/* */ +/* The segment intersection formulae are straightforward. If you want to */ +/* see them derived, see Franklin Antonio. "Faster Line Segment */ +/* Intersection." In Graphics Gems III (David Kirk, editor), pp. 199- */ +/* 202. Academic Press, Boston, 1992. */ +/* */ +/* If you make any improvements to this code, please please please let me */ +/* know, so that I may obtain the improvements. Even if you don't change */ +/* the code, I'd still love to hear what it's being used for. */ +/* */ +/* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */ +/* whatsoever. This code is provided "as-is". Use at your own risk. */ +/* */ +/*****************************************************************************/ + +/* For single precision (which will save some memory and reduce paging), */ +/* define the symbol SINGLE by using the -DSINGLE compiler switch or by */ +/* writing "#define SINGLE" below. */ +/* */ +/* For double precision (which will allow you to refine meshes to a smaller */ +/* edge length), leave SINGLE undefined. */ +/* */ +/* Double precision uses more memory, but improves the resolution of the */ +/* meshes you can generate with Triangle. It also reduces the likelihood */ +/* of a floating exception due to overflow. Finally, it is much faster */ +/* than single precision on 64-bit architectures like the DEC Alpha. I */ +/* recommend double precision unless you want to generate a mesh for which */ +/* you do not have enough memory. */ + +/* #define SINGLE */ + +#ifdef SINGLE +#define REAL float +#else /* not SINGLE */ +#define REAL double +#endif /* not SINGLE */ + +/* If yours is not a Unix system, define the NO_TIMER compiler switch to */ +/* remove the Unix-specific timing code. */ + +/* #define NO_TIMER */ + +/* To insert lots of self-checks for internal errors, define the SELF_CHECK */ +/* symbol. This will slow down the program significantly. It is best to */ +/* define the symbol using the -DSELF_CHECK compiler switch, but you could */ +/* write "#define SELF_CHECK" below. If you are modifying this code, I */ +/* recommend you turn self-checks on. */ + +/* #define SELF_CHECK */ + +/* To compile Triangle as a callable object library (triangle.o), define the */ +/* TRILIBRARY symbol. Read the file triangle.h for details on how to call */ +/* the procedure triangulate() that results. */ + +/* #define TRILIBRARY */ + +/* It is possible to generate a smaller version of Triangle using one or */ +/* both of the following symbols. Define the REDUCED symbol to eliminate */ +/* all features that are primarily of research interest; specifically, the */ +/* -i, -F, -s, and -C switches. Define the CDT_ONLY symbol to eliminate */ +/* all meshing algorithms above and beyond constrained Delaunay */ +/* triangulation; specifically, the -r, -q, -a, -S, and -s switches. */ +/* These reductions are most likely to be useful when generating an object */ +/* library (triangle.o) by defining the TRILIBRARY symbol. */ + +/* #define REDUCED */ +/* #define CDT_ONLY */ + +/* On some machines, the exact arithmetic routines might be defeated by the */ +/* use of internal extended precision floating-point registers. Sometimes */ +/* this problem can be fixed by defining certain values to be volatile, */ +/* thus forcing them to be stored to memory and rounded off. This isn't */ +/* a great solution, though, as it slows Triangle down. */ +/* */ +/* To try this out, write "#define INEXACT volatile" below. Normally, */ +/* however, INEXACT should be defined to be nothing. ("#define INEXACT".) */ + +#define INEXACT /* Nothing */ +/* #define INEXACT volatile */ + +/* Maximum number of characters in a file name (including the null). */ + +#define FILENAMESIZE 512 + +/* Maximum number of characters in a line read from a file (including the */ +/* null). */ + +#define INPUTLINESIZE 512 + +/* For efficiency, a variety of data structures are allocated in bulk. The */ +/* following constants determine how many of each structure is allocated */ +/* at once. */ + +#define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */ +#define SHELLEPERBLOCK 508 /* Number of shell edges allocated at once. */ +#define POINTPERBLOCK 4092 /* Number of points allocated at once. */ +#define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */ +/* Number of encroached segments allocated at once. */ +#define BADSEGMENTPERBLOCK 252 +/* Number of skinny triangles allocated at once. */ +#define BADTRIPERBLOCK 4092 +/* Number of splay tree nodes allocated at once. */ +#define SPLAYNODEPERBLOCK 508 + +/* The point marker DEADPOINT is an arbitrary number chosen large enough to */ +/* (hopefully) not conflict with user boundary markers. Make sure that it */ +/* is small enough to fit into your machine's integer size. */ + +#define DEADPOINT -1073741824 + +/* The next line is used to outsmart some very stupid compilers. If your */ +/* compiler is smarter, feel free to replace the "int" with "void". */ +/* Not that it matters. */ + +#define VOID int + +/* Two constants for algorithms based on random sampling. Both constants */ +/* have been chosen empirically to optimize their respective algorithms. */ + +/* Used for the point location scheme of Mucke, Saias, and Zhu, to decide */ +/* how large a random sample of triangles to inspect. */ +#define SAMPLEFACTOR 11 +/* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */ +/* of boundary edges should be maintained in the splay tree for point */ +/* location on the front. */ +#define SAMPLERATE 10 + +/* A number that speaks for itself, every kissable digit. */ + +#define PI 3.141592653589793238462643383279502884197169399375105820974944592308 + +/* Another fave. */ + +#define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732 + +/* And here's one for those of you who are intimidated by math. */ + +#define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333 + +#include +#include +#include +#ifndef NO_TIMER +#include +#endif /* NO_TIMER */ +#ifdef TRILIBRARY +#include "triangle.h" +#endif /* TRILIBRARY */ + +/* The following obscenity seems to be necessary to ensure that this program */ +/* will port to Dec Alphas running OSF/1, because their stdio.h file commits */ +/* the unpardonable sin of including stdlib.h. Hence, malloc(), free(), and */ +/* exit() may or may not already be defined at this point. I declare these */ +/* functions explicitly because some non-ANSI C compilers lack stdlib.h. */ + +#ifndef _STDLIB_H_ +extern void *malloc(); +extern void free(); +extern void exit(); +extern double strtod(); +extern long strtol(); +#endif /* _STDLIB_H_ */ + +/* A few forward declarations. */ + +void poolrestart(); +#ifndef TRILIBRARY +char *readline(); +char *findfield(); +#endif /* not TRILIBRARY */ + +/* Labels that signify whether a record consists primarily of pointers or of */ +/* floating-point words. Used to make decisions about data alignment. */ + +enum wordtype {POINTER, FLOATINGPOINT}; + +/* Labels that signify the result of point location. The result of a */ +/* search indicates that the point falls in the interior of a triangle, on */ +/* an edge, on a vertex, or outside the mesh. */ + +enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE}; + +/* Labels that signify the result of site insertion. The result indicates */ +/* that the point was inserted with complete success, was inserted but */ +/* encroaches on a segment, was not inserted because it lies on a segment, */ +/* or was not inserted because another point occupies the same location. */ + +enum insertsiteresult {SUCCESSFULPOINT, ENCROACHINGPOINT, VIOLATINGPOINT, + DUPLICATEPOINT}; + +/* Labels that signify the result of direction finding. The result */ +/* indicates that a segment connecting the two query points falls within */ +/* the direction triangle, along the left edge of the direction triangle, */ +/* or along the right edge of the direction triangle. */ + +enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR}; + +/* Labels that signify the result of the circumcenter computation routine. */ +/* The return value indicates which edge of the triangle is shortest. */ + +enum circumcenterresult {OPPOSITEORG, OPPOSITEDEST, OPPOSITEAPEX}; + +/*****************************************************************************/ +/* */ +/* The basic mesh data structures */ +/* */ +/* There are three: points, triangles, and shell edges (abbreviated */ +/* `shelle'). These three data structures, linked by pointers, comprise */ +/* the mesh. A point simply represents a point in space and its properties.*/ +/* A triangle is a triangle. A shell edge is a special data structure used */ +/* to represent impenetrable segments in the mesh (including the outer */ +/* boundary, boundaries of holes, and internal boundaries separating two */ +/* triangulated regions). Shell edges represent boundaries defined by the */ +/* user that triangles may not lie across. */ +/* */ +/* A triangle consists of a list of three vertices, a list of three */ +/* adjoining triangles, a list of three adjoining shell edges (when shell */ +/* edges are used), an arbitrary number of optional user-defined floating- */ +/* point attributes, and an optional area constraint. The latter is an */ +/* upper bound on the permissible area of each triangle in a region, used */ +/* for mesh refinement. */ +/* */ +/* For a triangle on a boundary of the mesh, some or all of the neighboring */ +/* triangles may not be present. For a triangle in the interior of the */ +/* mesh, often no neighboring shell edges are present. Such absent */ +/* triangles and shell edges are never represented by NULL pointers; they */ +/* are represented by two special records: `dummytri', the triangle that */ +/* fills "outer space", and `dummysh', the omnipresent shell edge. */ +/* `dummytri' and `dummysh' are used for several reasons; for instance, */ +/* they can be dereferenced and their contents examined without causing the */ +/* memory protection exception that would occur if NULL were dereferenced. */ +/* */ +/* However, it is important to understand that a triangle includes other */ +/* information as well. The pointers to adjoining vertices, triangles, and */ +/* shell edges are ordered in a way that indicates their geometric relation */ +/* to each other. Furthermore, each of these pointers contains orientation */ +/* information. Each pointer to an adjoining triangle indicates which face */ +/* of that triangle is contacted. Similarly, each pointer to an adjoining */ +/* shell edge indicates which side of that shell edge is contacted, and how */ +/* the shell edge is oriented relative to the triangle. */ +/* */ +/* Shell edges are found abutting edges of triangles; either sandwiched */ +/* between two triangles, or resting against one triangle on an exterior */ +/* boundary or hole boundary. */ +/* */ +/* A shell edge consists of a list of two vertices, a list of two */ +/* adjoining shell edges, and a list of two adjoining triangles. One of */ +/* the two adjoining triangles may not be present (though there should */ +/* always be one), and neighboring shell edges might not be present. */ +/* Shell edges also store a user-defined integer "boundary marker". */ +/* Typically, this integer is used to indicate what sort of boundary */ +/* conditions are to be applied at that location in a finite element */ +/* simulation. */ +/* */ +/* Like triangles, shell edges maintain information about the relative */ +/* orientation of neighboring objects. */ +/* */ +/* Points are relatively simple. A point is a list of floating point */ +/* numbers, starting with the x, and y coordinates, followed by an */ +/* arbitrary number of optional user-defined floating-point attributes, */ +/* followed by an integer boundary marker. During the segment insertion */ +/* phase, there is also a pointer from each point to a triangle that may */ +/* contain it. Each pointer is not always correct, but when one is, it */ +/* speeds up segment insertion. These pointers are assigned values once */ +/* at the beginning of the segment insertion phase, and are not used or */ +/* updated at any other time. Edge swapping during segment insertion will */ +/* render some of them incorrect. Hence, don't rely upon them for */ +/* anything. For the most part, points do not have any information about */ +/* what triangles or shell edges they are linked to. */ +/* */ +/*****************************************************************************/ + +/*****************************************************************************/ +/* */ +/* Handles */ +/* */ +/* The oriented triangle (`triedge') and oriented shell edge (`edge') data */ +/* structures defined below do not themselves store any part of the mesh. */ +/* The mesh itself is made of `triangle's, `shelle's, and `point's. */ +/* */ +/* Oriented triangles and oriented shell edges will usually be referred to */ +/* as "handles". A handle is essentially a pointer into the mesh; it */ +/* allows you to "hold" one particular part of the mesh. Handles are used */ +/* to specify the regions in which one is traversing and modifying the mesh.*/ +/* A single `triangle' may be held by many handles, or none at all. (The */ +/* latter case is not a memory leak, because the triangle is still */ +/* connected to other triangles in the mesh.) */ +/* */ +/* A `triedge' is a handle that holds a triangle. It holds a specific side */ +/* of the triangle. An `edge' is a handle that holds a shell edge. It */ +/* holds either the left or right side of the edge. */ +/* */ +/* Navigation about the mesh is accomplished through a set of mesh */ +/* manipulation primitives, further below. Many of these primitives take */ +/* a handle and produce a new handle that holds the mesh near the first */ +/* handle. Other primitives take two handles and glue the corresponding */ +/* parts of the mesh together. The exact position of the handles is */ +/* important. For instance, when two triangles are glued together by the */ +/* bond() primitive, they are glued by the sides on which the handles lie. */ +/* */ +/* Because points have no information about which triangles they are */ +/* attached to, I commonly represent a point by use of a handle whose */ +/* origin is the point. A single handle can simultaneously represent a */ +/* triangle, an edge, and a point. */ +/* */ +/*****************************************************************************/ + +/* The triangle data structure. Each triangle contains three pointers to */ +/* adjoining triangles, plus three pointers to vertex points, plus three */ +/* pointers to shell edges (defined below; these pointers are usually */ +/* `dummysh'). It may or may not also contain user-defined attributes */ +/* and/or a floating-point "area constraint". It may also contain extra */ +/* pointers for nodes, when the user asks for high-order elements. */ +/* Because the size and structure of a `triangle' is not decided until */ +/* runtime, I haven't simply defined the type `triangle' to be a struct. */ + +typedef REAL **triangle; /* Really: typedef triangle *triangle */ + +/* An oriented triangle: includes a pointer to a triangle and orientation. */ +/* The orientation denotes an edge of the triangle. Hence, there are */ +/* three possible orientations. By convention, each edge is always */ +/* directed to point counterclockwise about the corresponding triangle. */ + +struct triedge { + triangle *tri; + int orient; /* Ranges from 0 to 2. */ +}; + +/* The shell data structure. Each shell edge contains two pointers to */ +/* adjoining shell edges, plus two pointers to vertex points, plus two */ +/* pointers to adjoining triangles, plus one shell marker. */ + +typedef REAL **shelle; /* Really: typedef shelle *shelle */ + +/* An oriented shell edge: includes a pointer to a shell edge and an */ +/* orientation. The orientation denotes a side of the edge. Hence, there */ +/* are two possible orientations. By convention, the edge is always */ +/* directed so that the "side" denoted is the right side of the edge. */ + +struct edge { + shelle *sh; + int shorient; /* Ranges from 0 to 1. */ +}; + +/* The point data structure. Each point is actually an array of REALs. */ +/* The number of REALs is unknown until runtime. An integer boundary */ +/* marker, and sometimes a pointer to a triangle, is appended after the */ +/* REALs. */ + +typedef REAL *point; + +/* A queue used to store encroached segments. Each segment's vertices are */ +/* stored so that one can check whether a segment is still the same. */ + +struct badsegment { + struct edge encsegment; /* An encroached segment. */ + point segorg, segdest; /* The two vertices. */ + struct badsegment *nextsegment; /* Pointer to next encroached segment. */ +}; + +/* A queue used to store bad triangles. The key is the square of the cosine */ +/* of the smallest angle of the triangle. Each triangle's vertices are */ +/* stored so that one can check whether a triangle is still the same. */ + +struct badface { + struct triedge badfacetri; /* A bad triangle. */ + REAL key; /* cos^2 of smallest (apical) angle. */ + point faceorg, facedest, faceapex; /* The three vertices. */ + struct badface *nextface; /* Pointer to next bad triangle. */ +}; + +/* A node in a heap used to store events for the sweepline Delaunay */ +/* algorithm. Nodes do not point directly to their parents or children in */ +/* the heap. Instead, each node knows its position in the heap, and can */ +/* look up its parent and children in a separate array. The `eventptr' */ +/* points either to a `point' or to a triangle (in encoded format, so that */ +/* an orientation is included). In the latter case, the origin of the */ +/* oriented triangle is the apex of a "circle event" of the sweepline */ +/* algorithm. To distinguish site events from circle events, all circle */ +/* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */ + +struct event { + REAL xkey, ykey; /* Coordinates of the event. */ + VOID *eventptr; /* Can be a point or the location of a circle event. */ + int heapposition; /* Marks this event's position in the heap. */ +}; + +/* A node in the splay tree. Each node holds an oriented ghost triangle */ +/* that represents a boundary edge of the growing triangulation. When a */ +/* circle event covers two boundary edges with a triangle, so that they */ +/* are no longer boundary edges, those edges are not immediately deleted */ +/* from the tree; rather, they are lazily deleted when they are next */ +/* encountered. (Since only a random sample of boundary edges are kept */ +/* in the tree, lazy deletion is faster.) `keydest' is used to verify */ +/* that a triangle is still the same as when it entered the splay tree; if */ +/* it has been rotated (due to a circle event), it no longer represents a */ +/* boundary edge and should be deleted. */ + +struct splaynode { + struct triedge keyedge; /* Lprev of an edge on the front. */ + point keydest; /* Used to verify that splay node is still live. */ + struct splaynode *lchild, *rchild; /* Children in splay tree. */ +}; + +/* A type used to allocate memory. firstblock is the first block of items. */ +/* nowblock is the block from which items are currently being allocated. */ +/* nextitem points to the next slab of free memory for an item. */ +/* deaditemstack is the head of a linked list (stack) of deallocated items */ +/* that can be recycled. unallocateditems is the number of items that */ +/* remain to be allocated from nowblock. */ +/* */ +/* Traversal is the process of walking through the entire list of items, and */ +/* is separate from allocation. Note that a traversal will visit items on */ +/* the "deaditemstack" stack as well as live items. pathblock points to */ +/* the block currently being traversed. pathitem points to the next item */ +/* to be traversed. pathitemsleft is the number of items that remain to */ +/* be traversed in pathblock. */ +/* */ +/* itemwordtype is set to POINTER or FLOATINGPOINT, and is used to suggest */ +/* what sort of word the record is primarily made up of. alignbytes */ +/* determines how new records should be aligned in memory. itembytes and */ +/* itemwords are the length of a record in bytes (after rounding up) and */ +/* words. itemsperblock is the number of items allocated at once in a */ +/* single block. items is the number of currently allocated items. */ +/* maxitems is the maximum number of items that have been allocated at */ +/* once; it is the current number of items plus the number of records kept */ +/* on deaditemstack. */ + +struct memorypool { + VOID **firstblock, **nowblock; + VOID *nextitem; + VOID *deaditemstack; + VOID **pathblock; + VOID *pathitem; + enum wordtype itemwordtype; + int alignbytes; + int itembytes, itemwords; + int itemsperblock; + long items, maxitems; + int unallocateditems; + int pathitemsleft; +}; + +/* Variables used to allocate memory for triangles, shell edges, points, */ +/* viri (triangles being eaten), bad (encroached) segments, bad (skinny */ +/* or too large) triangles, and splay tree nodes. */ + +struct memorypool triangles; +struct memorypool shelles; +struct memorypool points; +struct memorypool viri; +struct memorypool badsegments; +struct memorypool badtriangles; +struct memorypool splaynodes; + +/* Variables that maintain the bad triangle queues. The tails are pointers */ +/* to the pointers that have to be filled in to enqueue an item. */ + +struct badface *queuefront[64]; +struct badface **queuetail[64]; + +REAL xmin, xmax, ymin, ymax; /* x and y bounds. */ +REAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */ +int inpoints; /* Number of input points. */ +int inelements; /* Number of input triangles. */ +int insegments; /* Number of input segments. */ +int holes; /* Number of input holes. */ +int regions; /* Number of input regions. */ +long edges; /* Number of output edges. */ +int mesh_dim; /* Dimension (ought to be 2). */ +int nextras; /* Number of attributes per point. */ +int eextras; /* Number of attributes per triangle. */ +long hullsize; /* Number of edges of convex hull. */ +int triwords; /* Total words per triangle. */ +int shwords; /* Total words per shell edge. */ +int pointmarkindex; /* Index to find boundary marker of a point. */ +int point2triindex; /* Index to find a triangle adjacent to a point. */ +int highorderindex; /* Index to find extra nodes for high-order elements. */ +int elemattribindex; /* Index to find attributes of a triangle. */ +int areaboundindex; /* Index to find area bound of a triangle. */ +int checksegments; /* Are there segments in the triangulation yet? */ +int readnodefile; /* Has a .node file been read? */ +long samples; /* Number of random samples for point location. */ +unsigned long randomseed; /* Current random number seed. */ + +REAL splitter; /* Used to split REAL factors for exact multiplication. */ +REAL epsilon; /* Floating-point machine epsilon. */ +REAL resulterrbound; +REAL ccwerrboundA, ccwerrboundB, ccwerrboundC; +REAL iccerrboundA, iccerrboundB, iccerrboundC; + +long incirclecount; /* Number of incircle tests performed. */ +long counterclockcount; /* Number of counterclockwise tests performed. */ +long hyperbolacount; /* Number of right-of-hyperbola tests performed. */ +long circumcentercount; /* Number of circumcenter calculations performed. */ +long circletopcount; /* Number of circle top calculations performed. */ + +/* Switches for the triangulator. */ +/* poly: -p switch. refine: -r switch. */ +/* quality: -q switch. */ +/* minangle: minimum angle bound, specified after -q switch. */ +/* goodangle: cosine squared of minangle. */ +/* vararea: -a switch without number. */ +/* fixedarea: -a switch with number. */ +/* maxarea: maximum area bound, specified after -a switch. */ +/* regionattrib: -A switch. convex: -c switch. */ +/* firstnumber: inverse of -z switch. All items are numbered starting */ +/* from firstnumber. */ +/* edgesout: -e switch. voronoi: -v switch. */ +/* neighbors: -n switch. geomview: -g switch. */ +/* nobound: -B switch. nopolywritten: -P switch. */ +/* nonodewritten: -N switch. noelewritten: -E switch. */ +/* noiterationnum: -I switch. noholes: -O switch. */ +/* noexact: -X switch. */ +/* order: element order, specified after -o switch. */ +/* nobisect: count of how often -Y switch is selected. */ +/* steiner: maximum number of Steiner points, specified after -S switch. */ +/* steinerleft: number of Steiner points not yet used. */ +/* incremental: -i switch. sweepline: -F switch. */ +/* dwyer: inverse of -l switch. */ +/* splitseg: -s switch. */ +/* docheck: -C switch. */ +/* quiet: -Q switch. verbose: count of how often -V switch is selected. */ +/* useshelles: -p, -r, -q, or -c switch; determines whether shell edges */ +/* are used at all. */ +/* */ +/* Read the instructions to find out the meaning of these switches. */ + +int poly, refine, quality, vararea, fixedarea, regionattrib, convex; +int firstnumber; +int edgesout, voronoi, neighbors, geomview; +int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum; +int noholes, noexact; +int incremental, sweepline, dwyer; +int splitseg; +int docheck; +int quiet, verbose; +int useshelles; +int order; +int nobisect; +int steiner, steinerleft; +REAL minangle, goodangle; +REAL maxarea; + +/* Variables for file names. */ + +#ifndef TRILIBRARY +char innodefilename[FILENAMESIZE]; +char inelefilename[FILENAMESIZE]; +char inpolyfilename[FILENAMESIZE]; +char areafilename[FILENAMESIZE]; +char outnodefilename[FILENAMESIZE]; +char outelefilename[FILENAMESIZE]; +char outpolyfilename[FILENAMESIZE]; +char edgefilename[FILENAMESIZE]; +char vnodefilename[FILENAMESIZE]; +char vedgefilename[FILENAMESIZE]; +char neighborfilename[FILENAMESIZE]; +char offfilename[FILENAMESIZE]; +#endif /* not TRILIBRARY */ + +/* Triangular bounding box points. */ + +point infpoint1, infpoint2, infpoint3; + +/* Pointer to the `triangle' that occupies all of "outer space". */ + +triangle *dummytri; +triangle *dummytribase; /* Keep base address so we can free() it later. */ + +/* Pointer to the omnipresent shell edge. Referenced by any triangle or */ +/* shell edge that isn't really connected to a shell edge at that */ +/* location. */ + +shelle *dummysh; +shelle *dummyshbase; /* Keep base address so we can free() it later. */ + +/* Pointer to a recently visited triangle. Improves point location if */ +/* proximate points are inserted sequentially. */ + +struct triedge recenttri; + +/*****************************************************************************/ +/* */ +/* Mesh manipulation primitives. Each triangle contains three pointers to */ +/* other triangles, with orientations. Each pointer points not to the */ +/* first byte of a triangle, but to one of the first three bytes of a */ +/* triangle. It is necessary to extract both the triangle itself and the */ +/* orientation. To save memory, I keep both pieces of information in one */ +/* pointer. To make this possible, I assume that all triangles are aligned */ +/* to four-byte boundaries. The `decode' routine below decodes a pointer, */ +/* extracting an orientation (in the range 0 to 2) and a pointer to the */ +/* beginning of a triangle. The `encode' routine compresses a pointer to a */ +/* triangle and an orientation into a single pointer. My assumptions that */ +/* triangles are four-byte-aligned and that the `unsigned long' type is */ +/* long enough to hold a pointer are two of the few kludges in this program.*/ +/* */ +/* Shell edges are manipulated similarly. A pointer to a shell edge */ +/* carries both an address and an orientation in the range 0 to 1. */ +/* */ +/* The other primitives take an oriented triangle or oriented shell edge, */ +/* and return an oriented triangle or oriented shell edge or point; or they */ +/* change the connections in the data structure. */ +/* */ +/*****************************************************************************/ + +/********* Mesh manipulation primitives begin here *********/ +/** **/ +/** **/ + +/* Fast lookup arrays to speed some of the mesh manipulation primitives. */ + +int plus1mod3[3] = {1, 2, 0}; +int minus1mod3[3] = {2, 0, 1}; + +/********* Primitives for triangles *********/ +/* */ +/* */ + +/* decode() converts a pointer to an oriented triangle. The orientation is */ +/* extracted from the two least significant bits of the pointer. */ + +#define decode(ptr, triedge) \ + (triedge).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l); \ + (triedge).tri = (triangle *) \ + ((unsigned long) (ptr) ^ (unsigned long) (triedge).orient) + +/* encode() compresses an oriented triangle into a single pointer. It */ +/* relies on the assumption that all triangles are aligned to four-byte */ +/* boundaries, so the two least significant bits of (triedge).tri are zero.*/ + +#define encode(triedge) \ + (triangle) ((unsigned long) (triedge).tri | (unsigned long) (triedge).orient) + +/* The following edge manipulation primitives are all described by Guibas */ +/* and Stolfi. However, they use an edge-based data structure, whereas I */ +/* am using a triangle-based data structure. */ + +/* sym() finds the abutting triangle, on the same edge. Note that the */ +/* edge direction is necessarily reversed, because triangle/edge handles */ +/* are always directed counterclockwise around the triangle. */ + +#define sym(triedge1, triedge2) \ + ptr = (triedge1).tri[(triedge1).orient]; \ + decode(ptr, triedge2); + +#define symself(triedge) \ + ptr = (triedge).tri[(triedge).orient]; \ + decode(ptr, triedge); + +/* lnext() finds the next edge (counterclockwise) of a triangle. */ + +#define lnext(triedge1, triedge2) \ + (triedge2).tri = (triedge1).tri; \ + (triedge2).orient = plus1mod3[(triedge1).orient] + +#define lnextself(triedge) \ + (triedge).orient = plus1mod3[(triedge).orient] + +/* lprev() finds the previous edge (clockwise) of a triangle. */ + +#define lprev(triedge1, triedge2) \ + (triedge2).tri = (triedge1).tri; \ + (triedge2).orient = minus1mod3[(triedge1).orient] + +#define lprevself(triedge) \ + (triedge).orient = minus1mod3[(triedge).orient] + +/* onext() spins counterclockwise around a point; that is, it finds the next */ +/* edge with the same origin in the counterclockwise direction. This edge */ +/* will be part of a different triangle. */ + +#define onext(triedge1, triedge2) \ + lprev(triedge1, triedge2); \ + symself(triedge2); + +#define onextself(triedge) \ + lprevself(triedge); \ + symself(triedge); + +/* oprev() spins clockwise around a point; that is, it finds the next edge */ +/* with the same origin in the clockwise direction. This edge will be */ +/* part of a different triangle. */ + +#define oprev(triedge1, triedge2) \ + sym(triedge1, triedge2); \ + lnextself(triedge2); + +#define oprevself(triedge) \ + symself(triedge); \ + lnextself(triedge); + +/* dnext() spins counterclockwise around a point; that is, it finds the next */ +/* edge with the same destination in the counterclockwise direction. This */ +/* edge will be part of a different triangle. */ + +#define dnext(triedge1, triedge2) \ + sym(triedge1, triedge2); \ + lprevself(triedge2); + +#define dnextself(triedge) \ + symself(triedge); \ + lprevself(triedge); + +/* dprev() spins clockwise around a point; that is, it finds the next edge */ +/* with the same destination in the clockwise direction. This edge will */ +/* be part of a different triangle. */ + +#define dprev(triedge1, triedge2) \ + lnext(triedge1, triedge2); \ + symself(triedge2); + +#define dprevself(triedge) \ + lnextself(triedge); \ + symself(triedge); + +/* rnext() moves one edge counterclockwise about the adjacent triangle. */ +/* (It's best understood by reading Guibas and Stolfi. It involves */ +/* changing triangles twice.) */ + +#define rnext(triedge1, triedge2) \ + sym(triedge1, triedge2); \ + lnextself(triedge2); \ + symself(triedge2); + +#define rnextself(triedge) \ + symself(triedge); \ + lnextself(triedge); \ + symself(triedge); + +/* rnext() moves one edge clockwise about the adjacent triangle. */ +/* (It's best understood by reading Guibas and Stolfi. It involves */ +/* changing triangles twice.) */ + +#define rprev(triedge1, triedge2) \ + sym(triedge1, triedge2); \ + lprevself(triedge2); \ + symself(triedge2); + +#define rprevself(triedge) \ + symself(triedge); \ + lprevself(triedge); \ + symself(triedge); + +/* These primitives determine or set the origin, destination, or apex of a */ +/* triangle. */ + +#define org(triedge, pointptr) \ + pointptr = (point) (triedge).tri[plus1mod3[(triedge).orient] + 3] + +#define dest(triedge, pointptr) \ + pointptr = (point) (triedge).tri[minus1mod3[(triedge).orient] + 3] + +#define apex(triedge, pointptr) \ + pointptr = (point) (triedge).tri[(triedge).orient + 3] + +#define setorg(triedge, pointptr) \ + (triedge).tri[plus1mod3[(triedge).orient] + 3] = (triangle) pointptr + +#define setdest(triedge, pointptr) \ + (triedge).tri[minus1mod3[(triedge).orient] + 3] = (triangle) pointptr + +#define setapex(triedge, pointptr) \ + (triedge).tri[(triedge).orient + 3] = (triangle) pointptr + +#define setvertices2null(triedge) \ + (triedge).tri[3] = (triangle) NULL; \ + (triedge).tri[4] = (triangle) NULL; \ + (triedge).tri[5] = (triangle) NULL; + +/* Bond two triangles together. */ + +#define bond(triedge1, triedge2) \ + (triedge1).tri[(triedge1).orient] = encode(triedge2); \ + (triedge2).tri[(triedge2).orient] = encode(triedge1) + +/* Dissolve a bond (from one side). Note that the other triangle will still */ +/* think it's connected to this triangle. Usually, however, the other */ +/* triangle is being deleted entirely, or bonded to another triangle, so */ +/* it doesn't matter. */ + +#define dissolve(triedge) \ + (triedge).tri[(triedge).orient] = (triangle) dummytri + +/* Copy a triangle/edge handle. */ + +#define triedgecopy(triedge1, triedge2) \ + (triedge2).tri = (triedge1).tri; \ + (triedge2).orient = (triedge1).orient + +/* Test for equality of triangle/edge handles. */ + +#define triedgeequal(triedge1, triedge2) \ + (((triedge1).tri == (triedge2).tri) && \ + ((triedge1).orient == (triedge2).orient)) + +/* Primitives to infect or cure a triangle with the virus. These rely on */ +/* the assumption that all shell edges are aligned to four-byte boundaries.*/ + +#define infect(triedge) \ + (triedge).tri[6] = (triangle) \ + ((unsigned long) (triedge).tri[6] | (unsigned long) 2l) + +#define uninfect(triedge) \ + (triedge).tri[6] = (triangle) \ + ((unsigned long) (triedge).tri[6] & ~ (unsigned long) 2l) + +/* Test a triangle for viral infection. */ + +#define infected(triedge) \ + (((unsigned long) (triedge).tri[6] & (unsigned long) 2l) != 0) + +/* Check or set a triangle's attributes. */ + +#define elemattribute(triedge, attnum) \ + ((REAL *) (triedge).tri)[elemattribindex + (attnum)] + +#define setelemattribute(triedge, attnum, value) \ + ((REAL *) (triedge).tri)[elemattribindex + (attnum)] = value + +/* Check or set a triangle's maximum area bound. */ + +#define areabound(triedge) ((REAL *) (triedge).tri)[areaboundindex] + +#define setareabound(triedge, value) \ + ((REAL *) (triedge).tri)[areaboundindex] = value + +/********* Primitives for shell edges *********/ +/* */ +/* */ + +/* sdecode() converts a pointer to an oriented shell edge. The orientation */ +/* is extracted from the least significant bit of the pointer. The two */ +/* least significant bits (one for orientation, one for viral infection) */ +/* are masked out to produce the real pointer. */ + +#define sdecode(sptr, edge) \ + (edge).shorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l); \ + (edge).sh = (shelle *) \ + ((unsigned long) (sptr) & ~ (unsigned long) 3l) + +/* sencode() compresses an oriented shell edge into a single pointer. It */ +/* relies on the assumption that all shell edges are aligned to two-byte */ +/* boundaries, so the least significant bit of (edge).sh is zero. */ + +#define sencode(edge) \ + (shelle) ((unsigned long) (edge).sh | (unsigned long) (edge).shorient) + +/* ssym() toggles the orientation of a shell edge. */ + +#define ssym(edge1, edge2) \ + (edge2).sh = (edge1).sh; \ + (edge2).shorient = 1 - (edge1).shorient + +#define ssymself(edge) \ + (edge).shorient = 1 - (edge).shorient + +/* spivot() finds the other shell edge (from the same segment) that shares */ +/* the same origin. */ + +#define spivot(edge1, edge2) \ + sptr = (edge1).sh[(edge1).shorient]; \ + sdecode(sptr, edge2) + +#define spivotself(edge) \ + sptr = (edge).sh[(edge).shorient]; \ + sdecode(sptr, edge) + +/* snext() finds the next shell edge (from the same segment) in sequence; */ +/* one whose origin is the input shell edge's destination. */ + +#define snext(edge1, edge2) \ + sptr = (edge1).sh[1 - (edge1).shorient]; \ + sdecode(sptr, edge2) + +#define snextself(edge) \ + sptr = (edge).sh[1 - (edge).shorient]; \ + sdecode(sptr, edge) + +/* These primitives determine or set the origin or destination of a shell */ +/* edge. */ + +#define sorg(edge, pointptr) \ + pointptr = (point) (edge).sh[2 + (edge).shorient] + +#define sdest(edge, pointptr) \ + pointptr = (point) (edge).sh[3 - (edge).shorient] + +#define setsorg(edge, pointptr) \ + (edge).sh[2 + (edge).shorient] = (shelle) pointptr + +#define setsdest(edge, pointptr) \ + (edge).sh[3 - (edge).shorient] = (shelle) pointptr + +/* These primitives read or set a shell marker. Shell markers are used to */ +/* hold user boundary information. */ + +#define mark(edge) (* (int *) ((edge).sh + 6)) + +#define setmark(edge, value) \ + * (int *) ((edge).sh + 6) = value + +/* Bond two shell edges together. */ + +#define sbond(edge1, edge2) \ + (edge1).sh[(edge1).shorient] = sencode(edge2); \ + (edge2).sh[(edge2).shorient] = sencode(edge1) + +/* Dissolve a shell edge bond (from one side). Note that the other shell */ +/* edge will still think it's connected to this shell edge. */ + +#define sdissolve(edge) \ + (edge).sh[(edge).shorient] = (shelle) dummysh + +/* Copy a shell edge. */ + +#define shellecopy(edge1, edge2) \ + (edge2).sh = (edge1).sh; \ + (edge2).shorient = (edge1).shorient + +/* Test for equality of shell edges. */ + +#define shelleequal(edge1, edge2) \ + (((edge1).sh == (edge2).sh) && \ + ((edge1).shorient == (edge2).shorient)) + +/********* Primitives for interacting triangles and shell edges *********/ +/* */ +/* */ + +/* tspivot() finds a shell edge abutting a triangle. */ + +#define tspivot(triedge, edge) \ + sptr = (shelle) (triedge).tri[6 + (triedge).orient]; \ + sdecode(sptr, edge) + +/* stpivot() finds a triangle abutting a shell edge. It requires that the */ +/* variable `ptr' of type `triangle' be defined. */ + +#define stpivot(edge, triedge) \ + ptr = (triangle) (edge).sh[4 + (edge).shorient]; \ + decode(ptr, triedge) + +/* Bond a triangle to a shell edge. */ + +#define tsbond(triedge, edge) \ + (triedge).tri[6 + (triedge).orient] = (triangle) sencode(edge); \ + (edge).sh[4 + (edge).shorient] = (shelle) encode(triedge) + +/* Dissolve a bond (from the triangle side). */ + +#define tsdissolve(triedge) \ + (triedge).tri[6 + (triedge).orient] = (triangle) dummysh + +/* Dissolve a bond (from the shell edge side). */ + +#define stdissolve(edge) \ + (edge).sh[4 + (edge).shorient] = (shelle) dummytri + +/********* Primitives for points *********/ +/* */ +/* */ + +#define pointmark(pt) ((int *) (pt))[pointmarkindex] + +#define setpointmark(pt, value) \ + ((int *) (pt))[pointmarkindex] = value + +#define point2tri(pt) ((triangle *) (pt))[point2triindex] + +#define setpoint2tri(pt, value) \ + ((triangle *) (pt))[point2triindex] = value + +/** **/ +/** **/ +/********* Mesh manipulation primitives end here *********/ + +/********* User interaction routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* syntax() Print list of command line switches. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +void syntax() +{ +#ifdef CDT_ONLY +#ifdef REDUCED + printf("triangle [-pAcevngBPNEIOXzo_lQVh] input_file\n"); +#else /* not REDUCED */ + printf("triangle [-pAcevngBPNEIOXzo_iFlCQVh] input_file\n"); +#endif /* not REDUCED */ +#else /* not CDT_ONLY */ +#ifdef REDUCED + printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__lQVh] input_file\n"); +#else /* not REDUCED */ + printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__iFlsCQVh] input_file\n"); +#endif /* not REDUCED */ +#endif /* not CDT_ONLY */ + + printf(" -p Triangulates a Planar Straight Line Graph (.poly file).\n"); +#ifndef CDT_ONLY + printf(" -r Refines a previously generated mesh.\n"); + printf( + " -q Quality mesh generation. A minimum angle may be specified.\n"); + printf(" -a Applies a maximum triangle area constraint.\n"); +#endif /* not CDT_ONLY */ + printf( + " -A Applies attributes to identify elements in certain regions.\n"); + printf(" -c Encloses the convex hull with segments.\n"); + printf(" -e Generates an edge list.\n"); + printf(" -v Generates a Voronoi diagram.\n"); + printf(" -n Generates a list of triangle neighbors.\n"); + printf(" -g Generates an .off file for Geomview.\n"); + printf(" -B Suppresses output of boundary information.\n"); + printf(" -P Suppresses output of .poly file.\n"); + printf(" -N Suppresses output of .node file.\n"); + printf(" -E Suppresses output of .ele file.\n"); + printf(" -I Suppresses mesh iteration numbers.\n"); + printf(" -O Ignores holes in .poly file.\n"); + printf(" -X Suppresses use of exact arithmetic.\n"); + printf(" -z Numbers all items starting from zero (rather than one).\n"); + printf(" -o2 Generates second-order subparametric elements.\n"); +#ifndef CDT_ONLY + printf(" -Y Suppresses boundary segment splitting.\n"); + printf(" -S Specifies maximum number of added Steiner points.\n"); +#endif /* not CDT_ONLY */ +#ifndef REDUCED + printf(" -i Uses incremental method, rather than divide-and-conquer.\n"); + printf(" -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n"); +#endif /* not REDUCED */ + printf(" -l Uses vertical cuts only, rather than alternating cuts.\n"); +#ifndef REDUCED +#ifndef CDT_ONLY + printf( + " -s Force segments into mesh by splitting (instead of using CDT).\n"); +#endif /* not CDT_ONLY */ + printf(" -C Check consistency of final mesh.\n"); +#endif /* not REDUCED */ + printf(" -Q Quiet: No terminal output except errors.\n"); + printf(" -V Verbose: Detailed information on what I'm doing.\n"); + printf(" -h Help: Detailed instructions for Triangle.\n"); + exit(0); +} + +#endif /* not TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* info() Print out complete instructions. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +void info() +{ + printf("Triangle\n"); + printf( +"A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n"); + printf("Version 1.3\n\n"); + printf( +"Copyright 1996 Jonathan Richard Shewchuk (bugs/comments to jrs@cs.cmu.edu)\n" +); + printf("School of Computer Science / Carnegie Mellon University\n"); + printf("5000 Forbes Avenue / Pittsburgh, Pennsylvania 15213-3891\n"); + printf( +"Created as part of the Archimedes project (tools for parallel FEM).\n"); + printf( +"Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n"); + printf("There is no warranty whatsoever. Use at your own risk.\n"); +#ifdef SINGLE + printf("This executable is compiled for single precision arithmetic.\n\n\n"); +#else /* not SINGLE */ + printf("This executable is compiled for double precision arithmetic.\n\n\n"); +#endif /* not SINGLE */ + printf( +"Triangle generates exact Delaunay triangulations, constrained Delaunay\n"); + printf( +"triangulations, and quality conforming Delaunay triangulations. The latter\n" +); + printf( +"can be generated with no small angles, and are thus suitable for finite\n"); + printf( +"element analysis. If no command line switches are specified, your .node\n"); + printf( +"input file will be read, and the Delaunay triangulation will be returned in\n" +); + printf(".node and .ele output files. The command syntax is:\n\n"); +#ifdef CDT_ONLY +#ifdef REDUCED + printf("triangle [-pAcevngBPNEIOXzo_lQVh] input_file\n\n"); +#else /* not REDUCED */ + printf("triangle [-pAcevngBPNEIOXzo_iFlCQVh] input_file\n\n"); +#endif /* not REDUCED */ +#else /* not CDT_ONLY */ +#ifdef REDUCED + printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__lQVh] input_file\n\n"); +#else /* not REDUCED */ + printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n"); +#endif /* not REDUCED */ +#endif /* not CDT_ONLY */ + printf( +"Underscores indicate that numbers may optionally follow certain switches;\n"); + printf( +"do not leave any space between a switch and its numeric parameter.\n"); + printf( +"input_file must be a file with extension .node, or extension .poly if the\n"); + printf( +"-p switch is used. If -r is used, you must supply .node and .ele files,\n"); + printf( +"and possibly a .poly file and .area file as well. The formats of these\n"); + printf("files are described below.\n\n"); + printf("Command Line Switches:\n\n"); + printf( +" -p Reads a Planar Straight Line Graph (.poly file), which can specify\n" +); + printf( +" points, segments, holes, and regional attributes and area\n"); + printf( +" constraints. Will generate a constrained Delaunay triangulation\n"); + printf( +" fitting the input; or, if -s, -q, or -a is used, a conforming\n"); + printf( +" Delaunay triangulation. If -p is not used, Triangle reads a .node\n" +); + printf(" file by default.\n"); + printf( +" -r Refines a previously generated mesh. The mesh is read from a .node\n" +); + printf( +" file and an .ele file. If -p is also used, a .poly file is read\n"); + printf( +" and used to constrain edges in the mesh. Further details on\n"); + printf(" refinement are given below.\n"); + printf( +" -q Quality mesh generation by Jim Ruppert's Delaunay refinement\n"); + printf( +" algorithm. Adds points to the mesh to ensure that no angles\n"); + printf( +" smaller than 20 degrees occur. An alternative minimum angle may be\n" +); + printf( +" specified after the `q'. If the minimum angle is 20.7 degrees or\n"); + printf( +" smaller, the triangulation algorithm is theoretically guaranteed to\n" +); + printf( +" terminate (assuming infinite precision arithmetic - Triangle may\n"); + printf( +" fail to terminate if you run out of precision). In practice, the\n"); + printf( +" algorithm often succeeds for minimum angles up to 33.8 degrees.\n"); + printf( +" For highly refined meshes, however, it may be necessary to reduce\n"); + printf( +" the minimum angle to well below 20 to avoid problems associated\n"); + printf( +" with insufficient floating-point precision. The specified angle\n"); + printf(" may include a decimal point.\n"); + printf( +" -a Imposes a maximum triangle area. If a number follows the `a', no\n"); + printf( +" triangle will be generated whose area is larger than that number.\n"); + printf( +" If no number is specified, an .area file (if -r is used) or .poly\n"); + printf( +" file (if -r is not used) specifies a number of maximum area\n"); + printf( +" constraints. An .area file contains a separate area constraint for\n" +); + printf( +" each triangle, and is useful for refining a finite element mesh\n"); + printf( +" based on a posteriori error estimates. A .poly file can optionally\n" +); + printf( +" contain an area constraint for each segment-bounded region, thereby\n" +); + printf( +" enforcing triangle densities in a first triangulation. You can\n"); + printf( +" impose both a fixed area constraint and a varying area constraint\n"); + printf( +" by invoking the -a switch twice, once with and once without a\n"); + printf( +" number following. Each area specified may include a decimal point.\n" +); + printf( +" -A Assigns an additional attribute to each triangle that identifies\n"); + printf( +" what segment-bounded region each triangle belongs to. Attributes\n"); + printf( +" are assigned to regions by the .poly file. If a region is not\n"); + printf( +" explicitly marked by the .poly file, triangles in that region are\n"); + printf( +" assigned an attribute of zero. The -A switch has an effect only\n"); + printf(" when the -p switch is used and the -r switch is not.\n"); + printf( +" -c Creates segments on the convex hull of the triangulation. If you\n"); + printf( +" are triangulating a point set, this switch causes a .poly file to\n"); + printf( +" be written, containing all edges in the convex hull. (By default,\n" +); + printf( +" a .poly file is written only if a .poly file is read.) If you are\n" +); + printf( +" triangulating a PSLG, this switch specifies that the interior of\n"); + printf( +" the convex hull of the PSLG should be triangulated. If you do not\n" +); + printf( +" use this switch when triangulating a PSLG, it is assumed that you\n"); + printf( +" have identified the region to be triangulated by surrounding it\n"); + printf( +" with segments of the input PSLG. Beware: if you are not careful,\n" +); + printf( +" this switch can cause the introduction of an extremely thin angle\n"); + printf( +" between a PSLG segment and a convex hull segment, which can cause\n"); + printf( +" overrefinement or failure if Triangle runs out of precision. If\n"); + printf( +" you are refining a mesh, the -c switch works differently; it\n"); + printf( +" generates the set of boundary edges of the mesh, rather than the\n"); + printf(" convex hull.\n"); + printf( +" -e Outputs (to an .edge file) a list of edges of the triangulation.\n"); + printf( +" -v Outputs the Voronoi diagram associated with the triangulation.\n"); + printf(" Does not attempt to detect degeneracies.\n"); + printf( +" -n Outputs (to a .neigh file) a list of triangles neighboring each\n"); + printf(" triangle.\n"); + printf( +" -g Outputs the mesh to an Object File Format (.off) file, suitable for\n" +); + printf(" viewing with the Geometry Center's Geomview package.\n"); + printf( +" -B No boundary markers in the output .node, .poly, and .edge output\n"); + printf( +" files. See the detailed discussion of boundary markers below.\n"); + printf( +" -P No output .poly file. Saves disk space, but you lose the ability\n"); + printf( +" to impose segment constraints on later refinements of the mesh.\n"); + printf(" -N No output .node file.\n"); + printf(" -E No output .ele file.\n"); + printf( +" -I No iteration numbers. Suppresses the output of .node and .poly\n"); + printf( +" files, so your input files won't be overwritten. (If your input is\n" +); + printf( +" a .poly file only, a .node file will be written.) Cannot be used\n"); + printf( +" with the -r switch, because that would overwrite your input .ele\n"); + printf( +" file. Shouldn't be used with the -s, -q, or -a switch if you are\n"); + printf( +" using a .node file for input, because no .node file will be\n"); + printf(" written, so there will be no record of any added points.\n"); + printf(" -O No holes. Ignores the holes in the .poly file.\n"); + printf( +" -X No exact arithmetic. Normally, Triangle uses exact floating-point\n" +); + printf( +" arithmetic for certain tests if it thinks the inexact tests are not\n" +); + printf( +" accurate enough. Exact arithmetic ensures the robustness of the\n"); + printf( +" triangulation algorithms, despite floating-point roundoff error.\n"); + printf( +" Disabling exact arithmetic with the -X switch will cause a small\n"); + printf( +" improvement in speed and create the possibility (albeit small) that\n" +); + printf( +" Triangle will fail to produce a valid mesh. Not recommended.\n"); + printf( +" -z Numbers all items starting from zero (rather than one). Note that\n" +); + printf( +" this switch is normally overrided by the value used to number the\n"); + printf( +" first point of the input .node or .poly file. However, this switch\n" +); + printf(" is useful when calling Triangle from another program.\n"); + printf( +" -o2 Generates second-order subparametric elements with six nodes each.\n" +); + printf( +" -Y No new points on the boundary. This switch is useful when the mesh\n" +); + printf( +" boundary must be preserved so that it conforms to some adjacent\n"); + printf( +" mesh. Be forewarned that you will probably sacrifice some of the\n"); + printf( +" quality of the mesh; Triangle will try, but the resulting mesh may\n" +); + printf( +" contain triangles of poor aspect ratio. Works well if all the\n"); + printf( +" boundary points are closely spaced. Specify this switch twice\n"); + printf( +" (`-YY') to prevent all segment splitting, including internal\n"); + printf(" boundaries.\n"); + printf( +" -S Specifies the maximum number of Steiner points (points that are not\n" +); + printf( +" in the input, but are added to meet the constraints of minimum\n"); + printf( +" angle and maximum area). The default is to allow an unlimited\n"); + printf( +" number. If you specify this switch with no number after it,\n"); + printf( +" the limit is set to zero. Triangle always adds points at segment\n"); + printf( +" intersections, even if it needs to use more points than the limit\n"); + printf( +" you set. When Triangle inserts segments by splitting (-s), it\n"); + printf( +" always adds enough points to ensure that all the segments appear in\n" +); + printf( +" the triangulation, again ignoring the limit. Be forewarned that\n"); + printf( +" the -S switch may result in a conforming triangulation that is not\n" +); + printf( +" truly Delaunay, because Triangle may be forced to stop adding\n"); + printf( +" points when the mesh is in a state where a segment is non-Delaunay\n" +); + printf( +" and needs to be split. If so, Triangle will print a warning.\n"); + printf( +" -i Uses an incremental rather than divide-and-conquer algorithm to\n"); + printf( +" form a Delaunay triangulation. Try it if the divide-and-conquer\n"); + printf(" algorithm fails.\n"); + printf( +" -F Uses Steven Fortune's sweepline algorithm to form a Delaunay\n"); + printf( +" triangulation. Warning: does not use exact arithmetic for all\n"); + printf(" calculations. An exact result is not guaranteed.\n"); + printf( +" -l Uses only vertical cuts in the divide-and-conquer algorithm. By\n"); + printf( +" default, Triangle uses alternating vertical and horizontal cuts,\n"); + printf( +" which usually improve the speed except with point sets that are\n"); + printf( +" small or short and wide. This switch is primarily of theoretical\n"); + printf(" interest.\n"); + printf( +" -s Specifies that segments should be forced into the triangulation by\n" +); + printf( +" recursively splitting them at their midpoints, rather than by\n"); + printf( +" generating a constrained Delaunay triangulation. Segment splitting\n" +); + printf( +" is true to Ruppert's original algorithm, but can create needlessly\n" +); + printf(" small triangles near external small features.\n"); + printf( +" -C Check the consistency of the final mesh. Uses exact arithmetic for\n" +); + printf( +" checking, even if the -X switch is used. Useful if you suspect\n"); + printf(" Triangle is buggy.\n"); + printf( +" -Q Quiet: Suppresses all explanation of what Triangle is doing, unless\n" +); + printf(" an error occurs.\n"); + printf( +" -V Verbose: Gives detailed information about what Triangle is doing.\n"); + printf( +" Add more `V's for increasing amount of detail. `-V' gives\n"); + printf( +" information on algorithmic progress and more detailed statistics.\n"); + printf( +" `-VV' gives point-by-point details, and will print so much that\n"); + printf( +" Triangle will run much more slowly. `-VVV' gives information only\n" +); + printf(" a debugger could love.\n"); + printf(" -h Help: Displays these instructions.\n"); + printf("\n"); + printf("Definitions:\n"); + printf("\n"); + printf( +" A Delaunay triangulation of a point set is a triangulation whose vertices\n" +); + printf( +" are the point set, having the property that no point in the point set\n"); + printf( +" falls in the interior of the circumcircle (circle that passes through all\n" +); + printf(" three vertices) of any triangle in the triangulation.\n\n"); + printf( +" A Voronoi diagram of a point set is a subdivision of the plane into\n"); + printf( +" polygonal regions (some of which may be infinite), where each region is\n"); + printf( +" the set of points in the plane that are closer to some input point than\n"); + printf( +" to any other input point. (The Voronoi diagram is the geometric dual of\n" +); + printf(" the Delaunay triangulation.)\n\n"); + printf( +" A Planar Straight Line Graph (PSLG) is a collection of points and\n"); + printf( +" segments. Segments are simply edges, whose endpoints are points in the\n"); + printf( +" PSLG. The file format for PSLGs (.poly files) is described below.\n"); + printf("\n"); + printf( +" A constrained Delaunay triangulation of a PSLG is similar to a Delaunay\n"); + printf( +" triangulation, but each PSLG segment is present as a single edge in the\n"); + printf( +" triangulation. (A constrained Delaunay triangulation is not truly a\n"); + printf(" Delaunay triangulation.)\n\n"); + printf( +" A conforming Delaunay triangulation of a PSLG is a true Delaunay\n"); + printf( +" triangulation in which each PSLG segment may have been subdivided into\n"); + printf( +" several edges by the insertion of additional points. These inserted\n"); + printf( +" points are necessary to allow the segments to exist in the mesh while\n"); + printf(" maintaining the Delaunay property.\n\n"); + printf("File Formats:\n\n"); + printf( +" All files may contain comments prefixed by the character '#'. Points,\n"); + printf( +" triangles, edges, holes, and maximum area constraints must be numbered\n"); + printf( +" consecutively, starting from either 1 or 0. Whichever you choose, all\n"); + printf( +" input files must be consistent; if the nodes are numbered from 1, so must\n" +); + printf( +" be all other objects. Triangle automatically detects your choice while\n"); + printf( +" reading the .node (or .poly) file. (When calling Triangle from another\n"); + printf( +" program, use the -z switch if you wish to number objects from zero.)\n"); + printf(" Examples of these file formats are given below.\n\n"); + printf(" .node files:\n"); + printf( +" First line: <# of points> <# of attributes>\n"); + printf( +" <# of boundary markers (0 or 1)>\n" +); + printf( +" Remaining lines: [attributes] [boundary marker]\n"); + printf("\n"); + printf( +" The attributes, which are typically floating-point values of physical\n"); + printf( +" quantities (such as mass or conductivity) associated with the nodes of\n" +); + printf( +" a finite element mesh, are copied unchanged to the output mesh. If -s,\n" +); + printf( +" -q, or -a is selected, each new Steiner point added to the mesh will\n"); + printf(" have attributes assigned to it by linear interpolation.\n\n"); + printf( +" If the fourth entry of the first line is `1', the last column of the\n"); + printf( +" remainder of the file is assumed to contain boundary markers. Boundary\n" +); + printf( +" markers are used to identify boundary points and points resting on PSLG\n" +); + printf( +" segments; a complete description appears in a section below. The .node\n" +); + printf( +" file produced by Triangle will contain boundary markers in the last\n"); + printf(" column unless they are suppressed by the -B switch.\n\n"); + printf(" .ele files:\n"); + printf( +" First line: <# of triangles> <# of attributes>\n"); + printf( +" Remaining lines: ... [attributes]\n" +); + printf("\n"); + printf( +" Points are indices into the corresponding .node file. The first three\n" +); + printf( +" points are the corners, and are listed in counterclockwise order around\n" +); + printf( +" each triangle. (The remaining points, if any, depend on the type of\n"); + printf( +" finite element used.) The attributes are just like those of .node\n"); + printf( +" files. Because there is no simple mapping from input to output\n"); + printf( +" triangles, an attempt is made to interpolate attributes, which may\n"); + printf( +" result in a good deal of diffusion of attributes among nearby triangles\n" +); + printf( +" as the triangulation is refined. Diffusion does not occur across\n"); + printf( +" segments, so attributes used to identify segment-bounded regions remain\n" +); + printf( +" intact. In output .ele files, all triangles have three points each\n"); + printf( +" unless the -o2 switch is used, in which case they have six, and the\n"); + printf( +" fourth, fifth, and sixth points lie on the midpoints of the edges\n"); + printf(" opposite the first, second, and third corners.\n\n"); + printf(" .poly files:\n"); + printf( +" First line: <# of points> <# of attributes>\n"); + printf( +" <# of boundary markers (0 or 1)>\n" +); + printf( +" Following lines: [attributes] [boundary marker]\n"); + printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n"); + printf( +" Following lines: [boundary marker]\n"); + printf(" One line: <# of holes>\n"); + printf(" Following lines: \n"); + printf( +" Optional line: <# of regional attributes and/or area constraints>\n"); + printf( +" Optional following lines: \n"); + printf("\n"); + printf( +" A .poly file represents a PSLG, as well as some additional information.\n" +); + printf( +" The first section lists all the points, and is identical to the format\n" +); + printf( +" of .node files. <# of points> may be set to zero to indicate that the\n" +); + printf( +" points are listed in a separate .node file; .poly files produced by\n"); + printf( +" Triangle always have this format. This has the advantage that a point\n" +); + printf( +" set may easily be triangulated with or without segments. (The same\n"); + printf( +" effect can be achieved, albeit using more disk space, by making a copy\n" +); + printf( +" of the .poly file with the extension .node; all sections of the file\n"); + printf(" but the first are ignored.)\n\n"); + printf( +" The second section lists the segments. Segments are edges whose\n"); + printf( +" presence in the triangulation is enforced. Each segment is specified\n"); + printf( +" by listing the indices of its two endpoints. This means that you must\n" +); + printf( +" include its endpoints in the point list. If -s, -q, and -a are not\n"); + printf( +" selected, Triangle will produce a constrained Delaunay triangulation,\n"); + printf( +" in which each segment appears as a single edge in the triangulation.\n"); + printf( +" If -q or -a is selected, Triangle will produce a conforming Delaunay\n"); + printf( +" triangulation, in which segments may be subdivided into smaller edges.\n" +); + printf(" Each segment, like each point, may have a boundary marker.\n\n"); + printf( +" The third section lists holes (and concavities, if -c is selected) in\n"); + printf( +" the triangulation. Holes are specified by identifying a point inside\n"); + printf( +" each hole. After the triangulation is formed, Triangle creates holes\n"); + printf( +" by eating triangles, spreading out from each hole point until its\n"); + printf( +" progress is blocked by PSLG segments; you must be careful to enclose\n"); + printf( +" each hole in segments, or your whole triangulation may be eaten away.\n"); + printf( +" If the two triangles abutting a segment are eaten, the segment itself\n"); + printf( +" is also eaten. Do not place a hole directly on a segment; if you do,\n"); + printf(" Triangle will choose one side of the segment arbitrarily.\n\n"); + printf( +" The optional fourth section lists regional attributes (to be assigned\n"); + printf( +" to all triangles in a region) and regional constraints on the maximum\n"); + printf( +" triangle area. Triangle will read this section only if the -A switch\n"); + printf( +" is used or the -a switch is used without a number following it, and the\n" +); + printf( +" -r switch is not used. Regional attributes and area constraints are\n"); + printf( +" propagated in the same manner as holes; you specify a point for each\n"); + printf( +" attribute and/or constraint, and the attribute and/or constraint will\n"); + printf( +" affect the whole region (bounded by segments) containing the point. If\n" +); + printf( +" two values are written on a line after the x and y coordinate, the\n"); + printf( +" former is assumed to be a regional attribute (but will only be applied\n" +); + printf( +" if the -A switch is selected), and the latter is assumed to be a\n"); + printf( +" regional area constraint (but will only be applied if the -a switch is\n" +); + printf( +" selected). You may also specify just one value after the coordinates,\n" +); + printf( +" which can serve as both an attribute and an area constraint, depending\n" +); + printf( +" on the choice of switches. If you are using the -A and -a switches\n"); + printf( +" simultaneously and wish to assign an attribute to some region without\n"); + printf(" imposing an area constraint, use a negative maximum area.\n\n"); + printf( +" When a triangulation is created from a .poly file, you must either\n"); + printf( +" enclose the entire region to be triangulated in PSLG segments, or\n"); + printf( +" use the -c switch, which encloses the convex hull of the input point\n"); + printf( +" set. If you do not use the -c switch, Triangle will eat all triangles\n" +); + printf( +" on the outer boundary that are not protected by segments; if you are\n"); + printf( +" not careful, your whole triangulation may be eaten away. If you do\n"); + printf( +" use the -c switch, you can still produce concavities by appropriate\n"); + printf(" placement of holes just inside the convex hull.\n\n"); + printf( +" An ideal PSLG has no intersecting segments, nor any points that lie\n"); + printf( +" upon segments (except, of course, the endpoints of each segment.) You\n" +); + printf( +" aren't required to make your .poly files ideal, but you should be aware\n" +); + printf( +" of what can go wrong. Segment intersections are relatively safe -\n"); + printf( +" Triangle will calculate the intersection points for you and add them to\n" +); + printf( +" the triangulation - as long as your machine's floating-point precision\n" +); + printf( +" doesn't become a problem. You are tempting the fates if you have three\n" +); + printf( +" segments that cross at the same location, and expect Triangle to figure\n" +); + printf( +" out where the intersection point is. Thanks to floating-point roundoff\n" +); + printf( +" error, Triangle will probably decide that the three segments intersect\n" +); + printf( +" at three different points, and you will find a minuscule triangle in\n"); + printf( +" your output - unless Triangle tries to refine the tiny triangle, uses\n"); + printf( +" up the last bit of machine precision, and fails to terminate at all.\n"); + printf( +" You're better off putting the intersection point in the input files,\n"); + printf( +" and manually breaking up each segment into two. Similarly, if you\n"); + printf( +" place a point at the middle of a segment, and hope that Triangle will\n"); + printf( +" break up the segment at that point, you might get lucky. On the other\n" +); + printf( +" hand, Triangle might decide that the point doesn't lie precisely on the\n" +); + printf( +" line, and you'll have a needle-sharp triangle in your output - or a lot\n" +); + printf(" of tiny triangles if you're generating a quality mesh.\n\n"); + printf( +" When Triangle reads a .poly file, it also writes a .poly file, which\n"); + printf( +" includes all edges that are part of input segments. If the -c switch\n"); + printf( +" is used, the output .poly file will also include all of the edges on\n"); + printf( +" the convex hull. Hence, the output .poly file is useful for finding\n"); + printf( +" edges associated with input segments and setting boundary conditions in\n" +); + printf( +" finite element simulations. More importantly, you will need it if you\n" +); + printf( +" plan to refine the output mesh, and don't want segments to be missing\n"); + printf(" in later triangulations.\n\n"); + printf(" .area files:\n"); + printf(" First line: <# of triangles>\n"); + printf(" Following lines: \n\n"); + printf( +" An .area file associates with each triangle a maximum area that is used\n" +); + printf( +" for mesh refinement. As with other file formats, every triangle must\n"); + printf( +" be represented, and they must be numbered consecutively. A triangle\n"); + printf( +" may be left unconstrained by assigning it a negative maximum area.\n"); + printf("\n"); + printf(" .edge files:\n"); + printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n"); + printf( +" Following lines: [boundary marker]\n"); + printf("\n"); + printf( +" Endpoints are indices into the corresponding .node file. Triangle can\n" +); + printf( +" produce .edge files (use the -e switch), but cannot read them. The\n"); + printf( +" optional column of boundary markers is suppressed by the -B switch.\n"); + printf("\n"); + printf( +" In Voronoi diagrams, one also finds a special kind of edge that is an\n"); + printf( +" infinite ray with only one endpoint. For these edges, a different\n"); + printf(" format is used:\n\n"); + printf(" -1 \n\n"); + printf( +" The `direction' is a floating-point vector that indicates the direction\n" +); + printf(" of the infinite ray.\n\n"); + printf(" .neigh files:\n"); + printf( +" First line: <# of triangles> <# of neighbors per triangle (always 3)>\n" +); + printf( +" Following lines: \n"); + printf("\n"); + printf( +" Neighbors are indices into the corresponding .ele file. An index of -1\n" +); + printf( +" indicates a mesh boundary, and therefore no neighbor. Triangle can\n"); + printf( +" produce .neigh files (use the -n switch), but cannot read them.\n"); + printf("\n"); + printf( +" The first neighbor of triangle i is opposite the first corner of\n"); + printf(" triangle i, and so on.\n\n"); + printf("Boundary Markers:\n\n"); + printf( +" Boundary markers are tags used mainly to identify which output points and\n" +); + printf( +" edges are associated with which PSLG segment, and to identify which\n"); + printf( +" points and edges occur on a boundary of the triangulation. A common use\n" +); + printf( +" is to determine where boundary conditions should be applied to a finite\n"); + printf( +" element mesh. You can prevent boundary markers from being written into\n"); + printf(" files produced by Triangle by using the -B switch.\n\n"); + printf( +" The boundary marker associated with each segment in an output .poly file\n" +); + printf(" or edge in an output .edge file is chosen as follows:\n"); + printf( +" - If an output edge is part or all of a PSLG segment with a nonzero\n"); + printf( +" boundary marker, then the edge is assigned the same marker.\n"); + printf( +" - Otherwise, if the edge occurs on a boundary of the triangulation\n"); + printf( +" (including boundaries of holes), then the edge is assigned the marker\n" +); + printf(" one (1).\n"); + printf(" - Otherwise, the edge is assigned the marker zero (0).\n"); + printf( +" The boundary marker associated with each point in an output .node file is\n" +); + printf(" chosen as follows:\n"); + printf( +" - If a point is assigned a nonzero boundary marker in the input file,\n"); + printf( +" then it is assigned the same marker in the output .node file.\n"); + printf( +" - Otherwise, if the point lies on a PSLG segment (including the\n"); + printf( +" segment's endpoints) with a nonzero boundary marker, then the point\n"); + printf( +" is assigned the same marker. If the point lies on several such\n"); + printf(" segments, one of the markers is chosen arbitrarily.\n"); + printf( +" - Otherwise, if the point occurs on a boundary of the triangulation,\n"); + printf(" then the point is assigned the marker one (1).\n"); + printf(" - Otherwise, the point is assigned the marker zero (0).\n"); + printf("\n"); + printf( +" If you want Triangle to determine for you which points and edges are on\n"); + printf( +" the boundary, assign them the boundary marker zero (or use no markers at\n" +); + printf( +" all) in your input files. Alternatively, you can mark some of them and\n"); + printf(" leave others marked zero, allowing Triangle to label them.\n\n"); + printf("Triangulation Iteration Numbers:\n\n"); + printf( +" Because Triangle can read and refine its own triangulations, input\n"); + printf( +" and output files have iteration numbers. For instance, Triangle might\n"); + printf( +" read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n"); + printf( +" triangulation, and output the files mesh.4.node, mesh.4.ele, and\n"); + printf(" mesh.4.poly. Files with no iteration number are treated as if\n"); + printf( +" their iteration number is zero; hence, Triangle might read the file\n"); + printf( +" points.node, triangulate it, and produce the files points.1.node and\n"); + printf(" points.1.ele.\n\n"); + printf( +" Iteration numbers allow you to create a sequence of successively finer\n"); + printf( +" meshes suitable for multigrid methods. They also allow you to produce a\n" +); + printf( +" sequence of meshes using error estimate-driven mesh refinement.\n"); + printf("\n"); + printf( +" If you're not using refinement or quality meshing, and you don't like\n"); + printf( +" iteration numbers, use the -I switch to disable them. This switch will\n"); + printf( +" also disable output of .node and .poly files to prevent your input files\n" +); + printf( +" from being overwritten. (If the input is a .poly file that contains its\n" +); + printf(" own points, a .node file will be written.)\n\n"); + printf("Examples of How to Use Triangle:\n\n"); + printf( +" `triangle dots' will read points from dots.node, and write their Delaunay\n" +); + printf( +" triangulation to dots.1.node and dots.1.ele. (dots.1.node will be\n"); + printf( +" identical to dots.node.) `triangle -I dots' writes the triangulation to\n" +); + printf( +" dots.ele instead. (No additional .node file is needed, so none is\n"); + printf(" written.)\n\n"); + printf( +" `triangle -pe object.1' will read a PSLG from object.1.poly (and possibly\n" +); + printf( +" object.1.node, if the points are omitted from object.1.poly) and write\n"); + printf(" their constrained Delaunay triangulation to object.2.node and\n"); + printf( +" object.2.ele. The segments will be copied to object.2.poly, and all\n"); + printf(" edges will be written to object.2.edge.\n\n"); + printf( +" `triangle -pq31.5a.1 object' will read a PSLG from object.poly (and\n"); + printf( +" possibly object.node), generate a mesh whose angles are all greater than\n" +); + printf( +" 31.5 degrees and whose triangles all have area smaller than 0.1, and\n"); + printf( +" write the mesh to object.1.node and object.1.ele. Each segment may have\n" +); + printf( +" been broken up into multiple edges; the resulting constrained edges are\n"); + printf(" written to object.1.poly.\n\n"); + printf( +" Here is a sample file `box.poly' describing a square with a square hole:\n" +); + printf("\n"); + printf( +" # A box with eight points in 2D, no attributes, one boundary marker.\n"); + printf(" 8 2 0 1\n"); + printf(" # Outer box has these vertices:\n"); + printf(" 1 0 0 0\n"); + printf(" 2 0 3 0\n"); + printf(" 3 3 0 0\n"); + printf(" 4 3 3 33 # A special marker for this point.\n"); + printf(" # Inner square has these vertices:\n"); + printf(" 5 1 1 0\n"); + printf(" 6 1 2 0\n"); + printf(" 7 2 1 0\n"); + printf(" 8 2 2 0\n"); + printf(" # Five segments with boundary markers.\n"); + printf(" 5 1\n"); + printf(" 1 1 2 5 # Left side of outer box.\n"); + printf(" 2 5 7 0 # Segments 2 through 5 enclose the hole.\n"); + printf(" 3 7 8 0\n"); + printf(" 4 8 6 10\n"); + printf(" 5 6 5 0\n"); + printf(" # One hole in the middle of the inner square.\n"); + printf(" 1\n"); + printf(" 1 1.5 1.5\n\n"); + printf( +" Note that some segments are missing from the outer square, so one must\n"); + printf( +" use the `-c' switch. After `triangle -pqc box.poly', here is the output\n" +); + printf( +" file `box.1.node', with twelve points. The last four points were added\n"); + printf( +" to meet the angle constraint. Points 1, 2, and 9 have markers from\n"); + printf( +" segment 1. Points 6 and 8 have markers from segment 4. All the other\n"); + printf( +" points but 4 have been marked to indicate that they lie on a boundary.\n"); + printf("\n"); + printf(" 12 2 0 1\n"); + printf(" 1 0 0 5\n"); + printf(" 2 0 3 5\n"); + printf(" 3 3 0 1\n"); + printf(" 4 3 3 33\n"); + printf(" 5 1 1 1\n"); + printf(" 6 1 2 10\n"); + printf(" 7 2 1 1\n"); + printf(" 8 2 2 10\n"); + printf(" 9 0 1.5 5\n"); + printf(" 10 1.5 0 1\n"); + printf(" 11 3 1.5 1\n"); + printf(" 12 1.5 3 1\n"); + printf(" # Generated by triangle -pqc box.poly\n\n"); + printf(" Here is the output file `box.1.ele', with twelve triangles.\n\n"); + printf(" 12 3 0\n"); + printf(" 1 5 6 9\n"); + printf(" 2 10 3 7\n"); + printf(" 3 6 8 12\n"); + printf(" 4 9 1 5\n"); + printf(" 5 6 2 9\n"); + printf(" 6 7 3 11\n"); + printf(" 7 11 4 8\n"); + printf(" 8 7 5 10\n"); + printf(" 9 12 2 6\n"); + printf(" 10 8 7 11\n"); + printf(" 11 5 1 10\n"); + printf(" 12 8 4 12\n"); + printf(" # Generated by triangle -pqc box.poly\n\n"); + printf( +" Here is the output file `box.1.poly'. Note that segments have been added\n" +); + printf( +" to represent the convex hull, and some segments have been split by newly\n" +); + printf( +" added points. Note also that <# of points> is set to zero to indicate\n"); + printf(" that the points should be read from the .node file.\n\n"); + printf(" 0 2 0 1\n"); + printf(" 12 1\n"); + printf(" 1 1 9 5\n"); + printf(" 2 5 7 1\n"); + printf(" 3 8 7 1\n"); + printf(" 4 6 8 10\n"); + printf(" 5 5 6 1\n"); + printf(" 6 3 10 1\n"); + printf(" 7 4 11 1\n"); + printf(" 8 2 12 1\n"); + printf(" 9 9 2 5\n"); + printf(" 10 10 1 1\n"); + printf(" 11 11 3 1\n"); + printf(" 12 12 4 1\n"); + printf(" 1\n"); + printf(" 1 1.5 1.5\n"); + printf(" # Generated by triangle -pqc box.poly\n\n"); + printf("Refinement and Area Constraints:\n\n"); + printf( +" The -r switch causes a mesh (.node and .ele files) to be read and\n"); + printf( +" refined. If the -p switch is also used, a .poly file is read and used to\n" +); + printf( +" specify edges that are constrained and cannot be eliminated (although\n"); + printf( +" they can be divided into smaller edges) by the refinement process.\n"); + printf("\n"); + printf( +" When you refine a mesh, you generally want to impose tighter quality\n"); + printf( +" constraints. One way to accomplish this is to use -q with a larger\n"); + printf( +" angle, or -a followed by a smaller area than you used to generate the\n"); + printf( +" mesh you are refining. Another way to do this is to create an .area\n"); + printf( +" file, which specifies a maximum area for each triangle, and use the -a\n"); + printf( +" switch (without a number following). Each triangle's area constraint is\n" +); + printf( +" applied to that triangle. Area constraints tend to diffuse as the mesh\n"); + printf( +" is refined, so if there are large variations in area constraint between\n"); + printf(" adjacent triangles, you may not get the results you want.\n\n"); + printf( +" If you are refining a mesh composed of linear (three-node) elements, the\n" +); + printf( +" output mesh will contain all the nodes present in the input mesh, in the\n" +); + printf( +" same order, with new nodes added at the end of the .node file. However,\n" +); + printf( +" there is no guarantee that each output element is contained in a single\n"); + printf( +" input element. Often, output elements will overlap two input elements,\n"); + printf( +" and input edges are not present in the output mesh. Hence, a sequence of\n" +); + printf( +" refined meshes will form a hierarchy of nodes, but not a hierarchy of\n"); + printf( +" elements. If you a refining a mesh of higher-order elements, the\n"); + printf( +" hierarchical property applies only to the nodes at the corners of an\n"); + printf(" element; other nodes may not be present in the refined mesh.\n\n"); + printf( +" It is important to understand that maximum area constraints in .poly\n"); + printf( +" files are handled differently from those in .area files. A maximum area\n" +); + printf( +" in a .poly file applies to the whole (segment-bounded) region in which a\n" +); + printf( +" point falls, whereas a maximum area in an .area file applies to only one\n" +); + printf( +" triangle. Area constraints in .poly files are used only when a mesh is\n"); + printf( +" first generated, whereas area constraints in .area files are used only to\n" +); + printf( +" refine an existing mesh, and are typically based on a posteriori error\n"); + printf( +" estimates resulting from a finite element simulation on that mesh.\n"); + printf("\n"); + printf( +" `triangle -rq25 object.1' will read object.1.node and object.1.ele, then\n" +); + printf( +" refine the triangulation to enforce a 25 degree minimum angle, and then\n"); + printf( +" write the refined triangulation to object.2.node and object.2.ele.\n"); + printf("\n"); + printf( +" `triangle -rpaa6.2 z.3' will read z.3.node, z.3.ele, z.3.poly, and\n"); + printf( +" z.3.area. After reconstructing the mesh and its segments, Triangle will\n" +); + printf( +" refine the mesh so that no triangle has area greater than 6.2, and\n"); + printf( +" furthermore the triangles satisfy the maximum area constraints in\n"); + printf( +" z.3.area. The output is written to z.4.node, z.4.ele, and z.4.poly.\n"); + printf("\n"); + printf( +" The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n"); + printf( +" x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n"); + printf(" suitable for multigrid.\n\n"); + printf("Convex Hulls and Mesh Boundaries:\n\n"); + printf( +" If the input is a point set (rather than a PSLG), Triangle produces its\n"); + printf( +" convex hull as a by-product in the output .poly file if you use the -c\n"); + printf( +" switch. There are faster algorithms for finding a two-dimensional convex\n" +); + printf( +" hull than triangulation, of course, but this one comes for free. If the\n" +); + printf( +" input is an unconstrained mesh (you are using the -r switch but not the\n"); + printf( +" -p switch), Triangle produces a list of its boundary edges (including\n"); + printf(" hole boundaries) as a by-product if you use the -c switch.\n\n"); + printf("Voronoi Diagrams:\n\n"); + printf( +" The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n"); + printf( +" .v.edge. For example, `triangle -v points' will read points.node,\n"); + printf( +" produce its Delaunay triangulation in points.1.node and points.1.ele,\n"); + printf( +" and produce its Voronoi diagram in points.1.v.node and points.1.v.edge.\n"); + printf( +" The .v.node file contains a list of all Voronoi vertices, and the .v.edge\n" +); + printf( +" file contains a list of all Voronoi edges, some of which may be infinite\n" +); + printf( +" rays. (The choice of filenames makes it easy to run the set of Voronoi\n"); + printf(" vertices through Triangle, if so desired.)\n\n"); + printf( +" This implementation does not use exact arithmetic to compute the Voronoi\n" +); + printf( +" vertices, and does not check whether neighboring vertices are identical.\n" +); + printf( +" Be forewarned that if the Delaunay triangulation is degenerate or\n"); + printf( +" near-degenerate, the Voronoi diagram may have duplicate points, crossing\n" +); + printf( +" edges, or infinite rays whose direction vector is zero. Also, if you\n"); + printf( +" generate a constrained (as opposed to conforming) Delaunay triangulation,\n" +); + printf( +" or if the triangulation has holes, the corresponding Voronoi diagram is\n"); + printf(" likely to have crossing edges and unlikely to make sense.\n\n"); + printf("Mesh Topology:\n\n"); + printf( +" You may wish to know which triangles are adjacent to a certain Delaunay\n"); + printf( +" edge in an .edge file, which Voronoi regions are adjacent to a certain\n"); + printf( +" Voronoi edge in a .v.edge file, or which Voronoi regions are adjacent to\n" +); + printf( +" each other. All of this information can be found by cross-referencing\n"); + printf( +" output files with the recollection that the Delaunay triangulation and\n"); + printf(" the Voronoi diagrams are planar duals.\n\n"); + printf( +" Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n"); + printf( +" the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n"); + printf( +" wise from the Voronoi edge. Triangle j of an .ele file is the dual of\n"); + printf( +" vertex j of the corresponding .v.node file; and Voronoi region k is the\n"); + printf(" dual of point k of the corresponding .node file.\n\n"); + printf( +" Hence, to find the triangles adjacent to a Delaunay edge, look at the\n"); + printf( +" vertices of the corresponding Voronoi edge; their dual triangles are on\n"); + printf( +" the left and right of the Delaunay edge, respectively. To find the\n"); + printf( +" Voronoi regions adjacent to a Voronoi edge, look at the endpoints of the\n" +); + printf( +" corresponding Delaunay edge; their dual regions are on the right and left\n" +); + printf( +" of the Voronoi edge, respectively. To find which Voronoi regions are\n"); + printf(" adjacent to each other, just read the list of Delaunay edges.\n"); + printf("\n"); + printf("Statistics:\n"); + printf("\n"); + printf( +" After generating a mesh, Triangle prints a count of the number of points,\n" +); + printf( +" triangles, edges, boundary edges, and segments in the output mesh. If\n"); + printf( +" you've forgotten the statistics for an existing mesh, the -rNEP switches\n" +); + printf( +" (or -rpNEP if you've got a .poly file for the existing mesh) will\n"); + printf(" regenerate these statistics without writing any output.\n\n"); + printf( +" The -V switch produces extended statistics, including a rough estimate\n"); + printf( +" of memory use and a histogram of triangle aspect ratios and angles in the\n" +); + printf(" mesh.\n\n"); + printf("Exact Arithmetic:\n\n"); + printf( +" Triangle uses adaptive exact arithmetic to perform what computational\n"); + printf( +" geometers call the `orientation' and `incircle' tests. If the floating-\n" +); + printf( +" point arithmetic of your machine conforms to the IEEE 754 standard (as\n"); + printf( +" most workstations do), and does not use extended precision internal\n"); + printf( +" registers, then your output is guaranteed to be an absolutely true\n"); + printf(" Delaunay or conforming Delaunay triangulation, roundoff error\n"); + printf( +" notwithstanding. The word `adaptive' implies that these arithmetic\n"); + printf( +" routines compute the result only to the precision necessary to guarantee\n" +); + printf( +" correctness, so they are usually nearly as fast as their approximate\n"); + printf( +" counterparts. The exact tests can be disabled with the -X switch. On\n"); + printf( +" most inputs, this switch will reduce the computation time by about eight\n" +); + printf( +" percent - it's not worth the risk. There are rare difficult inputs\n"); + printf( +" (having many collinear and cocircular points), however, for which the\n"); + printf( +" difference could be a factor of two. These are precisely the inputs most\n" +); + printf(" likely to cause errors if you use the -X switch.\n\n"); + printf( +" Unfortunately, these routines don't solve every numerical problem. Exact\n" +); + printf( +" arithmetic is not used to compute the positions of points, because the\n"); + printf( +" bit complexity of point coordinates would grow without bound. Hence,\n"); + printf( +" segment intersections aren't computed exactly; in very unusual cases,\n"); + printf( +" roundoff error in computing an intersection point might actually lead to\n" +); + printf( +" an inverted triangle and an invalid triangulation. (This is one reason\n"); + printf( +" to compute your own intersection points in your .poly files.) Similarly,\n" +); + printf( +" exact arithmetic is not used to compute the vertices of the Voronoi\n"); + printf(" diagram.\n\n"); + printf( +" Underflow and overflow can also cause difficulties; the exact arithmetic\n" +); + printf( +" routines do not ameliorate out-of-bounds exponents, which can arise\n"); + printf( +" during the orientation and incircle tests. As a rule of thumb, you\n"); + printf( +" should ensure that your input values are within a range such that their\n"); + printf( +" third powers can be taken without underflow or overflow. Underflow can\n"); + printf( +" silently prevent the tests from being performed exactly, while overflow\n"); + printf(" will typically cause a floating exception.\n\n"); + printf("Calling Triangle from Another Program:\n\n"); + printf(" Read the file triangle.h for details.\n\n"); + printf("Troubleshooting:\n\n"); + printf(" Please read this section before mailing me bugs.\n\n"); + printf(" `My output mesh has no triangles!'\n\n"); + printf( +" If you're using a PSLG, you've probably failed to specify a proper set\n" +); + printf( +" of bounding segments, or forgotten to use the -c switch. Or you may\n"); + printf( +" have placed a hole badly. To test these possibilities, try again with\n" +); + printf( +" the -c and -O switches. Alternatively, all your input points may be\n"); + printf( +" collinear, in which case you can hardly expect to triangulate them.\n"); + printf("\n"); + printf(" `Triangle doesn't terminate, or just crashes.'\n"); + printf("\n"); + printf( +" Bad things can happen when triangles get so small that the distance\n"); + printf( +" between their vertices isn't much larger than the precision of your\n"); + printf( +" machine's arithmetic. If you've compiled Triangle for single-precision\n" +); + printf( +" arithmetic, you might do better by recompiling it for double-precision.\n" +); + printf( +" Then again, you might just have to settle for more lenient constraints\n" +); + printf( +" on the minimum angle and the maximum area than you had planned.\n"); + printf("\n"); + printf( +" You can minimize precision problems by ensuring that the origin lies\n"); + printf( +" inside your point set, or even inside the densest part of your\n"); + printf( +" mesh. On the other hand, if you're triangulating an object whose x\n"); + printf( +" coordinates all fall between 6247133 and 6247134, you're not leaving\n"); + printf(" much floating-point precision for Triangle to work with.\n\n"); + printf( +" Precision problems can occur covertly if the input PSLG contains two\n"); + printf( +" segments that meet (or intersect) at a very small angle, or if such an\n" +); + printf( +" angle is introduced by the -c switch, which may occur if a point lies\n"); + printf( +" ever-so-slightly inside the convex hull, and is connected by a PSLG\n"); + printf( +" segment to a point on the convex hull. If you don't realize that a\n"); + printf( +" small angle is being formed, you might never discover why Triangle is\n"); + printf( +" crashing. To check for this possibility, use the -S switch (with an\n"); + printf( +" appropriate limit on the number of Steiner points, found by trial-and-\n" +); + printf( +" error) to stop Triangle early, and view the output .poly file with\n"); + printf( +" Show Me (described below). Look carefully for small angles between\n"); + printf( +" segments; zoom in closely, as such segments might look like a single\n"); + printf(" segment from a distance.\n\n"); + printf( +" If some of the input values are too large, Triangle may suffer a\n"); + printf( +" floating exception due to overflow when attempting to perform an\n"); + printf( +" orientation or incircle test. (Read the section on exact arithmetic\n"); + printf( +" above.) Again, I recommend compiling Triangle for double (rather\n"); + printf(" than single) precision arithmetic.\n\n"); + printf( +" `The numbering of the output points doesn't match the input points.'\n"); + printf("\n"); + printf( +" You may have eaten some of your input points with a hole, or by placing\n" +); + printf(" them outside the area enclosed by segments.\n\n"); + printf( +" `Triangle executes without incident, but when I look at the resulting\n"); + printf( +" mesh, it has overlapping triangles or other geometric inconsistencies.'\n"); + printf("\n"); + printf( +" If you select the -X switch, Triangle's divide-and-conquer Delaunay\n"); + printf( +" triangulation algorithm occasionally makes mistakes due to floating-\n"); + printf( +" point roundoff error. Although these errors are rare, don't use the -X\n" +); + printf(" switch. If you still have problems, please report the bug.\n"); + printf("\n"); + printf( +" Strange things can happen if you've taken liberties with your PSLG. Do\n"); + printf( +" you have a point lying in the middle of a segment? Triangle sometimes\n"); + printf( +" copes poorly with that sort of thing. Do you want to lay out a collinear\n" +); + printf( +" row of evenly spaced, segment-connected points? Have you simply defined\n" +); + printf( +" one long segment connecting the leftmost point to the rightmost point,\n"); + printf( +" and a bunch of points lying along it? This method occasionally works,\n"); + printf( +" especially with horizontal and vertical lines, but often it doesn't, and\n" +); + printf( +" you'll have to connect each adjacent pair of points with a separate\n"); + printf(" segment. If you don't like it, tough.\n\n"); + printf( +" Furthermore, if you have segments that intersect other than at their\n"); + printf( +" endpoints, try not to let the intersections fall extremely close to PSLG\n" +); + printf(" points or each other.\n\n"); + printf( +" If you have problems refining a triangulation not produced by Triangle:\n"); + printf( +" Are you sure the triangulation is geometrically valid? Is it formatted\n"); + printf( +" correctly for Triangle? Are the triangles all listed so the first three\n" +); + printf(" points are their corners in counterclockwise order?\n\n"); + printf("Show Me:\n\n"); + printf( +" Triangle comes with a separate program named `Show Me', whose primary\n"); + printf( +" purpose is to draw meshes on your screen or in PostScript. Its secondary\n" +); + printf( +" purpose is to check the validity of your input files, and do so more\n"); + printf( +" thoroughly than Triangle does. Show Me requires that you have the X\n"); + printf( +" Windows system. If you didn't receive Show Me with Triangle, complain to\n" +); + printf(" whomever you obtained Triangle from, then send me mail.\n\n"); + printf("Triangle on the Web:\n\n"); + printf( +" To see an illustrated, updated version of these instructions, check out\n"); + printf("\n"); + printf(" http://www.cs.cmu.edu/~quake/triangle.html\n"); + printf("\n"); + printf("A Brief Plea:\n"); + printf("\n"); + printf( +" If you use Triangle, and especially if you use it to accomplish real\n"); + printf( +" work, I would like very much to hear from you. A short letter or email\n"); + printf( +" (to jrs@cs.cmu.edu) describing how you use Triangle will mean a lot to\n"); + printf( +" me. The more people I know are using this program, the more easily I can\n" +); + printf( +" justify spending time on improvements and on the three-dimensional\n"); + printf( +" successor to Triangle, which in turn will benefit you. Also, I can put\n"); + printf( +" you on a list to receive email whenever a new version of Triangle is\n"); + printf(" available.\n\n"); + printf( +" If you use a mesh generated by Triangle in a publication, please include\n" +); + printf(" an acknowledgment as well.\n\n"); + printf("Research credit:\n\n"); + printf( +" Of course, I can take credit for only a fraction of the ideas that made\n"); + printf( +" this mesh generator possible. Triangle owes its existence to the efforts\n" +); + printf( +" of many fine computational geometers and other researchers, including\n"); + printf( +" Marshall Bern, L. Paul Chew, Boris Delaunay, Rex A. Dwyer, David\n"); + printf( +" Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E. Knuth, C. L.\n"); + printf( +" Lawson, Der-Tsai Lee, Ernst P. Mucke, Douglas M. Priest, Jim Ruppert,\n"); + printf( +" Isaac Saias, Bruce J. Schachter, Micha Sharir, Jorge Stolfi, Christopher\n" +); + printf( +" J. Van Wyk, David F. Watson, and Binhai Zhu. See the comments at the\n"); + printf(" beginning of the source code for references.\n\n"); + exit(0); +} + +#endif /* not TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* internalerror() Ask the user to send me the defective product. Exit. */ +/* */ +/*****************************************************************************/ + +void internalerror() +{ + printf(" Please report this bug to jrs@cs.cmu.edu\n"); + printf(" Include the message above, your input data set, and the exact\n"); + printf(" command line you used to run Triangle.\n"); + exit(1); +} + +/*****************************************************************************/ +/* */ +/* parsecommandline() Read the command line, identify switches, and set */ +/* up options and file names. */ +/* */ +/* The effects of this routine are felt entirely through global variables. */ +/* */ +/*****************************************************************************/ + +void parsecommandline(argc, argv) +int argc; +char **argv; +{ +#ifdef TRILIBRARY +#define STARTINDEX 0 +#else /* not TRILIBRARY */ +#define STARTINDEX 1 + int increment; + int meshnumber; +#endif /* not TRILIBRARY */ + int i, j, k; + char workstring[FILENAMESIZE]; + + poly = refine = quality = vararea = fixedarea = regionattrib = convex = 0; + firstnumber = 1; + edgesout = voronoi = neighbors = geomview = 0; + nobound = nopolywritten = nonodewritten = noelewritten = noiterationnum = 0; + noholes = noexact = 0; + incremental = sweepline = 0; + dwyer = 1; + splitseg = 0; + docheck = 0; + nobisect = 0; + steiner = -1; + order = 1; + minangle = 0.0; + maxarea = -1.0; + quiet = verbose = 0; +#ifndef TRILIBRARY + innodefilename[0] = '\0'; +#endif /* not TRILIBRARY */ + + for (i = STARTINDEX; i < argc; i++) { +#ifndef TRILIBRARY + if (argv[i][0] == '-') { +#endif /* not TRILIBRARY */ + for (j = STARTINDEX; argv[i][j] != '\0'; j++) { + if (argv[i][j] == 'p') { + poly = 1; + } +#ifndef CDT_ONLY + if (argv[i][j] == 'r') { + refine = 1; + } + if (argv[i][j] == 'q') { + quality = 1; + if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || + (argv[i][j + 1] == '.')) { + k = 0; + while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || + (argv[i][j + 1] == '.')) { + j++; + workstring[k] = argv[i][j]; + k++; + } + workstring[k] = '\0'; + minangle = (REAL) strtod(workstring, (char **) NULL); + } else { + minangle = 20.0; + } + } + if (argv[i][j] == 'a') { + quality = 1; + if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || + (argv[i][j + 1] == '.')) { + fixedarea = 1; + k = 0; + while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || + (argv[i][j + 1] == '.')) { + j++; + workstring[k] = argv[i][j]; + k++; + } + workstring[k] = '\0'; + maxarea = (REAL) strtod(workstring, (char **) NULL); + if (maxarea <= 0.0) { + printf("Error: Maximum area must be greater than zero.\n"); + exit(1); + } + } else { + vararea = 1; + } + } +#endif /* not CDT_ONLY */ + if (argv[i][j] == 'A') { + regionattrib = 1; + } + if (argv[i][j] == 'c') { + convex = 1; + } + if (argv[i][j] == 'z') { + firstnumber = 0; + } + if (argv[i][j] == 'e') { + edgesout = 1; + } + if (argv[i][j] == 'v') { + voronoi = 1; + } + if (argv[i][j] == 'n') { + neighbors = 1; + } + if (argv[i][j] == 'g') { + geomview = 1; + } + if (argv[i][j] == 'B') { + nobound = 1; + } + if (argv[i][j] == 'P') { + nopolywritten = 1; + } + if (argv[i][j] == 'N') { + nonodewritten = 1; + } + if (argv[i][j] == 'E') { + noelewritten = 1; + } +#ifndef TRILIBRARY + if (argv[i][j] == 'I') { + noiterationnum = 1; + } +#endif /* not TRILIBRARY */ + if (argv[i][j] == 'O') { + noholes = 1; + } + if (argv[i][j] == 'X') { + noexact = 1; + } + if (argv[i][j] == 'o') { + if (argv[i][j + 1] == '2') { + j++; + order = 2; + } + } +#ifndef CDT_ONLY + if (argv[i][j] == 'Y') { + nobisect++; + } + if (argv[i][j] == 'S') { + steiner = 0; + while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) { + j++; + steiner = steiner * 10 + (int) (argv[i][j] - '0'); + } + } +#endif /* not CDT_ONLY */ +#ifndef REDUCED + if (argv[i][j] == 'i') { + incremental = 1; + } + if (argv[i][j] == 'F') { + sweepline = 1; + } +#endif /* not REDUCED */ + if (argv[i][j] == 'l') { + dwyer = 0; + } +#ifndef REDUCED +#ifndef CDT_ONLY + if (argv[i][j] == 's') { + splitseg = 1; + } +#endif /* not CDT_ONLY */ + if (argv[i][j] == 'C') { + docheck = 1; + } +#endif /* not REDUCED */ + if (argv[i][j] == 'Q') { + quiet = 1; + } + if (argv[i][j] == 'V') { + verbose++; + } +#ifndef TRILIBRARY + if ((argv[i][j] == 'h') || (argv[i][j] == 'H') || + (argv[i][j] == '?')) { + info(); + } +#endif /* not TRILIBRARY */ + } +#ifndef TRILIBRARY + } else { + strncpy(innodefilename, argv[i], FILENAMESIZE - 1); + innodefilename[FILENAMESIZE - 1] = '\0'; + } +#endif /* not TRILIBRARY */ + } +#ifndef TRILIBRARY + if (innodefilename[0] == '\0') { + syntax(); + } + if (!strcmp(&innodefilename[strlen(innodefilename) - 5], ".node")) { + innodefilename[strlen(innodefilename) - 5] = '\0'; + } + if (!strcmp(&innodefilename[strlen(innodefilename) - 5], ".poly")) { + innodefilename[strlen(innodefilename) - 5] = '\0'; + poly = 1; + } +#ifndef CDT_ONLY + if (!strcmp(&innodefilename[strlen(innodefilename) - 4], ".ele")) { + innodefilename[strlen(innodefilename) - 4] = '\0'; + refine = 1; + } + if (!strcmp(&innodefilename[strlen(innodefilename) - 5], ".area")) { + innodefilename[strlen(innodefilename) - 5] = '\0'; + refine = 1; + quality = 1; + vararea = 1; + } +#endif /* not CDT_ONLY */ +#endif /* not TRILIBRARY */ + steinerleft = steiner; + useshelles = poly || refine || quality || convex; + goodangle = cos(minangle * PI / 180.0); + goodangle *= goodangle; + if (refine && noiterationnum) { + printf( + "Error: You cannot use the -I switch when refining a triangulation.\n"); + exit(1); + } + /* Be careful not to allocate space for element area constraints that */ + /* will never be assigned any value (other than the default -1.0). */ + if (!refine && !poly) { + vararea = 0; + } + /* Be careful not to add an extra attribute to each element unless the */ + /* input supports it (PSLG in, but not refining a preexisting mesh). */ + if (refine || !poly) { + regionattrib = 0; + } + +#ifndef TRILIBRARY + strcpy(inpolyfilename, innodefilename); + strcpy(inelefilename, innodefilename); + strcpy(areafilename, innodefilename); + increment = 0; + strcpy(workstring, innodefilename); + j = 1; + while (workstring[j] != '\0') { + if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) { + increment = j + 1; + } + j++; + } + meshnumber = 0; + if (increment > 0) { + j = increment; + do { + if ((workstring[j] >= '0') && (workstring[j] <= '9')) { + meshnumber = meshnumber * 10 + (int) (workstring[j] - '0'); + } else { + increment = 0; + } + j++; + } while (workstring[j] != '\0'); + } + if (noiterationnum) { + strcpy(outnodefilename, innodefilename); + strcpy(outelefilename, innodefilename); + strcpy(edgefilename, innodefilename); + strcpy(vnodefilename, innodefilename); + strcpy(vedgefilename, innodefilename); + strcpy(neighborfilename, innodefilename); + strcpy(offfilename, innodefilename); + strcat(outnodefilename, ".node"); + strcat(outelefilename, ".ele"); + strcat(edgefilename, ".edge"); + strcat(vnodefilename, ".v.node"); + strcat(vedgefilename, ".v.edge"); + strcat(neighborfilename, ".neigh"); + strcat(offfilename, ".off"); + } else if (increment == 0) { + strcpy(outnodefilename, innodefilename); + strcpy(outpolyfilename, innodefilename); + strcpy(outelefilename, innodefilename); + strcpy(edgefilename, innodefilename); + strcpy(vnodefilename, innodefilename); + strcpy(vedgefilename, innodefilename); + strcpy(neighborfilename, innodefilename); + strcpy(offfilename, innodefilename); + strcat(outnodefilename, ".1.node"); + strcat(outpolyfilename, ".1.poly"); + strcat(outelefilename, ".1.ele"); + strcat(edgefilename, ".1.edge"); + strcat(vnodefilename, ".1.v.node"); + strcat(vedgefilename, ".1.v.edge"); + strcat(neighborfilename, ".1.neigh"); + strcat(offfilename, ".1.off"); + } else { + workstring[increment] = '%'; + workstring[increment + 1] = 'd'; + workstring[increment + 2] = '\0'; + sprintf(outnodefilename, workstring, meshnumber + 1); + strcpy(outpolyfilename, outnodefilename); + strcpy(outelefilename, outnodefilename); + strcpy(edgefilename, outnodefilename); + strcpy(vnodefilename, outnodefilename); + strcpy(vedgefilename, outnodefilename); + strcpy(neighborfilename, outnodefilename); + strcpy(offfilename, outnodefilename); + strcat(outnodefilename, ".node"); + strcat(outpolyfilename, ".poly"); + strcat(outelefilename, ".ele"); + strcat(edgefilename, ".edge"); + strcat(vnodefilename, ".v.node"); + strcat(vedgefilename, ".v.edge"); + strcat(neighborfilename, ".neigh"); + strcat(offfilename, ".off"); + } + strcat(innodefilename, ".node"); + strcat(inpolyfilename, ".poly"); + strcat(inelefilename, ".ele"); + strcat(areafilename, ".area"); +#endif /* not TRILIBRARY */ +} + +/** **/ +/** **/ +/********* User interaction routines begin here *********/ + +/********* Debugging routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* printtriangle() Print out the details of a triangle/edge handle. */ +/* */ +/* I originally wrote this procedure to simplify debugging; it can be */ +/* called directly from the debugger, and presents information about a */ +/* triangle/edge handle in digestible form. It's also used when the */ +/* highest level of verbosity (`-VVV') is specified. */ +/* */ +/*****************************************************************************/ + +void printtriangle(t) +struct triedge *t; +{ + struct triedge printtri; + struct edge printsh; + point printpoint; + + printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri, + t->orient); + decode(t->tri[0], printtri); + if (printtri.tri == dummytri) { + printf(" [0] = Outer space\n"); + } else { + printf(" [0] = x%lx %d\n", (unsigned long) printtri.tri, + printtri.orient); + } + decode(t->tri[1], printtri); + if (printtri.tri == dummytri) { + printf(" [1] = Outer space\n"); + } else { + printf(" [1] = x%lx %d\n", (unsigned long) printtri.tri, + printtri.orient); + } + decode(t->tri[2], printtri); + if (printtri.tri == dummytri) { + printf(" [2] = Outer space\n"); + } else { + printf(" [2] = x%lx %d\n", (unsigned long) printtri.tri, + printtri.orient); + } + org(*t, printpoint); + if (printpoint == (point) NULL) + printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3); + else + printf(" Origin[%d] = x%lx (%.12g, %.12g)\n", + (t->orient + 1) % 3 + 3, (unsigned long) printpoint, + printpoint[0], printpoint[1]); + dest(*t, printpoint); + if (printpoint == (point) NULL) + printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3); + else + printf(" Dest [%d] = x%lx (%.12g, %.12g)\n", + (t->orient + 2) % 3 + 3, (unsigned long) printpoint, + printpoint[0], printpoint[1]); + apex(*t, printpoint); + if (printpoint == (point) NULL) + printf(" Apex [%d] = NULL\n", t->orient + 3); + else + printf(" Apex [%d] = x%lx (%.12g, %.12g)\n", + t->orient + 3, (unsigned long) printpoint, + printpoint[0], printpoint[1]); + if (useshelles) { + sdecode(t->tri[6], printsh); + if (printsh.sh != dummysh) { + printf(" [6] = x%lx %d\n", (unsigned long) printsh.sh, + printsh.shorient); + } + sdecode(t->tri[7], printsh); + if (printsh.sh != dummysh) { + printf(" [7] = x%lx %d\n", (unsigned long) printsh.sh, + printsh.shorient); + } + sdecode(t->tri[8], printsh); + if (printsh.sh != dummysh) { + printf(" [8] = x%lx %d\n", (unsigned long) printsh.sh, + printsh.shorient); + } + } + if (vararea) { + printf(" Area constraint: %.4g\n", areabound(*t)); + } +} + +/*****************************************************************************/ +/* */ +/* printshelle() Print out the details of a shell edge handle. */ +/* */ +/* I originally wrote this procedure to simplify debugging; it can be */ +/* called directly from the debugger, and presents information about a */ +/* shell edge handle in digestible form. It's also used when the highest */ +/* level of verbosity (`-VVV') is specified. */ +/* */ +/*****************************************************************************/ + +void printshelle(s) +struct edge *s; +{ + struct edge printsh; + struct triedge printtri; + point printpoint; + + printf("shell edge x%lx with orientation %d and mark %d:\n", + (unsigned long) s->sh, s->shorient, mark(*s)); + sdecode(s->sh[0], printsh); + if (printsh.sh == dummysh) { + printf(" [0] = No shell\n"); + } else { + printf(" [0] = x%lx %d\n", (unsigned long) printsh.sh, + printsh.shorient); + } + sdecode(s->sh[1], printsh); + if (printsh.sh == dummysh) { + printf(" [1] = No shell\n"); + } else { + printf(" [1] = x%lx %d\n", (unsigned long) printsh.sh, + printsh.shorient); + } + sorg(*s, printpoint); + if (printpoint == (point) NULL) + printf(" Origin[%d] = NULL\n", 2 + s->shorient); + else + printf(" Origin[%d] = x%lx (%.12g, %.12g)\n", + 2 + s->shorient, (unsigned long) printpoint, + printpoint[0], printpoint[1]); + sdest(*s, printpoint); + if (printpoint == (point) NULL) + printf(" Dest [%d] = NULL\n", 3 - s->shorient); + else + printf(" Dest [%d] = x%lx (%.12g, %.12g)\n", + 3 - s->shorient, (unsigned long) printpoint, + printpoint[0], printpoint[1]); + decode(s->sh[4], printtri); + if (printtri.tri == dummytri) { + printf(" [4] = Outer space\n"); + } else { + printf(" [4] = x%lx %d\n", (unsigned long) printtri.tri, + printtri.orient); + } + decode(s->sh[5], printtri); + if (printtri.tri == dummytri) { + printf(" [5] = Outer space\n"); + } else { + printf(" [5] = x%lx %d\n", (unsigned long) printtri.tri, + printtri.orient); + } +} + +/** **/ +/** **/ +/********* Debugging routines end here *********/ + +/********* Memory management routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* poolinit() Initialize a pool of memory for allocation of items. */ +/* */ +/* This routine initializes the machinery for allocating items. A `pool' */ +/* is created whose records have size at least `bytecount'. Items will be */ +/* allocated in `itemcount'-item blocks. Each item is assumed to be a */ +/* collection of words, and either pointers or floating-point values are */ +/* assumed to be the "primary" word type. (The "primary" word type is used */ +/* to determine alignment of items.) If `alignment' isn't zero, all items */ +/* will be `alignment'-byte aligned in memory. `alignment' must be either */ +/* a multiple or a factor of the primary word size; powers of two are safe. */ +/* `alignment' is normally used to create a few unused bits at the bottom */ +/* of each item's pointer, in which information may be stored. */ +/* */ +/* Don't change this routine unless you understand it. */ +/* */ +/*****************************************************************************/ + +void poolinit(pool, bytecount, itemcount, wtype, alignment) +struct memorypool *pool; +int bytecount; +int itemcount; +enum wordtype wtype; +int alignment; +{ + int wordsize; + + /* Initialize values in the pool. */ + pool->itemwordtype = wtype; + wordsize = (pool->itemwordtype == POINTER) ? sizeof(VOID *) : sizeof(REAL); + /* Find the proper alignment, which must be at least as large as: */ + /* - The parameter `alignment'. */ + /* - The primary word type, to avoid unaligned accesses. */ + /* - sizeof(VOID *), so the stack of dead items can be maintained */ + /* without unaligned accesses. */ + if (alignment > wordsize) { + pool->alignbytes = alignment; + } else { + pool->alignbytes = wordsize; + } + if (sizeof(VOID *) > pool->alignbytes) { + pool->alignbytes = sizeof(VOID *); + } + pool->itemwords = ((bytecount + pool->alignbytes - 1) / pool->alignbytes) + * (pool->alignbytes / wordsize); + pool->itembytes = pool->itemwords * wordsize; + pool->itemsperblock = itemcount; + + /* Allocate a block of items. Space for `itemsperblock' items and one */ + /* pointer (to point to the next block) are allocated, as well as space */ + /* to ensure alignment of the items. */ + pool->firstblock = (VOID **) malloc(pool->itemsperblock * pool->itembytes + + sizeof(VOID *) + pool->alignbytes); + if (pool->firstblock == (VOID **) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + /* Set the next block pointer to NULL. */ + *(pool->firstblock) = (VOID *) NULL; + poolrestart(pool); +} + +/*****************************************************************************/ +/* */ +/* poolrestart() Deallocate all items in a pool. */ +/* */ +/* The pool is returned to its starting state, except that no memory is */ +/* freed to the operating system. Rather, the previously allocated blocks */ +/* are ready to be reused. */ +/* */ +/*****************************************************************************/ + +void poolrestart(pool) +struct memorypool *pool; +{ + unsigned long alignptr; + + pool->items = 0; + pool->maxitems = 0; + + /* Set the currently active block. */ + pool->nowblock = pool->firstblock; + /* Find the first item in the pool. Increment by the size of (VOID *). */ + alignptr = (unsigned long) (pool->nowblock + 1); + /* Align the item on an `alignbytes'-byte boundary. */ + pool->nextitem = (VOID *) + (alignptr + (unsigned long) pool->alignbytes + - (alignptr % (unsigned long) pool->alignbytes)); + /* There are lots of unallocated items left in this block. */ + pool->unallocateditems = pool->itemsperblock; + /* The stack of deallocated items is empty. */ + pool->deaditemstack = (VOID *) NULL; +} + +/*****************************************************************************/ +/* */ +/* pooldeinit() Free to the operating system all memory taken by a pool. */ +/* */ +/*****************************************************************************/ + +void pooldeinit(pool) +struct memorypool *pool; +{ + while (pool->firstblock != (VOID **) NULL) { + pool->nowblock = (VOID **) *(pool->firstblock); + free(pool->firstblock); + pool->firstblock = pool->nowblock; + } +} + +/*****************************************************************************/ +/* */ +/* poolalloc() Allocate space for an item. */ +/* */ +/*****************************************************************************/ + +VOID *poolalloc(pool) +struct memorypool *pool; +{ + VOID *newitem; + VOID **newblock; + unsigned long alignptr; + + /* First check the linked list of dead items. If the list is not */ + /* empty, allocate an item from the list rather than a fresh one. */ + if (pool->deaditemstack != (VOID *) NULL) { + newitem = pool->deaditemstack; /* Take first item in list. */ + pool->deaditemstack = * (VOID **) pool->deaditemstack; + } else { + /* Check if there are any free items left in the current block. */ + if (pool->unallocateditems == 0) { + /* Check if another block must be allocated. */ + if (*(pool->nowblock) == (VOID *) NULL) { + /* Allocate a new block of items, pointed to by the previous block. */ + newblock = (VOID **) malloc(pool->itemsperblock * pool->itembytes + + sizeof(VOID *) + pool->alignbytes); + if (newblock == (VOID **) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + *(pool->nowblock) = (VOID *) newblock; + /* The next block pointer is NULL. */ + *newblock = (VOID *) NULL; + } + /* Move to the new block. */ + pool->nowblock = (VOID **) *(pool->nowblock); + /* Find the first item in the block. */ + /* Increment by the size of (VOID *). */ + alignptr = (unsigned long) (pool->nowblock + 1); + /* Align the item on an `alignbytes'-byte boundary. */ + pool->nextitem = (VOID *) + (alignptr + (unsigned long) pool->alignbytes + - (alignptr % (unsigned long) pool->alignbytes)); + /* There are lots of unallocated items left in this block. */ + pool->unallocateditems = pool->itemsperblock; + } + /* Allocate a new item. */ + newitem = pool->nextitem; + /* Advance `nextitem' pointer to next free item in block. */ + if (pool->itemwordtype == POINTER) { + pool->nextitem = (VOID *) ((VOID **) pool->nextitem + pool->itemwords); + } else { + pool->nextitem = (VOID *) ((REAL *) pool->nextitem + pool->itemwords); + } + pool->unallocateditems--; + pool->maxitems++; + } + pool->items++; + return newitem; +} + +/*****************************************************************************/ +/* */ +/* pooldealloc() Deallocate space for an item. */ +/* */ +/* The deallocated space is stored in a queue for later reuse. */ +/* */ +/*****************************************************************************/ + +void pooldealloc(pool, dyingitem) +struct memorypool *pool; +VOID *dyingitem; +{ + /* Push freshly killed item onto stack. */ + *((VOID **) dyingitem) = pool->deaditemstack; + pool->deaditemstack = dyingitem; + pool->items--; +} + +/*****************************************************************************/ +/* */ +/* traversalinit() Prepare to traverse the entire list of items. */ +/* */ +/* This routine is used in conjunction with traverse(). */ +/* */ +/*****************************************************************************/ + +void traversalinit(pool) +struct memorypool *pool; +{ + unsigned long alignptr; + + /* Begin the traversal in the first block. */ + pool->pathblock = pool->firstblock; + /* Find the first item in the block. Increment by the size of (VOID *). */ + alignptr = (unsigned long) (pool->pathblock + 1); + /* Align with item on an `alignbytes'-byte boundary. */ + pool->pathitem = (VOID *) + (alignptr + (unsigned long) pool->alignbytes + - (alignptr % (unsigned long) pool->alignbytes)); + /* Set the number of items left in the current block. */ + pool->pathitemsleft = pool->itemsperblock; +} + +/*****************************************************************************/ +/* */ +/* traverse() Find the next item in the list. */ +/* */ +/* This routine is used in conjunction with traversalinit(). Be forewarned */ +/* that this routine successively returns all items in the list, including */ +/* deallocated ones on the deaditemqueue. It's up to you to figure out */ +/* which ones are actually dead. Why? I don't want to allocate extra */ +/* space just to demarcate dead items. It can usually be done more */ +/* space-efficiently by a routine that knows something about the structure */ +/* of the item. */ +/* */ +/*****************************************************************************/ + +VOID *traverse(pool) +struct memorypool *pool; +{ + VOID *newitem; + unsigned long alignptr; + + /* Stop upon exhausting the list of items. */ + if (pool->pathitem == pool->nextitem) { + return (VOID *) NULL; + } + /* Check whether any untraversed items remain in the current block. */ + if (pool->pathitemsleft == 0) { + /* Find the next block. */ + pool->pathblock = (VOID **) *(pool->pathblock); + /* Find the first item in the block. Increment by the size of (VOID *). */ + alignptr = (unsigned long) (pool->pathblock + 1); + /* Align with item on an `alignbytes'-byte boundary. */ + pool->pathitem = (VOID *) + (alignptr + (unsigned long) pool->alignbytes + - (alignptr % (unsigned long) pool->alignbytes)); + /* Set the number of items left in the current block. */ + pool->pathitemsleft = pool->itemsperblock; + } + newitem = pool->pathitem; + /* Find the next item in the block. */ + if (pool->itemwordtype == POINTER) { + pool->pathitem = (VOID *) ((VOID **) pool->pathitem + pool->itemwords); + } else { + pool->pathitem = (VOID *) ((REAL *) pool->pathitem + pool->itemwords); + } + pool->pathitemsleft--; + return newitem; +} + +/*****************************************************************************/ +/* */ +/* dummyinit() Initialize the triangle that fills "outer space" and the */ +/* omnipresent shell edge. */ +/* */ +/* The triangle that fills "outer space", called `dummytri', is pointed to */ +/* by every triangle and shell edge on a boundary (be it outer or inner) of */ +/* the triangulation. Also, `dummytri' points to one of the triangles on */ +/* the convex hull (until the holes and concavities are carved), making it */ +/* possible to find a starting triangle for point location. */ +/* */ +/* The omnipresent shell edge, `dummysh', is pointed to by every triangle */ +/* or shell edge that doesn't have a full complement of real shell edges */ +/* to point to. */ +/* */ +/*****************************************************************************/ + +void dummyinit(trianglewords, shellewords) +int trianglewords; +int shellewords; +{ + unsigned long alignptr; + + /* `triwords' and `shwords' are used by the mesh manipulation primitives */ + /* to extract orientations of triangles and shell edges from pointers. */ + triwords = trianglewords; /* Initialize `triwords' once and for all. */ + shwords = shellewords; /* Initialize `shwords' once and for all. */ + + /* Set up `dummytri', the `triangle' that occupies "outer space". */ + dummytribase = (triangle *) malloc(triwords * sizeof(triangle) + + triangles.alignbytes); + if (dummytribase == (triangle *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */ + alignptr = (unsigned long) dummytribase; + dummytri = (triangle *) + (alignptr + (unsigned long) triangles.alignbytes + - (alignptr % (unsigned long) triangles.alignbytes)); + /* Initialize the three adjoining triangles to be "outer space". These */ + /* will eventually be changed by various bonding operations, but their */ + /* values don't really matter, as long as they can legally be */ + /* dereferenced. */ + dummytri[0] = (triangle) dummytri; + dummytri[1] = (triangle) dummytri; + dummytri[2] = (triangle) dummytri; + /* Three NULL vertex points. */ + dummytri[3] = (triangle) NULL; + dummytri[4] = (triangle) NULL; + dummytri[5] = (triangle) NULL; + + if (useshelles) { + /* Set up `dummysh', the omnipresent "shell edge" pointed to by any */ + /* triangle side or shell edge end that isn't attached to a real shell */ + /* edge. */ + dummyshbase = (shelle *) malloc(shwords * sizeof(shelle) + + shelles.alignbytes); + if (dummyshbase == (shelle *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + /* Align `dummysh' on a `shelles.alignbytes'-byte boundary. */ + alignptr = (unsigned long) dummyshbase; + dummysh = (shelle *) + (alignptr + (unsigned long) shelles.alignbytes + - (alignptr % (unsigned long) shelles.alignbytes)); + /* Initialize the two adjoining shell edges to be the omnipresent shell */ + /* edge. These will eventually be changed by various bonding */ + /* operations, but their values don't really matter, as long as they */ + /* can legally be dereferenced. */ + dummysh[0] = (shelle) dummysh; + dummysh[1] = (shelle) dummysh; + /* Two NULL vertex points. */ + dummysh[2] = (shelle) NULL; + dummysh[3] = (shelle) NULL; + /* Initialize the two adjoining triangles to be "outer space". */ + dummysh[4] = (shelle) dummytri; + dummysh[5] = (shelle) dummytri; + /* Set the boundary marker to zero. */ + * (int *) (dummysh + 6) = 0; + + /* Initialize the three adjoining shell edges of `dummytri' to be */ + /* the omnipresent shell edge. */ + dummytri[6] = (triangle) dummysh; + dummytri[7] = (triangle) dummysh; + dummytri[8] = (triangle) dummysh; + } +} + +/*****************************************************************************/ +/* */ +/* initializepointpool() Calculate the size of the point data structure */ +/* and initialize its memory pool. */ +/* */ +/* This routine also computes the `pointmarkindex' and `point2triindex' */ +/* indices used to find values within each point. */ +/* */ +/*****************************************************************************/ + +void initializepointpool() +{ + int pointsize; + + /* The index within each point at which the boundary marker is found. */ + /* Ensure the point marker is aligned to a sizeof(int)-byte address. */ + pointmarkindex = ((mesh_dim + nextras) * sizeof(REAL) + sizeof(int) - 1) + / sizeof(int); + pointsize = (pointmarkindex + 1) * sizeof(int); + if (poly) { + /* The index within each point at which a triangle pointer is found. */ + /* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */ + point2triindex = (pointsize + sizeof(triangle) - 1) / sizeof(triangle); + pointsize = (point2triindex + 1) * sizeof(triangle); + } + /* Initialize the pool of points. */ + poolinit(&points, pointsize, POINTPERBLOCK, + (sizeof(REAL) >= sizeof(triangle)) ? FLOATINGPOINT : POINTER, 0); +} + +/*****************************************************************************/ +/* */ +/* initializetrisegpools() Calculate the sizes of the triangle and shell */ +/* edge data structures and initialize their */ +/* memory pools. */ +/* */ +/* This routine also computes the `highorderindex', `elemattribindex', and */ +/* `areaboundindex' indices used to find values within each triangle. */ +/* */ +/*****************************************************************************/ + +void initializetrisegpools() +{ + int trisize; + + /* The index within each triangle at which the extra nodes (above three) */ + /* associated with high order elements are found. There are three */ + /* pointers to other triangles, three pointers to corners, and possibly */ + /* three pointers to shell edges before the extra nodes. */ + highorderindex = 6 + (useshelles * 3); + /* The number of bytes occupied by a triangle. */ + trisize = ((order + 1) * (order + 2) / 2 + (highorderindex - 3)) * + sizeof(triangle); + /* The index within each triangle at which its attributes are found, */ + /* where the index is measured in REALs. */ + elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL); + /* The index within each triangle at which the maximum area constraint */ + /* is found, where the index is measured in REALs. Note that if the */ + /* `regionattrib' flag is set, an additional attribute will be added. */ + areaboundindex = elemattribindex + eextras + regionattrib; + /* If triangle attributes or an area bound are needed, increase the number */ + /* of bytes occupied by a triangle. */ + if (vararea) { + trisize = (areaboundindex + 1) * sizeof(REAL); + } else if (eextras + regionattrib > 0) { + trisize = areaboundindex * sizeof(REAL); + } + /* If a Voronoi diagram or triangle neighbor graph is requested, make */ + /* sure there's room to store an integer index in each triangle. This */ + /* integer index can occupy the same space as the shell edges or */ + /* attributes or area constraint or extra nodes. */ + if ((voronoi || neighbors) && + (trisize < 6 * sizeof(triangle) + sizeof(int))) { + trisize = 6 * sizeof(triangle) + sizeof(int); + } + /* Having determined the memory size of a triangle, initialize the pool. */ + poolinit(&triangles, trisize, TRIPERBLOCK, POINTER, 4); + + if (useshelles) { + /* Initialize the pool of shell edges. */ + poolinit(&shelles, 6 * sizeof(triangle) + sizeof(int), SHELLEPERBLOCK, + POINTER, 4); + + /* Initialize the "outer space" triangle and omnipresent shell edge. */ + dummyinit(triangles.itemwords, shelles.itemwords); + } else { + /* Initialize the "outer space" triangle. */ + dummyinit(triangles.itemwords, 0); + } +} + +/*****************************************************************************/ +/* */ +/* triangledealloc() Deallocate space for a triangle, marking it dead. */ +/* */ +/*****************************************************************************/ + +void triangledealloc(dyingtriangle) +triangle *dyingtriangle; +{ + /* Set triangle's vertices to NULL. This makes it possible to */ + /* detect dead triangles when traversing the list of all triangles. */ + dyingtriangle[3] = (triangle) NULL; + dyingtriangle[4] = (triangle) NULL; + dyingtriangle[5] = (triangle) NULL; + pooldealloc(&triangles, (VOID *) dyingtriangle); +} + +/*****************************************************************************/ +/* */ +/* triangletraverse() Traverse the triangles, skipping dead ones. */ +/* */ +/*****************************************************************************/ + +triangle *triangletraverse() +{ + triangle *newtriangle; + + do { + newtriangle = (triangle *) traverse(&triangles); + if (newtriangle == (triangle *) NULL) { + return (triangle *) NULL; + } + } while (newtriangle[3] == (triangle) NULL); /* Skip dead ones. */ + return newtriangle; +} + +/*****************************************************************************/ +/* */ +/* shelledealloc() Deallocate space for a shell edge, marking it dead. */ +/* */ +/*****************************************************************************/ + +void shelledealloc(dyingshelle) +shelle *dyingshelle; +{ + /* Set shell edge's vertices to NULL. This makes it possible to */ + /* detect dead shells when traversing the list of all shells. */ + dyingshelle[2] = (shelle) NULL; + dyingshelle[3] = (shelle) NULL; + pooldealloc(&shelles, (VOID *) dyingshelle); +} + +/*****************************************************************************/ +/* */ +/* shelletraverse() Traverse the shell edges, skipping dead ones. */ +/* */ +/*****************************************************************************/ + +shelle *shelletraverse() +{ + shelle *newshelle; + + do { + newshelle = (shelle *) traverse(&shelles); + if (newshelle == (shelle *) NULL) { + return (shelle *) NULL; + } + } while (newshelle[2] == (shelle) NULL); /* Skip dead ones. */ + return newshelle; +} + +/*****************************************************************************/ +/* */ +/* pointdealloc() Deallocate space for a point, marking it dead. */ +/* */ +/*****************************************************************************/ + +void pointdealloc(dyingpoint) +point dyingpoint; +{ + /* Mark the point as dead. This makes it possible to detect dead points */ + /* when traversing the list of all points. */ + setpointmark(dyingpoint, DEADPOINT); + pooldealloc(&points, (VOID *) dyingpoint); +} + +/*****************************************************************************/ +/* */ +/* pointtraverse() Traverse the points, skipping dead ones. */ +/* */ +/*****************************************************************************/ + +point pointtraverse() +{ + point newpoint; + + do { + newpoint = (point) traverse(&points); + if (newpoint == (point) NULL) { + return (point) NULL; + } + } while (pointmark(newpoint) == DEADPOINT); /* Skip dead ones. */ + return newpoint; +} + +/*****************************************************************************/ +/* */ +/* badsegmentdealloc() Deallocate space for a bad segment, marking it */ +/* dead. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +void badsegmentdealloc(dyingseg) +struct edge *dyingseg; +{ + /* Set segment's orientation to -1. This makes it possible to */ + /* detect dead segments when traversing the list of all segments. */ + dyingseg->shorient = -1; + pooldealloc(&badsegments, (VOID *) dyingseg); +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* badsegmenttraverse() Traverse the bad segments, skipping dead ones. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +struct edge *badsegmenttraverse() +{ + struct edge *newseg; + + do { + newseg = (struct edge *) traverse(&badsegments); + if (newseg == (struct edge *) NULL) { + return (struct edge *) NULL; + } + } while (newseg->shorient == -1); /* Skip dead ones. */ + return newseg; +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* getpoint() Get a specific point, by number, from the list. */ +/* */ +/* The first point is number 'firstnumber'. */ +/* */ +/* Note that this takes O(n) time (with a small constant, if POINTPERBLOCK */ +/* is large). I don't care to take the trouble to make it work in constant */ +/* time. */ +/* */ +/*****************************************************************************/ + +point getpoint(number) +int number; +{ + VOID **getblock; + point foundpoint; + unsigned long alignptr; + int current; + + getblock = points.firstblock; + current = firstnumber; + /* Find the right block. */ + while (current + points.itemsperblock <= number) { + getblock = (VOID **) *getblock; + current += points.itemsperblock; + } + /* Now find the right point. */ + alignptr = (unsigned long) (getblock + 1); + foundpoint = (point) (alignptr + (unsigned long) points.alignbytes + - (alignptr % (unsigned long) points.alignbytes)); + while (current < number) { + foundpoint += points.itemwords; + current++; + } + return foundpoint; +} + +/*****************************************************************************/ +/* */ +/* triangledeinit() Free all remaining allocated memory. */ +/* */ +/*****************************************************************************/ + +void triangledeinit() +{ + pooldeinit(&triangles); + free(dummytribase); + if (useshelles) { + pooldeinit(&shelles); + free(dummyshbase); + } + pooldeinit(&points); +#ifndef CDT_ONLY + if (quality) { + pooldeinit(&badsegments); + if ((minangle > 0.0) || vararea || fixedarea) { + pooldeinit(&badtriangles); + } + } +#endif /* not CDT_ONLY */ +} + +/** **/ +/** **/ +/********* Memory management routines end here *********/ + +/********* Constructors begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* maketriangle() Create a new triangle with orientation zero. */ +/* */ +/*****************************************************************************/ + +void maketriangle(newtriedge) +struct triedge *newtriedge; +{ + int i; + + newtriedge->tri = (triangle *) poolalloc(&triangles); + /* Initialize the three adjoining triangles to be "outer space". */ + newtriedge->tri[0] = (triangle) dummytri; + newtriedge->tri[1] = (triangle) dummytri; + newtriedge->tri[2] = (triangle) dummytri; + /* Three NULL vertex points. */ + newtriedge->tri[3] = (triangle) NULL; + newtriedge->tri[4] = (triangle) NULL; + newtriedge->tri[5] = (triangle) NULL; + /* Initialize the three adjoining shell edges to be the omnipresent */ + /* shell edge. */ + if (useshelles) { + newtriedge->tri[6] = (triangle) dummysh; + newtriedge->tri[7] = (triangle) dummysh; + newtriedge->tri[8] = (triangle) dummysh; + } + for (i = 0; i < eextras; i++) { + setelemattribute(*newtriedge, i, 0.0); + } + if (vararea) { + setareabound(*newtriedge, -1.0); + } + + newtriedge->orient = 0; +} + +/*****************************************************************************/ +/* */ +/* makeshelle() Create a new shell edge with orientation zero. */ +/* */ +/*****************************************************************************/ + +void makeshelle(newedge) +struct edge *newedge; +{ + newedge->sh = (shelle *) poolalloc(&shelles); + /* Initialize the two adjoining shell edges to be the omnipresent */ + /* shell edge. */ + newedge->sh[0] = (shelle) dummysh; + newedge->sh[1] = (shelle) dummysh; + /* Two NULL vertex points. */ + newedge->sh[2] = (shelle) NULL; + newedge->sh[3] = (shelle) NULL; + /* Initialize the two adjoining triangles to be "outer space". */ + newedge->sh[4] = (shelle) dummytri; + newedge->sh[5] = (shelle) dummytri; + /* Set the boundary marker to zero. */ + setmark(*newedge, 0); + + newedge->shorient = 0; +} + +/** **/ +/** **/ +/********* Constructors end here *********/ + +/********* Determinant evaluation routines begin here *********/ +/** **/ +/** **/ + +/* The adaptive exact arithmetic geometric predicates implemented herein are */ +/* described in detail in my Technical Report CMU-CS-96-140. The complete */ +/* reference is given in the header. */ + +/* Which of the following two methods of finding the absolute values is */ +/* fastest is compiler-dependent. A few compilers can inline and optimize */ +/* the fabs() call; but most will incur the overhead of a function call, */ +/* which is disastrously slow. A faster way on IEEE machines might be to */ +/* mask the appropriate bit, but that's difficult to do in C. */ + +#define Absolute(a) ((a) >= 0.0 ? (a) : -(a)) +/* #define Absolute(a) fabs(a) */ + +/* Many of the operations are broken up into two pieces, a main part that */ +/* performs an approximate operation, and a "tail" that computes the */ +/* roundoff error of that operation. */ +/* */ +/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */ +/* Split(), and Two_Product() are all implemented as described in the */ +/* reference. Each of these macros requires certain variables to be */ +/* defined in the calling routine. The variables `bvirt', `c', `abig', */ +/* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */ +/* they store the result of an operation that may incur roundoff error. */ +/* The input parameter `x' (or the highest numbered `x_' parameter) must */ +/* also be declared `INEXACT'. */ + +#define Fast_Two_Sum_Tail(a, b, x, y) \ + bvirt = x - a; \ + y = b - bvirt + +#define Fast_Two_Sum(a, b, x, y) \ + x = (REAL) (a + b); \ + Fast_Two_Sum_Tail(a, b, x, y) + +#define Two_Sum_Tail(a, b, x, y) \ + bvirt = (REAL) (x - a); \ + avirt = x - bvirt; \ + bround = b - bvirt; \ + around = a - avirt; \ + y = around + bround + +#define Two_Sum(a, b, x, y) \ + x = (REAL) (a + b); \ + Two_Sum_Tail(a, b, x, y) + +#define Two_Diff_Tail(a, b, x, y) \ + bvirt = (REAL) (a - x); \ + avirt = x + bvirt; \ + bround = bvirt - b; \ + around = a - avirt; \ + y = around + bround + +#define Two_Diff(a, b, x, y) \ + x = (REAL) (a - b); \ + Two_Diff_Tail(a, b, x, y) + +#define Split(a, ahi, alo) \ + c = (REAL) (splitter * a); \ + abig = (REAL) (c - a); \ + ahi = c - abig; \ + alo = a - ahi + +#define Two_Product_Tail(a, b, x, y) \ + Split(a, ahi, alo); \ + Split(b, bhi, blo); \ + err1 = x - (ahi * bhi); \ + err2 = err1 - (alo * bhi); \ + err3 = err2 - (ahi * blo); \ + y = (alo * blo) - err3 + +#define Two_Product(a, b, x, y) \ + x = (REAL) (a * b); \ + Two_Product_Tail(a, b, x, y) + +/* Two_Product_Presplit() is Two_Product() where one of the inputs has */ +/* already been split. Avoids redundant splitting. */ + +#define Two_Product_Presplit(a, b, bhi, blo, x, y) \ + x = (REAL) (a * b); \ + Split(a, ahi, alo); \ + err1 = x - (ahi * bhi); \ + err2 = err1 - (alo * bhi); \ + err3 = err2 - (ahi * blo); \ + y = (alo * blo) - err3 + +/* Square() can be done more quickly than Two_Product(). */ + +#define Square_Tail(a, x, y) \ + Split(a, ahi, alo); \ + err1 = x - (ahi * ahi); \ + err3 = err1 - ((ahi + ahi) * alo); \ + y = (alo * alo) - err3 + +#define Square(a, x, y) \ + x = (REAL) (a * a); \ + Square_Tail(a, x, y) + +/* Macros for summing expansions of various fixed lengths. These are all */ +/* unrolled versions of Expansion_Sum(). */ + +#define Two_One_Sum(a1, a0, b, x2, x1, x0) \ + Two_Sum(a0, b , _i, x0); \ + Two_Sum(a1, _i, x2, x1) + +#define Two_One_Diff(a1, a0, b, x2, x1, x0) \ + Two_Diff(a0, b , _i, x0); \ + Two_Sum( a1, _i, x2, x1) + +#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \ + Two_One_Sum(a1, a0, b0, _j, _0, x0); \ + Two_One_Sum(_j, _0, b1, x3, x2, x1) + +#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \ + Two_One_Diff(a1, a0, b0, _j, _0, x0); \ + Two_One_Diff(_j, _0, b1, x3, x2, x1) + +/*****************************************************************************/ +/* */ +/* exactinit() Initialize the variables used for exact arithmetic. */ +/* */ +/* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in */ +/* floating-point arithmetic. `epsilon' bounds the relative roundoff */ +/* error. It is used for floating-point error analysis. */ +/* */ +/* `splitter' is used to split floating-point numbers into two half- */ +/* length significands for exact multiplication. */ +/* */ +/* I imagine that a highly optimizing compiler might be too smart for its */ +/* own good, and somehow cause this routine to fail, if it pretends that */ +/* floating-point arithmetic is too much like real arithmetic. */ +/* */ +/* Don't change this routine unless you fully understand it. */ +/* */ +/*****************************************************************************/ + +void exactinit() +{ + REAL half; + REAL check, lastcheck; + int every_other; + + every_other = 1; + half = 0.5; + epsilon = 1.0; + splitter = 1.0; + check = 1.0; + /* Repeatedly divide `epsilon' by two until it is too small to add to */ + /* one without causing roundoff. (Also check if the sum is equal to */ + /* the previous sum, for machines that round up instead of using exact */ + /* rounding. Not that these routines will work on such machines anyway. */ + do { + lastcheck = check; + epsilon *= half; + if (every_other) { + splitter *= 2.0; + } + every_other = !every_other; + check = 1.0 + epsilon; + } while ((check != 1.0) && (check != lastcheck)); + splitter += 1.0; + if (verbose > 1) { + printf("Floating point roundoff is of magnitude %.17g\n", epsilon); + printf("Floating point splitter is %.17g\n", splitter); + } + /* Error bounds for orientation and incircle tests. */ + resulterrbound = (3.0 + 8.0 * epsilon) * epsilon; + ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon; + ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon; + ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon; + iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon; + iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon; + iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon; +} + +/*****************************************************************************/ +/* */ +/* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */ +/* components from the output expansion. */ +/* */ +/* Sets h = e + f. See my Robust Predicates paper for details. */ +/* */ +/* If round-to-even is used (as with IEEE 754), maintains the strongly */ +/* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */ +/* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */ +/* properties. */ +/* */ +/*****************************************************************************/ + +int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */ +int elen; +REAL *e; +int flen; +REAL *f; +REAL *h; +{ + REAL Q; + INEXACT REAL Qnew; + INEXACT REAL hh; + INEXACT REAL bvirt; + REAL avirt, bround, around; + int eindex, findex, hindex; + REAL enow, fnow; + + enow = e[0]; + fnow = f[0]; + eindex = findex = 0; + if ((fnow > enow) == (fnow > -enow)) { + Q = enow; + enow = e[++eindex]; + } else { + Q = fnow; + fnow = f[++findex]; + } + hindex = 0; + if ((eindex < elen) && (findex < flen)) { + if ((fnow > enow) == (fnow > -enow)) { + Fast_Two_Sum(enow, Q, Qnew, hh); + enow = e[++eindex]; + } else { + Fast_Two_Sum(fnow, Q, Qnew, hh); + fnow = f[++findex]; + } + Q = Qnew; + if (hh != 0.0) { + h[hindex++] = hh; + } + while ((eindex < elen) && (findex < flen)) { + if ((fnow > enow) == (fnow > -enow)) { + Two_Sum(Q, enow, Qnew, hh); + enow = e[++eindex]; + } else { + Two_Sum(Q, fnow, Qnew, hh); + fnow = f[++findex]; + } + Q = Qnew; + if (hh != 0.0) { + h[hindex++] = hh; + } + } + } + while (eindex < elen) { + Two_Sum(Q, enow, Qnew, hh); + enow = e[++eindex]; + Q = Qnew; + if (hh != 0.0) { + h[hindex++] = hh; + } + } + while (findex < flen) { + Two_Sum(Q, fnow, Qnew, hh); + fnow = f[++findex]; + Q = Qnew; + if (hh != 0.0) { + h[hindex++] = hh; + } + } + if ((Q != 0.0) || (hindex == 0)) { + h[hindex++] = Q; + } + return hindex; +} + +/*****************************************************************************/ +/* */ +/* scale_expansion_zeroelim() Multiply an expansion by a scalar, */ +/* eliminating zero components from the */ +/* output expansion. */ +/* */ +/* Sets h = be. See my Robust Predicates paper for details. */ +/* */ +/* Maintains the nonoverlapping property. If round-to-even is used (as */ +/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */ +/* properties as well. (That is, if e has one of these properties, so */ +/* will h.) */ +/* */ +/*****************************************************************************/ + +int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */ +int elen; +REAL *e; +REAL b; +REAL *h; +{ + INEXACT REAL Q, sum; + REAL hh; + INEXACT REAL product1; + REAL product0; + int eindex, hindex; + REAL enow; + INEXACT REAL bvirt; + REAL avirt, bround, around; + INEXACT REAL c; + INEXACT REAL abig; + REAL ahi, alo, bhi, blo; + REAL err1, err2, err3; + + Split(b, bhi, blo); + Two_Product_Presplit(e[0], b, bhi, blo, Q, hh); + hindex = 0; + if (hh != 0) { + h[hindex++] = hh; + } + for (eindex = 1; eindex < elen; eindex++) { + enow = e[eindex]; + Two_Product_Presplit(enow, b, bhi, blo, product1, product0); + Two_Sum(Q, product0, sum, hh); + if (hh != 0) { + h[hindex++] = hh; + } + Fast_Two_Sum(product1, sum, Q, hh); + if (hh != 0) { + h[hindex++] = hh; + } + } + if ((Q != 0.0) || (hindex == 0)) { + h[hindex++] = Q; + } + return hindex; +} + +/*****************************************************************************/ +/* */ +/* estimate() Produce a one-word estimate of an expansion's value. */ +/* */ +/* See my Robust Predicates paper for details. */ +/* */ +/*****************************************************************************/ + +REAL estimate(elen, e) +int elen; +REAL *e; +{ + REAL Q; + int eindex; + + Q = e[0]; + for (eindex = 1; eindex < elen; eindex++) { + Q += e[eindex]; + } + return Q; +} + +/*****************************************************************************/ +/* */ +/* counterclockwise() Return a positive value if the points pa, pb, and */ +/* pc occur in counterclockwise order; a negative */ +/* value if they occur in clockwise order; and zero */ +/* if they are collinear. The result is also a rough */ +/* approximation of twice the signed area of the */ +/* triangle defined by the three points. */ +/* */ +/* Uses exact arithmetic if necessary to ensure a correct answer. The */ +/* result returned is the determinant of a matrix. This determinant is */ +/* computed adaptively, in the sense that exact arithmetic is used only to */ +/* the degree it is needed to ensure that the returned value has the */ +/* correct sign. Hence, this function is usually quite fast, but will run */ +/* more slowly when the input points are collinear or nearly so. */ +/* */ +/* See my Robust Predicates paper for details. */ +/* */ +/*****************************************************************************/ + +REAL counterclockwiseadapt(pa, pb, pc, detsum) +point pa; +point pb; +point pc; +REAL detsum; +{ + INEXACT REAL acx, acy, bcx, bcy; + REAL acxtail, acytail, bcxtail, bcytail; + INEXACT REAL detleft, detright; + REAL detlefttail, detrighttail; + REAL det, errbound; + REAL B[4], C1[8], C2[12], D[16]; + INEXACT REAL B3; + int C1length, C2length, Dlength; + REAL u[4]; + INEXACT REAL u3; + INEXACT REAL s1, t1; + REAL s0, t0; + + INEXACT REAL bvirt; + REAL avirt, bround, around; + INEXACT REAL c; + INEXACT REAL abig; + REAL ahi, alo, bhi, blo; + REAL err1, err2, err3; + INEXACT REAL _i, _j; + REAL _0; + + acx = (REAL) (pa[0] - pc[0]); + bcx = (REAL) (pb[0] - pc[0]); + acy = (REAL) (pa[1] - pc[1]); + bcy = (REAL) (pb[1] - pc[1]); + + Two_Product(acx, bcy, detleft, detlefttail); + Two_Product(acy, bcx, detright, detrighttail); + + Two_Two_Diff(detleft, detlefttail, detright, detrighttail, + B3, B[2], B[1], B[0]); + B[3] = B3; + + det = estimate(4, B); + errbound = ccwerrboundB * detsum; + if ((det >= errbound) || (-det >= errbound)) { + return det; + } + + Two_Diff_Tail(pa[0], pc[0], acx, acxtail); + Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail); + Two_Diff_Tail(pa[1], pc[1], acy, acytail); + Two_Diff_Tail(pb[1], pc[1], bcy, bcytail); + + if ((acxtail == 0.0) && (acytail == 0.0) + && (bcxtail == 0.0) && (bcytail == 0.0)) { + return det; + } + + errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det); + det += (acx * bcytail + bcy * acxtail) + - (acy * bcxtail + bcx * acytail); + if ((det >= errbound) || (-det >= errbound)) { + return det; + } + + Two_Product(acxtail, bcy, s1, s0); + Two_Product(acytail, bcx, t1, t0); + Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); + u[3] = u3; + C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1); + + Two_Product(acx, bcytail, s1, s0); + Two_Product(acy, bcxtail, t1, t0); + Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); + u[3] = u3; + C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2); + + Two_Product(acxtail, bcytail, s1, s0); + Two_Product(acytail, bcxtail, t1, t0); + Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); + u[3] = u3; + Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D); + + return(D[Dlength - 1]); +} + +REAL counterclockwise(pa, pb, pc) +point pa; +point pb; +point pc; +{ + REAL detleft, detright, det; + REAL detsum, errbound; + + counterclockcount++; + + detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]); + detright = (pa[1] - pc[1]) * (pb[0] - pc[0]); + det = detleft - detright; + + if (noexact) { + return det; + } + + if (detleft > 0.0) { + if (detright <= 0.0) { + return det; + } else { + detsum = detleft + detright; + } + } else if (detleft < 0.0) { + if (detright >= 0.0) { + return det; + } else { + detsum = -detleft - detright; + } + } else { + return det; + } + + errbound = ccwerrboundA * detsum; + if ((det >= errbound) || (-det >= errbound)) { + return det; + } + + return counterclockwiseadapt(pa, pb, pc, detsum); +} + +/*****************************************************************************/ +/* */ +/* incircle() Return a positive value if the point pd lies inside the */ +/* circle passing through pa, pb, and pc; a negative value if */ +/* it lies outside; and zero if the four points are cocircular.*/ +/* The points pa, pb, and pc must be in counterclockwise */ +/* order, or the sign of the result will be reversed. */ +/* */ +/* Uses exact arithmetic if necessary to ensure a correct answer. The */ +/* result returned is the determinant of a matrix. This determinant is */ +/* computed adaptively, in the sense that exact arithmetic is used only to */ +/* the degree it is needed to ensure that the returned value has the */ +/* correct sign. Hence, this function is usually quite fast, but will run */ +/* more slowly when the input points are cocircular or nearly so. */ +/* */ +/* See my Robust Predicates paper for details. */ +/* */ +/*****************************************************************************/ + +REAL incircleadapt(pa, pb, pc, pd, permanent) +point pa; +point pb; +point pc; +point pd; +REAL permanent; +{ + INEXACT REAL adx, bdx, cdx, ady, bdy, cdy; + REAL det, errbound; + + INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1; + REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0; + REAL bc[4], ca[4], ab[4]; + INEXACT REAL bc3, ca3, ab3; + REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32]; + int axbclen, axxbclen, aybclen, ayybclen, alen; + REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32]; + int bxcalen, bxxcalen, bycalen, byycalen, blen; + REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32]; + int cxablen, cxxablen, cyablen, cyyablen, clen; + REAL abdet[64]; + int ablen; + REAL fin1[1152], fin2[1152]; + REAL *finnow, *finother, *finswap; + int finlength; + + REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail; + INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1; + REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0; + REAL aa[4], bb[4], cc[4]; + INEXACT REAL aa3, bb3, cc3; + INEXACT REAL ti1, tj1; + REAL ti0, tj0; + REAL u[4], v[4]; + INEXACT REAL u3, v3; + REAL temp8[8], temp16a[16], temp16b[16], temp16c[16]; + REAL temp32a[32], temp32b[32], temp48[48], temp64[64]; + int temp8len, temp16alen, temp16blen, temp16clen; + int temp32alen, temp32blen, temp48len, temp64len; + REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8]; + int axtbblen, axtcclen, aytbblen, aytcclen; + REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8]; + int bxtaalen, bxtcclen, bytaalen, bytcclen; + REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8]; + int cxtaalen, cxtbblen, cytaalen, cytbblen; + REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8]; + int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen; + REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16]; + int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen; + REAL axtbctt[8], aytbctt[8], bxtcatt[8]; + REAL bytcatt[8], cxtabtt[8], cytabtt[8]; + int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen; + REAL abt[8], bct[8], cat[8]; + int abtlen, bctlen, catlen; + REAL abtt[4], bctt[4], catt[4]; + int abttlen, bcttlen, cattlen; + INEXACT REAL abtt3, bctt3, catt3; + REAL negate; + + INEXACT REAL bvirt; + REAL avirt, bround, around; + INEXACT REAL c; + INEXACT REAL abig; + REAL ahi, alo, bhi, blo; + REAL err1, err2, err3; + INEXACT REAL _i, _j; + REAL _0; + + adx = (REAL) (pa[0] - pd[0]); + bdx = (REAL) (pb[0] - pd[0]); + cdx = (REAL) (pc[0] - pd[0]); + ady = (REAL) (pa[1] - pd[1]); + bdy = (REAL) (pb[1] - pd[1]); + cdy = (REAL) (pc[1] - pd[1]); + + Two_Product(bdx, cdy, bdxcdy1, bdxcdy0); + Two_Product(cdx, bdy, cdxbdy1, cdxbdy0); + Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]); + bc[3] = bc3; + axbclen = scale_expansion_zeroelim(4, bc, adx, axbc); + axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc); + aybclen = scale_expansion_zeroelim(4, bc, ady, aybc); + ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc); + alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet); + + Two_Product(cdx, ady, cdxady1, cdxady0); + Two_Product(adx, cdy, adxcdy1, adxcdy0); + Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]); + ca[3] = ca3; + bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca); + bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca); + bycalen = scale_expansion_zeroelim(4, ca, bdy, byca); + byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca); + blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet); + + Two_Product(adx, bdy, adxbdy1, adxbdy0); + Two_Product(bdx, ady, bdxady1, bdxady0); + Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]); + ab[3] = ab3; + cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab); + cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab); + cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab); + cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab); + clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet); + + ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet); + finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1); + + det = estimate(finlength, fin1); + errbound = iccerrboundB * permanent; + if ((det >= errbound) || (-det >= errbound)) { + return det; + } + + Two_Diff_Tail(pa[0], pd[0], adx, adxtail); + Two_Diff_Tail(pa[1], pd[1], ady, adytail); + Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail); + Two_Diff_Tail(pb[1], pd[1], bdy, bdytail); + Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail); + Two_Diff_Tail(pc[1], pd[1], cdy, cdytail); + if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) + && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) { + return det; + } + + errbound = iccerrboundC * permanent + resulterrbound * Absolute(det); + det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail) + - (bdy * cdxtail + cdx * bdytail)) + + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx)) + + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail) + - (cdy * adxtail + adx * cdytail)) + + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx)) + + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail) + - (ady * bdxtail + bdx * adytail)) + + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx)); + if ((det >= errbound) || (-det >= errbound)) { + return det; + } + + finnow = fin1; + finother = fin2; + + if ((bdxtail != 0.0) || (bdytail != 0.0) + || (cdxtail != 0.0) || (cdytail != 0.0)) { + Square(adx, adxadx1, adxadx0); + Square(ady, adyady1, adyady0); + Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]); + aa[3] = aa3; + } + if ((cdxtail != 0.0) || (cdytail != 0.0) + || (adxtail != 0.0) || (adytail != 0.0)) { + Square(bdx, bdxbdx1, bdxbdx0); + Square(bdy, bdybdy1, bdybdy0); + Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]); + bb[3] = bb3; + } + if ((adxtail != 0.0) || (adytail != 0.0) + || (bdxtail != 0.0) || (bdytail != 0.0)) { + Square(cdx, cdxcdx1, cdxcdx0); + Square(cdy, cdycdy1, cdycdy0); + Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]); + cc[3] = cc3; + } + + if (adxtail != 0.0) { + axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc); + temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx, + temp16a); + + axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc); + temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b); + + axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb); + temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c); + + temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (adytail != 0.0) { + aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc); + temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady, + temp16a); + + aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb); + temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b); + + aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc); + temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c); + + temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (bdxtail != 0.0) { + bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca); + temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx, + temp16a); + + bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa); + temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b); + + bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc); + temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c); + + temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (bdytail != 0.0) { + bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca); + temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy, + temp16a); + + bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc); + temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b); + + bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa); + temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c); + + temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (cdxtail != 0.0) { + cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab); + temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx, + temp16a); + + cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb); + temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b); + + cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa); + temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c); + + temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (cdytail != 0.0) { + cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab); + temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy, + temp16a); + + cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa); + temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b); + + cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb); + temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c); + + temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + + if ((adxtail != 0.0) || (adytail != 0.0)) { + if ((bdxtail != 0.0) || (bdytail != 0.0) + || (cdxtail != 0.0) || (cdytail != 0.0)) { + Two_Product(bdxtail, cdy, ti1, ti0); + Two_Product(bdx, cdytail, tj1, tj0); + Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); + u[3] = u3; + negate = -bdy; + Two_Product(cdxtail, negate, ti1, ti0); + negate = -bdytail; + Two_Product(cdx, negate, tj1, tj0); + Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); + v[3] = v3; + bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct); + + Two_Product(bdxtail, cdytail, ti1, ti0); + Two_Product(cdxtail, bdytail, tj1, tj0); + Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]); + bctt[3] = bctt3; + bcttlen = 4; + } else { + bct[0] = 0.0; + bctlen = 1; + bctt[0] = 0.0; + bcttlen = 1; + } + + if (adxtail != 0.0) { + temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a); + axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct); + temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx, + temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + if (bdytail != 0.0) { + temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8); + temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, + temp16a); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, + temp16a, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (cdytail != 0.0) { + temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8); + temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, + temp16a); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, + temp16a, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + + temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail, + temp32a); + axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt); + temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx, + temp16a); + temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail, + temp16b); + temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32b); + temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, + temp32blen, temp32b, temp64); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, + temp64, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (adytail != 0.0) { + temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a); + aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct); + temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady, + temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + + + temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail, + temp32a); + aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt); + temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady, + temp16a); + temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail, + temp16b); + temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32b); + temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, + temp32blen, temp32b, temp64); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, + temp64, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + } + if ((bdxtail != 0.0) || (bdytail != 0.0)) { + if ((cdxtail != 0.0) || (cdytail != 0.0) + || (adxtail != 0.0) || (adytail != 0.0)) { + Two_Product(cdxtail, ady, ti1, ti0); + Two_Product(cdx, adytail, tj1, tj0); + Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); + u[3] = u3; + negate = -cdy; + Two_Product(adxtail, negate, ti1, ti0); + negate = -cdytail; + Two_Product(adx, negate, tj1, tj0); + Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); + v[3] = v3; + catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat); + + Two_Product(cdxtail, adytail, ti1, ti0); + Two_Product(adxtail, cdytail, tj1, tj0); + Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]); + catt[3] = catt3; + cattlen = 4; + } else { + cat[0] = 0.0; + catlen = 1; + catt[0] = 0.0; + cattlen = 1; + } + + if (bdxtail != 0.0) { + temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a); + bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat); + temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx, + temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + if (cdytail != 0.0) { + temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8); + temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, + temp16a); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, + temp16a, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (adytail != 0.0) { + temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8); + temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, + temp16a); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, + temp16a, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + + temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail, + temp32a); + bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt); + temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx, + temp16a); + temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail, + temp16b); + temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32b); + temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, + temp32blen, temp32b, temp64); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, + temp64, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (bdytail != 0.0) { + temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a); + bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat); + temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy, + temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + + + temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail, + temp32a); + bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt); + temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy, + temp16a); + temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail, + temp16b); + temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32b); + temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, + temp32blen, temp32b, temp64); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, + temp64, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + } + if ((cdxtail != 0.0) || (cdytail != 0.0)) { + if ((adxtail != 0.0) || (adytail != 0.0) + || (bdxtail != 0.0) || (bdytail != 0.0)) { + Two_Product(adxtail, bdy, ti1, ti0); + Two_Product(adx, bdytail, tj1, tj0); + Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); + u[3] = u3; + negate = -ady; + Two_Product(bdxtail, negate, ti1, ti0); + negate = -adytail; + Two_Product(bdx, negate, tj1, tj0); + Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); + v[3] = v3; + abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt); + + Two_Product(adxtail, bdytail, ti1, ti0); + Two_Product(bdxtail, adytail, tj1, tj0); + Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]); + abtt[3] = abtt3; + abttlen = 4; + } else { + abt[0] = 0.0; + abtlen = 1; + abtt[0] = 0.0; + abttlen = 1; + } + + if (cdxtail != 0.0) { + temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a); + cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt); + temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx, + temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + if (adytail != 0.0) { + temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8); + temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, + temp16a); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, + temp16a, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (bdytail != 0.0) { + temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8); + temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, + temp16a); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, + temp16a, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + + temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail, + temp32a); + cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt); + temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx, + temp16a); + temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail, + temp16b); + temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32b); + temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, + temp32blen, temp32b, temp64); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, + temp64, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (cdytail != 0.0) { + temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a); + cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt); + temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy, + temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + + + temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail, + temp32a); + cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt); + temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy, + temp16a); + temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail, + temp16b); + temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32b); + temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, + temp32blen, temp32b, temp64); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, + temp64, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + } + + return finnow[finlength - 1]; +} + +REAL incircle(pa, pb, pc, pd) +point pa; +point pb; +point pc; +point pd; +{ + REAL adx, bdx, cdx, ady, bdy, cdy; + REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady; + REAL alift, blift, clift; + REAL det; + REAL permanent, errbound; + + incirclecount++; + + adx = pa[0] - pd[0]; + bdx = pb[0] - pd[0]; + cdx = pc[0] - pd[0]; + ady = pa[1] - pd[1]; + bdy = pb[1] - pd[1]; + cdy = pc[1] - pd[1]; + + bdxcdy = bdx * cdy; + cdxbdy = cdx * bdy; + alift = adx * adx + ady * ady; + + cdxady = cdx * ady; + adxcdy = adx * cdy; + blift = bdx * bdx + bdy * bdy; + + adxbdy = adx * bdy; + bdxady = bdx * ady; + clift = cdx * cdx + cdy * cdy; + + det = alift * (bdxcdy - cdxbdy) + + blift * (cdxady - adxcdy) + + clift * (adxbdy - bdxady); + + if (noexact) { + return det; + } + + permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift + + (Absolute(cdxady) + Absolute(adxcdy)) * blift + + (Absolute(adxbdy) + Absolute(bdxady)) * clift; + errbound = iccerrboundA * permanent; + if ((det > errbound) || (-det > errbound)) { + return det; + } + + return incircleadapt(pa, pb, pc, pd, permanent); +} + +/** **/ +/** **/ +/********* Determinant evaluation routines end here *********/ + +/*****************************************************************************/ +/* */ +/* triangleinit() Initialize some variables. */ +/* */ +/*****************************************************************************/ + +void triangleinit() +{ + points.maxitems = triangles.maxitems = shelles.maxitems = viri.maxitems = + badsegments.maxitems = badtriangles.maxitems = splaynodes.maxitems = 0l; + points.itembytes = triangles.itembytes = shelles.itembytes = viri.itembytes = + badsegments.itembytes = badtriangles.itembytes = splaynodes.itembytes = 0; + recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */ + samples = 1; /* Point location should take at least one sample. */ + checksegments = 0; /* There are no segments in the triangulation yet. */ + incirclecount = counterclockcount = hyperbolacount = 0; + circumcentercount = circletopcount = 0; + randomseed = 1; + + exactinit(); /* Initialize exact arithmetic constants. */ +} + +/*****************************************************************************/ +/* */ +/* randomnation() Generate a random number between 0 and `choices' - 1. */ +/* */ +/* This is a simple linear congruential random number generator. Hence, it */ +/* is a bad random number generator, but good enough for most randomized */ +/* geometric algorithms. */ +/* */ +/*****************************************************************************/ + +unsigned long randomnation(choices) +unsigned int choices; +{ + randomseed = (randomseed * 1366l + 150889l) % 714025l; + return randomseed / (714025l / choices + 1); +} + +/********* Mesh quality testing routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* checkmesh() Test the mesh for topological consistency. */ +/* */ +/*****************************************************************************/ + +#ifndef REDUCED + +void checkmesh() +{ + struct triedge triangleloop; + struct triedge oppotri, oppooppotri; + point triorg, tridest, triapex; + point oppoorg, oppodest; + int horrors; + int saveexact; + triangle ptr; /* Temporary variable used by sym(). */ + + /* Temporarily turn on exact arithmetic if it's off. */ + saveexact = noexact; + noexact = 0; + if (!quiet) { + printf(" Checking consistency of mesh...\n"); + } + horrors = 0; + /* Run through the list of triangles, checking each one. */ + traversalinit(&triangles); + triangleloop.tri = triangletraverse(); + while (triangleloop.tri != (triangle *) NULL) { + /* Check all three edges of the triangle. */ + for (triangleloop.orient = 0; triangleloop.orient < 3; + triangleloop.orient++) { + org(triangleloop, triorg); + dest(triangleloop, tridest); + if (triangleloop.orient == 0) { /* Only test for inversion once. */ + /* Test if the triangle is flat or inverted. */ + apex(triangleloop, triapex); + if (counterclockwise(triorg, tridest, triapex) <= 0.0) { + printf(" !! !! Inverted "); + printtriangle(&triangleloop); + horrors++; + } + } + /* Find the neighboring triangle on this edge. */ + sym(triangleloop, oppotri); + if (oppotri.tri != dummytri) { + /* Check that the triangle's neighbor knows it's a neighbor. */ + sym(oppotri, oppooppotri); + if ((triangleloop.tri != oppooppotri.tri) + || (triangleloop.orient != oppooppotri.orient)) { + printf(" !! !! Asymmetric triangle-triangle bond:\n"); + if (triangleloop.tri == oppooppotri.tri) { + printf(" (Right triangle, wrong orientation)\n"); + } + printf(" First "); + printtriangle(&triangleloop); + printf(" Second (nonreciprocating) "); + printtriangle(&oppotri); + horrors++; + } + /* Check that both triangles agree on the identities */ + /* of their shared vertices. */ + org(oppotri, oppoorg); + dest(oppotri, oppodest); + if ((triorg != oppodest) || (tridest != oppoorg)) { + printf(" !! !! Mismatched edge coordinates between two triangles:\n" + ); + printf(" First mismatched "); + printtriangle(&triangleloop); + printf(" Second mismatched "); + printtriangle(&oppotri); + horrors++; + } + } + } + triangleloop.tri = triangletraverse(); + } + if (horrors == 0) { + if (!quiet) { + printf(" In my studied opinion, the mesh appears to be consistent.\n"); + } + } else if (horrors == 1) { + printf(" !! !! !! !! Precisely one festering wound discovered.\n"); + } else { + printf(" !! !! !! !! %d abominations witnessed.\n", horrors); + } + /* Restore the status of exact arithmetic. */ + noexact = saveexact; +} + +#endif /* not REDUCED */ + +/*****************************************************************************/ +/* */ +/* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. */ +/* */ +/*****************************************************************************/ + +#ifndef REDUCED + +void checkdelaunay() +{ + struct triedge triangleloop; + struct triedge oppotri; + struct edge opposhelle; + point triorg, tridest, triapex; + point oppoapex; + int shouldbedelaunay; + int horrors; + int saveexact; + triangle ptr; /* Temporary variable used by sym(). */ + shelle sptr; /* Temporary variable used by tspivot(). */ + + /* Temporarily turn on exact arithmetic if it's off. */ + saveexact = noexact; + noexact = 0; + if (!quiet) { + printf(" Checking Delaunay property of mesh...\n"); + } + horrors = 0; + /* Run through the list of triangles, checking each one. */ + traversalinit(&triangles); + triangleloop.tri = triangletraverse(); + while (triangleloop.tri != (triangle *) NULL) { + /* Check all three edges of the triangle. */ + for (triangleloop.orient = 0; triangleloop.orient < 3; + triangleloop.orient++) { + org(triangleloop, triorg); + dest(triangleloop, tridest); + apex(triangleloop, triapex); + sym(triangleloop, oppotri); + apex(oppotri, oppoapex); + /* Only test that the edge is locally Delaunay if there is an */ + /* adjoining triangle whose pointer is larger (to ensure that */ + /* each pair isn't tested twice). */ + shouldbedelaunay = (oppotri.tri != dummytri) + && (triapex != (point) NULL) && (oppoapex != (point) NULL) + && (triangleloop.tri < oppotri.tri); + if (checksegments && shouldbedelaunay) { + /* If a shell edge separates the triangles, then the edge is */ + /* constrained, so no local Delaunay test should be done. */ + tspivot(triangleloop, opposhelle); + if (opposhelle.sh != dummysh){ + shouldbedelaunay = 0; + } + } + if (shouldbedelaunay) { + if (incircle(triorg, tridest, triapex, oppoapex) > 0.0) { + printf(" !! !! Non-Delaunay pair of triangles:\n"); + printf(" First non-Delaunay "); + printtriangle(&triangleloop); + printf(" Second non-Delaunay "); + printtriangle(&oppotri); + horrors++; + } + } + } + triangleloop.tri = triangletraverse(); + } + if (horrors == 0) { + if (!quiet) { + printf( + " By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n"); + } + } else if (horrors == 1) { + printf( + " !! !! !! !! Precisely one terrifying transgression identified.\n"); + } else { + printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors); + } + /* Restore the status of exact arithmetic. */ + noexact = saveexact; +} + +#endif /* not REDUCED */ + +/*****************************************************************************/ +/* */ +/* enqueuebadtri() Add a bad triangle to the end of a queue. */ +/* */ +/* The queue is actually a set of 64 queues. I use multiple queues to give */ +/* priority to smaller angles. I originally implemented a heap, but the */ +/* queues are (to my surprise) much faster. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +void enqueuebadtri(instri, angle, insapex, insorg, insdest) +struct triedge *instri; +REAL angle; +point insapex; +point insorg; +point insdest; +{ + struct badface *newface; + int queuenumber; + + if (verbose > 2) { + printf(" Queueing bad triangle:\n"); + printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", insorg[0], + insorg[1], insdest[0], insdest[1], insapex[0], insapex[1]); + } + /* Allocate space for the bad triangle. */ + newface = (struct badface *) poolalloc(&badtriangles); + triedgecopy(*instri, newface->badfacetri); + newface->key = angle; + newface->faceapex = insapex; + newface->faceorg = insorg; + newface->facedest = insdest; + newface->nextface = (struct badface *) NULL; + /* Determine the appropriate queue to put the bad triangle into. */ + if (angle > 0.6) { + queuenumber = (int) (160.0 * (angle - 0.6)); + if (queuenumber > 63) { + queuenumber = 63; + } + } else { + /* It's not a bad angle; put the triangle in the lowest-priority queue. */ + queuenumber = 0; + } + /* Add the triangle to the end of a queue. */ + *queuetail[queuenumber] = newface; + /* Maintain a pointer to the NULL pointer at the end of the queue. */ + queuetail[queuenumber] = &newface->nextface; +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* dequeuebadtri() Remove a triangle from the front of the queue. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +struct badface *dequeuebadtri() +{ + struct badface *result; + int queuenumber; + + /* Look for a nonempty queue. */ + for (queuenumber = 63; queuenumber >= 0; queuenumber--) { + result = queuefront[queuenumber]; + if (result != (struct badface *) NULL) { + /* Remove the triangle from the queue. */ + queuefront[queuenumber] = result->nextface; + /* Maintain a pointer to the NULL pointer at the end of the queue. */ + if (queuefront[queuenumber] == (struct badface *) NULL) { + queuetail[queuenumber] = &queuefront[queuenumber]; + } + return result; + } + } + return (struct badface *) NULL; +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* checkedge4encroach() Check a segment to see if it is encroached; add */ +/* it to the list if it is. */ +/* */ +/* An encroached segment is an unflippable edge that has a point in its */ +/* diametral circle (that is, it faces an angle greater than 90 degrees). */ +/* This definition is due to Ruppert. */ +/* */ +/* Returns a nonzero value if the edge is encroached. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +int checkedge4encroach(testedge) +struct edge *testedge; +{ + struct triedge neighbortri; + struct edge testsym; + struct edge *badedge; + int addtolist; + int sides; + point eorg, edest, eapex; + triangle ptr; /* Temporary variable used by stpivot(). */ + + addtolist = 0; + sides = 0; + + sorg(*testedge, eorg); + sdest(*testedge, edest); + /* Check one neighbor of the shell edge. */ + stpivot(*testedge, neighbortri); + /* Does the neighbor exist, or is this a boundary edge? */ + if (neighbortri.tri != dummytri) { + sides++; + /* Find a vertex opposite this edge. */ + apex(neighbortri, eapex); + /* Check whether the vertex is inside the diametral circle of the */ + /* shell edge. Pythagoras' Theorem is used to check whether the */ + /* angle at the vertex is greater than 90 degrees. */ + if (eapex[0] * (eorg[0] + edest[0]) + eapex[1] * (eorg[1] + edest[1]) > + eapex[0] * eapex[0] + eorg[0] * edest[0] + + eapex[1] * eapex[1] + eorg[1] * edest[1]) { + addtolist = 1; + } + } + /* Check the other neighbor of the shell edge. */ + ssym(*testedge, testsym); + stpivot(testsym, neighbortri); + /* Does the neighbor exist, or is this a boundary edge? */ + if (neighbortri.tri != dummytri) { + sides++; + /* Find the other vertex opposite this edge. */ + apex(neighbortri, eapex); + /* Check whether the vertex is inside the diametral circle of the */ + /* shell edge. Pythagoras' Theorem is used to check whether the */ + /* angle at the vertex is greater than 90 degrees. */ + if (eapex[0] * (eorg[0] + edest[0]) + + eapex[1] * (eorg[1] + edest[1]) > + eapex[0] * eapex[0] + eorg[0] * edest[0] + + eapex[1] * eapex[1] + eorg[1] * edest[1]) { + addtolist += 2; + } + } + + if (addtolist && (!nobisect || ((nobisect == 1) && (sides == 2)))) { + if (verbose > 2) { + printf(" Queueing encroached segment (%.12g, %.12g) (%.12g, %.12g).\n", + eorg[0], eorg[1], edest[0], edest[1]); + } + /* Add the shell edge to the list of encroached segments. */ + /* Be sure to get the orientation right. */ + badedge = (struct edge *) poolalloc(&badsegments); + if (addtolist == 1) { + shellecopy(*testedge, *badedge); + } else { + shellecopy(testsym, *badedge); + } + } + return addtolist; +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* testtriangle() Test a face for quality measures. */ +/* */ +/* Tests a triangle to see if it satisfies the minimum angle condition and */ +/* the maximum area condition. Triangles that aren't up to spec are added */ +/* to the bad triangle queue. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +void testtriangle(testtri) +struct triedge *testtri; +{ + struct triedge sametesttri; + struct edge edge1, edge2; + point torg, tdest, tapex; + point anglevertex; + REAL dxod, dyod, dxda, dyda, dxao, dyao; + REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2; + REAL apexlen, orglen, destlen; + REAL angle; + REAL area; + shelle sptr; /* Temporary variable used by tspivot(). */ + + org(*testtri, torg); + dest(*testtri, tdest); + apex(*testtri, tapex); + dxod = torg[0] - tdest[0]; + dyod = torg[1] - tdest[1]; + dxda = tdest[0] - tapex[0]; + dyda = tdest[1] - tapex[1]; + dxao = tapex[0] - torg[0]; + dyao = tapex[1] - torg[1]; + dxod2 = dxod * dxod; + dyod2 = dyod * dyod; + dxda2 = dxda * dxda; + dyda2 = dyda * dyda; + dxao2 = dxao * dxao; + dyao2 = dyao * dyao; + /* Find the lengths of the triangle's three edges. */ + apexlen = dxod2 + dyod2; + orglen = dxda2 + dyda2; + destlen = dxao2 + dyao2; + if ((apexlen < orglen) && (apexlen < destlen)) { + /* The edge opposite the apex is shortest. */ + /* Find the square of the cosine of the angle at the apex. */ + angle = dxda * dxao + dyda * dyao; + angle = angle * angle / (orglen * destlen); + anglevertex = tapex; + lnext(*testtri, sametesttri); + tspivot(sametesttri, edge1); + lnextself(sametesttri); + tspivot(sametesttri, edge2); + } else if (orglen < destlen) { + /* The edge opposite the origin is shortest. */ + /* Find the square of the cosine of the angle at the origin. */ + angle = dxod * dxao + dyod * dyao; + angle = angle * angle / (apexlen * destlen); + anglevertex = torg; + tspivot(*testtri, edge1); + lprev(*testtri, sametesttri); + tspivot(sametesttri, edge2); + } else { + /* The edge opposite the destination is shortest. */ + /* Find the square of the cosine of the angle at the destination. */ + angle = dxod * dxda + dyod * dyda; + angle = angle * angle / (apexlen * orglen); + anglevertex = tdest; + tspivot(*testtri, edge1); + lnext(*testtri, sametesttri); + tspivot(sametesttri, edge2); + } + /* Check if both edges that form the angle are segments. */ + if ((edge1.sh != dummysh) && (edge2.sh != dummysh)) { + /* The angle is a segment intersection. */ + if ((angle > 0.9924) && !quiet) { /* Roughly 5 degrees. */ + if (angle > 1.0) { + /* Beware of a floating exception in acos(). */ + angle = 1.0; + } + /* Find the actual angle in degrees, for printing. */ + angle = acos(sqrt(angle)) * (180.0 / PI); + printf( + "Warning: Small angle (%.4g degrees) between segments at point\n", + angle); + printf(" (%.12g, %.12g)\n", anglevertex[0], anglevertex[1]); + } + /* Don't add this bad triangle to the list; there's nothing that */ + /* can be done about a small angle between two segments. */ + angle = 0.0; + } + /* Check whether the angle is smaller than permitted. */ + if (angle > goodangle) { + /* Add this triangle to the list of bad triangles. */ + enqueuebadtri(testtri, angle, tapex, torg, tdest); + return; + } + if (vararea || fixedarea) { + /* Check whether the area is larger than permitted. */ + area = 0.5 * (dxod * dyda - dyod * dxda); + +#if 0 + if ( area < 1.0 / (2.0 * 3600.0 * 3600.0) ) { + /* FGFS ADDITION!!! */ + /* small enough, don't add to list of bad triangles */ + printf("REJECTING TRIANGLE OF AREA %.6g\n", area); + } +#endif + + if (fixedarea && (area > maxarea)) { + /* Add this triangle to the list of bad triangles. */ + enqueuebadtri(testtri, angle, tapex, torg, tdest); + } else if (vararea) { + /* Nonpositive area constraints are treated as unconstrained. */ + if ((area > areabound(*testtri)) && (areabound(*testtri) > 0.0)) { + /* Add this triangle to the list of bad triangles. */ + enqueuebadtri(testtri, angle, tapex, torg, tdest); + } + } + } +} + +#endif /* not CDT_ONLY */ + +/** **/ +/** **/ +/********* Mesh quality testing routines end here *********/ + +/********* Point location routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* makepointmap() Construct a mapping from points to triangles to improve */ +/* the speed of point location for segment insertion. */ +/* */ +/* Traverses all the triangles, and provides each corner of each triangle */ +/* with a pointer to that triangle. Of course, pointers will be */ +/* overwritten by other pointers because (almost) each point is a corner */ +/* of several triangles, but in the end every point will point to some */ +/* triangle that contains it. */ +/* */ +/*****************************************************************************/ + +void makepointmap() +{ + struct triedge triangleloop; + point triorg; + + if (verbose) { + printf(" Constructing mapping from points to triangles.\n"); + } + traversalinit(&triangles); + triangleloop.tri = triangletraverse(); + while (triangleloop.tri != (triangle *) NULL) { + /* Check all three points of the triangle. */ + for (triangleloop.orient = 0; triangleloop.orient < 3; + triangleloop.orient++) { + org(triangleloop, triorg); + setpoint2tri(triorg, encode(triangleloop)); + } + triangleloop.tri = triangletraverse(); + } +} + +/*****************************************************************************/ +/* */ +/* preciselocate() Find a triangle or edge containing a given point. */ +/* */ +/* Begins its search from `searchtri'. It is important that `searchtri' */ +/* be a handle with the property that `searchpoint' is strictly to the left */ +/* of the edge denoted by `searchtri', or is collinear with that edge and */ +/* does not intersect that edge. (In particular, `searchpoint' should not */ +/* be the origin or destination of that edge.) */ +/* */ +/* These conditions are imposed because preciselocate() is normally used in */ +/* one of two situations: */ +/* */ +/* (1) To try to find the location to insert a new point. Normally, we */ +/* know an edge that the point is strictly to the left of. In the */ +/* incremental Delaunay algorithm, that edge is a bounding box edge. */ +/* In Ruppert's Delaunay refinement algorithm for quality meshing, */ +/* that edge is the shortest edge of the triangle whose circumcenter */ +/* is being inserted. */ +/* */ +/* (2) To try to find an existing point. In this case, any edge on the */ +/* convex hull is a good starting edge. The possibility that the */ +/* vertex one seeks is an endpoint of the starting edge must be */ +/* screened out before preciselocate() is called. */ +/* */ +/* On completion, `searchtri' is a triangle that contains `searchpoint'. */ +/* */ +/* This implementation differs from that given by Guibas and Stolfi. It */ +/* walks from triangle to triangle, crossing an edge only if `searchpoint' */ +/* is on the other side of the line containing that edge. After entering */ +/* a triangle, there are two edges by which one can leave that triangle. */ +/* If both edges are valid (`searchpoint' is on the other side of both */ +/* edges), one of the two is chosen by drawing a line perpendicular to */ +/* the entry edge (whose endpoints are `forg' and `fdest') passing through */ +/* `fapex'. Depending on which side of this perpendicular `searchpoint' */ +/* falls on, an exit edge is chosen. */ +/* */ +/* This implementation is empirically faster than the Guibas and Stolfi */ +/* point location routine (which I originally used), which tends to spiral */ +/* in toward its target. */ +/* */ +/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */ +/* is a handle whose origin is the existing vertex. */ +/* */ +/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */ +/* handle whose primary edge is the edge on which the point lies. */ +/* */ +/* Returns INTRIANGLE if the point lies strictly within a triangle. */ +/* `searchtri' is a handle on the triangle that contains the point. */ +/* */ +/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */ +/* handle whose primary edge the point is to the right of. This might */ +/* occur when the circumcenter of a triangle falls just slightly outside */ +/* the mesh due to floating-point roundoff error. It also occurs when */ +/* seeking a hole or region point that a foolish user has placed outside */ +/* the mesh. */ +/* */ +/* WARNING: This routine is designed for convex triangulations, and will */ +/* not generally work after the holes and concavities have been carved. */ +/* However, it can still be used to find the circumcenter of a triangle, as */ +/* long as the search is begun from the triangle in question. */ +/* */ +/*****************************************************************************/ + +enum locateresult preciselocate(searchpoint, searchtri) +point searchpoint; +struct triedge *searchtri; +{ + struct triedge backtracktri; + point forg, fdest, fapex; + point swappoint; + REAL orgorient, destorient; + int moveleft; + triangle ptr; /* Temporary variable used by sym(). */ + + if (verbose > 2) { + printf(" Searching for point (%.12g, %.12g).\n", + searchpoint[0], searchpoint[1]); + } + /* Where are we? */ + org(*searchtri, forg); + dest(*searchtri, fdest); + apex(*searchtri, fapex); + while (1) { + if (verbose > 2) { + printf(" At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", + forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]); + } + /* Check whether the apex is the point we seek. */ + if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) { + lprevself(*searchtri); + return ONVERTEX; + } + /* Does the point lie on the other side of the line defined by the */ + /* triangle edge opposite the triangle's destination? */ + destorient = counterclockwise(forg, fapex, searchpoint); + /* Does the point lie on the other side of the line defined by the */ + /* triangle edge opposite the triangle's origin? */ + orgorient = counterclockwise(fapex, fdest, searchpoint); + if (destorient > 0.0) { + if (orgorient > 0.0) { + /* Move left if the inner product of (fapex - searchpoint) and */ + /* (fdest - forg) is positive. This is equivalent to drawing */ + /* a line perpendicular to the line (forg, fdest) passing */ + /* through `fapex', and determining which side of this line */ + /* `searchpoint' falls on. */ + moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) + + (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0; + } else { + moveleft = 1; + } + } else { + if (orgorient > 0.0) { + moveleft = 0; + } else { + /* The point we seek must be on the boundary of or inside this */ + /* triangle. */ + if (destorient == 0.0) { + lprevself(*searchtri); + return ONEDGE; + } + if (orgorient == 0.0) { + lnextself(*searchtri); + return ONEDGE; + } + return INTRIANGLE; + } + } + + /* Move to another triangle. Leave a trace `backtracktri' in case */ + /* floating-point roundoff or some such bogey causes us to walk */ + /* off a boundary of the triangulation. We can just bounce off */ + /* the boundary as if it were an elastic band. */ + if (moveleft) { + lprev(*searchtri, backtracktri); + fdest = fapex; + } else { + lnext(*searchtri, backtracktri); + forg = fapex; + } + sym(backtracktri, *searchtri); + + /* Check for walking off the edge. */ + if (searchtri->tri == dummytri) { + /* Turn around. */ + triedgecopy(backtracktri, *searchtri); + swappoint = forg; + forg = fdest; + fdest = swappoint; + apex(*searchtri, fapex); + /* Check if the point really is beyond the triangulation boundary. */ + destorient = counterclockwise(forg, fapex, searchpoint); + orgorient = counterclockwise(fapex, fdest, searchpoint); + if ((orgorient < 0.0) && (destorient < 0.0)) { + return OUTSIDE; + } + } else { + apex(*searchtri, fapex); + } + } +} + +/*****************************************************************************/ +/* */ +/* locate() Find a triangle or edge containing a given point. */ +/* */ +/* Searching begins from one of: the input `searchtri', a recently */ +/* encountered triangle `recenttri', or from a triangle chosen from a */ +/* random sample. The choice is made by determining which triangle's */ +/* origin is closest to the point we are searcing for. Normally, */ +/* `searchtri' should be a handle on the convex hull of the triangulation. */ +/* */ +/* Details on the random sampling method can be found in the Mucke, Saias, */ +/* and Zhu paper cited in the header of this code. */ +/* */ +/* On completion, `searchtri' is a triangle that contains `searchpoint'. */ +/* */ +/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */ +/* is a handle whose origin is the existing vertex. */ +/* */ +/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */ +/* handle whose primary edge is the edge on which the point lies. */ +/* */ +/* Returns INTRIANGLE if the point lies strictly within a triangle. */ +/* `searchtri' is a handle on the triangle that contains the point. */ +/* */ +/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */ +/* handle whose primary edge the point is to the right of. This might */ +/* occur when the circumcenter of a triangle falls just slightly outside */ +/* the mesh due to floating-point roundoff error. It also occurs when */ +/* seeking a hole or region point that a foolish user has placed outside */ +/* the mesh. */ +/* */ +/* WARNING: This routine is designed for convex triangulations, and will */ +/* not generally work after the holes and concavities have been carved. */ +/* */ +/*****************************************************************************/ + +enum locateresult locate(searchpoint, searchtri) +point searchpoint; +struct triedge *searchtri; +{ + VOID **sampleblock; + triangle *firsttri; + struct triedge sampletri; + point torg, tdest; + unsigned long alignptr; + REAL searchdist, dist; + REAL ahead; + long sampleblocks, samplesperblock, samplenum; + long triblocks; + long i, j; + triangle ptr; /* Temporary variable used by sym(). */ + + if (verbose > 2) { + printf(" Randomly sampling for a triangle near point (%.12g, %.12g).\n", + searchpoint[0], searchpoint[1]); + } + /* Record the distance from the suggested starting triangle to the */ + /* point we seek. */ + org(*searchtri, torg); + searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + + (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); + if (verbose > 2) { + printf(" Boundary triangle has origin (%.12g, %.12g).\n", + torg[0], torg[1]); + } + + /* If a recently encountered triangle has been recorded and has not been */ + /* deallocated, test it as a good starting point. */ + if (recenttri.tri != (triangle *) NULL) { + if (recenttri.tri[3] != (triangle) NULL) { + org(recenttri, torg); + if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) { + triedgecopy(recenttri, *searchtri); + return ONVERTEX; + } + dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + + (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); + if (dist < searchdist) { + triedgecopy(recenttri, *searchtri); + searchdist = dist; + if (verbose > 2) { + printf(" Choosing recent triangle with origin (%.12g, %.12g).\n", + torg[0], torg[1]); + } + } + } + } + + /* The number of random samples taken is proportional to the cube root of */ + /* the number of triangles in the mesh. The next bit of code assumes */ + /* that the number of triangles increases monotonically. */ + while (SAMPLEFACTOR * samples * samples * samples < triangles.items) { + samples++; + } + triblocks = (triangles.maxitems + TRIPERBLOCK - 1) / TRIPERBLOCK; + samplesperblock = 1 + (samples / triblocks); + sampleblocks = samples / samplesperblock; + sampleblock = triangles.firstblock; + sampletri.orient = 0; + for (i = 0; i < sampleblocks; i++) { + alignptr = (unsigned long) (sampleblock + 1); + firsttri = (triangle *) (alignptr + (unsigned long) triangles.alignbytes + - (alignptr % (unsigned long) triangles.alignbytes)); + for (j = 0; j < samplesperblock; j++) { + if (i == triblocks - 1) { + samplenum = randomnation((int) + (triangles.maxitems - (i * TRIPERBLOCK))); + } else { + samplenum = randomnation(TRIPERBLOCK); + } + sampletri.tri = (triangle *) + (firsttri + (samplenum * triangles.itemwords)); + if (sampletri.tri[3] != (triangle) NULL) { + org(sampletri, torg); + dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + + (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); + if (dist < searchdist) { + triedgecopy(sampletri, *searchtri); + searchdist = dist; + if (verbose > 2) { + printf(" Choosing triangle with origin (%.12g, %.12g).\n", + torg[0], torg[1]); + } + } + } + } + sampleblock = (VOID **) *sampleblock; + } + /* Where are we? */ + org(*searchtri, torg); + dest(*searchtri, tdest); + /* Check the starting triangle's vertices. */ + if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) { + return ONVERTEX; + } + if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) { + lnextself(*searchtri); + return ONVERTEX; + } + /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */ + ahead = counterclockwise(torg, tdest, searchpoint); + if (ahead < 0.0) { + /* Turn around so that `searchpoint' is to the left of the */ + /* edge specified by `searchtri'. */ + symself(*searchtri); + } else if (ahead == 0.0) { + /* Check if `searchpoint' is between `torg' and `tdest'. */ + if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) + && ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) { + return ONEDGE; + } + } + return preciselocate(searchpoint, searchtri); +} + +/** **/ +/** **/ +/********* Point location routines end here *********/ + +/********* Mesh transformation routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* insertshelle() Create a new shell edge and insert it between two */ +/* triangles. */ +/* */ +/* The new shell edge is inserted at the edge described by the handle */ +/* `tri'. Its vertices are properly initialized. The marker `shellemark' */ +/* is applied to the shell edge and, if appropriate, its vertices. */ +/* */ +/*****************************************************************************/ + +void insertshelle(tri, shellemark) +struct triedge *tri; /* Edge at which to insert the new shell edge. */ +int shellemark; /* Marker for the new shell edge. */ +{ + struct triedge oppotri; + struct edge newshelle; + point triorg, tridest; + triangle ptr; /* Temporary variable used by sym(). */ + shelle sptr; /* Temporary variable used by tspivot(). */ + + /* Mark points if possible. */ + org(*tri, triorg); + dest(*tri, tridest); + if (pointmark(triorg) == 0) { + setpointmark(triorg, shellemark); + } + if (pointmark(tridest) == 0) { + setpointmark(tridest, shellemark); + } + /* Check if there's already a shell edge here. */ + tspivot(*tri, newshelle); + if (newshelle.sh == dummysh) { + /* Make new shell edge and initialize its vertices. */ + makeshelle(&newshelle); + setsorg(newshelle, tridest); + setsdest(newshelle, triorg); + /* Bond new shell edge to the two triangles it is sandwiched between. */ + /* Note that the facing triangle `oppotri' might be equal to */ + /* `dummytri' (outer space), but the new shell edge is bonded to it */ + /* all the same. */ + tsbond(*tri, newshelle); + sym(*tri, oppotri); + ssymself(newshelle); + tsbond(oppotri, newshelle); + setmark(newshelle, shellemark); + if (verbose > 2) { + printf(" Inserting new "); + printshelle(&newshelle); + } + } else { + if (mark(newshelle) == 0) { + setmark(newshelle, shellemark); + } + } +} + +/*****************************************************************************/ +/* */ +/* Terminology */ +/* */ +/* A "local transformation" replaces a small set of triangles with another */ +/* set of triangles. This may or may not involve inserting or deleting a */ +/* point. */ +/* */ +/* The term "casing" is used to describe the set of triangles that are */ +/* attached to the triangles being transformed, but are not transformed */ +/* themselves. Think of the casing as a fixed hollow structure inside */ +/* which all the action happens. A "casing" is only defined relative to */ +/* a single transformation; each occurrence of a transformation will */ +/* involve a different casing. */ +/* */ +/* A "shell" is similar to a "casing". The term "shell" describes the set */ +/* of shell edges (if any) that are attached to the triangles being */ +/* transformed. However, I sometimes use "shell" to refer to a single */ +/* shell edge, so don't get confused. */ +/* */ +/*****************************************************************************/ + +/*****************************************************************************/ +/* */ +/* flip() Transform two triangles to two different triangles by flipping */ +/* an edge within a quadrilateral. */ +/* */ +/* Imagine the original triangles, abc and bad, oriented so that the */ +/* shared edge ab lies in a horizontal plane, with the point b on the left */ +/* and the point a on the right. The point c lies below the edge, and the */ +/* point d lies above the edge. The `flipedge' handle holds the edge ab */ +/* of triangle abc, and is directed left, from vertex a to vertex b. */ +/* */ +/* The triangles abc and bad are deleted and replaced by the triangles cdb */ +/* and dca. The triangles that represent abc and bad are NOT deallocated; */ +/* they are reused for dca and cdb, respectively. Hence, any handles that */ +/* may have held the original triangles are still valid, although not */ +/* directed as they were before. */ +/* */ +/* Upon completion of this routine, the `flipedge' handle holds the edge */ +/* dc of triangle dca, and is directed down, from vertex d to vertex c. */ +/* (Hence, the two triangles have rotated counterclockwise.) */ +/* */ +/* WARNING: This transformation is geometrically valid only if the */ +/* quadrilateral adbc is convex. Furthermore, this transformation is */ +/* valid only if there is not a shell edge between the triangles abc and */ +/* bad. This routine does not check either of these preconditions, and */ +/* it is the responsibility of the calling routine to ensure that they are */ +/* met. If they are not, the streets shall be filled with wailing and */ +/* gnashing of teeth. */ +/* */ +/*****************************************************************************/ + +void flip(flipedge) +struct triedge *flipedge; /* Handle for the triangle abc. */ +{ + struct triedge botleft, botright; + struct triedge topleft, topright; + struct triedge top; + struct triedge botlcasing, botrcasing; + struct triedge toplcasing, toprcasing; + struct edge botlshelle, botrshelle; + struct edge toplshelle, toprshelle; + point leftpoint, rightpoint, botpoint; + point farpoint; + triangle ptr; /* Temporary variable used by sym(). */ + shelle sptr; /* Temporary variable used by tspivot(). */ + + /* Identify the vertices of the quadrilateral. */ + org(*flipedge, rightpoint); + dest(*flipedge, leftpoint); + apex(*flipedge, botpoint); + sym(*flipedge, top); +#ifdef SELF_CHECK + if (top.tri == dummytri) { + printf("Internal error in flip(): Attempt to flip on boundary.\n"); + lnextself(*flipedge); + return; + } + if (checksegments) { + tspivot(*flipedge, toplshelle); + if (toplshelle.sh != dummysh) { + printf("Internal error in flip(): Attempt to flip a segment.\n"); + lnextself(*flipedge); + return; + } + } +#endif /* SELF_CHECK */ + apex(top, farpoint); + + /* Identify the casing of the quadrilateral. */ + lprev(top, topleft); + sym(topleft, toplcasing); + lnext(top, topright); + sym(topright, toprcasing); + lnext(*flipedge, botleft); + sym(botleft, botlcasing); + lprev(*flipedge, botright); + sym(botright, botrcasing); + /* Rotate the quadrilateral one-quarter turn counterclockwise. */ + bond(topleft, botlcasing); + bond(botleft, botrcasing); + bond(botright, toprcasing); + bond(topright, toplcasing); + + if (checksegments) { + /* Check for shell edges and rebond them to the quadrilateral. */ + tspivot(topleft, toplshelle); + tspivot(botleft, botlshelle); + tspivot(botright, botrshelle); + tspivot(topright, toprshelle); + if (toplshelle.sh == dummysh) { + tsdissolve(topright); + } else { + tsbond(topright, toplshelle); + } + if (botlshelle.sh == dummysh) { + tsdissolve(topleft); + } else { + tsbond(topleft, botlshelle); + } + if (botrshelle.sh == dummysh) { + tsdissolve(botleft); + } else { + tsbond(botleft, botrshelle); + } + if (toprshelle.sh == dummysh) { + tsdissolve(botright); + } else { + tsbond(botright, toprshelle); + } + } + + /* New point assignments for the rotated quadrilateral. */ + setorg(*flipedge, farpoint); + setdest(*flipedge, botpoint); + setapex(*flipedge, rightpoint); + setorg(top, botpoint); + setdest(top, farpoint); + setapex(top, leftpoint); + if (verbose > 2) { + printf(" Edge flip results in left "); + lnextself(topleft); + printtriangle(&topleft); + printf(" and right "); + printtriangle(flipedge); + } +} + +/*****************************************************************************/ +/* */ +/* insertsite() Insert a vertex into a Delaunay triangulation, */ +/* performing flips as necessary to maintain the Delaunay */ +/* property. */ +/* */ +/* The point `insertpoint' is located. If `searchtri.tri' is not NULL, */ +/* the search for the containing triangle begins from `searchtri'. If */ +/* `searchtri.tri' is NULL, a full point location procedure is called. */ +/* If `insertpoint' is found inside a triangle, the triangle is split into */ +/* three; if `insertpoint' lies on an edge, the edge is split in two, */ +/* thereby splitting the two adjacent triangles into four. Edge flips are */ +/* used to restore the Delaunay property. If `insertpoint' lies on an */ +/* existing vertex, no action is taken, and the value DUPLICATEPOINT is */ +/* returned. On return, `searchtri' is set to a handle whose origin is the */ +/* existing vertex. */ +/* */ +/* Normally, the parameter `splitedge' is set to NULL, implying that no */ +/* segment should be split. In this case, if `insertpoint' is found to */ +/* lie on a segment, no action is taken, and the value VIOLATINGPOINT is */ +/* returned. On return, `searchtri' is set to a handle whose primary edge */ +/* is the violated segment. */ +/* */ +/* If the calling routine wishes to split a segment by inserting a point in */ +/* it, the parameter `splitedge' should be that segment. In this case, */ +/* `searchtri' MUST be the triangle handle reached by pivoting from that */ +/* segment; no point location is done. */ +/* */ +/* `segmentflaws' and `triflaws' are flags that indicate whether or not */ +/* there should be checks for the creation of encroached segments or bad */ +/* quality faces. If a newly inserted point encroaches upon segments, */ +/* these segments are added to the list of segments to be split if */ +/* `segmentflaws' is set. If bad triangles are created, these are added */ +/* to the queue if `triflaws' is set. */ +/* */ +/* If a duplicate point or violated segment does not prevent the point */ +/* from being inserted, the return value will be ENCROACHINGPOINT if the */ +/* point encroaches upon a segment (and checking is enabled), or */ +/* SUCCESSFULPOINT otherwise. In either case, `searchtri' is set to a */ +/* handle whose origin is the newly inserted vertex. */ +/* */ +/* insertsite() does not use flip() for reasons of speed; some */ +/* information can be reused from edge flip to edge flip, like the */ +/* locations of shell edges. */ +/* */ +/*****************************************************************************/ + +enum insertsiteresult insertsite(insertpoint, searchtri, splitedge, + segmentflaws, triflaws) +point insertpoint; +struct triedge *searchtri; +struct edge *splitedge; +int segmentflaws; +int triflaws; +{ + struct triedge horiz; + struct triedge top; + struct triedge botleft, botright; + struct triedge topleft, topright; + struct triedge newbotleft, newbotright; + struct triedge newtopright; + struct triedge botlcasing, botrcasing; + struct triedge toplcasing, toprcasing; + struct triedge testtri; + struct edge botlshelle, botrshelle; + struct edge toplshelle, toprshelle; + struct edge brokenshelle; + struct edge checkshelle; + struct edge rightedge; + struct edge newedge; + struct edge *encroached; + point first; + point leftpoint, rightpoint, botpoint, toppoint, farpoint; + REAL attrib; + REAL area; + enum insertsiteresult success; + enum locateresult intersect; + int doflip; + int mirrorflag; + int i; + triangle ptr; /* Temporary variable used by sym(). */ + shelle sptr; /* Temporary variable used by spivot() and tspivot(). */ + + if (verbose > 1) { + printf(" Inserting (%.12g, %.12g).\n", insertpoint[0], insertpoint[1]); + } + if (splitedge == (struct edge *) NULL) { + /* Find the location of the point to be inserted. Check if a good */ + /* starting triangle has already been provided by the caller. */ + if (searchtri->tri == (triangle *) NULL) { + /* Find a boundary triangle. */ + horiz.tri = dummytri; + horiz.orient = 0; + symself(horiz); + /* Search for a triangle containing `insertpoint'. */ + intersect = locate(insertpoint, &horiz); + } else { + /* Start searching from the triangle provided by the caller. */ + triedgecopy(*searchtri, horiz); + intersect = preciselocate(insertpoint, &horiz); + } + } else { + /* The calling routine provides the edge in which the point is inserted. */ + triedgecopy(*searchtri, horiz); + intersect = ONEDGE; + } + if (intersect == ONVERTEX) { + /* There's already a vertex there. Return in `searchtri' a triangle */ + /* whose origin is the existing vertex. */ + triedgecopy(horiz, *searchtri); + triedgecopy(horiz, recenttri); + return DUPLICATEPOINT; + } + if ((intersect == ONEDGE) || (intersect == OUTSIDE)) { + /* The vertex falls on an edge or boundary. */ + if (checksegments && (splitedge == (struct edge *) NULL)) { + /* Check whether the vertex falls on a shell edge. */ + tspivot(horiz, brokenshelle); + if (brokenshelle.sh != dummysh) { + /* The vertex falls on a shell edge. */ + if (segmentflaws) { + if (nobisect == 0) { + /* Add the shell edge to the list of encroached segments. */ + encroached = (struct edge *) poolalloc(&badsegments); + shellecopy(brokenshelle, *encroached); + } else if ((nobisect == 1) && (intersect == ONEDGE)) { + /* This segment may be split only if it is an internal boundary. */ + sym(horiz, testtri); + if (testtri.tri != dummytri) { + /* Add the shell edge to the list of encroached segments. */ + encroached = (struct edge *) poolalloc(&badsegments); + shellecopy(brokenshelle, *encroached); + } + } + } + /* Return a handle whose primary edge contains the point, */ + /* which has not been inserted. */ + triedgecopy(horiz, *searchtri); + triedgecopy(horiz, recenttri); + return VIOLATINGPOINT; + } + } + /* Insert the point on an edge, dividing one triangle into two (if */ + /* the edge lies on a boundary) or two triangles into four. */ + lprev(horiz, botright); + sym(botright, botrcasing); + sym(horiz, topright); + /* Is there a second triangle? (Or does this edge lie on a boundary?) */ + mirrorflag = topright.tri != dummytri; + if (mirrorflag) { + lnextself(topright); + sym(topright, toprcasing); + maketriangle(&newtopright); + } else { + /* Splitting the boundary edge increases the number of boundary edges. */ + hullsize++; + } + maketriangle(&newbotright); + + /* Set the vertices of changed and new triangles. */ + org(horiz, rightpoint); + dest(horiz, leftpoint); + apex(horiz, botpoint); + setorg(newbotright, botpoint); + setdest(newbotright, rightpoint); + setapex(newbotright, insertpoint); + setorg(horiz, insertpoint); + for (i = 0; i < eextras; i++) { + /* Set the element attributes of a new triangle. */ + setelemattribute(newbotright, i, elemattribute(botright, i)); + } + if (vararea) { + /* Set the area constraint of a new triangle. */ + setareabound(newbotright, areabound(botright)); + } + if (mirrorflag) { + dest(topright, toppoint); + setorg(newtopright, rightpoint); + setdest(newtopright, toppoint); + setapex(newtopright, insertpoint); + setorg(topright, insertpoint); + for (i = 0; i < eextras; i++) { + /* Set the element attributes of another new triangle. */ + setelemattribute(newtopright, i, elemattribute(topright, i)); + } + if (vararea) { + /* Set the area constraint of another new triangle. */ + setareabound(newtopright, areabound(topright)); + } + } + + /* There may be shell edges that need to be bonded */ + /* to the new triangle(s). */ + if (checksegments) { + tspivot(botright, botrshelle); + if (botrshelle.sh != dummysh) { + tsdissolve(botright); + tsbond(newbotright, botrshelle); + } + if (mirrorflag) { + tspivot(topright, toprshelle); + if (toprshelle.sh != dummysh) { + tsdissolve(topright); + tsbond(newtopright, toprshelle); + } + } + } + + /* Bond the new triangle(s) to the surrounding triangles. */ + bond(newbotright, botrcasing); + lprevself(newbotright); + bond(newbotright, botright); + lprevself(newbotright); + if (mirrorflag) { + bond(newtopright, toprcasing); + lnextself(newtopright); + bond(newtopright, topright); + lnextself(newtopright); + bond(newtopright, newbotright); + } + + if (splitedge != (struct edge *) NULL) { + /* Split the shell edge into two. */ + setsdest(*splitedge, insertpoint); + ssymself(*splitedge); + spivot(*splitedge, rightedge); + insertshelle(&newbotright, mark(*splitedge)); + tspivot(newbotright, newedge); + sbond(*splitedge, newedge); + ssymself(newedge); + sbond(newedge, rightedge); + ssymself(*splitedge); + } + +#ifdef SELF_CHECK + if (counterclockwise(rightpoint, leftpoint, botpoint) < 0.0) { + printf("Internal error in insertsite():\n"); + printf(" Clockwise triangle prior to edge point insertion (bottom).\n"); + } + if (mirrorflag) { + if (counterclockwise(leftpoint, rightpoint, toppoint) < 0.0) { + printf("Internal error in insertsite():\n"); + printf(" Clockwise triangle prior to edge point insertion (top).\n"); + } + if (counterclockwise(rightpoint, toppoint, insertpoint) < 0.0) { + printf("Internal error in insertsite():\n"); + printf(" Clockwise triangle after edge point insertion (top right).\n" + ); + } + if (counterclockwise(toppoint, leftpoint, insertpoint) < 0.0) { + printf("Internal error in insertsite():\n"); + printf(" Clockwise triangle after edge point insertion (top left).\n" + ); + } + } + if (counterclockwise(leftpoint, botpoint, insertpoint) < 0.0) { + printf("Internal error in insertsite():\n"); + printf(" Clockwise triangle after edge point insertion (bottom left).\n" + ); + } + if (counterclockwise(botpoint, rightpoint, insertpoint) < 0.0) { + printf("Internal error in insertsite():\n"); + printf( + " Clockwise triangle after edge point insertion (bottom right).\n"); + } +#endif /* SELF_CHECK */ + if (verbose > 2) { + printf(" Updating bottom left "); + printtriangle(&botright); + if (mirrorflag) { + printf(" Updating top left "); + printtriangle(&topright); + printf(" Creating top right "); + printtriangle(&newtopright); + } + printf(" Creating bottom right "); + printtriangle(&newbotright); + } + + /* Position `horiz' on the first edge to check for */ + /* the Delaunay property. */ + lnextself(horiz); + } else { + /* Insert the point in a triangle, splitting it into three. */ + lnext(horiz, botleft); + lprev(horiz, botright); + sym(botleft, botlcasing); + sym(botright, botrcasing); + maketriangle(&newbotleft); + maketriangle(&newbotright); + + /* Set the vertices of changed and new triangles. */ + org(horiz, rightpoint); + dest(horiz, leftpoint); + apex(horiz, botpoint); + setorg(newbotleft, leftpoint); + setdest(newbotleft, botpoint); + setapex(newbotleft, insertpoint); + setorg(newbotright, botpoint); + setdest(newbotright, rightpoint); + setapex(newbotright, insertpoint); + setapex(horiz, insertpoint); + for (i = 0; i < eextras; i++) { + /* Set the element attributes of the new triangles. */ + attrib = elemattribute(horiz, i); + setelemattribute(newbotleft, i, attrib); + setelemattribute(newbotright, i, attrib); + } + if (vararea) { + /* Set the area constraint of the new triangles. */ + area = areabound(horiz); + setareabound(newbotleft, area); + setareabound(newbotright, area); + } + + /* There may be shell edges that need to be bonded */ + /* to the new triangles. */ + if (checksegments) { + tspivot(botleft, botlshelle); + if (botlshelle.sh != dummysh) { + tsdissolve(botleft); + tsbond(newbotleft, botlshelle); + } + tspivot(botright, botrshelle); + if (botrshelle.sh != dummysh) { + tsdissolve(botright); + tsbond(newbotright, botrshelle); + } + } + + /* Bond the new triangles to the surrounding triangles. */ + bond(newbotleft, botlcasing); + bond(newbotright, botrcasing); + lnextself(newbotleft); + lprevself(newbotright); + bond(newbotleft, newbotright); + lnextself(newbotleft); + bond(botleft, newbotleft); + lprevself(newbotright); + bond(botright, newbotright); + +#ifdef SELF_CHECK + if (counterclockwise(rightpoint, leftpoint, botpoint) < 0.0) { + printf("Internal error in insertsite():\n"); + printf(" Clockwise triangle prior to point insertion.\n"); + } + if (counterclockwise(rightpoint, leftpoint, insertpoint) < 0.0) { + printf("Internal error in insertsite():\n"); + printf(" Clockwise triangle after point insertion (top).\n"); + } + if (counterclockwise(leftpoint, botpoint, insertpoint) < 0.0) { + printf("Internal error in insertsite():\n"); + printf(" Clockwise triangle after point insertion (left).\n"); + } + if (counterclockwise(botpoint, rightpoint, insertpoint) < 0.0) { + printf("Internal error in insertsite():\n"); + printf(" Clockwise triangle after point insertion (right).\n"); + } +#endif /* SELF_CHECK */ + if (verbose > 2) { + printf(" Updating top "); + printtriangle(&horiz); + printf(" Creating left "); + printtriangle(&newbotleft); + printf(" Creating right "); + printtriangle(&newbotright); + } + } + + /* The insertion is successful by default, unless an encroached */ + /* edge is found. */ + success = SUCCESSFULPOINT; + /* Circle around the newly inserted vertex, checking each edge opposite */ + /* it for the Delaunay property. Non-Delaunay edges are flipped. */ + /* `horiz' is always the edge being checked. `first' marks where to */ + /* stop circling. */ + org(horiz, first); + rightpoint = first; + dest(horiz, leftpoint); + /* Circle until finished. */ + while (1) { + /* By default, the edge will be flipped. */ + doflip = 1; + if (checksegments) { + /* Check for a segment, which cannot be flipped. */ + tspivot(horiz, checkshelle); + if (checkshelle.sh != dummysh) { + /* The edge is a segment and cannot be flipped. */ + doflip = 0; +#ifndef CDT_ONLY + if (segmentflaws) { + /* Does the new point encroach upon this segment? */ + if (checkedge4encroach(&checkshelle)) { + success = ENCROACHINGPOINT; + } + } +#endif /* not CDT_ONLY */ + } + } + if (doflip) { + /* Check if the edge is a boundary edge. */ + sym(horiz, top); + if (top.tri == dummytri) { + /* The edge is a boundary edge and cannot be flipped. */ + doflip = 0; + } else { + /* Find the point on the other side of the edge. */ + apex(top, farpoint); + /* In the incremental Delaunay triangulation algorithm, any of */ + /* `leftpoint', `rightpoint', and `farpoint' could be vertices */ + /* of the triangular bounding box. These vertices must be */ + /* treated as if they are infinitely distant, even though their */ + /* "coordinates" are not. */ + if ((leftpoint == infpoint1) || (leftpoint == infpoint2) + || (leftpoint == infpoint3)) { + /* `leftpoint' is infinitely distant. Check the convexity of */ + /* the boundary of the triangulation. 'farpoint' might be */ + /* infinite as well, but trust me, this same condition */ + /* should be applied. */ + doflip = counterclockwise(insertpoint, rightpoint, farpoint) > 0.0; + } else if ((rightpoint == infpoint1) || (rightpoint == infpoint2) + || (rightpoint == infpoint3)) { + /* `rightpoint' is infinitely distant. Check the convexity of */ + /* the boundary of the triangulation. 'farpoint' might be */ + /* infinite as well, but trust me, this same condition */ + /* should be applied. */ + doflip = counterclockwise(farpoint, leftpoint, insertpoint) > 0.0; + } else if ((farpoint == infpoint1) || (farpoint == infpoint2) + || (farpoint == infpoint3)) { + /* `farpoint' is infinitely distant and cannot be inside */ + /* the circumcircle of the triangle `horiz'. */ + doflip = 0; + } else { + /* Test whether the edge is locally Delaunay. */ + doflip = incircle(leftpoint, insertpoint, rightpoint, farpoint) + > 0.0; + } + if (doflip) { + /* We made it! Flip the edge `horiz' by rotating its containing */ + /* quadrilateral (the two triangles adjacent to `horiz'). */ + /* Identify the casing of the quadrilateral. */ + lprev(top, topleft); + sym(topleft, toplcasing); + lnext(top, topright); + sym(topright, toprcasing); + lnext(horiz, botleft); + sym(botleft, botlcasing); + lprev(horiz, botright); + sym(botright, botrcasing); + /* Rotate the quadrilateral one-quarter turn counterclockwise. */ + bond(topleft, botlcasing); + bond(botleft, botrcasing); + bond(botright, toprcasing); + bond(topright, toplcasing); + if (checksegments) { + /* Check for shell edges and rebond them to the quadrilateral. */ + tspivot(topleft, toplshelle); + tspivot(botleft, botlshelle); + tspivot(botright, botrshelle); + tspivot(topright, toprshelle); + if (toplshelle.sh == dummysh) { + tsdissolve(topright); + } else { + tsbond(topright, toplshelle); + } + if (botlshelle.sh == dummysh) { + tsdissolve(topleft); + } else { + tsbond(topleft, botlshelle); + } + if (botrshelle.sh == dummysh) { + tsdissolve(botleft); + } else { + tsbond(botleft, botrshelle); + } + if (toprshelle.sh == dummysh) { + tsdissolve(botright); + } else { + tsbond(botright, toprshelle); + } + } + /* New point assignments for the rotated quadrilateral. */ + setorg(horiz, farpoint); + setdest(horiz, insertpoint); + setapex(horiz, rightpoint); + setorg(top, insertpoint); + setdest(top, farpoint); + setapex(top, leftpoint); + for (i = 0; i < eextras; i++) { + /* Take the average of the two triangles' attributes. */ + attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i)); + setelemattribute(top, i, attrib); + setelemattribute(horiz, i, attrib); + } + if (vararea) { + if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) { + area = -1.0; + } else { + /* Take the average of the two triangles' area constraints. */ + /* This prevents small area constraints from migrating a */ + /* long, long way from their original location due to flips. */ + area = 0.5 * (areabound(top) + areabound(horiz)); + } + setareabound(top, area); + setareabound(horiz, area); + } +#ifdef SELF_CHECK + if (insertpoint != (point) NULL) { + if (counterclockwise(leftpoint, insertpoint, rightpoint) < 0.0) { + printf("Internal error in insertsite():\n"); + printf(" Clockwise triangle prior to edge flip (bottom).\n"); + } + /* The following test has been removed because constrainededge() */ + /* sometimes generates inverted triangles that insertsite() */ + /* removes. */ +/* + if (counterclockwise(rightpoint, farpoint, leftpoint) < 0.0) { + printf("Internal error in insertsite():\n"); + printf(" Clockwise triangle prior to edge flip (top).\n"); + } +*/ + if (counterclockwise(farpoint, leftpoint, insertpoint) < 0.0) { + printf("Internal error in insertsite():\n"); + printf(" Clockwise triangle after edge flip (left).\n"); + } + if (counterclockwise(insertpoint, rightpoint, farpoint) < 0.0) { + printf("Internal error in insertsite():\n"); + printf(" Clockwise triangle after edge flip (right).\n"); + } + } +#endif /* SELF_CHECK */ + if (verbose > 2) { + printf(" Edge flip results in left "); + lnextself(topleft); + printtriangle(&topleft); + printf(" and right "); + printtriangle(&horiz); + } + /* On the next iterations, consider the two edges that were */ + /* exposed (this is, are now visible to the newly inserted */ + /* point) by the edge flip. */ + lprevself(horiz); + leftpoint = farpoint; + } + } + } + if (!doflip) { + /* The handle `horiz' is accepted as locally Delaunay. */ +#ifndef CDT_ONLY + if (triflaws) { + /* Check the triangle `horiz' for quality. */ + testtriangle(&horiz); + } +#endif /* not CDT_ONLY */ + /* Look for the next edge around the newly inserted point. */ + lnextself(horiz); + sym(horiz, testtri); + /* Check for finishing a complete revolution about the new point, or */ + /* falling off the edge of the triangulation. The latter will */ + /* happen when a point is inserted at a boundary. */ + if ((leftpoint == first) || (testtri.tri == dummytri)) { + /* We're done. Return a triangle whose origin is the new point. */ + lnext(horiz, *searchtri); + lnext(horiz, recenttri); + return success; + } + /* Finish finding the next edge around the newly inserted point. */ + lnext(testtri, horiz); + rightpoint = leftpoint; + dest(horiz, leftpoint); + } + } +} + +/*****************************************************************************/ +/* */ +/* triangulatepolygon() Find the Delaunay triangulation of a polygon that */ +/* has a certain "nice" shape. This includes the */ +/* polygons that result from deletion of a point or */ +/* insertion of a segment. */ +/* */ +/* This is a conceptually difficult routine. The starting assumption is */ +/* that we have a polygon with n sides. n - 1 of these sides are currently */ +/* represented as edges in the mesh. One side, called the "base", need not */ +/* be. */ +/* */ +/* Inside the polygon is a structure I call a "fan", consisting of n - 1 */ +/* triangles that share a common origin. For each of these triangles, the */ +/* edge opposite the origin is one of the sides of the polygon. The */ +/* primary edge of each triangle is the edge directed from the origin to */ +/* the destination; note that this is not the same edge that is a side of */ +/* the polygon. `firstedge' is the primary edge of the first triangle. */ +/* From there, the triangles follow in counterclockwise order about the */ +/* polygon, until `lastedge', the primary edge of the last triangle. */ +/* `firstedge' and `lastedge' are probably connected to other triangles */ +/* beyond the extremes of the fan, but their identity is not important, as */ +/* long as the fan remains connected to them. */ +/* */ +/* Imagine the polygon oriented so that its base is at the bottom. This */ +/* puts `firstedge' on the far right, and `lastedge' on the far left. */ +/* The right vertex of the base is the destination of `firstedge', and the */ +/* left vertex of the base is the apex of `lastedge'. */ +/* */ +/* The challenge now is to find the right sequence of edge flips to */ +/* transform the fan into a Delaunay triangulation of the polygon. Each */ +/* edge flip effectively removes one triangle from the fan, committing it */ +/* to the polygon. The resulting polygon has one fewer edge. If `doflip' */ +/* is set, the final flip will be performed, resulting in a fan of one */ +/* (useless?) triangle. If `doflip' is not set, the final flip is not */ +/* performed, resulting in a fan of two triangles, and an unfinished */ +/* triangular polygon that is not yet filled out with a single triangle. */ +/* On completion of the routine, `lastedge' is the last remaining triangle, */ +/* or the leftmost of the last two. */ +/* */ +/* Although the flips are performed in the order described above, the */ +/* decisions about what flips to perform are made in precisely the reverse */ +/* order. The recursive triangulatepolygon() procedure makes a decision, */ +/* uses up to two recursive calls to triangulate the "subproblems" */ +/* (polygons with fewer edges), and then performs an edge flip. */ +/* */ +/* The "decision" it makes is which vertex of the polygon should be */ +/* connected to the base. This decision is made by testing every possible */ +/* vertex. Once the best vertex is found, the two edges that connect this */ +/* vertex to the base become the bases for two smaller polygons. These */ +/* are triangulated recursively. Unfortunately, this approach can take */ +/* O(n^2) time not only in the worst case, but in many common cases. It's */ +/* rarely a big deal for point deletion, where n is rarely larger than ten, */ +/* but it could be a big deal for segment insertion, especially if there's */ +/* a lot of long segments that each cut many triangles. I ought to code */ +/* a faster algorithm some time. */ +/* */ +/* The `edgecount' parameter is the number of sides of the polygon, */ +/* including its base. `triflaws' is a flag that determines whether the */ +/* new triangles should be tested for quality, and enqueued if they are */ +/* bad. */ +/* */ +/*****************************************************************************/ + +void triangulatepolygon(firstedge, lastedge, edgecount, doflip, triflaws) +struct triedge *firstedge; +struct triedge *lastedge; +int edgecount; +int doflip; +int triflaws; +{ + struct triedge testtri; + struct triedge besttri; + struct triedge tempedge; + point leftbasepoint, rightbasepoint; + point testpoint; + point bestpoint; + int bestnumber; + int i; + triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ + + /* Identify the base vertices. */ + apex(*lastedge, leftbasepoint); + dest(*firstedge, rightbasepoint); + if (verbose > 2) { + printf(" Triangulating interior polygon at edge\n"); + printf(" (%.12g, %.12g) (%.12g, %.12g)\n", leftbasepoint[0], + leftbasepoint[1], rightbasepoint[0], rightbasepoint[1]); + } + /* Find the best vertex to connect the base to. */ + onext(*firstedge, besttri); + dest(besttri, bestpoint); + triedgecopy(besttri, testtri); + bestnumber = 1; + for (i = 2; i <= edgecount - 2; i++) { + onextself(testtri); + dest(testtri, testpoint); + /* Is this a better vertex? */ + if (incircle(leftbasepoint, rightbasepoint, bestpoint, testpoint) > 0.0) { + triedgecopy(testtri, besttri); + bestpoint = testpoint; + bestnumber = i; + } + } + if (verbose > 2) { + printf(" Connecting edge to (%.12g, %.12g)\n", bestpoint[0], + bestpoint[1]); + } + if (bestnumber > 1) { + /* Recursively triangulate the smaller polygon on the right. */ + oprev(besttri, tempedge); + triangulatepolygon(firstedge, &tempedge, bestnumber + 1, 1, triflaws); + } + if (bestnumber < edgecount - 2) { + /* Recursively triangulate the smaller polygon on the left. */ + sym(besttri, tempedge); + triangulatepolygon(&besttri, lastedge, edgecount - bestnumber, 1, + triflaws); + /* Find `besttri' again; it may have been lost to edge flips. */ + sym(tempedge, besttri); + } + if (doflip) { + /* Do one final edge flip. */ + flip(&besttri); +#ifndef CDT_ONLY + if (triflaws) { + /* Check the quality of the newly committed triangle. */ + sym(besttri, testtri); + testtriangle(&testtri); + } +#endif /* not CDT_ONLY */ + } + /* Return the base triangle. */ + triedgecopy(besttri, *lastedge); +} + +/*****************************************************************************/ +/* */ +/* deletesite() Delete a vertex from a Delaunay triangulation, ensuring */ +/* that the triangulation remains Delaunay. */ +/* */ +/* The origin of `deltri' is deleted. The union of the triangles adjacent */ +/* to this point is a polygon, for which the Delaunay triangulation is */ +/* found. Two triangles are removed from the mesh. */ +/* */ +/* Only interior points that do not lie on segments (shell edges) or */ +/* boundaries may be deleted. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +void deletesite(deltri) +struct triedge *deltri; +{ + struct triedge countingtri; + struct triedge firstedge, lastedge; + struct triedge deltriright; + struct triedge lefttri, righttri; + struct triedge leftcasing, rightcasing; + struct edge leftshelle, rightshelle; + point delpoint; + point neworg; + int edgecount; + triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ + shelle sptr; /* Temporary variable used by tspivot(). */ + + org(*deltri, delpoint); + if (verbose > 1) { + printf(" Deleting (%.12g, %.12g).\n", delpoint[0], delpoint[1]); + } + pointdealloc(delpoint); + + /* Count the degree of the point being deleted. */ + onext(*deltri, countingtri); + edgecount = 1; + while (!triedgeequal(*deltri, countingtri)) { +#ifdef SELF_CHECK + if (countingtri.tri == dummytri) { + printf("Internal error in deletesite():\n"); + printf(" Attempt to delete boundary point.\n"); + internalerror(); + } +#endif /* SELF_CHECK */ + edgecount++; + onextself(countingtri); + } + +#ifdef SELF_CHECK + if (edgecount < 3) { + printf("Internal error in deletesite():\n Point has degree %d.\n", + edgecount); + internalerror(); + } +#endif /* SELF_CHECK */ + if (edgecount > 3) { + /* Triangulate the polygon defined by the union of all triangles */ + /* adjacent to the point being deleted. Check the quality of */ + /* the resulting triangles. */ + onext(*deltri, firstedge); + oprev(*deltri, lastedge); + triangulatepolygon(&firstedge, &lastedge, edgecount, 0, !nobisect); + } + /* Splice out two triangles. */ + lprev(*deltri, deltriright); + dnext(*deltri, lefttri); + sym(lefttri, leftcasing); + oprev(deltriright, righttri); + sym(righttri, rightcasing); + bond(*deltri, leftcasing); + bond(deltriright, rightcasing); + tspivot(lefttri, leftshelle); + if (leftshelle.sh != dummysh) { + tsbond(*deltri, leftshelle); + } + tspivot(righttri, rightshelle); + if (rightshelle.sh != dummysh) { + tsbond(deltriright, rightshelle); + } + + /* Set the new origin of `deltri' and check its quality. */ + org(lefttri, neworg); + setorg(*deltri, neworg); + if (!nobisect) { + testtriangle(deltri); + } + + /* Delete the two spliced-out triangles. */ + triangledealloc(lefttri.tri); + triangledealloc(righttri.tri); +} + +#endif /* not CDT_ONLY */ + +/** **/ +/** **/ +/********* Mesh transformation routines end here *********/ + +/********* Divide-and-conquer Delaunay triangulation begins here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* The divide-and-conquer bounding box */ +/* */ +/* I originally implemented the divide-and-conquer and incremental Delaunay */ +/* triangulations using the edge-based data structure presented by Guibas */ +/* and Stolfi. Switching to a triangle-based data structure doubled the */ +/* speed. However, I had to think of a few extra tricks to maintain the */ +/* elegance of the original algorithms. */ +/* */ +/* The "bounding box" used by my variant of the divide-and-conquer */ +/* algorithm uses one triangle for each edge of the convex hull of the */ +/* triangulation. These bounding triangles all share a common apical */ +/* vertex, which is represented by NULL and which represents nothing. */ +/* The bounding triangles are linked in a circular fan about this NULL */ +/* vertex, and the edges on the convex hull of the triangulation appear */ +/* opposite the NULL vertex. You might find it easiest to imagine that */ +/* the NULL vertex is a point in 3D space behind the center of the */ +/* triangulation, and that the bounding triangles form a sort of cone. */ +/* */ +/* This bounding box makes it easy to represent degenerate cases. For */ +/* instance, the triangulation of two vertices is a single edge. This edge */ +/* is represented by two bounding box triangles, one on each "side" of the */ +/* edge. These triangles are also linked together in a fan about the NULL */ +/* vertex. */ +/* */ +/* The bounding box also makes it easy to traverse the convex hull, as the */ +/* divide-and-conquer algorithm needs to do. */ +/* */ +/*****************************************************************************/ + +/*****************************************************************************/ +/* */ +/* pointsort() Sort an array of points by x-coordinate, using the */ +/* y-coordinate as a secondary key. */ +/* */ +/* Uses quicksort. Randomized O(n log n) time. No, I did not make any of */ +/* the usual quicksort mistakes. */ +/* */ +/*****************************************************************************/ + +void pointsort(sortarray, arraysize) +point *sortarray; +int arraysize; +{ + int left, right; + int pivot; + REAL pivotx, pivoty; + point temp; + + if (arraysize == 2) { + /* Recursive base case. */ + if ((sortarray[0][0] > sortarray[1][0]) || + ((sortarray[0][0] == sortarray[1][0]) && + (sortarray[0][1] > sortarray[1][1]))) { + temp = sortarray[1]; + sortarray[1] = sortarray[0]; + sortarray[0] = temp; + } + return; + } + /* Choose a random pivot to split the array. */ + pivot = (int) randomnation(arraysize); + pivotx = sortarray[pivot][0]; + pivoty = sortarray[pivot][1]; + /* Split the array. */ + left = -1; + right = arraysize; + while (left < right) { + /* Search for a point whose x-coordinate is too large for the left. */ + do { + left++; + } while ((left <= right) && ((sortarray[left][0] < pivotx) || + ((sortarray[left][0] == pivotx) && + (sortarray[left][1] < pivoty)))); + /* Search for a point whose x-coordinate is too small for the right. */ + do { + right--; + } while ((left <= right) && ((sortarray[right][0] > pivotx) || + ((sortarray[right][0] == pivotx) && + (sortarray[right][1] > pivoty)))); + if (left < right) { + /* Swap the left and right points. */ + temp = sortarray[left]; + sortarray[left] = sortarray[right]; + sortarray[right] = temp; + } + } + if (left > 1) { + /* Recursively sort the left subset. */ + pointsort(sortarray, left); + } + if (right < arraysize - 2) { + /* Recursively sort the right subset. */ + pointsort(&sortarray[right + 1], arraysize - right - 1); + } +} + +/*****************************************************************************/ +/* */ +/* pointmedian() An order statistic algorithm, almost. Shuffles an array */ +/* of points so that the first `median' points occur */ +/* lexicographically before the remaining points. */ +/* */ +/* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */ +/* if axis == 1. Very similar to the pointsort() procedure, but runs in */ +/* randomized linear time. */ +/* */ +/*****************************************************************************/ + +void pointmedian(sortarray, arraysize, median, axis) +point *sortarray; +int arraysize; +int median; +int axis; +{ + int left, right; + int pivot; + REAL pivot1, pivot2; + point temp; + + if (arraysize == 2) { + /* Recursive base case. */ + if ((sortarray[0][axis] > sortarray[1][axis]) || + ((sortarray[0][axis] == sortarray[1][axis]) && + (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) { + temp = sortarray[1]; + sortarray[1] = sortarray[0]; + sortarray[0] = temp; + } + return; + } + /* Choose a random pivot to split the array. */ + pivot = (int) randomnation(arraysize); + pivot1 = sortarray[pivot][axis]; + pivot2 = sortarray[pivot][1 - axis]; + /* Split the array. */ + left = -1; + right = arraysize; + while (left < right) { + /* Search for a point whose x-coordinate is too large for the left. */ + do { + left++; + } while ((left <= right) && ((sortarray[left][axis] < pivot1) || + ((sortarray[left][axis] == pivot1) && + (sortarray[left][1 - axis] < pivot2)))); + /* Search for a point whose x-coordinate is too small for the right. */ + do { + right--; + } while ((left <= right) && ((sortarray[right][axis] > pivot1) || + ((sortarray[right][axis] == pivot1) && + (sortarray[right][1 - axis] > pivot2)))); + if (left < right) { + /* Swap the left and right points. */ + temp = sortarray[left]; + sortarray[left] = sortarray[right]; + sortarray[right] = temp; + } + } + /* Unlike in pointsort(), at most one of the following */ + /* conditionals is true. */ + if (left > median) { + /* Recursively shuffle the left subset. */ + pointmedian(sortarray, left, median, axis); + } + if (right < median - 1) { + /* Recursively shuffle the right subset. */ + pointmedian(&sortarray[right + 1], arraysize - right - 1, + median - right - 1, axis); + } +} + +/*****************************************************************************/ +/* */ +/* alternateaxes() Sorts the points as appropriate for the divide-and- */ +/* conquer algorithm with alternating cuts. */ +/* */ +/* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. */ +/* For the base case, subsets containing only two or three points are */ +/* always sorted by x-coordinate. */ +/* */ +/*****************************************************************************/ + +void alternateaxes(sortarray, arraysize, axis) +point *sortarray; +int arraysize; +int axis; +{ + int divider; + + divider = arraysize >> 1; + if (arraysize <= 3) { + /* Recursive base case: subsets of two or three points will be */ + /* handled specially, and should always be sorted by x-coordinate. */ + axis = 0; + } + /* Partition with a horizontal or vertical cut. */ + pointmedian(sortarray, arraysize, divider, axis); + /* Recursively partition the subsets with a cross cut. */ + if (arraysize - divider >= 2) { + if (divider >= 2) { + alternateaxes(sortarray, divider, 1 - axis); + } + alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis); + } +} + +/*****************************************************************************/ +/* */ +/* mergehulls() Merge two adjacent Delaunay triangulations into a */ +/* single Delaunay triangulation. */ +/* */ +/* This is similar to the algorithm given by Guibas and Stolfi, but uses */ +/* a triangle-based, rather than edge-based, data structure. */ +/* */ +/* The algorithm walks up the gap between the two triangulations, knitting */ +/* them together. As they are merged, some of their bounding triangles */ +/* are converted into real triangles of the triangulation. The procedure */ +/* pulls each hull's bounding triangles apart, then knits them together */ +/* like the teeth of two gears. The Delaunay property determines, at each */ +/* step, whether the next "tooth" is a bounding triangle of the left hull */ +/* or the right. When a bounding triangle becomes real, its apex is */ +/* changed from NULL to a real point. */ +/* */ +/* Only two new triangles need to be allocated. These become new bounding */ +/* triangles at the top and bottom of the seam. They are used to connect */ +/* the remaining bounding triangles (those that have not been converted */ +/* into real triangles) into a single fan. */ +/* */ +/* On entry, `farleft' and `innerleft' are bounding triangles of the left */ +/* triangulation. The origin of `farleft' is the leftmost vertex, and */ +/* the destination of `innerleft' is the rightmost vertex of the */ +/* triangulation. Similarly, `innerright' and `farright' are bounding */ +/* triangles of the right triangulation. The origin of `innerright' and */ +/* destination of `farright' are the leftmost and rightmost vertices. */ +/* */ +/* On completion, the origin of `farleft' is the leftmost vertex of the */ +/* merged triangulation, and the destination of `farright' is the rightmost */ +/* vertex. */ +/* */ +/*****************************************************************************/ + +void mergehulls(farleft, innerleft, innerright, farright, axis) +struct triedge *farleft; +struct triedge *innerleft; +struct triedge *innerright; +struct triedge *farright; +int axis; +{ + struct triedge leftcand, rightcand; + struct triedge baseedge; + struct triedge nextedge; + struct triedge sidecasing, topcasing, outercasing; + struct triedge checkedge; + point innerleftdest; + point innerrightorg; + point innerleftapex, innerrightapex; + point farleftpt, farrightpt; + point farleftapex, farrightapex; + point lowerleft, lowerright; + point upperleft, upperright; + point nextapex; + point checkvertex; + int changemade; + int badedge; + int leftfinished, rightfinished; + triangle ptr; /* Temporary variable used by sym(). */ + + dest(*innerleft, innerleftdest); + apex(*innerleft, innerleftapex); + org(*innerright, innerrightorg); + apex(*innerright, innerrightapex); + /* Special treatment for horizontal cuts. */ + if (dwyer && (axis == 1)) { + org(*farleft, farleftpt); + apex(*farleft, farleftapex); + dest(*farright, farrightpt); + apex(*farright, farrightapex); + /* The pointers to the extremal points are shifted to point to the */ + /* topmost and bottommost point of each hull, rather than the */ + /* leftmost and rightmost points. */ + while (farleftapex[1] < farleftpt[1]) { + lnextself(*farleft); + symself(*farleft); + farleftpt = farleftapex; + apex(*farleft, farleftapex); + } + sym(*innerleft, checkedge); + apex(checkedge, checkvertex); + while (checkvertex[1] > innerleftdest[1]) { + lnext(checkedge, *innerleft); + innerleftapex = innerleftdest; + innerleftdest = checkvertex; + sym(*innerleft, checkedge); + apex(checkedge, checkvertex); + } + while (innerrightapex[1] < innerrightorg[1]) { + lnextself(*innerright); + symself(*innerright); + innerrightorg = innerrightapex; + apex(*innerright, innerrightapex); + } + sym(*farright, checkedge); + apex(checkedge, checkvertex); + while (checkvertex[1] > farrightpt[1]) { + lnext(checkedge, *farright); + farrightapex = farrightpt; + farrightpt = checkvertex; + sym(*farright, checkedge); + apex(checkedge, checkvertex); + } + } + /* Find a line tangent to and below both hulls. */ + do { + changemade = 0; + /* Make innerleftdest the "bottommost" point of the left hull. */ + if (counterclockwise(innerleftdest, innerleftapex, innerrightorg) > 0.0) { + lprevself(*innerleft); + symself(*innerleft); + innerleftdest = innerleftapex; + apex(*innerleft, innerleftapex); + changemade = 1; + } + /* Make innerrightorg the "bottommost" point of the right hull. */ + if (counterclockwise(innerrightapex, innerrightorg, innerleftdest) > 0.0) { + lnextself(*innerright); + symself(*innerright); + innerrightorg = innerrightapex; + apex(*innerright, innerrightapex); + changemade = 1; + } + } while (changemade); + /* Find the two candidates to be the next "gear tooth". */ + sym(*innerleft, leftcand); + sym(*innerright, rightcand); + /* Create the bottom new bounding triangle. */ + maketriangle(&baseedge); + /* Connect it to the bounding boxes of the left and right triangulations. */ + bond(baseedge, *innerleft); + lnextself(baseedge); + bond(baseedge, *innerright); + lnextself(baseedge); + setorg(baseedge, innerrightorg); + setdest(baseedge, innerleftdest); + /* Apex is intentionally left NULL. */ + if (verbose > 2) { + printf(" Creating base bounding "); + printtriangle(&baseedge); + } + /* Fix the extreme triangles if necessary. */ + org(*farleft, farleftpt); + if (innerleftdest == farleftpt) { + lnext(baseedge, *farleft); + } + dest(*farright, farrightpt); + if (innerrightorg == farrightpt) { + lprev(baseedge, *farright); + } + /* The vertices of the current knitting edge. */ + lowerleft = innerleftdest; + lowerright = innerrightorg; + /* The candidate vertices for knitting. */ + apex(leftcand, upperleft); + apex(rightcand, upperright); + /* Walk up the gap between the two triangulations, knitting them together. */ + while (1) { + /* Have we reached the top? (This isn't quite the right question, */ + /* because even though the left triangulation might seem finished now, */ + /* moving up on the right triangulation might reveal a new point of */ + /* the left triangulation. And vice-versa.) */ + leftfinished = counterclockwise(upperleft, lowerleft, lowerright) <= 0.0; + rightfinished = counterclockwise(upperright, lowerleft, lowerright) <= 0.0; + if (leftfinished && rightfinished) { + /* Create the top new bounding triangle. */ + maketriangle(&nextedge); + setorg(nextedge, lowerleft); + setdest(nextedge, lowerright); + /* Apex is intentionally left NULL. */ + /* Connect it to the bounding boxes of the two triangulations. */ + bond(nextedge, baseedge); + lnextself(nextedge); + bond(nextedge, rightcand); + lnextself(nextedge); + bond(nextedge, leftcand); + if (verbose > 2) { + printf(" Creating top bounding "); + printtriangle(&baseedge); + } + /* Special treatment for horizontal cuts. */ + if (dwyer && (axis == 1)) { + org(*farleft, farleftpt); + apex(*farleft, farleftapex); + dest(*farright, farrightpt); + apex(*farright, farrightapex); + sym(*farleft, checkedge); + apex(checkedge, checkvertex); + /* The pointers to the extremal points are restored to the leftmost */ + /* and rightmost points (rather than topmost and bottommost). */ + while (checkvertex[0] < farleftpt[0]) { + lprev(checkedge, *farleft); + farleftapex = farleftpt; + farleftpt = checkvertex; + sym(*farleft, checkedge); + apex(checkedge, checkvertex); + } + while (farrightapex[0] > farrightpt[0]) { + lprevself(*farright); + symself(*farright); + farrightpt = farrightapex; + apex(*farright, farrightapex); + } + } + return; + } + /* Consider eliminating edges from the left triangulation. */ + if (!leftfinished) { + /* What vertex would be exposed if an edge were deleted? */ + lprev(leftcand, nextedge); + symself(nextedge); + apex(nextedge, nextapex); + /* If nextapex is NULL, then no vertex would be exposed; the */ + /* triangulation would have been eaten right through. */ + if (nextapex != (point) NULL) { + /* Check whether the edge is Delaunay. */ + badedge = incircle(lowerleft, lowerright, upperleft, nextapex) > 0.0; + while (badedge) { + /* Eliminate the edge with an edge flip. As a result, the */ + /* left triangulation will have one more boundary triangle. */ + lnextself(nextedge); + sym(nextedge, topcasing); + lnextself(nextedge); + sym(nextedge, sidecasing); + bond(nextedge, topcasing); + bond(leftcand, sidecasing); + lnextself(leftcand); + sym(leftcand, outercasing); + lprevself(nextedge); + bond(nextedge, outercasing); + /* Correct the vertices to reflect the edge flip. */ + setorg(leftcand, lowerleft); + setdest(leftcand, NULL); + setapex(leftcand, nextapex); + setorg(nextedge, NULL); + setdest(nextedge, upperleft); + setapex(nextedge, nextapex); + /* Consider the newly exposed vertex. */ + upperleft = nextapex; + /* What vertex would be exposed if another edge were deleted? */ + triedgecopy(sidecasing, nextedge); + apex(nextedge, nextapex); + if (nextapex != (point) NULL) { + /* Check whether the edge is Delaunay. */ + badedge = incircle(lowerleft, lowerright, upperleft, nextapex) + > 0.0; + } else { + /* Avoid eating right through the triangulation. */ + badedge = 0; + } + } + } + } + /* Consider eliminating edges from the right triangulation. */ + if (!rightfinished) { + /* What vertex would be exposed if an edge were deleted? */ + lnext(rightcand, nextedge); + symself(nextedge); + apex(nextedge, nextapex); + /* If nextapex is NULL, then no vertex would be exposed; the */ + /* triangulation would have been eaten right through. */ + if (nextapex != (point) NULL) { + /* Check whether the edge is Delaunay. */ + badedge = incircle(lowerleft, lowerright, upperright, nextapex) > 0.0; + while (badedge) { + /* Eliminate the edge with an edge flip. As a result, the */ + /* right triangulation will have one more boundary triangle. */ + lprevself(nextedge); + sym(nextedge, topcasing); + lprevself(nextedge); + sym(nextedge, sidecasing); + bond(nextedge, topcasing); + bond(rightcand, sidecasing); + lprevself(rightcand); + sym(rightcand, outercasing); + lnextself(nextedge); + bond(nextedge, outercasing); + /* Correct the vertices to reflect the edge flip. */ + setorg(rightcand, NULL); + setdest(rightcand, lowerright); + setapex(rightcand, nextapex); + setorg(nextedge, upperright); + setdest(nextedge, NULL); + setapex(nextedge, nextapex); + /* Consider the newly exposed vertex. */ + upperright = nextapex; + /* What vertex would be exposed if another edge were deleted? */ + triedgecopy(sidecasing, nextedge); + apex(nextedge, nextapex); + if (nextapex != (point) NULL) { + /* Check whether the edge is Delaunay. */ + badedge = incircle(lowerleft, lowerright, upperright, nextapex) + > 0.0; + } else { + /* Avoid eating right through the triangulation. */ + badedge = 0; + } + } + } + } + if (leftfinished || (!rightfinished && + (incircle(upperleft, lowerleft, lowerright, upperright) > 0.0))) { + /* Knit the triangulations, adding an edge from `lowerleft' */ + /* to `upperright'. */ + bond(baseedge, rightcand); + lprev(rightcand, baseedge); + setdest(baseedge, lowerleft); + lowerright = upperright; + sym(baseedge, rightcand); + apex(rightcand, upperright); + } else { + /* Knit the triangulations, adding an edge from `upperleft' */ + /* to `lowerright'. */ + bond(baseedge, leftcand); + lnext(leftcand, baseedge); + setorg(baseedge, lowerright); + lowerleft = upperleft; + sym(baseedge, leftcand); + apex(leftcand, upperleft); + } + if (verbose > 2) { + printf(" Connecting "); + printtriangle(&baseedge); + } + } +} + +/*****************************************************************************/ +/* */ +/* divconqrecurse() Recursively form a Delaunay triangulation by the */ +/* divide-and-conquer method. */ +/* */ +/* Recursively breaks down the problem into smaller pieces, which are */ +/* knitted together by mergehulls(). The base cases (problems of two or */ +/* three points) are handled specially here. */ +/* */ +/* On completion, `farleft' and `farright' are bounding triangles such that */ +/* the origin of `farleft' is the leftmost vertex (breaking ties by */ +/* choosing the highest leftmost vertex), and the destination of */ +/* `farright' is the rightmost vertex (breaking ties by choosing the */ +/* lowest rightmost vertex). */ +/* */ +/*****************************************************************************/ + +void divconqrecurse(sortarray, vertices, axis, farleft, farright) +point *sortarray; +int vertices; +int axis; +struct triedge *farleft; +struct triedge *farright; +{ + struct triedge midtri, tri1, tri2, tri3; + struct triedge innerleft, innerright; + REAL area; + int divider; + + if (verbose > 2) { + printf(" Triangulating %d points.\n", vertices); + } + if (vertices == 2) { + /* The triangulation of two vertices is an edge. An edge is */ + /* represented by two bounding triangles. */ + maketriangle(farleft); + setorg(*farleft, sortarray[0]); + setdest(*farleft, sortarray[1]); + /* The apex is intentionally left NULL. */ + maketriangle(farright); + setorg(*farright, sortarray[1]); + setdest(*farright, sortarray[0]); + /* The apex is intentionally left NULL. */ + bond(*farleft, *farright); + lprevself(*farleft); + lnextself(*farright); + bond(*farleft, *farright); + lprevself(*farleft); + lnextself(*farright); + bond(*farleft, *farright); + if (verbose > 2) { + printf(" Creating "); + printtriangle(farleft); + printf(" Creating "); + printtriangle(farright); + } + /* Ensure that the origin of `farleft' is sortarray[0]. */ + lprev(*farright, *farleft); + return; + } else if (vertices == 3) { + /* The triangulation of three vertices is either a triangle (with */ + /* three bounding triangles) or two edges (with four bounding */ + /* triangles). In either case, four triangles are created. */ + maketriangle(&midtri); + maketriangle(&tri1); + maketriangle(&tri2); + maketriangle(&tri3); + area = counterclockwise(sortarray[0], sortarray[1], sortarray[2]); + if (area == 0.0) { + /* Three collinear points; the triangulation is two edges. */ + setorg(midtri, sortarray[0]); + setdest(midtri, sortarray[1]); + setorg(tri1, sortarray[1]); + setdest(tri1, sortarray[0]); + setorg(tri2, sortarray[2]); + setdest(tri2, sortarray[1]); + setorg(tri3, sortarray[1]); + setdest(tri3, sortarray[2]); + /* All apices are intentionally left NULL. */ + bond(midtri, tri1); + bond(tri2, tri3); + lnextself(midtri); + lprevself(tri1); + lnextself(tri2); + lprevself(tri3); + bond(midtri, tri3); + bond(tri1, tri2); + lnextself(midtri); + lprevself(tri1); + lnextself(tri2); + lprevself(tri3); + bond(midtri, tri1); + bond(tri2, tri3); + /* Ensure that the origin of `farleft' is sortarray[0]. */ + triedgecopy(tri1, *farleft); + /* Ensure that the destination of `farright' is sortarray[2]. */ + triedgecopy(tri2, *farright); + } else { + /* The three points are not collinear; the triangulation is one */ + /* triangle, namely `midtri'. */ + setorg(midtri, sortarray[0]); + setdest(tri1, sortarray[0]); + setorg(tri3, sortarray[0]); + /* Apices of tri1, tri2, and tri3 are left NULL. */ + if (area > 0.0) { + /* The vertices are in counterclockwise order. */ + setdest(midtri, sortarray[1]); + setorg(tri1, sortarray[1]); + setdest(tri2, sortarray[1]); + setapex(midtri, sortarray[2]); + setorg(tri2, sortarray[2]); + setdest(tri3, sortarray[2]); + } else { + /* The vertices are in clockwise order. */ + setdest(midtri, sortarray[2]); + setorg(tri1, sortarray[2]); + setdest(tri2, sortarray[2]); + setapex(midtri, sortarray[1]); + setorg(tri2, sortarray[1]); + setdest(tri3, sortarray[1]); + } + /* The topology does not depend on how the vertices are ordered. */ + bond(midtri, tri1); + lnextself(midtri); + bond(midtri, tri2); + lnextself(midtri); + bond(midtri, tri3); + lprevself(tri1); + lnextself(tri2); + bond(tri1, tri2); + lprevself(tri1); + lprevself(tri3); + bond(tri1, tri3); + lnextself(tri2); + lprevself(tri3); + bond(tri2, tri3); + /* Ensure that the origin of `farleft' is sortarray[0]. */ + triedgecopy(tri1, *farleft); + /* Ensure that the destination of `farright' is sortarray[2]. */ + if (area > 0.0) { + triedgecopy(tri2, *farright); + } else { + lnext(*farleft, *farright); + } + } + if (verbose > 2) { + printf(" Creating "); + printtriangle(&midtri); + printf(" Creating "); + printtriangle(&tri1); + printf(" Creating "); + printtriangle(&tri2); + printf(" Creating "); + printtriangle(&tri3); + } + return; + } else { + /* Split the vertices in half. */ + divider = vertices >> 1; + /* Recursively triangulate each half. */ + divconqrecurse(sortarray, divider, 1 - axis, farleft, &innerleft); + divconqrecurse(&sortarray[divider], vertices - divider, 1 - axis, + &innerright, farright); + if (verbose > 1) { + printf(" Joining triangulations with %d and %d vertices.\n", divider, + vertices - divider); + } + /* Merge the two triangulations into one. */ + mergehulls(farleft, &innerleft, &innerright, farright, axis); + } +} + +long removeghosts(startghost) +struct triedge *startghost; +{ + struct triedge searchedge; + struct triedge dissolveedge; + struct triedge deadtri; + point markorg; + long hullsize; + triangle ptr; /* Temporary variable used by sym(). */ + + if (verbose) { + printf(" Removing ghost triangles.\n"); + } + /* Find an edge on the convex hull to start point location from. */ + lprev(*startghost, searchedge); + symself(searchedge); + dummytri[0] = encode(searchedge); + /* Remove the bounding box and count the convex hull edges. */ + triedgecopy(*startghost, dissolveedge); + hullsize = 0; + do { + hullsize++; + lnext(dissolveedge, deadtri); + lprevself(dissolveedge); + symself(dissolveedge); + /* If no PSLG is involved, set the boundary markers of all the points */ + /* on the convex hull. If a PSLG is used, this step is done later. */ + if (!poly) { + /* Watch out for the case where all the input points are collinear. */ + if (dissolveedge.tri != dummytri) { + org(dissolveedge, markorg); + if (pointmark(markorg) == 0) { + setpointmark(markorg, 1); + } + } + } + /* Remove a bounding triangle from a convex hull triangle. */ + dissolve(dissolveedge); + /* Find the next bounding triangle. */ + sym(deadtri, dissolveedge); + /* Delete the bounding triangle. */ + triangledealloc(deadtri.tri); + } while (!triedgeequal(dissolveedge, *startghost)); + return hullsize; +} + +/*****************************************************************************/ +/* */ +/* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */ +/* conquer method. */ +/* */ +/* Sorts the points, calls a recursive procedure to triangulate them, and */ +/* removes the bounding box, setting boundary markers as appropriate. */ +/* */ +/*****************************************************************************/ + +long divconqdelaunay() +{ + point *sortarray; + struct triedge hullleft, hullright; + int divider; + int i, j; + + /* Allocate an array of pointers to points for sorting. */ + sortarray = (point *) malloc(inpoints * sizeof(point)); + if (sortarray == (point *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + traversalinit(&points); + for (i = 0; i < inpoints; i++) { + sortarray[i] = pointtraverse(); + } + if (verbose) { + printf(" Sorting points.\n"); + } + /* Sort the points. */ + pointsort(sortarray, inpoints); + /* Discard duplicate points, which can really mess up the algorithm. */ + i = 0; + for (j = 1; j < inpoints; j++) { + if ((sortarray[i][0] == sortarray[j][0]) + && (sortarray[i][1] == sortarray[j][1])) { + if (!quiet) { + printf( +"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n", + sortarray[j][0], sortarray[j][1]); + } +/* Commented out - would eliminate point from output .node file, but causes + a failure if some segment has this point as an endpoint. + setpointmark(sortarray[j], DEADPOINT); +*/ + } else { + i++; + sortarray[i] = sortarray[j]; + } + } + i++; + if (dwyer) { + /* Re-sort the array of points to accommodate alternating cuts. */ + divider = i >> 1; + if (i - divider >= 2) { + if (divider >= 2) { + alternateaxes(sortarray, divider, 1); + } + alternateaxes(&sortarray[divider], i - divider, 1); + } + } + if (verbose) { + printf(" Forming triangulation.\n"); + } + /* Form the Delaunay triangulation. */ + divconqrecurse(sortarray, i, 0, &hullleft, &hullright); + free(sortarray); + + return removeghosts(&hullleft); +} + +/** **/ +/** **/ +/********* Divide-and-conquer Delaunay triangulation ends here *********/ + +/********* Incremental Delaunay triangulation begins here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* boundingbox() Form an "infinite" bounding triangle to insert points */ +/* into. */ +/* */ +/* The points at "infinity" are assigned finite coordinates, which are used */ +/* by the point location routines, but (mostly) ignored by the Delaunay */ +/* edge flip routines. */ +/* */ +/*****************************************************************************/ + +#ifndef REDUCED + +void boundingbox() +{ + struct triedge inftri; /* Handle for the triangular bounding box. */ + REAL width; + + if (verbose) { + printf(" Creating triangular bounding box.\n"); + } + /* Find the width (or height, whichever is larger) of the triangulation. */ + width = xmax - xmin; + if (ymax - ymin > width) { + width = ymax - ymin; + } + if (width == 0.0) { + width = 1.0; + } + /* Create the vertices of the bounding box. */ + infpoint1 = (point) malloc(points.itembytes); + infpoint2 = (point) malloc(points.itembytes); + infpoint3 = (point) malloc(points.itembytes); + if ((infpoint1 == (point) NULL) || (infpoint2 == (point) NULL) + || (infpoint3 == (point) NULL)) { + printf("Error: Out of memory.\n"); + exit(1); + } + infpoint1[0] = xmin - 50.0 * width; + infpoint1[1] = ymin - 40.0 * width; + infpoint2[0] = xmax + 50.0 * width; + infpoint2[1] = ymin - 40.0 * width; + infpoint3[0] = 0.5 * (xmin + xmax); + infpoint3[1] = ymax + 60.0 * width; + + /* Create the bounding box. */ + maketriangle(&inftri); + setorg(inftri, infpoint1); + setdest(inftri, infpoint2); + setapex(inftri, infpoint3); + /* Link dummytri to the bounding box so we can always find an */ + /* edge to begin searching (point location) from. */ + dummytri[0] = (triangle) inftri.tri; + if (verbose > 2) { + printf(" Creating "); + printtriangle(&inftri); + } +} + +#endif /* not REDUCED */ + +/*****************************************************************************/ +/* */ +/* removebox() Remove the "infinite" bounding triangle, setting boundary */ +/* markers as appropriate. */ +/* */ +/* The triangular bounding box has three boundary triangles (one for each */ +/* side of the bounding box), and a bunch of triangles fanning out from */ +/* the three bounding box vertices (one triangle for each edge of the */ +/* convex hull of the inner mesh). This routine removes these triangles. */ +/* */ +/*****************************************************************************/ + +#ifndef REDUCED + +long removebox() +{ + struct triedge deadtri; + struct triedge searchedge; + struct triedge checkedge; + struct triedge nextedge, finaledge, dissolveedge; + point markorg; + long hullsize; + triangle ptr; /* Temporary variable used by sym(). */ + + if (verbose) { + printf(" Removing triangular bounding box.\n"); + } + /* Find a boundary triangle. */ + nextedge.tri = dummytri; + nextedge.orient = 0; + symself(nextedge); + /* Mark a place to stop. */ + lprev(nextedge, finaledge); + lnextself(nextedge); + symself(nextedge); + /* Find a triangle (on the boundary of the point set) that isn't */ + /* a bounding box triangle. */ + lprev(nextedge, searchedge); + symself(searchedge); + /* Check whether nextedge is another boundary triangle */ + /* adjacent to the first one. */ + lnext(nextedge, checkedge); + symself(checkedge); + if (checkedge.tri == dummytri) { + /* Go on to the next triangle. There are only three boundary */ + /* triangles, and this next triangle cannot be the third one, */ + /* so it's safe to stop here. */ + lprevself(searchedge); + symself(searchedge); + } + /* Find a new boundary edge to search from, as the current search */ + /* edge lies on a bounding box triangle and will be deleted. */ + dummytri[0] = encode(searchedge); + hullsize = -2l; + while (!triedgeequal(nextedge, finaledge)) { + hullsize++; + lprev(nextedge, dissolveedge); + symself(dissolveedge); + /* If not using a PSLG, the vertices should be marked now. */ + /* (If using a PSLG, markhull() will do the job.) */ + if (!poly) { + /* Be careful! One must check for the case where all the input */ + /* points are collinear, and thus all the triangles are part of */ + /* the bounding box. Otherwise, the setpointmark() call below */ + /* will cause a bad pointer reference. */ + if (dissolveedge.tri != dummytri) { + org(dissolveedge, markorg); + if (pointmark(markorg) == 0) { + setpointmark(markorg, 1); + } + } + } + /* Disconnect the bounding box triangle from the mesh triangle. */ + dissolve(dissolveedge); + lnext(nextedge, deadtri); + sym(deadtri, nextedge); + /* Get rid of the bounding box triangle. */ + triangledealloc(deadtri.tri); + /* Do we need to turn the corner? */ + if (nextedge.tri == dummytri) { + /* Turn the corner. */ + triedgecopy(dissolveedge, nextedge); + } + } + triangledealloc(finaledge.tri); + + free(infpoint1); /* Deallocate the bounding box vertices. */ + free(infpoint2); + free(infpoint3); + + return hullsize; +} + +#endif /* not REDUCED */ + +/*****************************************************************************/ +/* */ +/* incrementaldelaunay() Form a Delaunay triangulation by incrementally */ +/* adding vertices. */ +/* */ +/*****************************************************************************/ + +#ifndef REDUCED + +long incrementaldelaunay() +{ + struct triedge starttri; + point pointloop; + int i; + + /* Create a triangular bounding box. */ + boundingbox(); + if (verbose) { + printf(" Incrementally inserting points.\n"); + } + traversalinit(&points); + pointloop = pointtraverse(); + i = 1; + while (pointloop != (point) NULL) { + /* Find a boundary triangle to search from. */ + starttri.tri = (triangle *) NULL; + if (insertsite(pointloop, &starttri, (struct edge *) NULL, 0, 0) == + DUPLICATEPOINT) { + if (!quiet) { + printf( +"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n", + pointloop[0], pointloop[1]); + } +/* Commented out - would eliminate point from output .node file. + setpointmark(pointloop, DEADPOINT); +*/ + } + pointloop = pointtraverse(); + i++; + } + /* Remove the bounding box. */ + return removebox(); +} + +#endif /* not REDUCED */ + +/** **/ +/** **/ +/********* Incremental Delaunay triangulation ends here *********/ + +/********* Sweepline Delaunay triangulation begins here *********/ +/** **/ +/** **/ + +#ifndef REDUCED + +void eventheapinsert(heap, heapsize, newevent) +struct event **heap; +int heapsize; +struct event *newevent; +{ + REAL eventx, eventy; + int eventnum; + int parent; + int notdone; + + eventx = newevent->xkey; + eventy = newevent->ykey; + eventnum = heapsize; + notdone = eventnum > 0; + while (notdone) { + parent = (eventnum - 1) >> 1; + if ((heap[parent]->ykey < eventy) || + ((heap[parent]->ykey == eventy) + && (heap[parent]->xkey <= eventx))) { + notdone = 0; + } else { + heap[eventnum] = heap[parent]; + heap[eventnum]->heapposition = eventnum; + + eventnum = parent; + notdone = eventnum > 0; + } + } + heap[eventnum] = newevent; + newevent->heapposition = eventnum; +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +void eventheapify(heap, heapsize, eventnum) +struct event **heap; +int heapsize; +int eventnum; +{ + struct event *thisevent; + REAL eventx, eventy; + int leftchild, rightchild; + int smallest; + int notdone; + + thisevent = heap[eventnum]; + eventx = thisevent->xkey; + eventy = thisevent->ykey; + leftchild = 2 * eventnum + 1; + notdone = leftchild < heapsize; + while (notdone) { + if ((heap[leftchild]->ykey < eventy) || + ((heap[leftchild]->ykey == eventy) + && (heap[leftchild]->xkey < eventx))) { + smallest = leftchild; + } else { + smallest = eventnum; + } + rightchild = leftchild + 1; + if (rightchild < heapsize) { + if ((heap[rightchild]->ykey < heap[smallest]->ykey) || + ((heap[rightchild]->ykey == heap[smallest]->ykey) + && (heap[rightchild]->xkey < heap[smallest]->xkey))) { + smallest = rightchild; + } + } + if (smallest == eventnum) { + notdone = 0; + } else { + heap[eventnum] = heap[smallest]; + heap[eventnum]->heapposition = eventnum; + heap[smallest] = thisevent; + thisevent->heapposition = smallest; + + eventnum = smallest; + leftchild = 2 * eventnum + 1; + notdone = leftchild < heapsize; + } + } +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +void eventheapdelete(heap, heapsize, eventnum) +struct event **heap; +int heapsize; +int eventnum; +{ + struct event *moveevent; + REAL eventx, eventy; + int parent; + int notdone; + + moveevent = heap[heapsize - 1]; + if (eventnum > 0) { + eventx = moveevent->xkey; + eventy = moveevent->ykey; + do { + parent = (eventnum - 1) >> 1; + if ((heap[parent]->ykey < eventy) || + ((heap[parent]->ykey == eventy) + && (heap[parent]->xkey <= eventx))) { + notdone = 0; + } else { + heap[eventnum] = heap[parent]; + heap[eventnum]->heapposition = eventnum; + + eventnum = parent; + notdone = eventnum > 0; + } + } while (notdone); + } + heap[eventnum] = moveevent; + moveevent->heapposition = eventnum; + eventheapify(heap, heapsize - 1, eventnum); +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +void createeventheap(eventheap, events, freeevents) +struct event ***eventheap; +struct event **events; +struct event **freeevents; +{ + point thispoint; + int maxevents; + int i; + + maxevents = (3 * inpoints) / 2; + *eventheap = (struct event **) malloc(maxevents * sizeof(struct event *)); + if (*eventheap == (struct event **) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + *events = (struct event *) malloc(maxevents * sizeof(struct event)); + if (*events == (struct event *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + traversalinit(&points); + for (i = 0; i < inpoints; i++) { + thispoint = pointtraverse(); + (*events)[i].eventptr = (VOID *) thispoint; + (*events)[i].xkey = thispoint[0]; + (*events)[i].ykey = thispoint[1]; + eventheapinsert(*eventheap, i, *events + i); + } + *freeevents = (struct event *) NULL; + for (i = maxevents - 1; i >= inpoints; i--) { + (*events)[i].eventptr = (VOID *) *freeevents; + *freeevents = *events + i; + } +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +int rightofhyperbola(fronttri, newsite) +struct triedge *fronttri; +point newsite; +{ + point leftpoint, rightpoint; + REAL dxa, dya, dxb, dyb; + + hyperbolacount++; + + dest(*fronttri, leftpoint); + apex(*fronttri, rightpoint); + if ((leftpoint[1] < rightpoint[1]) + || ((leftpoint[1] == rightpoint[1]) && (leftpoint[0] < rightpoint[0]))) { + if (newsite[0] >= rightpoint[0]) { + return 1; + } + } else { + if (newsite[0] <= leftpoint[0]) { + return 0; + } + } + dxa = leftpoint[0] - newsite[0]; + dya = leftpoint[1] - newsite[1]; + dxb = rightpoint[0] - newsite[0]; + dyb = rightpoint[1] - newsite[1]; + return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya); +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +REAL circletop(pa, pb, pc, ccwabc) +point pa; +point pb; +point pc; +REAL ccwabc; +{ + REAL xac, yac, xbc, ybc, xab, yab; + REAL aclen2, bclen2, ablen2; + + circletopcount++; + + xac = pa[0] - pc[0]; + yac = pa[1] - pc[1]; + xbc = pb[0] - pc[0]; + ybc = pb[1] - pc[1]; + xab = pa[0] - pb[0]; + yab = pa[1] - pb[1]; + aclen2 = xac * xac + yac * yac; + bclen2 = xbc * xbc + ybc * ybc; + ablen2 = xab * xab + yab * yab; + return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2)) + / (2.0 * ccwabc); +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +void check4deadevent(checktri, freeevents, eventheap, heapsize) +struct triedge *checktri; +struct event **freeevents; +struct event **eventheap; +int *heapsize; +{ + struct event *deadevent; + point eventpoint; + int eventnum; + + org(*checktri, eventpoint); + if (eventpoint != (point) NULL) { + deadevent = (struct event *) eventpoint; + eventnum = deadevent->heapposition; + deadevent->eventptr = (VOID *) *freeevents; + *freeevents = deadevent; + eventheapdelete(eventheap, *heapsize, eventnum); + (*heapsize)--; + setorg(*checktri, NULL); + } +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +struct splaynode *splay(splaytree, searchpoint, searchtri) +struct splaynode *splaytree; +point searchpoint; +struct triedge *searchtri; +{ + struct splaynode *child, *grandchild; + struct splaynode *lefttree, *righttree; + struct splaynode *leftright; + point checkpoint; + int rightofroot, rightofchild; + + if (splaytree == (struct splaynode *) NULL) { + return (struct splaynode *) NULL; + } + dest(splaytree->keyedge, checkpoint); + if (checkpoint == splaytree->keydest) { + rightofroot = rightofhyperbola(&splaytree->keyedge, searchpoint); + if (rightofroot) { + triedgecopy(splaytree->keyedge, *searchtri); + child = splaytree->rchild; + } else { + child = splaytree->lchild; + } + if (child == (struct splaynode *) NULL) { + return splaytree; + } + dest(child->keyedge, checkpoint); + if (checkpoint != child->keydest) { + child = splay(child, searchpoint, searchtri); + if (child == (struct splaynode *) NULL) { + if (rightofroot) { + splaytree->rchild = (struct splaynode *) NULL; + } else { + splaytree->lchild = (struct splaynode *) NULL; + } + return splaytree; + } + } + rightofchild = rightofhyperbola(&child->keyedge, searchpoint); + if (rightofchild) { + triedgecopy(child->keyedge, *searchtri); + grandchild = splay(child->rchild, searchpoint, searchtri); + child->rchild = grandchild; + } else { + grandchild = splay(child->lchild, searchpoint, searchtri); + child->lchild = grandchild; + } + if (grandchild == (struct splaynode *) NULL) { + if (rightofroot) { + splaytree->rchild = child->lchild; + child->lchild = splaytree; + } else { + splaytree->lchild = child->rchild; + child->rchild = splaytree; + } + return child; + } + if (rightofchild) { + if (rightofroot) { + splaytree->rchild = child->lchild; + child->lchild = splaytree; + } else { + splaytree->lchild = grandchild->rchild; + grandchild->rchild = splaytree; + } + child->rchild = grandchild->lchild; + grandchild->lchild = child; + } else { + if (rightofroot) { + splaytree->rchild = grandchild->lchild; + grandchild->lchild = splaytree; + } else { + splaytree->lchild = child->rchild; + child->rchild = splaytree; + } + child->lchild = grandchild->rchild; + grandchild->rchild = child; + } + return grandchild; + } else { + lefttree = splay(splaytree->lchild, searchpoint, searchtri); + righttree = splay(splaytree->rchild, searchpoint, searchtri); + + pooldealloc(&splaynodes, (VOID *) splaytree); + if (lefttree == (struct splaynode *) NULL) { + return righttree; + } else if (righttree == (struct splaynode *) NULL) { + return lefttree; + } else if (lefttree->rchild == (struct splaynode *) NULL) { + lefttree->rchild = righttree->lchild; + righttree->lchild = lefttree; + return righttree; + } else if (righttree->lchild == (struct splaynode *) NULL) { + righttree->lchild = lefttree->rchild; + lefttree->rchild = righttree; + return lefttree; + } else { +/* printf("Holy Toledo!!!\n"); */ + leftright = lefttree->rchild; + while (leftright->rchild != (struct splaynode *) NULL) { + leftright = leftright->rchild; + } + leftright->rchild = righttree; + return lefttree; + } + } +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +struct splaynode *splayinsert(splayroot, newkey, searchpoint) +struct splaynode *splayroot; +struct triedge *newkey; +point searchpoint; +{ + struct splaynode *newsplaynode; + + newsplaynode = (struct splaynode *) poolalloc(&splaynodes); + triedgecopy(*newkey, newsplaynode->keyedge); + dest(*newkey, newsplaynode->keydest); + if (splayroot == (struct splaynode *) NULL) { + newsplaynode->lchild = (struct splaynode *) NULL; + newsplaynode->rchild = (struct splaynode *) NULL; + } else if (rightofhyperbola(&splayroot->keyedge, searchpoint)) { + newsplaynode->lchild = splayroot; + newsplaynode->rchild = splayroot->rchild; + splayroot->rchild = (struct splaynode *) NULL; + } else { + newsplaynode->lchild = splayroot->lchild; + newsplaynode->rchild = splayroot; + splayroot->lchild = (struct splaynode *) NULL; + } + return newsplaynode; +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +struct splaynode *circletopinsert(splayroot, newkey, pa, pb, pc, topy) +struct splaynode *splayroot; +struct triedge *newkey; +point pa; +point pb; +point pc; +REAL topy; +{ + REAL ccwabc; + REAL xac, yac, xbc, ybc; + REAL aclen2, bclen2; + REAL searchpoint[2]; + struct triedge dummytri; + + ccwabc = counterclockwise(pa, pb, pc); + xac = pa[0] - pc[0]; + yac = pa[1] - pc[1]; + xbc = pb[0] - pc[0]; + ybc = pb[1] - pc[1]; + aclen2 = xac * xac + yac * yac; + bclen2 = xbc * xbc + ybc * ybc; + searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc); + searchpoint[1] = topy; + return splayinsert(splay(splayroot, (point) searchpoint, &dummytri), newkey, + (point) searchpoint); +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +struct splaynode *frontlocate(splayroot, bottommost, searchpoint, searchtri, + farright) +struct splaynode *splayroot; +struct triedge *bottommost; +point searchpoint; +struct triedge *searchtri; +int *farright; +{ + int farrightflag; + triangle ptr; /* Temporary variable used by onext(). */ + + triedgecopy(*bottommost, *searchtri); + splayroot = splay(splayroot, searchpoint, searchtri); + + farrightflag = 0; + while (!farrightflag && rightofhyperbola(searchtri, searchpoint)) { + onextself(*searchtri); + farrightflag = triedgeequal(*searchtri, *bottommost); + } + *farright = farrightflag; + return splayroot; +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +long sweeplinedelaunay() +{ + struct event **eventheap; + struct event *events; + struct event *freeevents; + struct event *nextevent; + struct event *newevent; + struct splaynode *splayroot; + struct triedge bottommost; + struct triedge searchtri; + struct triedge fliptri; + struct triedge lefttri, righttri, farlefttri, farrighttri; + struct triedge inserttri; + point firstpoint, secondpoint; + point nextpoint, lastpoint; + point connectpoint; + point leftpoint, midpoint, rightpoint; + REAL lefttest, righttest; + int heapsize; + int check4events, farrightflag; + triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ + + poolinit(&splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK, POINTER, + 0); + splayroot = (struct splaynode *) NULL; + + if (verbose) { + printf(" Placing points in event heap.\n"); + } + createeventheap(&eventheap, &events, &freeevents); + heapsize = inpoints; + + if (verbose) { + printf(" Forming triangulation.\n"); + } + maketriangle(&lefttri); + maketriangle(&righttri); + bond(lefttri, righttri); + lnextself(lefttri); + lprevself(righttri); + bond(lefttri, righttri); + lnextself(lefttri); + lprevself(righttri); + bond(lefttri, righttri); + firstpoint = (point) eventheap[0]->eventptr; + eventheap[0]->eventptr = (VOID *) freeevents; + freeevents = eventheap[0]; + eventheapdelete(eventheap, heapsize, 0); + heapsize--; + do { + if (heapsize == 0) { + printf("Error: Input points are all identical.\n"); + exit(1); + } + secondpoint = (point) eventheap[0]->eventptr; + eventheap[0]->eventptr = (VOID *) freeevents; + freeevents = eventheap[0]; + eventheapdelete(eventheap, heapsize, 0); + heapsize--; + if ((firstpoint[0] == secondpoint[0]) + && (firstpoint[1] == secondpoint[1])) { + printf( +"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n", + secondpoint[0], secondpoint[1]); +/* Commented out - would eliminate point from output .node file. + setpointmark(secondpoint, DEADPOINT); +*/ + } + } while ((firstpoint[0] == secondpoint[0]) + && (firstpoint[1] == secondpoint[1])); + setorg(lefttri, firstpoint); + setdest(lefttri, secondpoint); + setorg(righttri, secondpoint); + setdest(righttri, firstpoint); + lprev(lefttri, bottommost); + lastpoint = secondpoint; + while (heapsize > 0) { + nextevent = eventheap[0]; + eventheapdelete(eventheap, heapsize, 0); + heapsize--; + check4events = 1; + if (nextevent->xkey < xmin) { + decode(nextevent->eventptr, fliptri); + oprev(fliptri, farlefttri); + check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize); + onext(fliptri, farrighttri); + check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize); + + if (triedgeequal(farlefttri, bottommost)) { + lprev(fliptri, bottommost); + } + flip(&fliptri); + setapex(fliptri, NULL); + lprev(fliptri, lefttri); + lnext(fliptri, righttri); + sym(lefttri, farlefttri); + + if (randomnation(SAMPLERATE) == 0) { + symself(fliptri); + dest(fliptri, leftpoint); + apex(fliptri, midpoint); + org(fliptri, rightpoint); + splayroot = circletopinsert(splayroot, &lefttri, leftpoint, midpoint, + rightpoint, nextevent->ykey); + } + } else { + nextpoint = (point) nextevent->eventptr; + if ((nextpoint[0] == lastpoint[0]) && (nextpoint[1] == lastpoint[1])) { + printf( +"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n", + nextpoint[0], nextpoint[1]); +/* Commented out - would eliminate point from output .node file. + setpointmark(nextpoint, DEADPOINT); +*/ + check4events = 0; + } else { + lastpoint = nextpoint; + + splayroot = frontlocate(splayroot, &bottommost, nextpoint, &searchtri, + &farrightflag); +/* + triedgecopy(bottommost, searchtri); + farrightflag = 0; + while (!farrightflag && rightofhyperbola(&searchtri, nextpoint)) { + onextself(searchtri); + farrightflag = triedgeequal(searchtri, bottommost); + } +*/ + + check4deadevent(&searchtri, &freeevents, eventheap, &heapsize); + + triedgecopy(searchtri, farrighttri); + sym(searchtri, farlefttri); + maketriangle(&lefttri); + maketriangle(&righttri); + dest(farrighttri, connectpoint); + setorg(lefttri, connectpoint); + setdest(lefttri, nextpoint); + setorg(righttri, nextpoint); + setdest(righttri, connectpoint); + bond(lefttri, righttri); + lnextself(lefttri); + lprevself(righttri); + bond(lefttri, righttri); + lnextself(lefttri); + lprevself(righttri); + bond(lefttri, farlefttri); + bond(righttri, farrighttri); + if (!farrightflag && triedgeequal(farrighttri, bottommost)) { + triedgecopy(lefttri, bottommost); + } + + if (randomnation(SAMPLERATE) == 0) { + splayroot = splayinsert(splayroot, &lefttri, nextpoint); + } else if (randomnation(SAMPLERATE) == 0) { + lnext(righttri, inserttri); + splayroot = splayinsert(splayroot, &inserttri, nextpoint); + } + } + } + nextevent->eventptr = (VOID *) freeevents; + freeevents = nextevent; + + if (check4events) { + apex(farlefttri, leftpoint); + dest(lefttri, midpoint); + apex(lefttri, rightpoint); + lefttest = counterclockwise(leftpoint, midpoint, rightpoint); + if (lefttest > 0.0) { + newevent = freeevents; + freeevents = (struct event *) freeevents->eventptr; + newevent->xkey = xminextreme; + newevent->ykey = circletop(leftpoint, midpoint, rightpoint, + lefttest); + newevent->eventptr = (VOID *) encode(lefttri); + eventheapinsert(eventheap, heapsize, newevent); + heapsize++; + setorg(lefttri, newevent); + } + apex(righttri, leftpoint); + org(righttri, midpoint); + apex(farrighttri, rightpoint); + righttest = counterclockwise(leftpoint, midpoint, rightpoint); + if (righttest > 0.0) { + newevent = freeevents; + freeevents = (struct event *) freeevents->eventptr; + newevent->xkey = xminextreme; + newevent->ykey = circletop(leftpoint, midpoint, rightpoint, + righttest); + newevent->eventptr = (VOID *) encode(farrighttri); + eventheapinsert(eventheap, heapsize, newevent); + heapsize++; + setorg(farrighttri, newevent); + } + } + } + + pooldeinit(&splaynodes); + lprevself(bottommost); + return removeghosts(&bottommost); +} + +#endif /* not REDUCED */ + +/** **/ +/** **/ +/********* Sweepline Delaunay triangulation ends here *********/ + +/********* General mesh construction routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* delaunay() Form a Delaunay triangulation. */ +/* */ +/*****************************************************************************/ + +long delaunay() +{ + eextras = 0; + initializetrisegpools(); + +#ifdef REDUCED + if (!quiet) { + printf( + "Constructing Delaunay triangulation by divide-and-conquer method.\n"); + } + return divconqdelaunay(); +#else /* not REDUCED */ + if (!quiet) { + printf("Constructing Delaunay triangulation "); + if (incremental) { + printf("by incremental method.\n"); + } else if (sweepline) { + printf("by sweepline method.\n"); + } else { + printf("by divide-and-conquer method.\n"); + } + } + if (incremental) { + return incrementaldelaunay(); + } else if (sweepline) { + return sweeplinedelaunay(); + } else { + return divconqdelaunay(); + } +#endif /* not REDUCED */ +} + +/*****************************************************************************/ +/* */ +/* reconstruct() Reconstruct a triangulation from its .ele (and possibly */ +/* .poly) file. Used when the -r switch is used. */ +/* */ +/* Reads an .ele file and reconstructs the original mesh. If the -p switch */ +/* is used, this procedure will also read a .poly file and reconstruct the */ +/* shell edges of the original mesh. If the -a switch is used, this */ +/* procedure will also read an .area file and set a maximum area constraint */ +/* on each triangle. */ +/* */ +/* Points that are not corners of triangles, such as nodes on edges of */ +/* subparametric elements, are discarded. */ +/* */ +/* This routine finds the adjacencies between triangles (and shell edges) */ +/* by forming one stack of triangles for each vertex. Each triangle is on */ +/* three different stacks simultaneously. Each triangle's shell edge */ +/* pointers are used to link the items in each stack. This memory-saving */ +/* feature makes the code harder to read. The most important thing to keep */ +/* in mind is that each triangle is removed from a stack precisely when */ +/* the corresponding pointer is adjusted to refer to a shell edge rather */ +/* than the next triangle of the stack. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef TRILIBRARY + +int reconstruct(trianglelist, triangleattriblist, trianglearealist, elements, + corners, attribs, segmentlist, segmentmarkerlist, + numberofsegments) +int *trianglelist; +REAL *triangleattriblist; +REAL *trianglearealist; +int elements; +int corners; +int attribs; +int *segmentlist; +int *segmentmarkerlist; +int numberofsegments; + +#else /* not TRILIBRARY */ + +long reconstruct(elefilename, areafilename, polyfilename, polyfile) +char *elefilename; +char *areafilename; +char *polyfilename; +FILE *polyfile; + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + int pointindex; + int attribindex; +#else /* not TRILIBRARY */ + FILE *elefile; + FILE *areafile; + char inputline[INPUTLINESIZE]; + char *stringptr; + int areaelements; +#endif /* not TRILIBRARY */ + struct triedge triangleloop; + struct triedge triangleleft; + struct triedge checktri; + struct triedge checkleft; + struct triedge checkneighbor; + struct edge shelleloop; + triangle *vertexarray; + triangle *prevlink; + triangle nexttri; + point tdest, tapex; + point checkdest, checkapex; + point shorg; + point killpoint; + REAL area; + int corner[3]; + int end[2]; + int killpointindex; + int incorners; + int segmentmarkers; + int boundmarker; + int aroundpoint; + long hullsize; + int notfound; + int elementnumber, segmentnumber; + int i, j; + triangle ptr; /* Temporary variable used by sym(). */ + +#ifdef TRILIBRARY + inelements = elements; + incorners = corners; + if (incorners < 3) { + printf("Error: Triangles must have at least 3 points.\n"); + exit(1); + } + eextras = attribs; +#else /* not TRILIBRARY */ + /* Read the triangles from an .ele file. */ + if (!quiet) { + printf("Opening %s.\n", elefilename); + } + elefile = fopen(elefilename, "r"); + if (elefile == (FILE *) NULL) { + printf(" Error: Cannot access file %s.\n", elefilename); + exit(1); + } + /* Read number of triangles, number of points per triangle, and */ + /* number of triangle attributes from .ele file. */ + stringptr = readline(inputline, elefile, elefilename); + inelements = (int) strtol (stringptr, &stringptr, 0); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + incorners = 3; + } else { + incorners = (int) strtol (stringptr, &stringptr, 0); + if (incorners < 3) { + printf("Error: Triangles in %s must have at least 3 points.\n", + elefilename); + exit(1); + } + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + eextras = 0; + } else { + eextras = (int) strtol (stringptr, &stringptr, 0); + } +#endif /* not TRILIBRARY */ + + initializetrisegpools(); + + /* Create the triangles. */ + for (elementnumber = 1; elementnumber <= inelements; elementnumber++) { + maketriangle(&triangleloop); + /* Mark the triangle as living. */ + triangleloop.tri[3] = (triangle) triangleloop.tri; + } + + if (poly) { +#ifdef TRILIBRARY + insegments = numberofsegments; + segmentmarkers = segmentmarkerlist != (int *) NULL; +#else /* not TRILIBRARY */ + /* Read number of segments and number of segment */ + /* boundary markers from .poly file. */ + stringptr = readline(inputline, polyfile, inpolyfilename); + insegments = (int) strtol (stringptr, &stringptr, 0); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + segmentmarkers = 0; + } else { + segmentmarkers = (int) strtol (stringptr, &stringptr, 0); + } +#endif /* not TRILIBRARY */ + + /* Create the shell edges. */ + for (segmentnumber = 1; segmentnumber <= insegments; segmentnumber++) { + makeshelle(&shelleloop); + /* Mark the shell edge as living. */ + shelleloop.sh[2] = (shelle) shelleloop.sh; + } + } + +#ifdef TRILIBRARY + pointindex = 0; + attribindex = 0; +#else /* not TRILIBRARY */ + if (vararea) { + /* Open an .area file, check for consistency with the .ele file. */ + if (!quiet) { + printf("Opening %s.\n", areafilename); + } + areafile = fopen(areafilename, "r"); + if (areafile == (FILE *) NULL) { + printf(" Error: Cannot access file %s.\n", areafilename); + exit(1); + } + stringptr = readline(inputline, areafile, areafilename); + areaelements = (int) strtol (stringptr, &stringptr, 0); + if (areaelements != inelements) { + printf("Error: %s and %s disagree on number of triangles.\n", + elefilename, areafilename); + exit(1); + } + } +#endif /* not TRILIBRARY */ + + if (!quiet) { + printf("Reconstructing mesh.\n"); + } + /* Allocate a temporary array that maps each point to some adjacent */ + /* triangle. I took care to allocate all the permanent memory for */ + /* triangles and shell edges first. */ + vertexarray = (triangle *) malloc(points.items * sizeof(triangle)); + if (vertexarray == (triangle *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + /* Each point is initially unrepresented. */ + for (i = 0; i < points.items; i++) { + vertexarray[i] = (triangle) dummytri; + } + + if (verbose) { + printf(" Assembling triangles.\n"); + } + /* Read the triangles from the .ele file, and link */ + /* together those that share an edge. */ + traversalinit(&triangles); + triangleloop.tri = triangletraverse(); + elementnumber = firstnumber; + while (triangleloop.tri != (triangle *) NULL) { +#ifdef TRILIBRARY + /* Copy the triangle's three corners. */ + for (j = 0; j < 3; j++) { + corner[j] = trianglelist[pointindex++]; + if ((corner[j] < firstnumber) || (corner[j] >= firstnumber + inpoints)) { + printf("Error: Triangle %d has an invalid vertex index.\n", + elementnumber); + exit(1); + } + } +#else /* not TRILIBRARY */ + /* Read triangle number and the triangle's three corners. */ + stringptr = readline(inputline, elefile, elefilename); + for (j = 0; j < 3; j++) { + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Triangle %d is missing point %d in %s.\n", + elementnumber, j + 1, elefilename); + exit(1); + } else { + corner[j] = (int) strtol (stringptr, &stringptr, 0); + if ((corner[j] < firstnumber) || + (corner[j] >= firstnumber + inpoints)) { + printf("Error: Triangle %d has an invalid vertex index.\n", + elementnumber); + exit(1); + } + } + } +#endif /* not TRILIBRARY */ + + /* Find out about (and throw away) extra nodes. */ + for (j = 3; j < incorners; j++) { +#ifdef TRILIBRARY + killpointindex = trianglelist[pointindex++]; +#else /* not TRILIBRARY */ + stringptr = findfield(stringptr); + if (*stringptr != '\0') { + killpointindex = (int) strtol (stringptr, &stringptr, 0); +#endif /* not TRILIBRARY */ + if ((killpointindex >= firstnumber) && + (killpointindex < firstnumber + inpoints)) { + /* Delete the non-corner point if it's not already deleted. */ + killpoint = getpoint(killpointindex); + if (pointmark(killpoint) != DEADPOINT) { + pointdealloc(killpoint); + } + } +#ifndef TRILIBRARY + } +#endif /* not TRILIBRARY */ + } + + /* Read the triangle's attributes. */ + for (j = 0; j < eextras; j++) { +#ifdef TRILIBRARY + setelemattribute(triangleloop, j, triangleattriblist[attribindex++]); +#else /* not TRILIBRARY */ + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + setelemattribute(triangleloop, j, 0); + } else { + setelemattribute(triangleloop, j, + (REAL) strtod (stringptr, &stringptr)); + } +#endif /* not TRILIBRARY */ + } + + if (vararea) { +#ifdef TRILIBRARY + area = trianglearealist[elementnumber - firstnumber]; +#else /* not TRILIBRARY */ + /* Read an area constraint from the .area file. */ + stringptr = readline(inputline, areafile, areafilename); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + area = -1.0; /* No constraint on this triangle. */ + } else { + area = (REAL) strtod(stringptr, &stringptr); + } +#endif /* not TRILIBRARY */ + setareabound(triangleloop, area); + } + + /* Set the triangle's vertices. */ + triangleloop.orient = 0; + setorg(triangleloop, getpoint(corner[0])); + setdest(triangleloop, getpoint(corner[1])); + setapex(triangleloop, getpoint(corner[2])); + /* Try linking the triangle to others that share these vertices. */ + for (triangleloop.orient = 0; triangleloop.orient < 3; + triangleloop.orient++) { + /* Take the number for the origin of triangleloop. */ + aroundpoint = corner[triangleloop.orient]; + /* Look for other triangles having this vertex. */ + nexttri = vertexarray[aroundpoint - firstnumber]; + /* Link the current triangle to the next one in the stack. */ + triangleloop.tri[6 + triangleloop.orient] = nexttri; + /* Push the current triangle onto the stack. */ + vertexarray[aroundpoint - firstnumber] = encode(triangleloop); + decode(nexttri, checktri); + if (checktri.tri != dummytri) { + dest(triangleloop, tdest); + apex(triangleloop, tapex); + /* Look for other triangles that share an edge. */ + do { + dest(checktri, checkdest); + apex(checktri, checkapex); + if (tapex == checkdest) { + /* The two triangles share an edge; bond them together. */ + lprev(triangleloop, triangleleft); + bond(triangleleft, checktri); + } + if (tdest == checkapex) { + /* The two triangles share an edge; bond them together. */ + lprev(checktri, checkleft); + bond(triangleloop, checkleft); + } + /* Find the next triangle in the stack. */ + nexttri = checktri.tri[6 + checktri.orient]; + decode(nexttri, checktri); + } while (checktri.tri != dummytri); + } + } + triangleloop.tri = triangletraverse(); + elementnumber++; + } + +#ifdef TRILIBRARY + pointindex = 0; +#else /* not TRILIBRARY */ + fclose(elefile); + if (vararea) { + fclose(areafile); + } +#endif /* not TRILIBRARY */ + + hullsize = 0; /* Prepare to count the boundary edges. */ + if (poly) { + if (verbose) { + printf(" Marking segments in triangulation.\n"); + } + /* Read the segments from the .poly file, and link them */ + /* to their neighboring triangles. */ + boundmarker = 0; + traversalinit(&shelles); + shelleloop.sh = shelletraverse(); + segmentnumber = firstnumber; + while (shelleloop.sh != (shelle *) NULL) { +#ifdef TRILIBRARY + end[0] = segmentlist[pointindex++]; + end[1] = segmentlist[pointindex++]; + if (segmentmarkers) { + boundmarker = segmentmarkerlist[segmentnumber - firstnumber]; + } +#else /* not TRILIBRARY */ + /* Read the endpoints of each segment, and possibly a boundary marker. */ + stringptr = readline(inputline, polyfile, inpolyfilename); + /* Skip the first (segment number) field. */ + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Segment %d has no endpoints in %s.\n", segmentnumber, + polyfilename); + exit(1); + } else { + end[0] = (int) strtol (stringptr, &stringptr, 0); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Segment %d is missing its second endpoint in %s.\n", + segmentnumber, polyfilename); + exit(1); + } else { + end[1] = (int) strtol (stringptr, &stringptr, 0); + } + if (segmentmarkers) { + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + boundmarker = 0; + } else { + boundmarker = (int) strtol (stringptr, &stringptr, 0); + } + } +#endif /* not TRILIBRARY */ + for (j = 0; j < 2; j++) { + if ((end[j] < firstnumber) || (end[j] >= firstnumber + inpoints)) { + printf("Error: Segment %d has an invalid vertex index.\n", + segmentnumber); + exit(1); + } + } + + /* set the shell edge's vertices. */ + shelleloop.shorient = 0; + setsorg(shelleloop, getpoint(end[0])); + setsdest(shelleloop, getpoint(end[1])); + setmark(shelleloop, boundmarker); + /* Try linking the shell edge to triangles that share these vertices. */ + for (shelleloop.shorient = 0; shelleloop.shorient < 2; + shelleloop.shorient++) { + /* Take the number for the destination of shelleloop. */ + aroundpoint = end[1 - shelleloop.shorient]; + /* Look for triangles having this vertex. */ + prevlink = &vertexarray[aroundpoint - firstnumber]; + nexttri = vertexarray[aroundpoint - firstnumber]; + decode(nexttri, checktri); + sorg(shelleloop, shorg); + notfound = 1; + /* Look for triangles having this edge. Note that I'm only */ + /* comparing each triangle's destination with the shell edge; */ + /* each triangle's apex is handled through a different vertex. */ + /* Because each triangle appears on three vertices' lists, each */ + /* occurrence of a triangle on a list can (and does) represent */ + /* an edge. In this way, most edges are represented twice, and */ + /* every triangle-segment bond is represented once. */ + while (notfound && (checktri.tri != dummytri)) { + dest(checktri, checkdest); + if (shorg == checkdest) { + /* We have a match. Remove this triangle from the list. */ + *prevlink = checktri.tri[6 + checktri.orient]; + /* Bond the shell edge to the triangle. */ + tsbond(checktri, shelleloop); + /* Check if this is a boundary edge. */ + sym(checktri, checkneighbor); + if (checkneighbor.tri == dummytri) { + /* The next line doesn't insert a shell edge (because there's */ + /* already one there), but it sets the boundary markers of */ + /* the existing shell edge and its vertices. */ + insertshelle(&checktri, 1); + hullsize++; + } + notfound = 0; + } + /* Find the next triangle in the stack. */ + prevlink = &checktri.tri[6 + checktri.orient]; + nexttri = checktri.tri[6 + checktri.orient]; + decode(nexttri, checktri); + } + } + shelleloop.sh = shelletraverse(); + segmentnumber++; + } + } + + /* Mark the remaining edges as not being attached to any shell edge. */ + /* Also, count the (yet uncounted) boundary edges. */ + for (i = 0; i < points.items; i++) { + /* Search the stack of triangles adjacent to a point. */ + nexttri = vertexarray[i]; + decode(nexttri, checktri); + while (checktri.tri != dummytri) { + /* Find the next triangle in the stack before this */ + /* information gets overwritten. */ + nexttri = checktri.tri[6 + checktri.orient]; + /* No adjacent shell edge. (This overwrites the stack info.) */ + tsdissolve(checktri); + sym(checktri, checkneighbor); + if (checkneighbor.tri == dummytri) { + insertshelle(&checktri, 1); + hullsize++; + } + decode(nexttri, checktri); + } + } + + free(vertexarray); + return hullsize; +} + +#endif /* not CDT_ONLY */ + +/** **/ +/** **/ +/********* General mesh construction routines end here *********/ + +/********* Segment (shell edge) insertion begins here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* finddirection() Find the first triangle on the path from one point */ +/* to another. */ +/* */ +/* Finds the triangle that intersects a line segment drawn from the */ +/* origin of `searchtri' to the point `endpoint', and returns the result */ +/* in `searchtri'. The origin of `searchtri' does not change, even though */ +/* the triangle returned may differ from the one passed in. This routine */ +/* is used to find the direction to move in to get from one point to */ +/* another. */ +/* */ +/* The return value notes whether the destination or apex of the found */ +/* triangle is collinear with the two points in question. */ +/* */ +/*****************************************************************************/ + +enum finddirectionresult finddirection(searchtri, endpoint) +struct triedge *searchtri; +point endpoint; +{ + struct triedge checktri; + point startpoint; + point leftpoint, rightpoint; + REAL leftccw, rightccw; + int leftflag, rightflag; + triangle ptr; /* Temporary variable used by onext() and oprev(). */ + + org(*searchtri, startpoint); + dest(*searchtri, rightpoint); + apex(*searchtri, leftpoint); + /* Is `endpoint' to the left? */ + leftccw = counterclockwise(endpoint, startpoint, leftpoint); + leftflag = leftccw > 0.0; + /* Is `endpoint' to the right? */ + rightccw = counterclockwise(startpoint, endpoint, rightpoint); + rightflag = rightccw > 0.0; + if (leftflag && rightflag) { + /* `searchtri' faces directly away from `endpoint'. We could go */ + /* left or right. Ask whether it's a triangle or a boundary */ + /* on the left. */ + onext(*searchtri, checktri); + if (checktri.tri == dummytri) { + leftflag = 0; + } else { + rightflag = 0; + } + } + while (leftflag) { + /* Turn left until satisfied. */ + onextself(*searchtri); + if (searchtri->tri == dummytri) { + printf("Internal error in finddirection(): Unable to find a\n"); + printf(" triangle leading from (%.12g, %.12g) to", startpoint[0], + startpoint[1]); + printf(" (%.12g, %.12g).\n", endpoint[0], endpoint[1]); + internalerror(); + } + apex(*searchtri, leftpoint); + rightccw = leftccw; + leftccw = counterclockwise(endpoint, startpoint, leftpoint); + leftflag = leftccw > 0.0; + } + while (rightflag) { + /* Turn right until satisfied. */ + oprevself(*searchtri); + if (searchtri->tri == dummytri) { + printf("Internal error in finddirection(): Unable to find a\n"); + printf(" triangle leading from (%.12g, %.12g) to", startpoint[0], + startpoint[1]); + printf(" (%.12g, %.12g).\n", endpoint[0], endpoint[1]); + internalerror(); + } + dest(*searchtri, rightpoint); + leftccw = rightccw; + rightccw = counterclockwise(startpoint, endpoint, rightpoint); + rightflag = rightccw > 0.0; + } + if (leftccw == 0.0) { + return LEFTCOLLINEAR; + } else if (rightccw == 0.0) { + return RIGHTCOLLINEAR; + } else { + return WITHIN; + } +} + +/*****************************************************************************/ +/* */ +/* segmentintersection() Find the intersection of an existing segment */ +/* and a segment that is being inserted. Insert */ +/* a point at the intersection, splitting an */ +/* existing shell edge. */ +/* */ +/* The segment being inserted connects the apex of splittri to endpoint2. */ +/* splitshelle is the shell edge being split, and MUST be opposite */ +/* splittri. Hence, the edge being split connects the origin and */ +/* destination of splittri. */ +/* */ +/* On completion, splittri is a handle having the newly inserted */ +/* intersection point as its origin, and endpoint1 as its destination. */ +/* */ +/*****************************************************************************/ + +void segmentintersection(splittri, splitshelle, endpoint2) +struct triedge *splittri; +struct edge *splitshelle; +point endpoint2; +{ + point endpoint1; + point torg, tdest; + point leftpoint, rightpoint; + point newpoint; + enum insertsiteresult success; + enum finddirectionresult collinear; + REAL ex, ey; + REAL tx, ty; + REAL etx, ety; + REAL split, denom; + int i; + triangle ptr; /* Temporary variable used by onext(). */ + + /* Find the other three segment endpoints. */ + apex(*splittri, endpoint1); + org(*splittri, torg); + dest(*splittri, tdest); + /* Segment intersection formulae; see the Antonio reference. */ + tx = tdest[0] - torg[0]; + ty = tdest[1] - torg[1]; + ex = endpoint2[0] - endpoint1[0]; + ey = endpoint2[1] - endpoint1[1]; + etx = torg[0] - endpoint2[0]; + ety = torg[1] - endpoint2[1]; + denom = ty * ex - tx * ey; + if (denom == 0.0) { + printf("Internal error in segmentintersection():"); + printf(" Attempt to find intersection of parallel segments.\n"); + internalerror(); + } + split = (ey * etx - ex * ety) / denom; + /* Create the new point. */ + newpoint = (point) poolalloc(&points); + /* Interpolate its coordinate and attributes. */ + for (i = 0; i < 2 + nextras; i++) { + newpoint[i] = torg[i] + split * (tdest[i] - torg[i]); + } + setpointmark(newpoint, mark(*splitshelle)); + if (verbose > 1) { + printf( + " Splitting edge (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n", + torg[0], torg[1], tdest[0], tdest[1], newpoint[0], newpoint[1]); + } + /* Insert the intersection point. This should always succeed. */ + success = insertsite(newpoint, splittri, splitshelle, 0, 0); + if (success != SUCCESSFULPOINT) { + printf("Internal error in segmentintersection():\n"); + printf(" Failure to split a segment.\n"); + internalerror(); + } + if (steinerleft > 0) { + steinerleft--; + } + /* Inserting the point may have caused edge flips. We wish to rediscover */ + /* the edge connecting endpoint1 to the new intersection point. */ + collinear = finddirection(splittri, endpoint1); + dest(*splittri, rightpoint); + apex(*splittri, leftpoint); + if ((leftpoint[0] == endpoint1[0]) && (leftpoint[1] == endpoint1[1])) { + onextself(*splittri); + } else if ((rightpoint[0] != endpoint1[0]) || + (rightpoint[1] != endpoint1[1])) { + printf("Internal error in segmentintersection():\n"); + printf(" Topological inconsistency after splitting a segment.\n"); + internalerror(); + } + /* `splittri' should have destination endpoint1. */ +} + +/*****************************************************************************/ +/* */ +/* scoutsegment() Scout the first triangle on the path from one endpoint */ +/* to another, and check for completion (reaching the */ +/* second endpoint), a collinear point, and the */ +/* intersection of two segments. */ +/* */ +/* Returns one if the entire segment is successfully inserted, and zero if */ +/* the job must be finished by conformingedge() or constrainededge(). */ +/* */ +/* If the first triangle on the path has the second endpoint as its */ +/* destination or apex, a shell edge is inserted and the job is done. */ +/* */ +/* If the first triangle on the path has a destination or apex that lies on */ +/* the segment, a shell edge is inserted connecting the first endpoint to */ +/* the collinear point, and the search is continued from the collinear */ +/* point. */ +/* */ +/* If the first triangle on the path has a shell edge opposite its origin, */ +/* then there is a segment that intersects the segment being inserted. */ +/* Their intersection point is inserted, splitting the shell edge. */ +/* */ +/* Otherwise, return zero. */ +/* */ +/*****************************************************************************/ + +int scoutsegment(searchtri, endpoint2, newmark) +struct triedge *searchtri; +point endpoint2; +int newmark; +{ + struct triedge crosstri; + struct edge crossedge; + point leftpoint, rightpoint; + point endpoint1; + enum finddirectionresult collinear; + shelle sptr; /* Temporary variable used by tspivot(). */ + + collinear = finddirection(searchtri, endpoint2); + dest(*searchtri, rightpoint); + apex(*searchtri, leftpoint); + if (((leftpoint[0] == endpoint2[0]) && (leftpoint[1] == endpoint2[1])) || + ((rightpoint[0] == endpoint2[0]) && (rightpoint[1] == endpoint2[1]))) { + /* The segment is already an edge in the mesh. */ + if ((leftpoint[0] == endpoint2[0]) && (leftpoint[1] == endpoint2[1])) { + lprevself(*searchtri); + } + /* Insert a shell edge, if there isn't already one there. */ + insertshelle(searchtri, newmark); + return 1; + } else if (collinear == LEFTCOLLINEAR) { + /* We've collided with a point between the segment's endpoints. */ + /* Make the collinear point be the triangle's origin. */ + lprevself(*searchtri); + insertshelle(searchtri, newmark); + /* Insert the remainder of the segment. */ + return scoutsegment(searchtri, endpoint2, newmark); + } else if (collinear == RIGHTCOLLINEAR) { + /* We've collided with a point between the segment's endpoints. */ + insertshelle(searchtri, newmark); + /* Make the collinear point be the triangle's origin. */ + lnextself(*searchtri); + /* Insert the remainder of the segment. */ + return scoutsegment(searchtri, endpoint2, newmark); + } else { + lnext(*searchtri, crosstri); + tspivot(crosstri, crossedge); + /* Check for a crossing segment. */ + if (crossedge.sh == dummysh) { + return 0; + } else { + org(*searchtri, endpoint1); + /* Insert a point at the intersection. */ + segmentintersection(&crosstri, &crossedge, endpoint2); + triedgecopy(crosstri, *searchtri); + insertshelle(searchtri, newmark); + /* Insert the remainder of the segment. */ + return scoutsegment(searchtri, endpoint2, newmark); + } + } +} + +/*****************************************************************************/ +/* */ +/* conformingedge() Force a segment into a conforming Delaunay */ +/* triangulation by inserting a point at its midpoint, */ +/* and recursively forcing in the two half-segments if */ +/* necessary. */ +/* */ +/* Generates a sequence of edges connecting `endpoint1' to `endpoint2'. */ +/* `newmark' is the boundary marker of the segment, assigned to each new */ +/* splitting point and shell edge. */ +/* */ +/* Note that conformingedge() does not always maintain the conforming */ +/* Delaunay property. Once inserted, segments are locked into place; */ +/* points inserted later (to force other segments in) may render these */ +/* fixed segments non-Delaunay. The conforming Delaunay property will be */ +/* restored by enforcequality() by splitting encroached segments. */ +/* */ +/*****************************************************************************/ + +#ifndef REDUCED +#ifndef CDT_ONLY + +void conformingedge(endpoint1, endpoint2, newmark) +point endpoint1; +point endpoint2; +int newmark; +{ + struct triedge searchtri1, searchtri2; + struct edge brokenshelle; + point newpoint; + point midpoint1, midpoint2; + enum insertsiteresult success; + int result1, result2; + int i; + shelle sptr; /* Temporary variable used by tspivot(). */ + + if (verbose > 2) { + printf("Forcing segment into triangulation by recursive splitting:\n"); + printf(" (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1], + endpoint2[0], endpoint2[1]); + } + /* Create a new point to insert in the middle of the segment. */ + newpoint = (point) poolalloc(&points); + /* Interpolate coordinates and attributes. */ + for (i = 0; i < 2 + nextras; i++) { + newpoint[i] = 0.5 * (endpoint1[i] + endpoint2[i]); + } + setpointmark(newpoint, newmark); + /* Find a boundary triangle to search from. */ + searchtri1.tri = (triangle *) NULL; + /* Attempt to insert the new point. */ + success = insertsite(newpoint, &searchtri1, (struct edge *) NULL, 0, 0); + if (success == DUPLICATEPOINT) { + if (verbose > 2) { + printf(" Segment intersects existing point (%.12g, %.12g).\n", + newpoint[0], newpoint[1]); + } + /* Use the point that's already there. */ + pointdealloc(newpoint); + org(searchtri1, newpoint); + } else { + if (success == VIOLATINGPOINT) { + if (verbose > 2) { + printf(" Two segments intersect at (%.12g, %.12g).\n", + newpoint[0], newpoint[1]); + } + /* By fluke, we've landed right on another segment. Split it. */ + tspivot(searchtri1, brokenshelle); + success = insertsite(newpoint, &searchtri1, &brokenshelle, 0, 0); + if (success != SUCCESSFULPOINT) { + printf("Internal error in conformingedge():\n"); + printf(" Failure to split a segment.\n"); + internalerror(); + } + } + /* The point has been inserted successfully. */ + if (steinerleft > 0) { + steinerleft--; + } + } + triedgecopy(searchtri1, searchtri2); + result1 = scoutsegment(&searchtri1, endpoint1, newmark); + result2 = scoutsegment(&searchtri2, endpoint2, newmark); + if (!result1) { + /* The origin of searchtri1 may have changed if a collision with an */ + /* intervening vertex on the segment occurred. */ + org(searchtri1, midpoint1); + conformingedge(midpoint1, endpoint1, newmark); + } + if (!result2) { + /* The origin of searchtri2 may have changed if a collision with an */ + /* intervening vertex on the segment occurred. */ + org(searchtri2, midpoint2); + conformingedge(midpoint2, endpoint2, newmark); + } +} + +#endif /* not CDT_ONLY */ +#endif /* not REDUCED */ + +/*****************************************************************************/ +/* */ +/* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */ +/* recursively from an existing point. Pay special */ +/* attention to stacking inverted triangles. */ +/* */ +/* This is a support routine for inserting segments into a constrained */ +/* Delaunay triangulation. */ +/* */ +/* The origin of fixuptri is treated as if it has just been inserted, and */ +/* the local Delaunay condition needs to be enforced. It is only enforced */ +/* in one sector, however, that being the angular range defined by */ +/* fixuptri. */ +/* */ +/* This routine also needs to make decisions regarding the "stacking" of */ +/* triangles. (Read the description of constrainededge() below before */ +/* reading on here, so you understand the algorithm.) If the position of */ +/* the new point (the origin of fixuptri) indicates that the vertex before */ +/* it on the polygon is a reflex vertex, then "stack" the triangle by */ +/* doing nothing. (fixuptri is an inverted triangle, which is how stacked */ +/* triangles are identified.) */ +/* */ +/* Otherwise, check whether the vertex before that was a reflex vertex. */ +/* If so, perform an edge flip, thereby eliminating an inverted triangle */ +/* (popping it off the stack). The edge flip may result in the creation */ +/* of a new inverted triangle, depending on whether or not the new vertex */ +/* is visible to the vertex three edges behind on the polygon. */ +/* */ +/* If neither of the two vertices behind the new vertex are reflex */ +/* vertices, fixuptri and fartri, the triangle opposite it, are not */ +/* inverted; hence, ensure that the edge between them is locally Delaunay. */ +/* */ +/* `leftside' indicates whether or not fixuptri is to the left of the */ +/* segment being inserted. (Imagine that the segment is pointing up from */ +/* endpoint1 to endpoint2.) */ +/* */ +/*****************************************************************************/ + +void delaunayfixup(fixuptri, leftside) +struct triedge *fixuptri; +int leftside; +{ + struct triedge neartri; + struct triedge fartri; + struct edge faredge; + point nearpoint, leftpoint, rightpoint, farpoint; + triangle ptr; /* Temporary variable used by sym(). */ + shelle sptr; /* Temporary variable used by tspivot(). */ + + lnext(*fixuptri, neartri); + sym(neartri, fartri); + /* Check if the edge opposite the origin of fixuptri can be flipped. */ + if (fartri.tri == dummytri) { + return; + } + tspivot(neartri, faredge); + if (faredge.sh != dummysh) { + return; + } + /* Find all the relevant vertices. */ + apex(neartri, nearpoint); + org(neartri, leftpoint); + dest(neartri, rightpoint); + apex(fartri, farpoint); + /* Check whether the previous polygon vertex is a reflex vertex. */ + if (leftside) { + if (counterclockwise(nearpoint, leftpoint, farpoint) <= 0.0) { + /* leftpoint is a reflex vertex too. Nothing can */ + /* be done until a convex section is found. */ + return; + } + } else { + if (counterclockwise(farpoint, rightpoint, nearpoint) <= 0.0) { + /* rightpoint is a reflex vertex too. Nothing can */ + /* be done until a convex section is found. */ + return; + } + } + if (counterclockwise(rightpoint, leftpoint, farpoint) > 0.0) { + /* fartri is not an inverted triangle, and farpoint is not a reflex */ + /* vertex. As there are no reflex vertices, fixuptri isn't an */ + /* inverted triangle, either. Hence, test the edge between the */ + /* triangles to ensure it is locally Delaunay. */ + if (incircle(leftpoint, farpoint, rightpoint, nearpoint) <= 0.0) { + return; + } + /* Not locally Delaunay; go on to an edge flip. */ + } /* else fartri is inverted; remove it from the stack by flipping. */ + flip(&neartri); + lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */ + /* Recursively process the two triangles that result from the flip. */ + delaunayfixup(fixuptri, leftside); + delaunayfixup(&fartri, leftside); +} + +/*****************************************************************************/ +/* */ +/* constrainededge() Force a segment into a constrained Delaunay */ +/* triangulation by deleting the triangles it */ +/* intersects, and triangulating the polygons that */ +/* form on each side of it. */ +/* */ +/* Generates a single edge connecting `endpoint1' to `endpoint2'. The */ +/* triangle `starttri' has `endpoint1' as its origin. `newmark' is the */ +/* boundary marker of the segment. */ +/* */ +/* To insert a segment, every triangle whose interior intersects the */ +/* segment is deleted. The union of these deleted triangles is a polygon */ +/* (which is not necessarily monotone, but is close enough), which is */ +/* divided into two polygons by the new segment. This routine's task is */ +/* to generate the Delaunay triangulation of these two polygons. */ +/* */ +/* You might think of this routine's behavior as a two-step process. The */ +/* first step is to walk from endpoint1 to endpoint2, flipping each edge */ +/* encountered. This step creates a fan of edges connected to endpoint1, */ +/* including the desired edge to endpoint2. The second step enforces the */ +/* Delaunay condition on each side of the segment in an incremental manner: */ +/* proceeding along the polygon from endpoint1 to endpoint2 (this is done */ +/* independently on each side of the segment), each vertex is "enforced" */ +/* as if it had just been inserted, but affecting only the previous */ +/* vertices. The result is the same as if the vertices had been inserted */ +/* in the order they appear on the polygon, so the result is Delaunay. */ +/* */ +/* In truth, constrainededge() interleaves these two steps. The procedure */ +/* walks from endpoint1 to endpoint2, and each time an edge is encountered */ +/* and flipped, the newly exposed vertex (at the far end of the flipped */ +/* edge) is "enforced" upon the previously flipped edges, usually affecting */ +/* only one side of the polygon (depending upon which side of the segment */ +/* the vertex falls on). */ +/* */ +/* The algorithm is complicated by the need to handle polygons that are not */ +/* convex. Although the polygon is not necessarily monotone, it can be */ +/* triangulated in a manner similar to the stack-based algorithms for */ +/* monotone polygons. For each reflex vertex (local concavity) of the */ +/* polygon, there will be an inverted triangle formed by one of the edge */ +/* flips. (An inverted triangle is one with negative area - that is, its */ +/* vertices are arranged in clockwise order - and is best thought of as a */ +/* wrinkle in the fabric of the mesh.) Each inverted triangle can be */ +/* thought of as a reflex vertex pushed on the stack, waiting to be fixed */ +/* later. */ +/* */ +/* A reflex vertex is popped from the stack when a vertex is inserted that */ +/* is visible to the reflex vertex. (However, if the vertex behind the */ +/* reflex vertex is not visible to the reflex vertex, a new inverted */ +/* triangle will take its place on the stack.) These details are handled */ +/* by the delaunayfixup() routine above. */ +/* */ +/*****************************************************************************/ + +void constrainededge(starttri, endpoint2, newmark) +struct triedge *starttri; +point endpoint2; +int newmark; +{ + struct triedge fixuptri, fixuptri2; + struct edge fixupedge; + point endpoint1; + point farpoint; + REAL area; + int collision; + int done; + triangle ptr; /* Temporary variable used by sym() and oprev(). */ + shelle sptr; /* Temporary variable used by tspivot(). */ + + org(*starttri, endpoint1); + lnext(*starttri, fixuptri); + flip(&fixuptri); + /* `collision' indicates whether we have found a point directly */ + /* between endpoint1 and endpoint2. */ + collision = 0; + done = 0; + do { + org(fixuptri, farpoint); + /* `farpoint' is the extreme point of the polygon we are "digging" */ + /* to get from endpoint1 to endpoint2. */ + if ((farpoint[0] == endpoint2[0]) && (farpoint[1] == endpoint2[1])) { + oprev(fixuptri, fixuptri2); + /* Enforce the Delaunay condition around endpoint2. */ + delaunayfixup(&fixuptri, 0); + delaunayfixup(&fixuptri2, 1); + done = 1; + } else { + /* Check whether farpoint is to the left or right of the segment */ + /* being inserted, to decide which edge of fixuptri to dig */ + /* through next. */ + area = counterclockwise(endpoint1, endpoint2, farpoint); + if (area == 0.0) { + /* We've collided with a point between endpoint1 and endpoint2. */ + collision = 1; + oprev(fixuptri, fixuptri2); + /* Enforce the Delaunay condition around farpoint. */ + delaunayfixup(&fixuptri, 0); + delaunayfixup(&fixuptri2, 1); + done = 1; + } else { + if (area > 0.0) { /* farpoint is to the left of the segment. */ + oprev(fixuptri, fixuptri2); + /* Enforce the Delaunay condition around farpoint, on the */ + /* left side of the segment only. */ + delaunayfixup(&fixuptri2, 1); + /* Flip the edge that crosses the segment. After the edge is */ + /* flipped, one of its endpoints is the fan vertex, and the */ + /* destination of fixuptri is the fan vertex. */ + lprevself(fixuptri); + } else { /* farpoint is to the right of the segment. */ + delaunayfixup(&fixuptri, 0); + /* Flip the edge that crosses the segment. After the edge is */ + /* flipped, one of its endpoints is the fan vertex, and the */ + /* destination of fixuptri is the fan vertex. */ + oprevself(fixuptri); + } + /* Check for two intersecting segments. */ + tspivot(fixuptri, fixupedge); + if (fixupedge.sh == dummysh) { + flip(&fixuptri); /* May create an inverted triangle on the left. */ + } else { + /* We've collided with a segment between endpoint1 and endpoint2. */ + collision = 1; + /* Insert a point at the intersection. */ + segmentintersection(&fixuptri, &fixupedge, endpoint2); + done = 1; + } + } + } + } while (!done); + /* Insert a shell edge to make the segment permanent. */ + insertshelle(&fixuptri, newmark); + /* If there was a collision with an interceding vertex, install another */ + /* segment connecting that vertex with endpoint2. */ + if (collision) { + /* Insert the remainder of the segment. */ + if (!scoutsegment(&fixuptri, endpoint2, newmark)) { + constrainededge(&fixuptri, endpoint2, newmark); + } + } +} + +/*****************************************************************************/ +/* */ +/* insertsegment() Insert a PSLG segment into a triangulation. */ +/* */ +/*****************************************************************************/ + +void insertsegment(endpoint1, endpoint2, newmark) +point endpoint1; +point endpoint2; +int newmark; +{ + struct triedge searchtri1, searchtri2; + triangle encodedtri; + point checkpoint; + triangle ptr; /* Temporary variable used by sym(). */ + + if (verbose > 1) { + printf(" Connecting (%.12g, %.12g) to (%.12g, %.12g).\n", + endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]); + } + + /* Find a triangle whose origin is the segment's first endpoint. */ + checkpoint = (point) NULL; + encodedtri = point2tri(endpoint1); + if (encodedtri != (triangle) NULL) { + decode(encodedtri, searchtri1); + org(searchtri1, checkpoint); + } + if (checkpoint != endpoint1) { + /* Find a boundary triangle to search from. */ + searchtri1.tri = dummytri; + searchtri1.orient = 0; + symself(searchtri1); + /* Search for the segment's first endpoint by point location. */ + if (locate(endpoint1, &searchtri1) != ONVERTEX) { + printf( + "Internal error in insertsegment(): Unable to locate PSLG point\n"); + printf(" (%.12g, %.12g) in triangulation.\n", + endpoint1[0], endpoint1[1]); + internalerror(); + } + } + /* Remember this triangle to improve subsequent point location. */ + triedgecopy(searchtri1, recenttri); + /* Scout the beginnings of a path from the first endpoint */ + /* toward the second. */ + if (scoutsegment(&searchtri1, endpoint2, newmark)) { + /* The segment was easily inserted. */ + return; + } + /* The first endpoint may have changed if a collision with an intervening */ + /* vertex on the segment occurred. */ + org(searchtri1, endpoint1); + + /* Find a triangle whose origin is the segment's second endpoint. */ + checkpoint = (point) NULL; + encodedtri = point2tri(endpoint2); + if (encodedtri != (triangle) NULL) { + decode(encodedtri, searchtri2); + org(searchtri2, checkpoint); + } + if (checkpoint != endpoint2) { + /* Find a boundary triangle to search from. */ + searchtri2.tri = dummytri; + searchtri2.orient = 0; + symself(searchtri2); + /* Search for the segment's second endpoint by point location. */ + if (locate(endpoint2, &searchtri2) != ONVERTEX) { + printf( + "Internal error in insertsegment(): Unable to locate PSLG point\n"); + printf(" (%.12g, %.12g) in triangulation.\n", + endpoint2[0], endpoint2[1]); + internalerror(); + } + } + /* Remember this triangle to improve subsequent point location. */ + triedgecopy(searchtri2, recenttri); + /* Scout the beginnings of a path from the second endpoint */ + /* toward the first. */ + if (scoutsegment(&searchtri2, endpoint1, newmark)) { + /* The segment was easily inserted. */ + return; + } + /* The second endpoint may have changed if a collision with an intervening */ + /* vertex on the segment occurred. */ + org(searchtri2, endpoint2); + +#ifndef REDUCED +#ifndef CDT_ONLY + if (splitseg) { + /* Insert vertices to force the segment into the triangulation. */ + conformingedge(endpoint1, endpoint2, newmark); + } else { +#endif /* not CDT_ONLY */ +#endif /* not REDUCED */ + /* Insert the segment directly into the triangulation. */ + constrainededge(&searchtri1, endpoint2, newmark); +#ifndef REDUCED +#ifndef CDT_ONLY + } +#endif /* not CDT_ONLY */ +#endif /* not REDUCED */ +} + +/*****************************************************************************/ +/* */ +/* markhull() Cover the convex hull of a triangulation with shell edges. */ +/* */ +/*****************************************************************************/ + +void markhull() +{ + struct triedge hulltri; + struct triedge nexttri; + struct triedge starttri; + triangle ptr; /* Temporary variable used by sym() and oprev(). */ + + /* Find a triangle handle on the hull. */ + hulltri.tri = dummytri; + hulltri.orient = 0; + symself(hulltri); + /* Remember where we started so we know when to stop. */ + triedgecopy(hulltri, starttri); + /* Go once counterclockwise around the convex hull. */ + do { + /* Create a shell edge if there isn't already one here. */ + insertshelle(&hulltri, 1); + /* To find the next hull edge, go clockwise around the next vertex. */ + lnextself(hulltri); + oprev(hulltri, nexttri); + while (nexttri.tri != dummytri) { + triedgecopy(nexttri, hulltri); + oprev(hulltri, nexttri); + } + } while (!triedgeequal(hulltri, starttri)); +} + +/*****************************************************************************/ +/* */ +/* formskeleton() Create the shell edges of a triangulation, including */ +/* PSLG edges and edges on the convex hull. */ +/* */ +/* The PSLG edges are read from a .poly file. The return value is the */ +/* number of segments in the file. */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +int formskeleton(segmentlist, segmentmarkerlist, numberofsegments) +int *segmentlist; +int *segmentmarkerlist; +int numberofsegments; + +#else /* not TRILIBRARY */ + +int formskeleton(polyfile, polyfilename) +FILE *polyfile; +char *polyfilename; + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + char polyfilename[6]; + int index; +#else /* not TRILIBRARY */ + char inputline[INPUTLINESIZE]; + char *stringptr; +#endif /* not TRILIBRARY */ + point endpoint1, endpoint2; + int segments; + int segmentmarkers; + int end1, end2; + int boundmarker; + int i; + + if (poly) { + if (!quiet) { + printf("Inserting segments into Delaunay triangulation.\n"); + } +#ifdef TRILIBRARY + strcpy(polyfilename, "input"); + segments = numberofsegments; + segmentmarkers = segmentmarkerlist != (int *) NULL; + index = 0; +#else /* not TRILIBRARY */ + /* Read the segments from a .poly file. */ + /* Read number of segments and number of boundary markers. */ + stringptr = readline(inputline, polyfile, polyfilename); + segments = (int) strtol (stringptr, &stringptr, 0); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + segmentmarkers = 0; + } else { + segmentmarkers = (int) strtol (stringptr, &stringptr, 0); + } +#endif /* not TRILIBRARY */ + /* If segments are to be inserted, compute a mapping */ + /* from points to triangles. */ + if (segments > 0) { + if (verbose) { + printf(" Inserting PSLG segments.\n"); + } + makepointmap(); + } + + boundmarker = 0; + /* Read and insert the segments. */ + for (i = 1; i <= segments; i++) { +#ifdef TRILIBRARY + end1 = segmentlist[index++]; + end2 = segmentlist[index++]; + if (segmentmarkers) { + boundmarker = segmentmarkerlist[i - 1]; + } +#else /* not TRILIBRARY */ + stringptr = readline(inputline, polyfile, inpolyfilename); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Segment %d has no endpoints in %s.\n", i, + polyfilename); + exit(1); + } else { + end1 = (int) strtol (stringptr, &stringptr, 0); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Segment %d is missing its second endpoint in %s.\n", i, + polyfilename); + exit(1); + } else { + end2 = (int) strtol (stringptr, &stringptr, 0); + } + if (segmentmarkers) { + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + boundmarker = 0; + } else { + boundmarker = (int) strtol (stringptr, &stringptr, 0); + } + } +#endif /* not TRILIBRARY */ + if ((end1 < firstnumber) || (end1 >= firstnumber + inpoints)) { + if (!quiet) { + printf("Warning: Invalid first endpoint of segment %d in %s.\n", i, + polyfilename); + } + } else if ((end2 < firstnumber) || (end2 >= firstnumber + inpoints)) { + if (!quiet) { + printf("Warning: Invalid second endpoint of segment %d in %s.\n", i, + polyfilename); + } + } else { + endpoint1 = getpoint(end1); + endpoint2 = getpoint(end2); + if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) { + if (!quiet) { + printf("Warning: Endpoints of segment %d are coincident in %s.\n", + i, polyfilename); + } + } else { + insertsegment(endpoint1, endpoint2, boundmarker); + } + } + } + } else { + segments = 0; + } + if (convex || !poly) { + /* Enclose the convex hull with shell edges. */ + if (verbose) { + printf(" Enclosing convex hull with segments.\n"); + } + markhull(); + } + return segments; +} + +/** **/ +/** **/ +/********* Segment (shell edge) insertion ends here *********/ + +/********* Carving out holes and concavities begins here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* infecthull() Virally infect all of the triangles of the convex hull */ +/* that are not protected by shell edges. Where there are */ +/* shell edges, set boundary markers as appropriate. */ +/* */ +/*****************************************************************************/ + +void infecthull() +{ + struct triedge hulltri; + struct triedge nexttri; + struct triedge starttri; + struct edge hulledge; + triangle **deadtri; + point horg, hdest; + triangle ptr; /* Temporary variable used by sym(). */ + shelle sptr; /* Temporary variable used by tspivot(). */ + + if (verbose) { + printf(" Marking concavities (external triangles) for elimination.\n"); + } + /* Find a triangle handle on the hull. */ + hulltri.tri = dummytri; + hulltri.orient = 0; + symself(hulltri); + /* Remember where we started so we know when to stop. */ + triedgecopy(hulltri, starttri); + /* Go once counterclockwise around the convex hull. */ + do { + /* Ignore triangles that are already infected. */ + if (!infected(hulltri)) { + /* Is the triangle protected by a shell edge? */ + tspivot(hulltri, hulledge); + if (hulledge.sh == dummysh) { + /* The triangle is not protected; infect it. */ + infect(hulltri); + deadtri = (triangle **) poolalloc(&viri); + *deadtri = hulltri.tri; + } else { + /* The triangle is protected; set boundary markers if appropriate. */ + if (mark(hulledge) == 0) { + setmark(hulledge, 1); + org(hulltri, horg); + dest(hulltri, hdest); + if (pointmark(horg) == 0) { + setpointmark(horg, 1); + } + if (pointmark(hdest) == 0) { + setpointmark(hdest, 1); + } + } + } + } + /* To find the next hull edge, go clockwise around the next vertex. */ + lnextself(hulltri); + oprev(hulltri, nexttri); + while (nexttri.tri != dummytri) { + triedgecopy(nexttri, hulltri); + oprev(hulltri, nexttri); + } + } while (!triedgeequal(hulltri, starttri)); +} + +/*****************************************************************************/ +/* */ +/* plague() Spread the virus from all infected triangles to any neighbors */ +/* not protected by shell edges. Delete all infected triangles. */ +/* */ +/* This is the procedure that actually creates holes and concavities. */ +/* */ +/* This procedure operates in two phases. The first phase identifies all */ +/* the triangles that will die, and marks them as infected. They are */ +/* marked to ensure that each triangle is added to the virus pool only */ +/* once, so the procedure will terminate. */ +/* */ +/* The second phase actually eliminates the infected triangles. It also */ +/* eliminates orphaned points. */ +/* */ +/*****************************************************************************/ + +void plague() +{ + struct triedge testtri; + struct triedge neighbor; + triangle **virusloop; + triangle **deadtri; + struct edge neighborshelle; + point testpoint; + point norg, ndest; + point deadorg, deaddest, deadapex; + int killorg; + triangle ptr; /* Temporary variable used by sym() and onext(). */ + shelle sptr; /* Temporary variable used by tspivot(). */ + + if (verbose) { + printf(" Marking neighbors of marked triangles.\n"); + } + /* Loop through all the infected triangles, spreading the virus to */ + /* their neighbors, then to their neighbors' neighbors. */ + traversalinit(&viri); + virusloop = (triangle **) traverse(&viri); + while (virusloop != (triangle **) NULL) { + testtri.tri = *virusloop; + /* A triangle is marked as infected by messing with one of its shell */ + /* edges, setting it to an illegal value. Hence, we have to */ + /* temporarily uninfect this triangle so that we can examine its */ + /* adjacent shell edges. */ + uninfect(testtri); + if (verbose > 2) { + /* Assign the triangle an orientation for convenience in */ + /* checking its points. */ + testtri.orient = 0; + org(testtri, deadorg); + dest(testtri, deaddest); + apex(testtri, deadapex); + printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", + deadorg[0], deadorg[1], deaddest[0], deaddest[1], + deadapex[0], deadapex[1]); + } + /* Check each of the triangle's three neighbors. */ + for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { + /* Find the neighbor. */ + sym(testtri, neighbor); + /* Check for a shell between the triangle and its neighbor. */ + tspivot(testtri, neighborshelle); + /* Check if the neighbor is nonexistent or already infected. */ + if ((neighbor.tri == dummytri) || infected(neighbor)) { + if (neighborshelle.sh != dummysh) { + /* There is a shell edge separating the triangle from its */ + /* neighbor, but both triangles are dying, so the shell */ + /* edge dies too. */ + shelledealloc(neighborshelle.sh); + if (neighbor.tri != dummytri) { + /* Make sure the shell edge doesn't get deallocated again */ + /* later when the infected neighbor is visited. */ + uninfect(neighbor); + tsdissolve(neighbor); + infect(neighbor); + } + } + } else { /* The neighbor exists and is not infected. */ + if (neighborshelle.sh == dummysh) { + /* There is no shell edge protecting the neighbor, so */ + /* the neighbor becomes infected. */ + if (verbose > 2) { + org(neighbor, deadorg); + dest(neighbor, deaddest); + apex(neighbor, deadapex); + printf( + " Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", + deadorg[0], deadorg[1], deaddest[0], deaddest[1], + deadapex[0], deadapex[1]); + } + infect(neighbor); + /* Ensure that the neighbor's neighbors will be infected. */ + deadtri = (triangle **) poolalloc(&viri); + *deadtri = neighbor.tri; + } else { /* The neighbor is protected by a shell edge. */ + /* Remove this triangle from the shell edge. */ + stdissolve(neighborshelle); + /* The shell edge becomes a boundary. Set markers accordingly. */ + if (mark(neighborshelle) == 0) { + setmark(neighborshelle, 1); + } + org(neighbor, norg); + dest(neighbor, ndest); + if (pointmark(norg) == 0) { + setpointmark(norg, 1); + } + if (pointmark(ndest) == 0) { + setpointmark(ndest, 1); + } + } + } + } + /* Remark the triangle as infected, so it doesn't get added to the */ + /* virus pool again. */ + infect(testtri); + virusloop = (triangle **) traverse(&viri); + } + + if (verbose) { + printf(" Deleting marked triangles.\n"); + } + traversalinit(&viri); + virusloop = (triangle **) traverse(&viri); + while (virusloop != (triangle **) NULL) { + testtri.tri = *virusloop; + + /* Check each of the three corners of the triangle for elimination. */ + /* This is done by walking around each point, checking if it is */ + /* still connected to at least one live triangle. */ + for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { + org(testtri, testpoint); + /* Check if the point has already been tested. */ + if (testpoint != (point) NULL) { + killorg = 1; + /* Mark the corner of the triangle as having been tested. */ + setorg(testtri, NULL); + /* Walk counterclockwise about the point. */ + onext(testtri, neighbor); + /* Stop upon reaching a boundary or the starting triangle. */ + while ((neighbor.tri != dummytri) + && (!triedgeequal(neighbor, testtri))) { + if (infected(neighbor)) { + /* Mark the corner of this triangle as having been tested. */ + setorg(neighbor, NULL); + } else { + /* A live triangle. The point survives. */ + killorg = 0; + } + /* Walk counterclockwise about the point. */ + onextself(neighbor); + } + /* If we reached a boundary, we must walk clockwise as well. */ + if (neighbor.tri == dummytri) { + /* Walk clockwise about the point. */ + oprev(testtri, neighbor); + /* Stop upon reaching a boundary. */ + while (neighbor.tri != dummytri) { + if (infected(neighbor)) { + /* Mark the corner of this triangle as having been tested. */ + setorg(neighbor, NULL); + } else { + /* A live triangle. The point survives. */ + killorg = 0; + } + /* Walk clockwise about the point. */ + oprevself(neighbor); + } + } + if (killorg) { + if (verbose > 1) { + printf(" Deleting point (%.12g, %.12g)\n", + testpoint[0], testpoint[1]); + } + pointdealloc(testpoint); + } + } + } + + /* Record changes in the number of boundary edges, and disconnect */ + /* dead triangles from their neighbors. */ + for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { + sym(testtri, neighbor); + if (neighbor.tri == dummytri) { + /* There is no neighboring triangle on this edge, so this edge */ + /* is a boundary edge. This triangle is being deleted, so this */ + /* boundary edge is deleted. */ + hullsize--; + } else { + /* Disconnect the triangle from its neighbor. */ + dissolve(neighbor); + /* There is a neighboring triangle on this edge, so this edge */ + /* becomes a boundary edge when this triangle is deleted. */ + hullsize++; + } + } + /* Return the dead triangle to the pool of triangles. */ + triangledealloc(testtri.tri); + virusloop = (triangle **) traverse(&viri); + } + /* Empty the virus pool. */ + poolrestart(&viri); +} + +/*****************************************************************************/ +/* */ +/* regionplague() Spread regional attributes and/or area constraints */ +/* (from a .poly file) throughout the mesh. */ +/* */ +/* This procedure operates in two phases. The first phase spreads an */ +/* attribute and/or an area constraint through a (segment-bounded) region. */ +/* The triangles are marked to ensure that each triangle is added to the */ +/* virus pool only once, so the procedure will terminate. */ +/* */ +/* The second phase uninfects all infected triangles, returning them to */ +/* normal. */ +/* */ +/*****************************************************************************/ + +void regionplague(attribute, area) +REAL attribute; +REAL area; +{ + struct triedge testtri; + struct triedge neighbor; + triangle **virusloop; + triangle **regiontri; + struct edge neighborshelle; + point regionorg, regiondest, regionapex; + triangle ptr; /* Temporary variable used by sym() and onext(). */ + shelle sptr; /* Temporary variable used by tspivot(). */ + + if (verbose > 1) { + printf(" Marking neighbors of marked triangles.\n"); + } + /* Loop through all the infected triangles, spreading the attribute */ + /* and/or area constraint to their neighbors, then to their neighbors' */ + /* neighbors. */ + traversalinit(&viri); + virusloop = (triangle **) traverse(&viri); + while (virusloop != (triangle **) NULL) { + testtri.tri = *virusloop; + /* A triangle is marked as infected by messing with one of its shell */ + /* edges, setting it to an illegal value. Hence, we have to */ + /* temporarily uninfect this triangle so that we can examine its */ + /* adjacent shell edges. */ + uninfect(testtri); + if (regionattrib) { + /* Set an attribute. */ + setelemattribute(testtri, eextras, attribute); + } + if (vararea) { + /* Set an area constraint. */ + setareabound(testtri, area); + } + if (verbose > 2) { + /* Assign the triangle an orientation for convenience in */ + /* checking its points. */ + testtri.orient = 0; + org(testtri, regionorg); + dest(testtri, regiondest); + apex(testtri, regionapex); + printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", + regionorg[0], regionorg[1], regiondest[0], regiondest[1], + regionapex[0], regionapex[1]); + } + /* Check each of the triangle's three neighbors. */ + for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { + /* Find the neighbor. */ + sym(testtri, neighbor); + /* Check for a shell between the triangle and its neighbor. */ + tspivot(testtri, neighborshelle); + /* Make sure the neighbor exists, is not already infected, and */ + /* isn't protected by a shell edge. */ + if ((neighbor.tri != dummytri) && !infected(neighbor) + && (neighborshelle.sh == dummysh)) { + if (verbose > 2) { + org(neighbor, regionorg); + dest(neighbor, regiondest); + apex(neighbor, regionapex); + printf(" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", + regionorg[0], regionorg[1], regiondest[0], regiondest[1], + regionapex[0], regionapex[1]); + } + /* Infect the neighbor. */ + infect(neighbor); + /* Ensure that the neighbor's neighbors will be infected. */ + regiontri = (triangle **) poolalloc(&viri); + *regiontri = neighbor.tri; + } + } + /* Remark the triangle as infected, so it doesn't get added to the */ + /* virus pool again. */ + infect(testtri); + virusloop = (triangle **) traverse(&viri); + } + + /* Uninfect all triangles. */ + if (verbose > 1) { + printf(" Unmarking marked triangles.\n"); + } + traversalinit(&viri); + virusloop = (triangle **) traverse(&viri); + while (virusloop != (triangle **) NULL) { + testtri.tri = *virusloop; + uninfect(testtri); + virusloop = (triangle **) traverse(&viri); + } + /* Empty the virus pool. */ + poolrestart(&viri); +} + +/*****************************************************************************/ +/* */ +/* carveholes() Find the holes and infect them. Find the area */ +/* constraints and infect them. Infect the convex hull. */ +/* Spread the infection and kill triangles. Spread the */ +/* area constraints. */ +/* */ +/* This routine mainly calls other routines to carry out all these */ +/* functions. */ +/* */ +/*****************************************************************************/ + +void carveholes(holelist, holes, regionlist, regions) +REAL *holelist; +int holes; +REAL *regionlist; +int regions; +{ + struct triedge searchtri; + struct triedge triangleloop; + struct triedge *regiontris; + triangle **holetri; + triangle **regiontri; + point searchorg, searchdest; + enum locateresult intersect; + int i; + triangle ptr; /* Temporary variable used by sym(). */ + + if (!(quiet || (noholes && convex))) { + printf("Removing unwanted triangles.\n"); + if (verbose && (holes > 0)) { + printf(" Marking holes for elimination.\n"); + } + } + + if (regions > 0) { + /* Allocate storage for the triangles in which region points fall. */ + regiontris = (struct triedge *) malloc(regions * sizeof(struct triedge)); + if (regiontris == (struct triedge *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + + if (((holes > 0) && !noholes) || !convex || (regions > 0)) { + /* Initialize a pool of viri to be used for holes, concavities, */ + /* regional attributes, and/or regional area constraints. */ + poolinit(&viri, sizeof(triangle *), VIRUSPERBLOCK, POINTER, 0); + } + + if (!convex) { + /* Mark as infected any unprotected triangles on the boundary. */ + /* This is one way by which concavities are created. */ + infecthull(); + } + + if ((holes > 0) && !noholes) { + /* Infect each triangle in which a hole lies. */ + for (i = 0; i < 2 * holes; i += 2) { + /* Ignore holes that aren't within the bounds of the mesh. */ + if ((holelist[i] >= xmin) && (holelist[i] <= xmax) + && (holelist[i + 1] >= ymin) && (holelist[i + 1] <= ymax)) { + /* Start searching from some triangle on the outer boundary. */ + searchtri.tri = dummytri; + searchtri.orient = 0; + symself(searchtri); + /* Ensure that the hole is to the left of this boundary edge; */ + /* otherwise, locate() will falsely report that the hole */ + /* falls within the starting triangle. */ + org(searchtri, searchorg); + dest(searchtri, searchdest); + if (counterclockwise(searchorg, searchdest, &holelist[i]) > 0.0) { + /* Find a triangle that contains the hole. */ + intersect = locate(&holelist[i], &searchtri); + if ((intersect != OUTSIDE) && (!infected(searchtri))) { + /* Infect the triangle. This is done by marking the triangle */ + /* as infect and including the triangle in the virus pool. */ + infect(searchtri); + holetri = (triangle **) poolalloc(&viri); + *holetri = searchtri.tri; + } + } + } + } + } + + /* Now, we have to find all the regions BEFORE we carve the holes, because */ + /* locate() won't work when the triangulation is no longer convex. */ + /* (Incidentally, this is the reason why regional attributes and area */ + /* constraints can't be used when refining a preexisting mesh, which */ + /* might not be convex; they can only be used with a freshly */ + /* triangulated PSLG.) */ + if (regions > 0) { + /* Find the starting triangle for each region. */ + for (i = 0; i < regions; i++) { + regiontris[i].tri = dummytri; + /* Ignore region points that aren't within the bounds of the mesh. */ + if ((regionlist[4 * i] >= xmin) && (regionlist[4 * i] <= xmax) && + (regionlist[4 * i + 1] >= ymin) && (regionlist[4 * i + 1] <= ymax)) { + /* Start searching from some triangle on the outer boundary. */ + searchtri.tri = dummytri; + searchtri.orient = 0; + symself(searchtri); + /* Ensure that the region point is to the left of this boundary */ + /* edge; otherwise, locate() will falsely report that the */ + /* region point falls within the starting triangle. */ + org(searchtri, searchorg); + dest(searchtri, searchdest); + if (counterclockwise(searchorg, searchdest, ®ionlist[4 * i]) > + 0.0) { + /* Find a triangle that contains the region point. */ + intersect = locate(®ionlist[4 * i], &searchtri); + if ((intersect != OUTSIDE) && (!infected(searchtri))) { + /* Record the triangle for processing after the */ + /* holes have been carved. */ + triedgecopy(searchtri, regiontris[i]); + } + } + } + } + } + + if (viri.items > 0) { + /* Carve the holes and concavities. */ + plague(); + } + /* The virus pool should be empty now. */ + + if (regions > 0) { + if (!quiet) { + if (regionattrib) { + if (vararea) { + printf("Spreading regional attributes and area constraints.\n"); + } else { + printf("Spreading regional attributes.\n"); + } + } else { + printf("Spreading regional area constraints.\n"); + } + } + if (regionattrib && !refine) { + /* Assign every triangle a regional attribute of zero. */ + traversalinit(&triangles); + triangleloop.orient = 0; + triangleloop.tri = triangletraverse(); + while (triangleloop.tri != (triangle *) NULL) { + setelemattribute(triangleloop, eextras, 0.0); + triangleloop.tri = triangletraverse(); + } + } + for (i = 0; i < regions; i++) { + if (regiontris[i].tri != dummytri) { + /* Make sure the triangle under consideration still exists. */ + /* It may have been eaten by the virus. */ + if (regiontris[i].tri[3] != (triangle) NULL) { + /* Put one triangle in the virus pool. */ + infect(regiontris[i]); + regiontri = (triangle **) poolalloc(&viri); + *regiontri = regiontris[i].tri; + /* Apply one region's attribute and/or area constraint. */ + regionplague(regionlist[4 * i + 2], regionlist[4 * i + 3]); + /* The virus pool should be empty now. */ + } + } + } + if (regionattrib && !refine) { + /* Note the fact that each triangle has an additional attribute. */ + eextras++; + } + } + + /* Free up memory. */ + if (((holes > 0) && !noholes) || !convex || (regions > 0)) { + pooldeinit(&viri); + } + if (regions > 0) { + free(regiontris); + } +} + +/** **/ +/** **/ +/********* Carving out holes and concavities ends here *********/ + +/********* Mesh quality maintenance begins here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* tallyencs() Traverse the entire list of shell edges, check each edge */ +/* to see if it is encroached. If so, add it to the list. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +void tallyencs() +{ + struct edge edgeloop; + int dummy; + + traversalinit(&shelles); + edgeloop.shorient = 0; + edgeloop.sh = shelletraverse(); + while (edgeloop.sh != (shelle *) NULL) { + /* If the segment is encroached, add it to the list. */ + dummy = checkedge4encroach(&edgeloop); + edgeloop.sh = shelletraverse(); + } +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* precisionerror() Print an error message for precision problems. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +void precisionerror() +{ + printf("Try increasing the area criterion and/or reducing the minimum\n"); + printf(" allowable angle so that tiny triangles are not created.\n"); +#ifdef SINGLE + printf("Alternatively, try recompiling me with double precision\n"); + printf(" arithmetic (by removing \"#define SINGLE\" from the\n"); + printf(" source file or \"-DSINGLE\" from the makefile).\n"); +#endif /* SINGLE */ +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* repairencs() Find and repair all the encroached segments. */ +/* */ +/* Encroached segments are repaired by splitting them by inserting a point */ +/* at or near their centers. */ +/* */ +/* `flaws' is a flag that specifies whether one should take note of new */ +/* encroached segments and bad triangles that result from inserting points */ +/* to repair existing encroached segments. */ +/* */ +/* When a segment is split, the two resulting subsegments are always */ +/* tested to see if they are encroached upon, regardless of the value */ +/* of `flaws'. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +void repairencs(flaws) +int flaws; +{ + struct triedge enctri; + struct triedge testtri; + struct edge *encloop; + struct edge testsh; + point eorg, edest; + point newpoint; + enum insertsiteresult success; + REAL segmentlength, nearestpoweroftwo; + REAL split; + int acuteorg, acutedest; + int dummy; + int i; + triangle ptr; /* Temporary variable used by stpivot(). */ + shelle sptr; /* Temporary variable used by snext(). */ + + while ((badsegments.items > 0) && (steinerleft != 0)) { + traversalinit(&badsegments); + encloop = badsegmenttraverse(); + while ((encloop != (struct edge *) NULL) && (steinerleft != 0)) { + /* To decide where to split a segment, we need to know if the */ + /* segment shares an endpoint with an adjacent segment. */ + /* The concern is that, if we simply split every encroached */ + /* segment in its center, two adjacent segments with a small */ + /* angle between them might lead to an infinite loop; each */ + /* point added to split one segment will encroach upon the */ + /* other segment, which must then be split with a point that */ + /* will encroach upon the first segment, and so on forever. */ + /* To avoid this, imagine a set of concentric circles, whose */ + /* radii are powers of two, about each segment endpoint. */ + /* These concentric circles determine where the segment is */ + /* split. (If both endpoints are shared with adjacent */ + /* segments, split the segment in the middle, and apply the */ + /* concentric shells for later splittings.) */ + + /* Is the origin shared with another segment? */ + stpivot(*encloop, enctri); + lnext(enctri, testtri); + tspivot(testtri, testsh); + acuteorg = testsh.sh != dummysh; + /* Is the destination shared with another segment? */ + lnextself(testtri); + tspivot(testtri, testsh); + acutedest = testsh.sh != dummysh; + /* Now, check the other side of the segment, if there's a triangle */ + /* there. */ + sym(enctri, testtri); + if (testtri.tri != dummytri) { + /* Is the destination shared with another segment? */ + lnextself(testtri); + tspivot(testtri, testsh); + acutedest = acutedest || (testsh.sh != dummysh); + /* Is the origin shared with another segment? */ + lnextself(testtri); + tspivot(testtri, testsh); + acuteorg = acuteorg || (testsh.sh != dummysh); + } + + sorg(*encloop, eorg); + sdest(*encloop, edest); + /* Use the concentric circles if exactly one endpoint is shared */ + /* with another adjacent segment. */ + if (acuteorg ^ acutedest) { + segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0]) + + (edest[1] - eorg[1]) * (edest[1] - eorg[1])); + /* Find the power of two nearest the segment's length. */ + nearestpoweroftwo = 1.0; + while (segmentlength > SQUAREROOTTWO * nearestpoweroftwo) { + nearestpoweroftwo *= 2.0; + } + while (segmentlength < (0.5 * SQUAREROOTTWO) * nearestpoweroftwo) { + nearestpoweroftwo *= 0.5; + } + /* Where do we split the segment? */ + split = 0.5 * nearestpoweroftwo / segmentlength; + if (acutedest) { + split = 1.0 - split; + } + } else { + /* If we're not worried about adjacent segments, split */ + /* this segment in the middle. */ + split = 0.5; + } + + /* Create the new point. */ + newpoint = (point) poolalloc(&points); + /* Interpolate its coordinate and attributes. */ + for (i = 0; i < 2 + nextras; i++) { + newpoint[i] = (1.0 - split) * eorg[i] + split * edest[i]; + } + setpointmark(newpoint, mark(*encloop)); + if (verbose > 1) { + printf( + " Splitting edge (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n", + eorg[0], eorg[1], edest[0], edest[1], newpoint[0], newpoint[1]); + } + /* Check whether the new point lies on an endpoint. */ + if (((newpoint[0] == eorg[0]) && (newpoint[1] == eorg[1])) + || ((newpoint[0] == edest[0]) && (newpoint[1] == edest[1]))) { + printf("Error: Ran out of precision at (%.12g, %.12g).\n", + newpoint[0], newpoint[1]); + printf("I attempted to split a segment to a smaller size than can\n"); + printf(" be accommodated by the finite precision of floating point\n" + ); + printf(" arithmetic.\n"); + precisionerror(); + exit(1); + } + /* Insert the splitting point. This should always succeed. */ + success = insertsite(newpoint, &enctri, encloop, flaws, flaws); + if ((success != SUCCESSFULPOINT) && (success != ENCROACHINGPOINT)) { + printf("Internal error in repairencs():\n"); + printf(" Failure to split a segment.\n"); + internalerror(); + } + if (steinerleft > 0) { + steinerleft--; + } + /* Check the two new subsegments to see if they're encroached. */ + dummy = checkedge4encroach(encloop); + snextself(*encloop); + dummy = checkedge4encroach(encloop); + + badsegmentdealloc(encloop); + encloop = badsegmenttraverse(); + } + } +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* tallyfaces() Test every triangle in the mesh for quality measures. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +void tallyfaces() +{ + struct triedge triangleloop; + + if (verbose) { + printf(" Making a list of bad triangles.\n"); + } + traversalinit(&triangles); + triangleloop.orient = 0; + triangleloop.tri = triangletraverse(); + while (triangleloop.tri != (triangle *) NULL) { + /* If the triangle is bad, enqueue it. */ + testtriangle(&triangleloop); + triangleloop.tri = triangletraverse(); + } +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* findcircumcenter() Find the circumcenter of a triangle. */ +/* */ +/* The result is returned both in terms of x-y coordinates and xi-eta */ +/* coordinates. The xi-eta coordinate system is defined in terms of the */ +/* triangle: the origin of the triangle is the origin of the coordinate */ +/* system; the destination of the triangle is one unit along the xi axis; */ +/* and the apex of the triangle is one unit along the eta axis. */ +/* */ +/* The return value indicates which edge of the triangle is shortest. */ +/* */ +/*****************************************************************************/ + +enum circumcenterresult findcircumcenter(torg, tdest, tapex, circumcenter, + xi, eta) +point torg; +point tdest; +point tapex; +point circumcenter; +REAL *xi; +REAL *eta; +{ + REAL xdo, ydo, xao, yao, xad, yad; + REAL dodist, aodist, addist; + REAL denominator; + REAL dx, dy; + + circumcentercount++; + + /* Compute the circumcenter of the triangle. */ + xdo = tdest[0] - torg[0]; + ydo = tdest[1] - torg[1]; + xao = tapex[0] - torg[0]; + yao = tapex[1] - torg[1]; + dodist = xdo * xdo + ydo * ydo; + aodist = xao * xao + yao * yao; + if (noexact) { + denominator = 0.5 / (xdo * yao - xao * ydo); + } else { + /* Use the counterclockwise() routine to ensure a positive (and */ + /* reasonably accurate) result, avoiding any possibility of */ + /* division by zero. */ + denominator = 0.5 / counterclockwise(tdest, tapex, torg); + /* Don't count the above as an orientation test. */ + counterclockcount--; + } + circumcenter[0] = torg[0] - (ydo * aodist - yao * dodist) * denominator; + circumcenter[1] = torg[1] + (xdo * aodist - xao * dodist) * denominator; + + /* To interpolate point attributes for the new point inserted at */ + /* the circumcenter, define a coordinate system with a xi-axis, */ + /* directed from the triangle's origin to its destination, and */ + /* an eta-axis, directed from its origin to its apex. */ + /* Calculate the xi and eta coordinates of the circumcenter. */ + dx = circumcenter[0] - torg[0]; + dy = circumcenter[1] - torg[1]; + *xi = (dx * yao - xao * dy) * (2.0 * denominator); + *eta = (xdo * dy - dx * ydo) * (2.0 * denominator); + + xad = tapex[0] - tdest[0]; + yad = tapex[1] - tdest[1]; + addist = xad * xad + yad * yad; + if ((addist < dodist) && (addist < aodist)) { + return OPPOSITEORG; + } else if (dodist < aodist) { + return OPPOSITEAPEX; + } else { + return OPPOSITEDEST; + } +} + +/*****************************************************************************/ +/* */ +/* splittriangle() Inserts a point at the circumcenter of a triangle. */ +/* Deletes the newly inserted point if it encroaches upon */ +/* a segment. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +void splittriangle(badtri) +struct badface *badtri; +{ + point borg, bdest, bapex; + point newpoint; + REAL xi, eta; + enum insertsiteresult success; + enum circumcenterresult shortedge; + int errorflag; + int i; + + org(badtri->badfacetri, borg); + dest(badtri->badfacetri, bdest); + apex(badtri->badfacetri, bapex); + /* Make sure that this triangle is still the same triangle it was */ + /* when it was tested and determined to be of bad quality. */ + /* Subsequent transformations may have made it a different triangle. */ + if ((borg == badtri->faceorg) && (bdest == badtri->facedest) && + (bapex == badtri->faceapex)) { + if (verbose > 1) { + printf(" Splitting this triangle at its circumcenter:\n"); + printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0], + borg[1], bdest[0], bdest[1], bapex[0], bapex[1]); + } + errorflag = 0; + /* Create a new point at the triangle's circumcenter. */ + newpoint = (point) poolalloc(&points); + shortedge = findcircumcenter(borg, bdest, bapex, newpoint, &xi, &eta); + /* Check whether the new point lies on a triangle vertex. */ + if (((newpoint[0] == borg[0]) && (newpoint[1] == borg[1])) + || ((newpoint[0] == bdest[0]) && (newpoint[1] == bdest[1])) + || ((newpoint[0] == bapex[0]) && (newpoint[1] == bapex[1]))) { + if (!quiet) { + printf("Warning: New point (%.12g, %.12g) falls on existing vertex.\n" + , newpoint[0], newpoint[1]); + errorflag = 1; + } + pointdealloc(newpoint); + } else { + for (i = 2; i < 2 + nextras; i++) { + /* Interpolate the point attributes at the circumcenter. */ + newpoint[i] = borg[i] + xi * (bdest[i] - borg[i]) + + eta * (bapex[i] - borg[i]); + } + /* The new point must be in the interior, and have a marker of zero. */ + setpointmark(newpoint, 0); + /* Ensure that the handle `badtri->badfacetri' represents the shortest */ + /* edge of the triangle. This ensures that the circumcenter must */ + /* fall to the left of this edge, so point location will work. */ + if (shortedge == OPPOSITEORG) { + lnextself(badtri->badfacetri); + } else if (shortedge == OPPOSITEDEST) { + lprevself(badtri->badfacetri); + } + /* Insert the circumcenter, searching from the edge of the triangle, */ + /* and maintain the Delaunay property of the triangulation. */ + success = insertsite(newpoint, &(badtri->badfacetri), + (struct edge *) NULL, 1, 1); + if (success == SUCCESSFULPOINT) { + if (steinerleft > 0) { + steinerleft--; + } + } else if (success == ENCROACHINGPOINT) { + /* If the newly inserted point encroaches upon a segment, delete it. */ + deletesite(&(badtri->badfacetri)); + } else if (success == VIOLATINGPOINT) { + /* Failed to insert the new point, but some segment was */ + /* marked as being encroached. */ + pointdealloc(newpoint); + } else { /* success == DUPLICATEPOINT */ + /* Failed to insert the new point because a vertex is already there. */ + if (!quiet) { + printf( + "Warning: New point (%.12g, %.12g) falls on existing vertex.\n" + , newpoint[0], newpoint[1]); + errorflag = 1; + } + pointdealloc(newpoint); + } + } + if (errorflag) { + if (verbose) { + printf(" The new point is at the circumcenter of triangle\n"); + printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", + borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]); + } + printf("This probably means that I am trying to refine triangles\n"); + printf(" to a smaller size than can be accommodated by the finite\n"); + printf(" precision of floating point arithmetic. (You can be\n"); + printf(" sure of this if I fail to terminate.)\n"); + precisionerror(); + } + } + /* Return the bad triangle to the pool. */ + pooldealloc(&badtriangles, (VOID *) badtri); +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* enforcequality() Remove all the encroached edges and bad triangles */ +/* from the triangulation. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +void enforcequality() +{ + int i; + + if (!quiet) { + printf("Adding Steiner points to enforce quality.\n"); + } + /* Initialize the pool of encroached segments. */ + poolinit(&badsegments, sizeof(struct edge), BADSEGMENTPERBLOCK, POINTER, 0); + if (verbose) { + printf(" Looking for encroached segments.\n"); + } + /* Test all segments to see if they're encroached. */ + tallyencs(); + if (verbose && (badsegments.items > 0)) { + printf(" Splitting encroached segments.\n"); + } + /* Note that steinerleft == -1 if an unlimited number */ + /* of Steiner points is allowed. */ + while ((badsegments.items > 0) && (steinerleft != 0)) { + /* Fix the segments without noting newly encroached segments or */ + /* bad triangles. The reason we don't want to note newly */ + /* encroached segments is because some encroached segments are */ + /* likely to be noted multiple times, and would then be blindly */ + /* split multiple times. I should fix that some time. */ + repairencs(0); + /* Now, find all the segments that became encroached while adding */ + /* points to split encroached segments. */ + tallyencs(); + } + /* At this point, if we haven't run out of Steiner points, the */ + /* triangulation should be (conforming) Delaunay. */ + + /* Next, we worry about enforcing triangle quality. */ + if ((minangle > 0.0) || vararea || fixedarea) { + /* Initialize the pool of bad triangles. */ + poolinit(&badtriangles, sizeof(struct badface), BADTRIPERBLOCK, POINTER, + 0); + /* Initialize the queues of bad triangles. */ + for (i = 0; i < 64; i++) { + queuefront[i] = (struct badface *) NULL; + queuetail[i] = &queuefront[i]; + } + /* Test all triangles to see if they're bad. */ + tallyfaces(); + if (verbose) { + printf(" Splitting bad triangles.\n"); + } + while ((badtriangles.items > 0) && (steinerleft != 0)) { + /* Fix one bad triangle by inserting a point at its circumcenter. */ + splittriangle(dequeuebadtri()); + /* Fix any encroached segments that may have resulted. Record */ + /* any new bad triangles or encroached segments that result. */ + if (badsegments.items > 0) { + repairencs(1); + } + } + } + /* At this point, if we haven't run out of Steiner points, the */ + /* triangulation should be (conforming) Delaunay and have no */ + /* low-quality triangles. */ + + /* Might we have run out of Steiner points too soon? */ + if (!quiet && (badsegments.items > 0) && (steinerleft == 0)) { + printf("\nWarning: I ran out of Steiner points, but the mesh has\n"); + if (badsegments.items == 1) { + printf(" an encroached segment, and therefore might not be truly\n"); + } else { + printf(" %ld encroached segments, and therefore might not be truly\n", + badsegments.items); + } + printf(" Delaunay. If the Delaunay property is important to you,\n"); + printf(" try increasing the number of Steiner points (controlled by\n"); + printf(" the -S switch) slightly and try again.\n\n"); + } +} + +#endif /* not CDT_ONLY */ + +/** **/ +/** **/ +/********* Mesh quality maintenance ends here *********/ + +/*****************************************************************************/ +/* */ +/* highorder() Create extra nodes for quadratic subparametric elements. */ +/* */ +/*****************************************************************************/ + +void highorder() +{ + struct triedge triangleloop, trisym; + struct edge checkmark; + point newpoint; + point torg, tdest; + int i; + triangle ptr; /* Temporary variable used by sym(). */ + shelle sptr; /* Temporary variable used by tspivot(). */ + + if (!quiet) { + printf("Adding vertices for second-order triangles.\n"); + } + /* The following line ensures that dead items in the pool of nodes */ + /* cannot be allocated for the extra nodes associated with high */ + /* order elements. This ensures that the primary nodes (at the */ + /* corners of elements) will occur earlier in the output files, and */ + /* have lower indices, than the extra nodes. */ + points.deaditemstack = (VOID *) NULL; + + traversalinit(&triangles); + triangleloop.tri = triangletraverse(); + /* To loop over the set of edges, loop over all triangles, and look at */ + /* the three edges of each triangle. If there isn't another triangle */ + /* adjacent to the edge, operate on the edge. If there is another */ + /* adjacent triangle, operate on the edge only if the current triangle */ + /* has a smaller pointer than its neighbor. This way, each edge is */ + /* considered only once. */ + while (triangleloop.tri != (triangle *) NULL) { + for (triangleloop.orient = 0; triangleloop.orient < 3; + triangleloop.orient++) { + sym(triangleloop, trisym); + if ((triangleloop.tri < trisym.tri) || (trisym.tri == dummytri)) { + org(triangleloop, torg); + dest(triangleloop, tdest); + /* Create a new node in the middle of the edge. Interpolate */ + /* its attributes. */ + newpoint = (point) poolalloc(&points); + for (i = 0; i < 2 + nextras; i++) { + newpoint[i] = 0.5 * (torg[i] + tdest[i]); + } + /* Set the new node's marker to zero or one, depending on */ + /* whether it lies on a boundary. */ + setpointmark(newpoint, trisym.tri == dummytri); + if (useshelles) { + tspivot(triangleloop, checkmark); + /* If this edge is a segment, transfer the marker to the new node. */ + if (checkmark.sh != dummysh) { + setpointmark(newpoint, mark(checkmark)); + } + } + if (verbose > 1) { + printf(" Creating (%.12g, %.12g).\n", newpoint[0], newpoint[1]); + } + /* Record the new node in the (one or two) adjacent elements. */ + triangleloop.tri[highorderindex + triangleloop.orient] = + (triangle) newpoint; + if (trisym.tri != dummytri) { + trisym.tri[highorderindex + trisym.orient] = (triangle) newpoint; + } + } + } + triangleloop.tri = triangletraverse(); + } +} + +/********* File I/O routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* readline() Read a nonempty line from a file. */ +/* */ +/* A line is considered "nonempty" if it contains something that looks like */ +/* a number. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +char *readline(string, infile, infilename) +char *string; +FILE *infile; +char *infilename; +{ + char *result; + + /* Search for something that looks like a number. */ + do { + result = fgets(string, INPUTLINESIZE, infile); + if (result == (char *) NULL) { + printf(" Error: Unexpected end of file in %s.\n", infilename); + exit(1); + } + /* Skip anything that doesn't look like a number, a comment, */ + /* or the end of a line. */ + while ((*result != '\0') && (*result != '#') + && (*result != '.') && (*result != '+') && (*result != '-') + && ((*result < '0') || (*result > '9'))) { + result++; + } + /* If it's a comment or end of line, read another line and try again. */ + } while ((*result == '#') || (*result == '\0')); + return result; +} + +#endif /* not TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* findfield() Find the next field of a string. */ +/* */ +/* Jumps past the current field by searching for whitespace, then jumps */ +/* past the whitespace to find the next field. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +char *findfield(string) +char *string; +{ + char *result; + + result = string; + /* Skip the current field. Stop upon reaching whitespace. */ + while ((*result != '\0') && (*result != '#') + && (*result != ' ') && (*result != '\t')) { + result++; + } + /* Now skip the whitespace and anything else that doesn't look like a */ + /* number, a comment, or the end of a line. */ + while ((*result != '\0') && (*result != '#') + && (*result != '.') && (*result != '+') && (*result != '-') + && ((*result < '0') || (*result > '9'))) { + result++; + } + /* Check for a comment (prefixed with `#'). */ + if (*result == '#') { + *result = '\0'; + } + return result; +} + +#endif /* not TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* readnodes() Read the points from a file, which may be a .node or .poly */ +/* file. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +void readnodes(nodefilename, polyfilename, polyfile) +char *nodefilename; +char *polyfilename; +FILE **polyfile; +{ + FILE *infile; + point pointloop; + char inputline[INPUTLINESIZE]; + char *stringptr; + char *infilename; + REAL x, y; + int firstnode; + int nodemarkers; + int currentmarker; + int i, j; + + if (poly) { + /* Read the points from a .poly file. */ + if (!quiet) { + printf("Opening %s.\n", polyfilename); + } + *polyfile = fopen(polyfilename, "r"); + if (*polyfile == (FILE *) NULL) { + printf(" Error: Cannot access file %s.\n", polyfilename); + exit(1); + } + /* Read number of points, number of dimensions, number of point */ + /* attributes, and number of boundary markers. */ + stringptr = readline(inputline, *polyfile, polyfilename); + inpoints = (int) strtol (stringptr, &stringptr, 0); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + mesh_dim = 2; + } else { + mesh_dim = (int) strtol (stringptr, &stringptr, 0); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + nextras = 0; + } else { + nextras = (int) strtol (stringptr, &stringptr, 0); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + nodemarkers = 0; + } else { + nodemarkers = (int) strtol (stringptr, &stringptr, 0); + } + if (inpoints > 0) { + infile = *polyfile; + infilename = polyfilename; + readnodefile = 0; + } else { + /* If the .poly file claims there are zero points, that means that */ + /* the points should be read from a separate .node file. */ + readnodefile = 1; + infilename = innodefilename; + } + } else { + readnodefile = 1; + infilename = innodefilename; + *polyfile = (FILE *) NULL; + } + + if (readnodefile) { + /* Read the points from a .node file. */ + if (!quiet) { + printf("Opening %s.\n", innodefilename); + } + infile = fopen(innodefilename, "r"); + if (infile == (FILE *) NULL) { + printf(" Error: Cannot access file %s.\n", innodefilename); + exit(1); + } + /* Read number of points, number of dimensions, number of point */ + /* attributes, and number of boundary markers. */ + stringptr = readline(inputline, infile, innodefilename); + inpoints = (int) strtol (stringptr, &stringptr, 0); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + mesh_dim = 2; + } else { + mesh_dim = (int) strtol (stringptr, &stringptr, 0); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + nextras = 0; + } else { + nextras = (int) strtol (stringptr, &stringptr, 0); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + nodemarkers = 0; + } else { + nodemarkers = (int) strtol (stringptr, &stringptr, 0); + } + } + + if (inpoints < 3) { + printf("Error: Input must have at least three input points.\n"); + exit(1); + } + if (mesh_dim != 2) { + printf("Error: Triangle only works with two-dimensional meshes.\n"); + exit(1); + } + + initializepointpool(); + + /* Read the points. */ + for (i = 0; i < inpoints; i++) { + pointloop = (point) poolalloc(&points); + stringptr = readline(inputline, infile, infilename); + if (i == 0) { + firstnode = (int) strtol (stringptr, &stringptr, 0); + if ((firstnode == 0) || (firstnode == 1)) { + firstnumber = firstnode; + } + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Point %d has no x coordinate.\n", firstnumber + i); + exit(1); + } + x = (REAL) strtod(stringptr, &stringptr); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Point %d has no y coordinate.\n", firstnumber + i); + exit(1); + } + y = (REAL) strtod(stringptr, &stringptr); + pointloop[0] = x; + pointloop[1] = y; + /* Read the point attributes. */ + for (j = 2; j < 2 + nextras; j++) { + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + pointloop[j] = 0.0; + } else { + pointloop[j] = (REAL) strtod(stringptr, &stringptr); + } + } + if (nodemarkers) { + /* Read a point marker. */ + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + setpointmark(pointloop, 0); + } else { + currentmarker = (int) strtol (stringptr, &stringptr, 0); + setpointmark(pointloop, currentmarker); + } + } else { + /* If no markers are specified in the file, they default to zero. */ + setpointmark(pointloop, 0); + } + /* Determine the smallest and largest x and y coordinates. */ + if (i == 0) { + xmin = xmax = x; + ymin = ymax = y; + } else { + xmin = (x < xmin) ? x : xmin; + xmax = (x > xmax) ? x : xmax; + ymin = (y < ymin) ? y : ymin; + ymax = (y > ymax) ? y : ymax; + } + } + if (readnodefile) { + fclose(infile); + } + + /* Nonexistent x value used as a flag to mark circle events in sweepline */ + /* Delaunay algorithm. */ + xminextreme = 10 * xmin - 9 * xmax; +} + +#endif /* not TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* transfernodes() Read the points from memory. */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +void transfernodes(pointlist, pointattriblist, pointmarkerlist, numberofpoints, + numberofpointattribs) +REAL *pointlist; +REAL *pointattriblist; +int *pointmarkerlist; +int numberofpoints; +int numberofpointattribs; +{ + point pointloop; + REAL x, y; + int i, j; + int coordindex; + int attribindex; + + inpoints = numberofpoints; + mesh_dim = 2; + nextras = numberofpointattribs; + readnodefile = 0; + if (inpoints < 3) { + printf("Error: Input must have at least three input points.\n"); + exit(1); + } + + initializepointpool(); + + /* Read the points. */ + coordindex = 0; + attribindex = 0; + for (i = 0; i < inpoints; i++) { + pointloop = (point) poolalloc(&points); + /* Read the point coordinates. */ + x = pointloop[0] = pointlist[coordindex++]; + y = pointloop[1] = pointlist[coordindex++]; + /* Read the point attributes. */ + for (j = 0; j < numberofpointattribs; j++) { + pointloop[2 + j] = pointattriblist[attribindex++]; + } + if (pointmarkerlist != (int *) NULL) { + /* Read a point marker. */ + setpointmark(pointloop, pointmarkerlist[i]); + } else { + /* If no markers are specified, they default to zero. */ + setpointmark(pointloop, 0); + } + x = pointloop[0]; + y = pointloop[1]; + /* Determine the smallest and largest x and y coordinates. */ + if (i == 0) { + xmin = xmax = x; + ymin = ymax = y; + } else { + xmin = (x < xmin) ? x : xmin; + xmax = (x > xmax) ? x : xmax; + ymin = (y < ymin) ? y : ymin; + ymax = (y > ymax) ? y : ymax; + } + } + + /* Nonexistent x value used as a flag to mark circle events in sweepline */ + /* Delaunay algorithm. */ + xminextreme = 10 * xmin - 9 * xmax; +} + +#endif /* TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* readholes() Read the holes, and possibly regional attributes and area */ +/* constraints, from a .poly file. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +void readholes(polyfile, polyfilename, hlist, holes, rlist, regions) +FILE *polyfile; +char *polyfilename; +REAL **hlist; +int *holes; +REAL **rlist; +int *regions; +{ + REAL *holelist; + REAL *regionlist; + char inputline[INPUTLINESIZE]; + char *stringptr; + int index; + int i; + + /* Read the holes. */ + stringptr = readline(inputline, polyfile, polyfilename); + *holes = (int) strtol (stringptr, &stringptr, 0); + if (*holes > 0) { + holelist = (REAL *) malloc(2 * *holes * sizeof(REAL)); + *hlist = holelist; + if (holelist == (REAL *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + for (i = 0; i < 2 * *holes; i += 2) { + stringptr = readline(inputline, polyfile, polyfilename); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Hole %d has no x coordinate.\n", + firstnumber + (i >> 1)); + exit(1); + } else { + holelist[i] = (REAL) strtod(stringptr, &stringptr); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Hole %d has no y coordinate.\n", + firstnumber + (i >> 1)); + exit(1); + } else { + holelist[i + 1] = (REAL) strtod(stringptr, &stringptr); + } + } + } else { + *hlist = (REAL *) NULL; + } + +#ifndef CDT_ONLY + if ((regionattrib || vararea) && !refine) { + /* Read the area constraints. */ + stringptr = readline(inputline, polyfile, polyfilename); + *regions = (int) strtol (stringptr, &stringptr, 0); + if (*regions > 0) { + regionlist = (REAL *) malloc(4 * *regions * sizeof(REAL)); + *rlist = regionlist; + if (regionlist == (REAL *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + index = 0; + for (i = 0; i < *regions; i++) { + stringptr = readline(inputline, polyfile, polyfilename); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Region %d has no x coordinate.\n", + firstnumber + i); + exit(1); + } else { + regionlist[index++] = (REAL) strtod(stringptr, &stringptr); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Region %d has no y coordinate.\n", + firstnumber + i); + exit(1); + } else { + regionlist[index++] = (REAL) strtod(stringptr, &stringptr); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf( + "Error: Region %d has no region attribute or area constraint.\n", + firstnumber + i); + exit(1); + } else { + regionlist[index++] = (REAL) strtod(stringptr, &stringptr); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + regionlist[index] = regionlist[index - 1]; + } else { + regionlist[index] = (REAL) strtod(stringptr, &stringptr); + } + index++; + } + } + } else { + /* Set `*regions' to zero to avoid an accidental free() later. */ + *regions = 0; + *rlist = (REAL *) NULL; + } +#endif /* not CDT_ONLY */ + + fclose(polyfile); +} + +#endif /* not TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* finishfile() Write the command line to the output file so the user */ +/* can remember how the file was generated. Close the file. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +void finishfile(outfile, argc, argv) +FILE *outfile; +int argc; +char **argv; +{ + int i; + + fprintf(outfile, "# Generated by"); + for (i = 0; i < argc; i++) { + fprintf(outfile, " "); + fputs(argv[i], outfile); + } + fprintf(outfile, "\n"); + fclose(outfile); +} + +#endif /* not TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* writenodes() Number the points and write them to a .node file. */ +/* */ +/* To save memory, the point numbers are written over the shell markers */ +/* after the points are written to a file. */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +void writenodes(pointlist, pointattriblist, pointmarkerlist) +REAL **pointlist; +REAL **pointattriblist; +int **pointmarkerlist; + +#else /* not TRILIBRARY */ + +void writenodes(nodefilename, argc, argv) +char *nodefilename; +int argc; +char **argv; + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + REAL *plist; + REAL *palist; + int *pmlist; + int coordindex; + int attribindex; +#else /* not TRILIBRARY */ + FILE *outfile; +#endif /* not TRILIBRARY */ + point pointloop; + int pointnumber; + int i; + +#ifdef TRILIBRARY + if (!quiet) { + printf("Writing points.\n"); + } + /* Allocate memory for output points if necessary. */ + if (*pointlist == (REAL *) NULL) { + *pointlist = (REAL *) malloc(points.items * 2 * sizeof(REAL)); + if (*pointlist == (REAL *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + /* Allocate memory for output point attributes if necessary. */ + if ((nextras > 0) && (*pointattriblist == (REAL *) NULL)) { + *pointattriblist = (REAL *) malloc(points.items * nextras * sizeof(REAL)); + if (*pointattriblist == (REAL *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + /* Allocate memory for output point markers if necessary. */ + if (!nobound && (*pointmarkerlist == (int *) NULL)) { + *pointmarkerlist = (int *) malloc(points.items * sizeof(int)); + if (*pointmarkerlist == (int *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + plist = *pointlist; + palist = *pointattriblist; + pmlist = *pointmarkerlist; + coordindex = 0; + attribindex = 0; +#else /* not TRILIBRARY */ + if (!quiet) { + printf("Writing %s.\n", nodefilename); + } + outfile = fopen(nodefilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", nodefilename); + exit(1); + } + /* Number of points, number of dimensions, number of point attributes, */ + /* and number of boundary markers (zero or one). */ + fprintf(outfile, "%ld %d %d %d\n", points.items, mesh_dim, nextras, + 1 - nobound); +#endif /* not TRILIBRARY */ + + traversalinit(&points); + pointloop = pointtraverse(); + pointnumber = firstnumber; + while (pointloop != (point) NULL) { +#ifdef TRILIBRARY + /* X and y coordinates. */ + plist[coordindex++] = pointloop[0]; + plist[coordindex++] = pointloop[1]; + /* Point attributes. */ + for (i = 0; i < nextras; i++) { + palist[attribindex++] = pointloop[2 + i]; + } + if (!nobound) { + /* Copy the boundary marker. */ + pmlist[pointnumber - firstnumber] = pointmark(pointloop); + } +#else /* not TRILIBRARY */ + /* Point number, x and y coordinates. */ + fprintf(outfile, "%4d %.17g %.17g", pointnumber, pointloop[0], + pointloop[1]); + for (i = 0; i < nextras; i++) { + /* Write an attribute. */ + fprintf(outfile, " %.17g", pointloop[i + 2]); + } + if (nobound) { + fprintf(outfile, "\n"); + } else { + /* Write the boundary marker. */ + fprintf(outfile, " %d\n", pointmark(pointloop)); + } +#endif /* not TRILIBRARY */ + + setpointmark(pointloop, pointnumber); + pointloop = pointtraverse(); + pointnumber++; + } + +#ifndef TRILIBRARY + finishfile(outfile, argc, argv); +#endif /* not TRILIBRARY */ +} + +/*****************************************************************************/ +/* */ +/* numbernodes() Number the points. */ +/* */ +/* Each point is assigned a marker equal to its number. */ +/* */ +/* Used when writenodes() is not called because no .node file is written. */ +/* */ +/*****************************************************************************/ + +void numbernodes() +{ + point pointloop; + int pointnumber; + + traversalinit(&points); + pointloop = pointtraverse(); + pointnumber = firstnumber; + while (pointloop != (point) NULL) { + setpointmark(pointloop, pointnumber); + pointloop = pointtraverse(); + pointnumber++; + } +} + +/*****************************************************************************/ +/* */ +/* writeelements() Write the triangles to an .ele file. */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +void writeelements(trianglelist, triangleattriblist) +int **trianglelist; +REAL **triangleattriblist; + +#else /* not TRILIBRARY */ + +void writeelements(elefilename, argc, argv) +char *elefilename; +int argc; +char **argv; + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + int *tlist; + REAL *talist; + int pointindex; + int attribindex; +#else /* not TRILIBRARY */ + FILE *outfile; +#endif /* not TRILIBRARY */ + struct triedge triangleloop; + point p1, p2, p3; + point mid1, mid2, mid3; + int elementnumber; + int i; + +#ifdef TRILIBRARY + if (!quiet) { + printf("Writing triangles.\n"); + } + /* Allocate memory for output triangles if necessary. */ + if (*trianglelist == (int *) NULL) { + *trianglelist = (int *) malloc(triangles.items * + ((order + 1) * (order + 2) / 2) * sizeof(int)); + if (*trianglelist == (int *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + /* Allocate memory for output triangle attributes if necessary. */ + if ((eextras > 0) && (*triangleattriblist == (REAL *) NULL)) { + *triangleattriblist = (REAL *) malloc(triangles.items * eextras * + sizeof(REAL)); + if (*triangleattriblist == (REAL *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + tlist = *trianglelist; + talist = *triangleattriblist; + pointindex = 0; + attribindex = 0; +#else /* not TRILIBRARY */ + if (!quiet) { + printf("Writing %s.\n", elefilename); + } + outfile = fopen(elefilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", elefilename); + exit(1); + } + /* Number of triangles, points per triangle, attributes per triangle. */ + fprintf(outfile, "%ld %d %d\n", triangles.items, + (order + 1) * (order + 2) / 2, eextras); +#endif /* not TRILIBRARY */ + + traversalinit(&triangles); + triangleloop.tri = triangletraverse(); + triangleloop.orient = 0; + elementnumber = firstnumber; + while (triangleloop.tri != (triangle *) NULL) { + org(triangleloop, p1); + dest(triangleloop, p2); + apex(triangleloop, p3); + if (order == 1) { +#ifdef TRILIBRARY + tlist[pointindex++] = pointmark(p1); + tlist[pointindex++] = pointmark(p2); + tlist[pointindex++] = pointmark(p3); +#else /* not TRILIBRARY */ + /* Triangle number, indices for three points. */ + fprintf(outfile, "%4d %4d %4d %4d", elementnumber, + pointmark(p1), pointmark(p2), pointmark(p3)); +#endif /* not TRILIBRARY */ + } else { + mid1 = (point) triangleloop.tri[highorderindex + 1]; + mid2 = (point) triangleloop.tri[highorderindex + 2]; + mid3 = (point) triangleloop.tri[highorderindex]; +#ifdef TRILIBRARY + tlist[pointindex++] = pointmark(p1); + tlist[pointindex++] = pointmark(p2); + tlist[pointindex++] = pointmark(p3); + tlist[pointindex++] = pointmark(mid1); + tlist[pointindex++] = pointmark(mid2); + tlist[pointindex++] = pointmark(mid3); +#else /* not TRILIBRARY */ + /* Triangle number, indices for six points. */ + fprintf(outfile, "%4d %4d %4d %4d %4d %4d %4d", elementnumber, + pointmark(p1), pointmark(p2), pointmark(p3), pointmark(mid1), + pointmark(mid2), pointmark(mid3)); +#endif /* not TRILIBRARY */ + } + +#ifdef TRILIBRARY + for (i = 0; i < eextras; i++) { + talist[attribindex++] = elemattribute(triangleloop, i); + } +#else /* not TRILIBRARY */ + for (i = 0; i < eextras; i++) { + fprintf(outfile, " %.17g", elemattribute(triangleloop, i)); + } + fprintf(outfile, "\n"); +#endif /* not TRILIBRARY */ + + triangleloop.tri = triangletraverse(); + elementnumber++; + } + +#ifndef TRILIBRARY + finishfile(outfile, argc, argv); +#endif /* not TRILIBRARY */ +} + +/*****************************************************************************/ +/* */ +/* writepoly() Write the segments and holes to a .poly file. */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +void writepoly(segmentlist, segmentmarkerlist) +int **segmentlist; +int **segmentmarkerlist; + +#else /* not TRILIBRARY */ + +void writepoly(polyfilename, holelist, holes, regionlist, regions, argc, argv) +char *polyfilename; +REAL *holelist; +int holes; +REAL *regionlist; +int regions; +int argc; +char **argv; + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + int *slist; + int *smlist; + int index; +#else /* not TRILIBRARY */ + FILE *outfile; + int i; +#endif /* not TRILIBRARY */ + struct edge shelleloop; + point endpoint1, endpoint2; + int shellenumber; + +#ifdef TRILIBRARY + if (!quiet) { + printf("Writing segments.\n"); + } + /* Allocate memory for output segments if necessary. */ + if (*segmentlist == (int *) NULL) { + *segmentlist = (int *) malloc(shelles.items * 2 * sizeof(int)); + if (*segmentlist == (int *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + /* Allocate memory for output segment markers if necessary. */ + if (!nobound && (*segmentmarkerlist == (int *) NULL)) { + *segmentmarkerlist = (int *) malloc(shelles.items * sizeof(int)); + if (*segmentmarkerlist == (int *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + slist = *segmentlist; + smlist = *segmentmarkerlist; + index = 0; +#else /* not TRILIBRARY */ + if (!quiet) { + printf("Writing %s.\n", polyfilename); + } + outfile = fopen(polyfilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", polyfilename); + exit(1); + } + /* The zero indicates that the points are in a separate .node file. */ + /* Followed by number of dimensions, number of point attributes, */ + /* and number of boundary markers (zero or one). */ + fprintf(outfile, "%d %d %d %d\n", 0, mesh_dim, nextras, 1 - nobound); + /* Number of segments, number of boundary markers (zero or one). */ + fprintf(outfile, "%ld %d\n", shelles.items, 1 - nobound); +#endif /* not TRILIBRARY */ + + traversalinit(&shelles); + shelleloop.sh = shelletraverse(); + shelleloop.shorient = 0; + shellenumber = firstnumber; + while (shelleloop.sh != (shelle *) NULL) { + sorg(shelleloop, endpoint1); + sdest(shelleloop, endpoint2); +#ifdef TRILIBRARY + /* Copy indices of the segment's two endpoints. */ + slist[index++] = pointmark(endpoint1); + slist[index++] = pointmark(endpoint2); + if (!nobound) { + /* Copy the boundary marker. */ + smlist[shellenumber - firstnumber] = mark(shelleloop); + } +#else /* not TRILIBRARY */ + /* Segment number, indices of its two endpoints, and possibly a marker. */ + if (nobound) { + fprintf(outfile, "%4d %4d %4d\n", shellenumber, + pointmark(endpoint1), pointmark(endpoint2)); + } else { + fprintf(outfile, "%4d %4d %4d %4d\n", shellenumber, + pointmark(endpoint1), pointmark(endpoint2), mark(shelleloop)); + } +#endif /* not TRILIBRARY */ + + shelleloop.sh = shelletraverse(); + shellenumber++; + } + +#ifndef TRILIBRARY +#ifndef CDT_ONLY + fprintf(outfile, "%d\n", holes); + if (holes > 0) { + for (i = 0; i < holes; i++) { + /* Hole number, x and y coordinates. */ + fprintf(outfile, "%4d %.17g %.17g\n", firstnumber + i, + holelist[2 * i], holelist[2 * i + 1]); + } + } + if (regions > 0) { + fprintf(outfile, "%d\n", regions); + for (i = 0; i < regions; i++) { + /* Region number, x and y coordinates, attribute, maximum area. */ + fprintf(outfile, "%4d %.17g %.17g %.17g %.17g\n", firstnumber + i, + regionlist[4 * i], regionlist[4 * i + 1], + regionlist[4 * i + 2], regionlist[4 * i + 3]); + } + } +#endif /* not CDT_ONLY */ + + finishfile(outfile, argc, argv); +#endif /* not TRILIBRARY */ +} + +/*****************************************************************************/ +/* */ +/* writeedges() Write the edges to a .edge file. */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +void writeedges(edgelist, edgemarkerlist) +int **edgelist; +int **edgemarkerlist; + +#else /* not TRILIBRARY */ + +void writeedges(edgefilename, argc, argv) +char *edgefilename; +int argc; +char **argv; + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + int *elist; + int *emlist; + int index; +#else /* not TRILIBRARY */ + FILE *outfile; +#endif /* not TRILIBRARY */ + struct triedge triangleloop, trisym; + struct edge checkmark; + point p1, p2; + int edgenumber; + triangle ptr; /* Temporary variable used by sym(). */ + shelle sptr; /* Temporary variable used by tspivot(). */ + +#ifdef TRILIBRARY + if (!quiet) { + printf("Writing edges.\n"); + } + /* Allocate memory for edges if necessary. */ + if (*edgelist == (int *) NULL) { + *edgelist = (int *) malloc(edges * 2 * sizeof(int)); + if (*edgelist == (int *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + /* Allocate memory for edge markers if necessary. */ + if (!nobound && (*edgemarkerlist == (int *) NULL)) { + *edgemarkerlist = (int *) malloc(edges * sizeof(int)); + if (*edgemarkerlist == (int *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + elist = *edgelist; + emlist = *edgemarkerlist; + index = 0; +#else /* not TRILIBRARY */ + if (!quiet) { + printf("Writing %s.\n", edgefilename); + } + outfile = fopen(edgefilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", edgefilename); + exit(1); + } + /* Number of edges, number of boundary markers (zero or one). */ + fprintf(outfile, "%ld %d\n", edges, 1 - nobound); +#endif /* not TRILIBRARY */ + + traversalinit(&triangles); + triangleloop.tri = triangletraverse(); + edgenumber = firstnumber; + /* To loop over the set of edges, loop over all triangles, and look at */ + /* the three edges of each triangle. If there isn't another triangle */ + /* adjacent to the edge, operate on the edge. If there is another */ + /* adjacent triangle, operate on the edge only if the current triangle */ + /* has a smaller pointer than its neighbor. This way, each edge is */ + /* considered only once. */ + while (triangleloop.tri != (triangle *) NULL) { + for (triangleloop.orient = 0; triangleloop.orient < 3; + triangleloop.orient++) { + sym(triangleloop, trisym); + if ((triangleloop.tri < trisym.tri) || (trisym.tri == dummytri)) { + org(triangleloop, p1); + dest(triangleloop, p2); +#ifdef TRILIBRARY + elist[index++] = pointmark(p1); + elist[index++] = pointmark(p2); +#endif /* TRILIBRARY */ + if (nobound) { +#ifndef TRILIBRARY + /* Edge number, indices of two endpoints. */ + fprintf(outfile, "%4d %d %d\n", edgenumber, + pointmark(p1), pointmark(p2)); +#endif /* not TRILIBRARY */ + } else { + /* Edge number, indices of two endpoints, and a boundary marker. */ + /* If there's no shell edge, the boundary marker is zero. */ + if (useshelles) { + tspivot(triangleloop, checkmark); + if (checkmark.sh == dummysh) { +#ifdef TRILIBRARY + emlist[edgenumber - firstnumber] = 0; +#else /* not TRILIBRARY */ + fprintf(outfile, "%4d %d %d %d\n", edgenumber, + pointmark(p1), pointmark(p2), 0); +#endif /* not TRILIBRARY */ + } else { +#ifdef TRILIBRARY + emlist[edgenumber - firstnumber] = mark(checkmark); +#else /* not TRILIBRARY */ + fprintf(outfile, "%4d %d %d %d\n", edgenumber, + pointmark(p1), pointmark(p2), mark(checkmark)); +#endif /* not TRILIBRARY */ + } + } else { +#ifdef TRILIBRARY + emlist[edgenumber - firstnumber] = trisym.tri == dummytri; +#else /* not TRILIBRARY */ + fprintf(outfile, "%4d %d %d %d\n", edgenumber, + pointmark(p1), pointmark(p2), trisym.tri == dummytri); +#endif /* not TRILIBRARY */ + } + } + edgenumber++; + } + } + triangleloop.tri = triangletraverse(); + } + +#ifndef TRILIBRARY + finishfile(outfile, argc, argv); +#endif /* not TRILIBRARY */ +} + +/*****************************************************************************/ +/* */ +/* writevoronoi() Write the Voronoi diagram to a .v.node and .v.edge */ +/* file. */ +/* */ +/* The Voronoi diagram is the geometric dual of the Delaunay triangulation. */ +/* Hence, the Voronoi vertices are listed by traversing the Delaunay */ +/* triangles, and the Voronoi edges are listed by traversing the Delaunay */ +/* edges. */ +/* */ +/* WARNING: In order to assign numbers to the Voronoi vertices, this */ +/* procedure messes up the shell edges or the extra nodes of every */ +/* element. Hence, you should call this procedure last. */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +void writevoronoi(vpointlist, vpointattriblist, vpointmarkerlist, vedgelist, + vedgemarkerlist, vnormlist) +REAL **vpointlist; +REAL **vpointattriblist; +int **vpointmarkerlist; +int **vedgelist; +int **vedgemarkerlist; +REAL **vnormlist; + +#else /* not TRILIBRARY */ + +void writevoronoi(vnodefilename, vedgefilename, argc, argv) +char *vnodefilename; +char *vedgefilename; +int argc; +char **argv; + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + REAL *plist; + REAL *palist; + int *elist; + REAL *normlist; + int coordindex; + int attribindex; +#else /* not TRILIBRARY */ + FILE *outfile; +#endif /* not TRILIBRARY */ + struct triedge triangleloop, trisym; + point torg, tdest, tapex; + REAL circumcenter[2]; + REAL xi, eta; + int vnodenumber, vedgenumber; + int p1, p2; + int i; + triangle ptr; /* Temporary variable used by sym(). */ + +#ifdef TRILIBRARY + if (!quiet) { + printf("Writing Voronoi vertices.\n"); + } + /* Allocate memory for Voronoi vertices if necessary. */ + if (*vpointlist == (REAL *) NULL) { + *vpointlist = (REAL *) malloc(triangles.items * 2 * sizeof(REAL)); + if (*vpointlist == (REAL *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + /* Allocate memory for Voronoi vertex attributes if necessary. */ + if (*vpointattriblist == (REAL *) NULL) { + *vpointattriblist = (REAL *) malloc(triangles.items * nextras * + sizeof(REAL)); + if (*vpointattriblist == (REAL *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + *vpointmarkerlist = (int *) NULL; + plist = *vpointlist; + palist = *vpointattriblist; + coordindex = 0; + attribindex = 0; +#else /* not TRILIBRARY */ + if (!quiet) { + printf("Writing %s.\n", vnodefilename); + } + outfile = fopen(vnodefilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", vnodefilename); + exit(1); + } + /* Number of triangles, two dimensions, number of point attributes, */ + /* zero markers. */ + fprintf(outfile, "%ld %d %d %d\n", triangles.items, 2, nextras, 0); +#endif /* not TRILIBRARY */ + + traversalinit(&triangles); + triangleloop.tri = triangletraverse(); + triangleloop.orient = 0; + vnodenumber = firstnumber; + while (triangleloop.tri != (triangle *) NULL) { + org(triangleloop, torg); + dest(triangleloop, tdest); + apex(triangleloop, tapex); + findcircumcenter(torg, tdest, tapex, circumcenter, &xi, &eta); +#ifdef TRILIBRARY + /* X and y coordinates. */ + plist[coordindex++] = circumcenter[0]; + plist[coordindex++] = circumcenter[1]; + for (i = 2; i < 2 + nextras; i++) { + /* Interpolate the point attributes at the circumcenter. */ + palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i]) + + eta * (tapex[i] - torg[i]); + } +#else /* not TRILIBRARY */ + /* Voronoi vertex number, x and y coordinates. */ + fprintf(outfile, "%4d %.17g %.17g", vnodenumber, circumcenter[0], + circumcenter[1]); + for (i = 2; i < 2 + nextras; i++) { + /* Interpolate the point attributes at the circumcenter. */ + fprintf(outfile, " %.17g", torg[i] + xi * (tdest[i] - torg[i]) + + eta * (tapex[i] - torg[i])); + } + fprintf(outfile, "\n"); +#endif /* not TRILIBRARY */ + + * (int *) (triangleloop.tri + 6) = vnodenumber; + triangleloop.tri = triangletraverse(); + vnodenumber++; + } + +#ifndef TRILIBRARY + finishfile(outfile, argc, argv); +#endif /* not TRILIBRARY */ + +#ifdef TRILIBRARY + if (!quiet) { + printf("Writing Voronoi edges.\n"); + } + /* Allocate memory for output Voronoi edges if necessary. */ + if (*vedgelist == (int *) NULL) { + *vedgelist = (int *) malloc(edges * 2 * sizeof(int)); + if (*vedgelist == (int *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + *vedgemarkerlist = (int *) NULL; + /* Allocate memory for output Voronoi norms if necessary. */ + if (*vnormlist == (REAL *) NULL) { + *vnormlist = (REAL *) malloc(edges * 2 * sizeof(REAL)); + if (*vnormlist == (REAL *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + elist = *vedgelist; + normlist = *vnormlist; + coordindex = 0; +#else /* not TRILIBRARY */ + if (!quiet) { + printf("Writing %s.\n", vedgefilename); + } + outfile = fopen(vedgefilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", vedgefilename); + exit(1); + } + /* Number of edges, zero boundary markers. */ + fprintf(outfile, "%ld %d\n", edges, 0); +#endif /* not TRILIBRARY */ + + traversalinit(&triangles); + triangleloop.tri = triangletraverse(); + vedgenumber = firstnumber; + /* To loop over the set of edges, loop over all triangles, and look at */ + /* the three edges of each triangle. If there isn't another triangle */ + /* adjacent to the edge, operate on the edge. If there is another */ + /* adjacent triangle, operate on the edge only if the current triangle */ + /* has a smaller pointer than its neighbor. This way, each edge is */ + /* considered only once. */ + while (triangleloop.tri != (triangle *) NULL) { + for (triangleloop.orient = 0; triangleloop.orient < 3; + triangleloop.orient++) { + sym(triangleloop, trisym); + if ((triangleloop.tri < trisym.tri) || (trisym.tri == dummytri)) { + /* Find the number of this triangle (and Voronoi vertex). */ + p1 = * (int *) (triangleloop.tri + 6); + if (trisym.tri == dummytri) { + org(triangleloop, torg); + dest(triangleloop, tdest); +#ifdef TRILIBRARY + /* Copy an infinite ray. Index of one endpoint, and -1. */ + elist[coordindex] = p1; + normlist[coordindex++] = tdest[1] - torg[1]; + elist[coordindex] = -1; + normlist[coordindex++] = torg[0] - tdest[0]; +#else /* not TRILIBRARY */ + /* Write an infinite ray. Edge number, index of one endpoint, -1, */ + /* and x and y coordinates of a vector representing the */ + /* direction of the ray. */ + fprintf(outfile, "%4d %d %d %.17g %.17g\n", vedgenumber, + p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]); +#endif /* not TRILIBRARY */ + } else { + /* Find the number of the adjacent triangle (and Voronoi vertex). */ + p2 = * (int *) (trisym.tri + 6); + /* Finite edge. Write indices of two endpoints. */ +#ifdef TRILIBRARY + elist[coordindex] = p1; + normlist[coordindex++] = 0.0; + elist[coordindex] = p2; + normlist[coordindex++] = 0.0; +#else /* not TRILIBRARY */ + fprintf(outfile, "%4d %d %d\n", vedgenumber, p1, p2); +#endif /* not TRILIBRARY */ + } + vedgenumber++; + } + } + triangleloop.tri = triangletraverse(); + } + +#ifndef TRILIBRARY + finishfile(outfile, argc, argv); +#endif /* not TRILIBRARY */ +} + +#ifdef TRILIBRARY + +void writeneighbors(neighborlist) +int **neighborlist; + +#else /* not TRILIBRARY */ + +void writeneighbors(neighborfilename, argc, argv) +char *neighborfilename; +int argc; +char **argv; + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + int *nlist; + int index; +#else /* not TRILIBRARY */ + FILE *outfile; +#endif /* not TRILIBRARY */ + struct triedge triangleloop, trisym; + int elementnumber; + int neighbor1, neighbor2, neighbor3; + triangle ptr; /* Temporary variable used by sym(). */ + +#ifdef TRILIBRARY + if (!quiet) { + printf("Writing neighbors.\n"); + } + /* Allocate memory for neighbors if necessary. */ + if (*neighborlist == (int *) NULL) { + *neighborlist = (int *) malloc(triangles.items * 3 * sizeof(int)); + if (*neighborlist == (int *) NULL) { + printf("Error: Out of memory.\n"); + exit(1); + } + } + nlist = *neighborlist; + index = 0; +#else /* not TRILIBRARY */ + if (!quiet) { + printf("Writing %s.\n", neighborfilename); + } + outfile = fopen(neighborfilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", neighborfilename); + exit(1); + } + /* Number of triangles, three edges per triangle. */ + fprintf(outfile, "%ld %d\n", triangles.items, 3); +#endif /* not TRILIBRARY */ + + traversalinit(&triangles); + triangleloop.tri = triangletraverse(); + triangleloop.orient = 0; + elementnumber = firstnumber; + while (triangleloop.tri != (triangle *) NULL) { + * (int *) (triangleloop.tri + 6) = elementnumber; + triangleloop.tri = triangletraverse(); + elementnumber++; + } + * (int *) (dummytri + 6) = -1; + + traversalinit(&triangles); + triangleloop.tri = triangletraverse(); + elementnumber = firstnumber; + while (triangleloop.tri != (triangle *) NULL) { + triangleloop.orient = 1; + sym(triangleloop, trisym); + neighbor1 = * (int *) (trisym.tri + 6); + triangleloop.orient = 2; + sym(triangleloop, trisym); + neighbor2 = * (int *) (trisym.tri + 6); + triangleloop.orient = 0; + sym(triangleloop, trisym); + neighbor3 = * (int *) (trisym.tri + 6); +#ifdef TRILIBRARY + nlist[index++] = neighbor1; + nlist[index++] = neighbor2; + nlist[index++] = neighbor3; +#else /* not TRILIBRARY */ + /* Triangle number, neighboring triangle numbers. */ + fprintf(outfile, "%4d %d %d %d\n", elementnumber, + neighbor1, neighbor2, neighbor3); +#endif /* not TRILIBRARY */ + + triangleloop.tri = triangletraverse(); + elementnumber++; + } + +#ifndef TRILIBRARY + finishfile(outfile, argc, argv); +#endif /* TRILIBRARY */ +} + +/*****************************************************************************/ +/* */ +/* writeoff() Write the triangulation to an .off file. */ +/* */ +/* OFF stands for the Object File Format, a format used by the Geometry */ +/* Center's Geomview package. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +void writeoff(offfilename, argc, argv) +char *offfilename; +int argc; +char **argv; +{ + FILE *outfile; + struct triedge triangleloop; + point pointloop; + point p1, p2, p3; + + if (!quiet) { + printf("Writing %s.\n", offfilename); + } + outfile = fopen(offfilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", offfilename); + exit(1); + } + /* Number of points, triangles, and edges. */ + fprintf(outfile, "OFF\n%ld %ld %ld\n", points.items, triangles.items, + edges); + + /* Write the points. */ + traversalinit(&points); + pointloop = pointtraverse(); + while (pointloop != (point) NULL) { + /* The "0.0" is here because the OFF format uses 3D coordinates. */ + fprintf(outfile, " %.17g %.17g %.17g\n", pointloop[0], + pointloop[1], 0.0); + pointloop = pointtraverse(); + } + + /* Write the triangles. */ + traversalinit(&triangles); + triangleloop.tri = triangletraverse(); + triangleloop.orient = 0; + while (triangleloop.tri != (triangle *) NULL) { + org(triangleloop, p1); + dest(triangleloop, p2); + apex(triangleloop, p3); + /* The "3" means a three-vertex polygon. */ + fprintf(outfile, " 3 %4d %4d %4d\n", pointmark(p1) - 1, + pointmark(p2) - 1, pointmark(p3) - 1); + triangleloop.tri = triangletraverse(); + } + finishfile(outfile, argc, argv); +} + +#endif /* not TRILIBRARY */ + +/** **/ +/** **/ +/********* File I/O routines end here *********/ + +/*****************************************************************************/ +/* */ +/* quality_statistics() Print statistics about the quality of the mesh. */ +/* */ +/*****************************************************************************/ + +void quality_statistics() +{ + struct triedge triangleloop; + point p[3]; + REAL cossquaretable[8]; + REAL ratiotable[16]; + REAL dx[3], dy[3]; + REAL edgelength[3]; + REAL dotproduct; + REAL cossquare; + REAL triarea; + REAL shortest, longest; + REAL trilongest2; + REAL smallestarea, biggestarea; + REAL triminaltitude2; + REAL minaltitude; + REAL triaspect2; + REAL worstaspect; + REAL smallestangle, biggestangle; + REAL radconst, degconst; + int angletable[18]; + int aspecttable[16]; + int aspectindex; + int tendegree; + int acutebiggest; + int i, ii, j, k; + + printf("Mesh quality statistics:\n\n"); + radconst = PI / 18.0; + degconst = 180.0 / PI; + for (i = 0; i < 8; i++) { + cossquaretable[i] = cos(radconst * (REAL) (i + 1)); + cossquaretable[i] = cossquaretable[i] * cossquaretable[i]; + } + for (i = 0; i < 18; i++) { + angletable[i] = 0; + } + + ratiotable[0] = 1.5; ratiotable[1] = 2.0; + ratiotable[2] = 2.5; ratiotable[3] = 3.0; + ratiotable[4] = 4.0; ratiotable[5] = 6.0; + ratiotable[6] = 10.0; ratiotable[7] = 15.0; + ratiotable[8] = 25.0; ratiotable[9] = 50.0; + ratiotable[10] = 100.0; ratiotable[11] = 300.0; + ratiotable[12] = 1000.0; ratiotable[13] = 10000.0; + ratiotable[14] = 100000.0; ratiotable[15] = 0.0; + for (i = 0; i < 16; i++) { + aspecttable[i] = 0; + } + + worstaspect = 0.0; + minaltitude = xmax - xmin + ymax - ymin; + minaltitude = minaltitude * minaltitude; + shortest = minaltitude; + longest = 0.0; + smallestarea = minaltitude; + biggestarea = 0.0; + worstaspect = 0.0; + smallestangle = 0.0; + biggestangle = 2.0; + acutebiggest = 1; + + traversalinit(&triangles); + triangleloop.tri = triangletraverse(); + triangleloop.orient = 0; + while (triangleloop.tri != (triangle *) NULL) { + org(triangleloop, p[0]); + dest(triangleloop, p[1]); + apex(triangleloop, p[2]); + trilongest2 = 0.0; + + for (i = 0; i < 3; i++) { + j = plus1mod3[i]; + k = minus1mod3[i]; + dx[i] = p[j][0] - p[k][0]; + dy[i] = p[j][1] - p[k][1]; + edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i]; + if (edgelength[i] > trilongest2) { + trilongest2 = edgelength[i]; + } + if (edgelength[i] > longest) { + longest = edgelength[i]; + } + if (edgelength[i] < shortest) { + shortest = edgelength[i]; + } + } + + triarea = counterclockwise(p[0], p[1], p[2]); + if (triarea < smallestarea) { + smallestarea = triarea; + } + if (triarea > biggestarea) { + biggestarea = triarea; + } + triminaltitude2 = triarea * triarea / trilongest2; + if (triminaltitude2 < minaltitude) { + minaltitude = triminaltitude2; + } + triaspect2 = trilongest2 / triminaltitude2; + if (triaspect2 > worstaspect) { + worstaspect = triaspect2; + } + aspectindex = 0; + while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex]) + && (aspectindex < 15)) { + aspectindex++; + } + aspecttable[aspectindex]++; + + for (i = 0; i < 3; i++) { + j = plus1mod3[i]; + k = minus1mod3[i]; + dotproduct = dx[j] * dx[k] + dy[j] * dy[k]; + cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]); + tendegree = 8; + for (ii = 7; ii >= 0; ii--) { + if (cossquare > cossquaretable[ii]) { + tendegree = ii; + } + } + if (dotproduct <= 0.0) { + angletable[tendegree]++; + if (cossquare > smallestangle) { + smallestangle = cossquare; + } + if (acutebiggest && (cossquare < biggestangle)) { + biggestangle = cossquare; + } + } else { + angletable[17 - tendegree]++; + if (acutebiggest || (cossquare > biggestangle)) { + biggestangle = cossquare; + acutebiggest = 0; + } + } + } + triangleloop.tri = triangletraverse(); + } + + shortest = sqrt(shortest); + longest = sqrt(longest); + minaltitude = sqrt(minaltitude); + worstaspect = sqrt(worstaspect); + smallestarea *= 2.0; + biggestarea *= 2.0; + if (smallestangle >= 1.0) { + smallestangle = 0.0; + } else { + smallestangle = degconst * acos(sqrt(smallestangle)); + } + if (biggestangle >= 1.0) { + biggestangle = 180.0; + } else { + if (acutebiggest) { + biggestangle = degconst * acos(sqrt(biggestangle)); + } else { + biggestangle = 180.0 - degconst * acos(sqrt(biggestangle)); + } + } + + printf(" Smallest area: %16.5g | Largest area: %16.5g\n", + smallestarea, biggestarea); + printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n", + shortest, longest); + printf(" Shortest altitude: %12.5g | Largest aspect ratio: %8.5g\n\n", + minaltitude, worstaspect); + printf(" Aspect ratio histogram:\n"); + printf(" 1.1547 - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n", + ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8], + aspecttable[8]); + for (i = 1; i < 7; i++) { + printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n", + ratiotable[i - 1], ratiotable[i], aspecttable[i], + ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]); + } + printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n", + ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14], + aspecttable[15]); + printf( +" (Triangle aspect ratio is longest edge divided by shortest altitude)\n\n"); + printf(" Smallest angle: %15.5g | Largest angle: %15.5g\n\n", + smallestangle, biggestangle); + printf(" Angle histogram:\n"); + for (i = 0; i < 9; i++) { + printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n", + i * 10, i * 10 + 10, angletable[i], + i * 10 + 90, i * 10 + 100, angletable[i + 9]); + } + printf("\n"); +} + +/*****************************************************************************/ +/* */ +/* statistics() Print all sorts of cool facts. */ +/* */ +/*****************************************************************************/ + +void statistics() +{ + printf("\nStatistics:\n\n"); + printf(" Input points: %d\n", inpoints); + if (refine) { + printf(" Input triangles: %d\n", inelements); + } + if (poly) { + printf(" Input segments: %d\n", insegments); + if (!refine) { + printf(" Input holes: %d\n", holes); + } + } + + printf("\n Mesh points: %ld\n", points.items); + printf(" Mesh triangles: %ld\n", triangles.items); + printf(" Mesh edges: %ld\n", edges); + if (poly || refine) { + printf(" Mesh boundary edges: %ld\n", hullsize); + printf(" Mesh segments: %ld\n\n", shelles.items); + } else { + printf(" Mesh convex hull edges: %ld\n\n", hullsize); + } + if (verbose) { + quality_statistics(); + printf("Memory allocation statistics:\n\n"); + printf(" Maximum number of points: %ld\n", points.maxitems); + printf(" Maximum number of triangles: %ld\n", triangles.maxitems); + if (shelles.maxitems > 0) { + printf(" Maximum number of segments: %ld\n", shelles.maxitems); + } + if (viri.maxitems > 0) { + printf(" Maximum number of viri: %ld\n", viri.maxitems); + } + if (badsegments.maxitems > 0) { + printf(" Maximum number of encroached segments: %ld\n", + badsegments.maxitems); + } + if (badtriangles.maxitems > 0) { + printf(" Maximum number of bad triangles: %ld\n", + badtriangles.maxitems); + } + if (splaynodes.maxitems > 0) { + printf(" Maximum number of splay tree nodes: %ld\n", + splaynodes.maxitems); + } + printf(" Approximate heap memory use (bytes): %ld\n\n", + points.maxitems * points.itembytes + + triangles.maxitems * triangles.itembytes + + shelles.maxitems * shelles.itembytes + + viri.maxitems * viri.itembytes + + badsegments.maxitems * badsegments.itembytes + + badtriangles.maxitems * badtriangles.itembytes + + splaynodes.maxitems * splaynodes.itembytes); + + printf("Algorithmic statistics:\n\n"); + printf(" Number of incircle tests: %ld\n", incirclecount); + printf(" Number of orientation tests: %ld\n", counterclockcount); + if (hyperbolacount > 0) { + printf(" Number of right-of-hyperbola tests: %ld\n", + hyperbolacount); + } + if (circumcentercount > 0) { + printf(" Number of circumcenter computations: %ld\n", + circumcentercount); + } + if (circletopcount > 0) { + printf(" Number of circle top computations: %ld\n", + circletopcount); + } + printf("\n"); + } +} + +/*****************************************************************************/ +/* */ +/* main() or triangulate() Gosh, do everything. */ +/* */ +/* The sequence is roughly as follows. Many of these steps can be skipped, */ +/* depending on the command line switches. */ +/* */ +/* - Initialize constants and parse the command line. */ +/* - Read the points from a file and either */ +/* - triangulate them (no -r), or */ +/* - read an old mesh from files and reconstruct it (-r). */ +/* - Insert the PSLG segments (-p), and possibly segments on the convex */ +/* hull (-c). */ +/* - Read the holes (-p), regional attributes (-pA), and regional area */ +/* constraints (-pa). Carve the holes and concavities, and spread the */ +/* regional attributes and area constraints. */ +/* - Enforce the constraints on minimum angle (-q) and maximum area (-a). */ +/* Also enforce the conforming Delaunay property (-q and -a). */ +/* - Compute the number of edges in the resulting mesh. */ +/* - Promote the mesh's linear triangles to higher order elements (-o). */ +/* - Write the output files and print the statistics. */ +/* - Check the consistency and Delaunay property of the mesh (-C). */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +void triangulate(triswitches, in, out, vorout) +char *triswitches; +struct triangulateio *in; +struct triangulateio *out; +struct triangulateio *vorout; + +#else /* not TRILIBRARY */ + +int main(argc, argv) +int argc; +char **argv; + +#endif /* not TRILIBRARY */ + +{ + REAL *holearray; /* Array of holes. */ + REAL *regionarray; /* Array of regional attributes and area constraints. */ +#ifndef TRILIBRARY + FILE *polyfile; +#endif /* not TRILIBRARY */ +#ifndef NO_TIMER + /* Variables for timing the performance of Triangle. The types are */ + /* defined in sys/time.h. */ + struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6; + struct timezone tz; +#endif /* NO_TIMER */ + +#ifndef NO_TIMER + gettimeofday(&tv0, &tz); +#endif /* NO_TIMER */ + + triangleinit(); +#ifdef TRILIBRARY + parsecommandline(1, &triswitches); +#else /* not TRILIBRARY */ + parsecommandline(argc, argv); +#endif /* not TRILIBRARY */ + +#ifdef TRILIBRARY + transfernodes(in->pointlist, in->pointattributelist, in->pointmarkerlist, + in->numberofpoints, in->numberofpointattributes); +#else /* not TRILIBRARY */ + readnodes(innodefilename, inpolyfilename, &polyfile); +#endif /* not TRILIBRARY */ + +#ifndef NO_TIMER + if (!quiet) { + gettimeofday(&tv1, &tz); + } +#endif /* NO_TIMER */ + +#ifdef CDT_ONLY + hullsize = delaunay(); /* Triangulate the points. */ +#else /* not CDT_ONLY */ + if (refine) { + /* Read and reconstruct a mesh. */ +#ifdef TRILIBRARY + hullsize = reconstruct(in->trianglelist, in->triangleattributelist, + in->trianglearealist, in->numberoftriangles, + in->numberofcorners, in->numberoftriangleattributes, + in->segmentlist, in->segmentmarkerlist, + in->numberofsegments); +#else /* not TRILIBRARY */ + hullsize = reconstruct(inelefilename, areafilename, inpolyfilename, + polyfile); +#endif /* not TRILIBRARY */ + } else { + hullsize = delaunay(); /* Triangulate the points. */ + } +#endif /* not CDT_ONLY */ + +#ifndef NO_TIMER + if (!quiet) { + gettimeofday(&tv2, &tz); + if (refine) { + printf("Mesh reconstruction"); + } else { + printf("Delaunay"); + } + printf(" milliseconds: %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec) + + (tv2.tv_usec - tv1.tv_usec) / 1000l); + } +#endif /* NO_TIMER */ + + /* Ensure that no point can be mistaken for a triangular bounding */ + /* box point in insertsite(). */ + infpoint1 = (point) NULL; + infpoint2 = (point) NULL; + infpoint3 = (point) NULL; + + if (useshelles) { + checksegments = 1; /* Segments will be introduced next. */ + if (!refine) { + /* Insert PSLG segments and/or convex hull segments. */ +#ifdef TRILIBRARY + insegments = formskeleton(in->segmentlist, in->segmentmarkerlist, + in->numberofsegments); +#else /* not TRILIBRARY */ + insegments = formskeleton(polyfile, inpolyfilename); +#endif /* not TRILIBRARY */ + } + } + +#ifndef NO_TIMER + if (!quiet) { + gettimeofday(&tv3, &tz); + if (useshelles && !refine) { + printf("Segment milliseconds: %ld\n", + 1000l * (tv3.tv_sec - tv2.tv_sec) + + (tv3.tv_usec - tv2.tv_usec) / 1000l); + } + } +#endif /* NO_TIMER */ + + if (poly) { +#ifdef TRILIBRARY + holearray = in->holelist; + holes = in->numberofholes; + regionarray = in->regionlist; + regions = in->numberofregions; +#else /* not TRILIBRARY */ + readholes(polyfile, inpolyfilename, &holearray, &holes, + ®ionarray, ®ions); +#endif /* not TRILIBRARY */ + if (!refine) { + /* Carve out holes and concavities. */ + carveholes(holearray, holes, regionarray, regions); + } + } else { + /* Without a PSLG, there can be no holes or regional attributes */ + /* or area constraints. The following are set to zero to avoid */ + /* an accidental free() later. */ + holes = 0; + regions = 0; + } + +#ifndef NO_TIMER + if (!quiet) { + gettimeofday(&tv4, &tz); + if (poly && !refine) { + printf("Hole milliseconds: %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec) + + (tv4.tv_usec - tv3.tv_usec) / 1000l); + } + } +#endif /* NO_TIMER */ + +#ifndef CDT_ONLY + if (quality) { + enforcequality(); /* Enforce angle and area constraints. */ + } +#endif /* not CDT_ONLY */ + +#ifndef NO_TIMER + if (!quiet) { + gettimeofday(&tv5, &tz); +#ifndef CDT_ONLY + if (quality) { + printf("Quality milliseconds: %ld\n", + 1000l * (tv5.tv_sec - tv4.tv_sec) + + (tv5.tv_usec - tv4.tv_usec) / 1000l); + } +#endif /* not CDT_ONLY */ + } +#endif /* NO_TIMER */ + + /* Compute the number of edges. */ + edges = (3l * triangles.items + hullsize) / 2l; + + if (order > 1) { + highorder(); /* Promote elements to higher polynomial order. */ + } + if (!quiet) { + printf("\n"); + } + +#ifdef TRILIBRARY + out->numberofpoints = points.items; + out->numberofpointattributes = nextras; + out->numberoftriangles = triangles.items; + out->numberofcorners = (order + 1) * (order + 2) / 2; + out->numberoftriangleattributes = eextras; + out->numberofedges = edges; + if (useshelles) { + out->numberofsegments = shelles.items; + } else { + out->numberofsegments = hullsize; + } + if (vorout != (struct triangulateio *) NULL) { + vorout->numberofpoints = triangles.items; + vorout->numberofpointattributes = nextras; + vorout->numberofedges = edges; + } +#endif /* TRILIBRARY */ + /* If not using iteration numbers, don't write a .node file if one was */ + /* read, because the original one would be overwritten! */ + if (nonodewritten || (noiterationnum && readnodefile)) { + if (!quiet) { +#ifdef TRILIBRARY + printf("NOT writing points.\n"); +#else /* not TRILIBRARY */ + printf("NOT writing a .node file.\n"); +#endif /* not TRILIBRARY */ + } + numbernodes(); /* We must remember to number the points. */ + } else { +#ifdef TRILIBRARY + writenodes(&out->pointlist, &out->pointattributelist, + &out->pointmarkerlist); +#else /* not TRILIBRARY */ + writenodes(outnodefilename, argc, argv); /* Numbers the points too. */ +#endif /* TRILIBRARY */ + } + if (noelewritten) { + if (!quiet) { +#ifdef TRILIBRARY + printf("NOT writing triangles.\n"); +#else /* not TRILIBRARY */ + printf("NOT writing an .ele file.\n"); +#endif /* not TRILIBRARY */ + } + } else { +#ifdef TRILIBRARY + writeelements(&out->trianglelist, &out->triangleattributelist); +#else /* not TRILIBRARY */ + writeelements(outelefilename, argc, argv); +#endif /* not TRILIBRARY */ + } + /* The -c switch (convex switch) causes a PSLG to be written */ + /* even if none was read. */ + if (poly || convex) { + /* If not using iteration numbers, don't overwrite the .poly file. */ + if (nopolywritten || noiterationnum) { + if (!quiet) { +#ifdef TRILIBRARY + printf("NOT writing segments.\n"); +#else /* not TRILIBRARY */ + printf("NOT writing a .poly file.\n"); +#endif /* not TRILIBRARY */ + } + } else { +#ifdef TRILIBRARY + writepoly(&out->segmentlist, &out->segmentmarkerlist); + out->numberofholes = holes; + out->numberofregions = regions; + if (poly) { + out->holelist = in->holelist; + out->regionlist = in->regionlist; + } else { + out->holelist = (REAL *) NULL; + out->regionlist = (REAL *) NULL; + } +#else /* not TRILIBRARY */ + writepoly(outpolyfilename, holearray, holes, regionarray, regions, + argc, argv); +#endif /* not TRILIBRARY */ + } + } +#ifndef TRILIBRARY +#ifndef CDT_ONLY + if (regions > 0) { + free(regionarray); + } +#endif /* not CDT_ONLY */ + if (holes > 0) { + free(holearray); + } + if (geomview) { + writeoff(offfilename, argc, argv); + } +#endif /* not TRILIBRARY */ + if (edgesout) { +#ifdef TRILIBRARY + writeedges(&out->edgelist, &out->edgemarkerlist); +#else /* not TRILIBRARY */ + writeedges(edgefilename, argc, argv); +#endif /* not TRILIBRARY */ + } + if (voronoi) { +#ifdef TRILIBRARY + writevoronoi(&vorout->pointlist, &vorout->pointattributelist, + &vorout->pointmarkerlist, &vorout->edgelist, + &vorout->edgemarkerlist, &vorout->normlist); +#else /* not TRILIBRARY */ + writevoronoi(vnodefilename, vedgefilename, argc, argv); +#endif /* not TRILIBRARY */ + } + if (neighbors) { +#ifdef TRILIBRARY + writeneighbors(&out->neighborlist); +#else /* not TRILIBRARY */ + writeneighbors(neighborfilename, argc, argv); +#endif /* not TRILIBRARY */ + } + + if (!quiet) { +#ifndef NO_TIMER + gettimeofday(&tv6, &tz); + printf("\nOutput milliseconds: %ld\n", + 1000l * (tv6.tv_sec - tv5.tv_sec) + + (tv6.tv_usec - tv5.tv_usec) / 1000l); + printf("Total running milliseconds: %ld\n", + 1000l * (tv6.tv_sec - tv0.tv_sec) + + (tv6.tv_usec - tv0.tv_usec) / 1000l); +#endif /* NO_TIMER */ + + statistics(); + } + +#ifndef REDUCED + if (docheck) { + checkmesh(); + checkdelaunay(); + } +#endif /* not REDUCED */ + + triangledeinit(); +#ifndef TRILIBRARY + return 0; +#endif /* not TRILIBRARY */ +} diff --git a/src/Lib/TriangleJRS/triangle.h b/src/Lib/TriangleJRS/triangle.h new file mode 100644 index 00000000..b9be696c --- /dev/null +++ b/src/Lib/TriangleJRS/triangle.h @@ -0,0 +1,289 @@ +/*****************************************************************************/ +/* */ +/* (triangle.h) */ +/* */ +/* Include file for programs that call Triangle. */ +/* */ +/* Accompanies Triangle Version 1.3 */ +/* July 19, 1996 */ +/* */ +/* Copyright 1996 */ +/* Jonathan Richard Shewchuk */ +/* School of Computer Science */ +/* Carnegie Mellon University */ +/* 5000 Forbes Avenue */ +/* Pittsburgh, Pennsylvania 15213-3891 */ +/* jrs@cs.cmu.edu */ +/* */ +/*****************************************************************************/ + +/*****************************************************************************/ +/* */ +/* How to call Triangle from another program */ +/* */ +/* */ +/* If you haven't read Triangle's instructions (run "triangle -h" to read */ +/* them), you won't understand what follows. */ +/* */ +/* Triangle must be compiled into an object file (triangle.o) with the */ +/* TRILIBRARY symbol defined (preferably by using the -DTRILIBRARY compiler */ +/* switch). The makefile included with Triangle will do this for you if */ +/* you run "make trilibrary". The resulting object file can be called via */ +/* the procedure triangulate(). */ +/* */ +/* If the size of the object file is important to you, you may wish to */ +/* generate a reduced version of triangle.o. The REDUCED symbol gets rid */ +/* of all features that are primarily of research interest. Specifically, */ +/* the -DREDUCED switch eliminates Triangle's -i, -F, -s, and -C switches. */ +/* The CDT_ONLY symbol gets rid of all meshing algorithms above and beyond */ +/* constrained Delaunay triangulation. Specifically, the -DCDT_ONLY switch */ +/* eliminates Triangle's -r, -q, -a, -S, and -s switches. */ +/* */ +/* IMPORTANT: These definitions (TRILIBRARY, REDUCED, CDT_ONLY) must be */ +/* made in the makefile or in triangle.c itself. Putting these definitions */ +/* in this file will not create the desired effect. */ +/* */ +/* */ +/* The calling convention for triangulate() follows. */ +/* */ +/* void triangulate(triswitches, in, out, vorout) */ +/* char *triswitches; */ +/* struct triangulateio *in; */ +/* struct triangulateio *out; */ +/* struct triangulateio *vorout; */ +/* */ +/* `triswitches' is a string containing the command line switches you wish */ +/* to invoke. No initial dash is required. Some suggestions: */ +/* */ +/* - You'll probably find it convenient to use the `z' switch so that */ +/* points (and other items) are numbered from zero. This simplifies */ +/* indexing, because the first item of any type always starts at index */ +/* [0] of the corresponding array, whether that item's number is zero or */ +/* one. */ +/* - You'll probably want to use the `Q' (quiet) switch in your final code, */ +/* but you can take advantage of Triangle's printed output (including the */ +/* `V' switch) while debugging. */ +/* - If you are not using the `q' or `a' switches, then the output points */ +/* will be identical to the input points, except possibly for the */ +/* boundary markers. If you don't need the boundary markers, you should */ +/* use the `N' (no nodes output) switch to save memory. (If you do need */ +/* boundary markers, but need to save memory, a good nasty trick is to */ +/* set out->pointlist equal to in->pointlist before calling triangulate(),*/ +/* so that Triangle overwrites the input points with identical copies.) */ +/* - The `I' (no iteration numbers) and `g' (.off file output) switches */ +/* have no effect when Triangle is compiled with TRILIBRARY defined. */ +/* */ +/* `in', `out', and `vorout' are descriptions of the input, the output, */ +/* and the Voronoi output. If the `v' (Voronoi output) switch is not used, */ +/* `vorout' may be NULL. `in' and `out' may never be NULL. */ +/* */ +/* Certain fields of the input and output structures must be initialized, */ +/* as described below. */ +/* */ +/*****************************************************************************/ + +/*****************************************************************************/ +/* */ +/* The `triangulateio' structure. */ +/* */ +/* Used to pass data into and out of the triangulate() procedure. */ +/* */ +/* */ +/* Arrays are used to store points, triangles, markers, and so forth. In */ +/* all cases, the first item in any array is stored starting at index [0]. */ +/* However, that item is item number `1' unless the `z' switch is used, in */ +/* which case it is item number `0'. Hence, you may find it easier to */ +/* index points (and triangles in the neighbor list) if you use the `z' */ +/* switch. Unless, of course, you're calling Triangle from a Fortran */ +/* program. */ +/* */ +/* Description of fields (except the `numberof' fields, which are obvious): */ +/* */ +/* `pointlist': An array of point coordinates. The first point's x */ +/* coordinate is at index [0] and its y coordinate at index [1], followed */ +/* by the coordinates of the remaining points. Each point occupies two */ +/* REALs. */ +/* `pointattributelist': An array of point attributes. Each point's */ +/* attributes occupy `numberofpointattributes' REALs. */ +/* `pointmarkerlist': An array of point markers; one int per point. */ +/* */ +/* `trianglelist': An array of triangle corners. The first triangle's */ +/* first corner is at index [0], followed by its other two corners in */ +/* counterclockwise order, followed by any other nodes if the triangle */ +/* represents a nonlinear element. Each triangle occupies */ +/* `numberofcorners' ints. */ +/* `triangleattributelist': An array of triangle attributes. Each */ +/* triangle's attributes occupy `numberoftriangleattributes' REALs. */ +/* `trianglearealist': An array of triangle area constraints; one REAL per */ +/* triangle. Input only. */ +/* `neighborlist': An array of triangle neighbors; three ints per */ +/* triangle. Output only. */ +/* */ +/* `segmentlist': An array of segment endpoints. The first segment's */ +/* endpoints are at indices [0] and [1], followed by the remaining */ +/* segments. Two ints per segment. */ +/* `segmentmarkerlist': An array of segment markers; one int per segment. */ +/* */ +/* `holelist': An array of holes. The first hole's x and y coordinates */ +/* are at indices [0] and [1], followed by the remaining holes. Two */ +/* REALs per hole. Input only, although the pointer is copied to the */ +/* output structure for your convenience. */ +/* */ +/* `regionlist': An array of regional attributes and area constraints. */ +/* The first constraint's x and y coordinates are at indices [0] and [1], */ +/* followed by the regional attribute and index [2], followed by the */ +/* maximum area at index [3], followed by the remaining area constraints. */ +/* Four REALs per area constraint. Note that each regional attribute is */ +/* used only if you select the `A' switch, and each area constraint is */ +/* used only if you select the `a' switch (with no number following), but */ +/* omitting one of these switches does not change the memory layout. */ +/* Input only, although the pointer is copied to the output structure for */ +/* your convenience. */ +/* */ +/* `edgelist': An array of edge endpoints. The first edge's endpoints are */ +/* at indices [0] and [1], followed by the remaining edges. Two ints per */ +/* edge. Output only. */ +/* `edgemarkerlist': An array of edge markers; one int per edge. Output */ +/* only. */ +/* `normlist': An array of normal vectors, used for infinite rays in */ +/* Voronoi diagrams. The first normal vector's x and y magnitudes are */ +/* at indices [0] and [1], followed by the remaining vectors. For each */ +/* finite edge in a Voronoi diagram, the normal vector written is the */ +/* zero vector. Two REALs per edge. Output only. */ +/* */ +/* */ +/* Any input fields that Triangle will examine must be initialized. */ +/* Furthermore, for each output array that Triangle will write to, you */ +/* must either provide space by setting the appropriate pointer to point */ +/* to the space you want the data written to, or you must initialize the */ +/* pointer to NULL, which tells Triangle to allocate space for the results. */ +/* The latter option is preferable, because Triangle always knows exactly */ +/* how much space to allocate. The former option is provided mainly for */ +/* people who need to call Triangle from Fortran code, though it also makes */ +/* possible some nasty space-saving tricks, like writing the output to the */ +/* same arrays as the input. */ +/* */ +/* Triangle will not free() any input or output arrays, including those it */ +/* allocates itself; that's up to you. */ +/* */ +/* Here's a guide to help you decide which fields you must initialize */ +/* before you call triangulate(). */ +/* */ +/* `in': */ +/* */ +/* - `pointlist' must always point to a list of points; `numberofpoints' */ +/* and `numberofpointattributes' must be properly set. */ +/* `pointmarkerlist' must either be set to NULL (in which case all */ +/* markers default to zero), or must point to a list of markers. If */ +/* `numberofpointattributes' is not zero, `pointattributelist' must */ +/* point to a list of point attributes. */ +/* - If the `r' switch is used, `trianglelist' must point to a list of */ +/* triangles, and `numberoftriangles', `numberofcorners', and */ +/* `numberoftriangleattributes' must be properly set. If */ +/* `numberoftriangleattributes' is not zero, `triangleattributelist' */ +/* must point to a list of triangle attributes. If the `a' switch is */ +/* used (with no number following), `trianglearealist' must point to a */ +/* list of triangle area constraints. `neighborlist' may be ignored. */ +/* - If the `p' switch is used, `segmentlist' must point to a list of */ +/* segments, `numberofsegments' must be properly set, and */ +/* `segmentmarkerlist' must either be set to NULL (in which case all */ +/* markers default to zero), or must point to a list of markers. */ +/* - If the `p' switch is used without the `r' switch, then */ +/* `numberofholes' and `numberofregions' must be properly set. If */ +/* `numberofholes' is not zero, `holelist' must point to a list of */ +/* holes. If `numberofregions' is not zero, `regionlist' must point to */ +/* a list of region constraints. */ +/* - If the `p' switch is used, `holelist', `numberofholes', */ +/* `regionlist', and `numberofregions' is copied to `out'. (You can */ +/* nonetheless get away with not initializing them if the `r' switch is */ +/* used.) */ +/* - `edgelist', `edgemarkerlist', `normlist', and `numberofedges' may be */ +/* ignored. */ +/* */ +/* `out': */ +/* */ +/* - `pointlist' must be initialized (NULL or pointing to memory) unless */ +/* the `N' switch is used. `pointmarkerlist' must be initialized */ +/* unless the `N' or `B' switch is used. If `N' is not used and */ +/* `in->numberofpointattributes' is not zero, `pointattributelist' must */ +/* be initialized. */ +/* - `trianglelist' must be initialized unless the `E' switch is used. */ +/* `neighborlist' must be initialized if the `n' switch is used. If */ +/* the `E' switch is not used and (`in->numberofelementattributes' is */ +/* not zero or the `A' switch is used), `elementattributelist' must be */ +/* initialized. `trianglearealist' may be ignored. */ +/* - `segmentlist' must be initialized if the `p' or `c' switch is used, */ +/* and the `P' switch is not used. `segmentmarkerlist' must also be */ +/* initialized under these circumstances unless the `B' switch is used. */ +/* - `edgelist' must be initialized if the `e' switch is used. */ +/* `edgemarkerlist' must be initialized if the `e' switch is used and */ +/* the `B' switch is not. */ +/* - `holelist', `regionlist', `normlist', and all scalars may be ignored.*/ +/* */ +/* `vorout' (only needed if `v' switch is used): */ +/* */ +/* - `pointlist' must be initialized. If `in->numberofpointattributes' */ +/* is not zero, `pointattributelist' must be initialized. */ +/* `pointmarkerlist' may be ignored. */ +/* - `edgelist' and `normlist' must both be initialized. */ +/* `edgemarkerlist' may be ignored. */ +/* - Everything else may be ignored. */ +/* */ +/* After a call to triangulate(), the valid fields of `out' and `vorout' */ +/* will depend, in an obvious way, on the choice of switches used. Note */ +/* that when the `p' switch is used, the pointers `holelist' and */ +/* `regionlist' are copied from `in' to `out', but no new space is */ +/* allocated; be careful that you don't free() the same array twice. On */ +/* the other hand, Triangle will never copy the `pointlist' pointer (or any */ +/* others); new space is allocated for `out->pointlist', or if the `N' */ +/* switch is used, `out->pointlist' remains uninitialized. */ +/* */ +/* All of the meaningful `numberof' fields will be properly set; for */ +/* instance, `numberofedges' will represent the number of edges in the */ +/* triangulation whether or not the edges were written. If segments are */ +/* not used, `numberofsegments' will indicate the number of boundary edges. */ +/* */ +/*****************************************************************************/ + +/* CLO: 3/21/99 - this could be done as a compile flag, but I always want +this defined and I don't want to sprinkle extra stuff throughout the +Makefile system if I don't have to. */ +#define ANSI_DECLARATORS 1 + +struct triangulateio { + REAL *pointlist; /* In / out */ + REAL *pointattributelist; /* In / out */ + int *pointmarkerlist; /* In / out */ + int numberofpoints; /* In / out */ + int numberofpointattributes; /* In / out */ + + int *trianglelist; /* In / out */ + REAL *triangleattributelist; /* In / out */ + REAL *trianglearealist; /* In only */ + int *neighborlist; /* Out only */ + int numberoftriangles; /* In / out */ + int numberofcorners; /* In / out */ + int numberoftriangleattributes; /* In / out */ + + int *segmentlist; /* In / out */ + int *segmentmarkerlist; /* In / out */ + int numberofsegments; /* In / out */ + + REAL *holelist; /* In / pointer to array copied out */ + int numberofholes; /* In / copied out */ + + REAL *regionlist; /* In / pointer to array copied out */ + int numberofregions; /* In / copied out */ + + int *edgelist; /* Out only */ + int *edgemarkerlist; /* Not used with Voronoi diagram; out only */ + REAL *normlist; /* Used only with Voronoi diagram; out only */ + int numberofedges; /* Out only */ +}; + +#ifdef ANSI_DECLARATORS +void triangulate(char *, struct triangulateio *, struct triangulateio *, + struct triangulateio *); +#else /* not ANSI_DECLARATORS */ +void triangulate(); +#endif /* not ANSI_DECLARATORS */ diff --git a/src/Lib/poly2tri/Makefile.am b/src/Lib/poly2tri/Makefile.am new file mode 100644 index 00000000..8acaf613 --- /dev/null +++ b/src/Lib/poly2tri/Makefile.am @@ -0,0 +1,19 @@ +EXTRA_DIST = README makefile.orig data_1 + +# if OLD_AUTOMAKE +# CFLAGS += -DSTANDALONE +# else +# AM_CFLAGS = -DSTANDALONE +# endif + +noinst_LIBRARIES = libpoly2tri.a + +libpoly2tri_a_SOURCES = \ + construct.c \ + interface.h \ + misc.c \ + monotone.c \ + tri.c \ + triangulate.h + +# INCLUDES += -I$(top_builddir) -I$(top_builddir)/Lib diff --git a/src/Lib/poly2tri/README b/src/Lib/poly2tri/README new file mode 100644 index 00000000..161cbeb1 --- /dev/null +++ b/src/Lib/poly2tri/README @@ -0,0 +1,96 @@ + This program is an implementation of a fast polygon +triangulation algorithm based on the paper "A simple and fast +incremental randomized algorithm for computing trapezoidal +decompositions and for triangulating polygons" by Raimund Seidel. + +(A copy of the implementation report is available as + http://www.cs.unc.edu/~manocha/CODE/GEM/chapter.html) + + The algorithm handles simple polygons with holes. The input is +specified as contours. The outermost contour is anti-clockwise, while +all the inner contours must be clockwise. No point should be repeated +in the input. A sample input file 'data_1' is provided. + + + The output is a list of triangles. Each triangle gives a pair +(i, j, k) where i, j, and k are indices of the vertices specified in +the input array. (The index numbering starts from 1, since the first +location v[0] in the input array of vertices is unused). The number of +output triangles produced for a polygon with n points is, + (n - 2) + 2*(#holes) + + + The algorithm also generates a qyery structure which can be +used to answer point-location queries very fast. + + int triangulate_polygon(...) +Time for triangulation: O(n log*n) + + int is_point_inside_polygon(...) +Time for query : O(log n) + + Both the routines are defined in 'tri.c'. See that file for +interfacing details. If not used stand_alone, include the header file +"interface.h" which contains the declarations for these +functions. Inclusion of "triangulation.h" is not necessary. + + + The implementation uses statically allocated arrays. Choose +appropriate value for SEGSIZE /* in triangulate.h */ depending on +input size. + + + There sould not be any compilation problem. If log2() is not +defined in your math library, you will have to supply the definition. + + +USAGE: + triangulate /* For standalone */ + + +------------------------------------------------------------------ +Bibliography: + + +@article{Sei91, + AUTHOR = "R. Seidel", + TITLE = "A simple and Fast Randomized Algorithm for Computing Trapezoidal Decompositions and for Triangulating Polygons", + JOURNAL = "Computational Geometry Theory \& Applications", + PAGES = "51-64", + NUMBER = 1, + YEAR = 1991, + VOLUME = 1 } + + +@book{o-cgc-94 +, author = "J. O'Rourke" +, title = "Computational Geometry in {C}" +, publisher = "Cambridge University Press" +, year = 1994 +, note = "ISBN 0-521-44592-2/Pb \$24.95, + ISBN 0-521-44034-3/Hc \$49.95. + Cambridge University Press + 40 West 20th Street + New York, NY 10011-4211 + 1-800-872-7423 + 346+xi pages, 228 exercises, 200 figures, 219 references" +, update = "94.05 orourke, 94.01 orourke" +, annote = "Textbook" +} + + + +Implementation report: Narkhede A. and Manocha D., Fast polygon + triangulation algorithm based on Seidel's Algorithm, UNC-CH, 1994. + +------------------------------------------------------------------- + +UNC-CH GIVES NO WARRANTY, EXPRESSED OR IMPLIED, FOR THE SOFTWARE +AND/OR DOCUMENTATION PROVIDED, INCLUDING, WITHOUT LIMITATION, WARRANTY +OF MERCHANTABILITY AND WARRANTY OF FITNESS FOR A PARTICULAR PURPOSE. + +This software is for non-commercial use only. + + + + - Atul Narkhede (narkhede@cs.unc.edu) diff --git a/src/Lib/poly2tri/construct.c b/src/Lib/poly2tri/construct.c new file mode 100644 index 00000000..6c18041f --- /dev/null +++ b/src/Lib/poly2tri/construct.c @@ -0,0 +1,1055 @@ +#include +#include + + +node_t qs[QSIZE]; /* Query structure */ +trap_t tr[TRSIZE]; /* Trapezoid structure */ +segment_t seg[SEGSIZE]; /* Segment table */ + +static int q_idx; +static int tr_idx; + +/* Return a new node to be added into the query tree */ +static int newnode() +{ + if (q_idx < QSIZE) + return q_idx++; + else + { + fprintf(stderr, "newnode: Query-table overflow\n"); + return -1; + } +} + +/* Return a free trapezoid */ +static int newtrap() +{ + if (tr_idx < TRSIZE) + { + tr[tr_idx].lseg = -1; + tr[tr_idx].rseg = -1; + tr[tr_idx].state = ST_VALID; + return tr_idx++; + } + else + { + fprintf(stderr, "newtrap: Trapezoid-table overflow\n"); + return -1; + } +} + + +/* Return the maximum of the two points into the yval structure */ +static int _max(yval, v0, v1) + point_t *yval; + point_t *v0; + point_t *v1; +{ + if (v0->y > v1->y + C_EPS) + *yval = *v0; + else if (FP_EQUAL(v0->y, v1->y)) + { + if (v0->x > v1->x + C_EPS) + *yval = *v0; + else + *yval = *v1; + } + else + *yval = *v1; + + return 0; +} + + +/* Return the minimum of the two points into the yval structure */ +static int _min(yval, v0, v1) + point_t *yval; + point_t *v0; + point_t *v1; +{ + if (v0->y < v1->y - C_EPS) + *yval = *v0; + else if (FP_EQUAL(v0->y, v1->y)) + { + if (v0->x < v1->x) + *yval = *v0; + else + *yval = *v1; + } + else + *yval = *v1; + + return 0; +} + + +int _greater_than(v0, v1) + point_t *v0; + point_t *v1; +{ + if (v0->y > v1->y + C_EPS) + return TRUE; + else if (v0->y < v1->y - C_EPS) + return FALSE; + else + return (v0->x > v1->x); +} + + +int _equal_to(v0, v1) + point_t *v0; + point_t *v1; +{ + return (FP_EQUAL(v0->y, v1->y) && FP_EQUAL(v0->x, v1->x)); +} + +int _greater_than_equal_to(v0, v1) + point_t *v0; + point_t *v1; +{ + if (v0->y > v1->y + C_EPS) + return TRUE; + else if (v0->y < v1->y - C_EPS) + return FALSE; + else + return (v0->x >= v1->x); +} + +int _less_than(v0, v1) + point_t *v0; + point_t *v1; +{ + if (v0->y < v1->y - C_EPS) + return TRUE; + else if (v0->y > v1->y + C_EPS) + return FALSE; + else + return (v0->x < v1->x); +} + + +/* Initilialise the query structure (Q) and the trapezoid table (T) + * when the first segment is added to start the trapezoidation. The + * query-tree starts out with 4 trapezoids, one S-node and 2 Y-nodes + * + * 4 + * ----------------------------------- + * \ + * 1 \ 2 + * \ + * ----------------------------------- + * 3 + */ + +static int init_query_structure(segnum) + int segnum; +{ + int i1, i2, i3, i4, i5, i6, i7, root; + int t1, t2, t3, t4; + segment_t *s = &seg[segnum]; + + q_idx = tr_idx = 1; + memset((void *)tr, 0, sizeof(tr)); + memset((void *)qs, 0, sizeof(qs)); + + i1 = newnode(); + qs[i1].nodetype = T_Y; + _max(&qs[i1].yval, &s->v0, &s->v1); /* root */ + root = i1; + + qs[i1].right = i2 = newnode(); + qs[i2].nodetype = T_SINK; + qs[i2].parent = i1; + + qs[i1].left = i3 = newnode(); + qs[i3].nodetype = T_Y; + _min(&qs[i3].yval, &s->v0, &s->v1); /* root */ + qs[i3].parent = i1; + + qs[i3].left = i4 = newnode(); + qs[i4].nodetype = T_SINK; + qs[i4].parent = i3; + + qs[i3].right = i5 = newnode(); + qs[i5].nodetype = T_X; + qs[i5].segnum = segnum; + qs[i5].parent = i3; + + qs[i5].left = i6 = newnode(); + qs[i6].nodetype = T_SINK; + qs[i6].parent = i5; + + qs[i5].right = i7 = newnode(); + qs[i7].nodetype = T_SINK; + qs[i7].parent = i5; + + t1 = newtrap(); /* middle left */ + t2 = newtrap(); /* middle right */ + t3 = newtrap(); /* bottom-most */ + t4 = newtrap(); /* topmost */ + + tr[t1].hi = tr[t2].hi = tr[t4].lo = qs[i1].yval; + tr[t1].lo = tr[t2].lo = tr[t3].hi = qs[i3].yval; + tr[t4].hi.y = (double) (INFINITY); + tr[t4].hi.x = (double) (INFINITY); + tr[t3].lo.y = (double) -1* (INFINITY); + tr[t3].lo.x = (double) -1* (INFINITY); + tr[t1].rseg = tr[t2].lseg = segnum; + tr[t1].u0 = tr[t2].u0 = t4; + tr[t1].d0 = tr[t2].d0 = t3; + tr[t4].d0 = tr[t3].u0 = t1; + tr[t4].d1 = tr[t3].u1 = t2; + + tr[t1].sink = i6; + tr[t2].sink = i7; + tr[t3].sink = i4; + tr[t4].sink = i2; + + tr[t1].state = tr[t2].state = ST_VALID; + tr[t3].state = tr[t4].state = ST_VALID; + + qs[i2].trnum = t4; + qs[i4].trnum = t3; + qs[i6].trnum = t1; + qs[i7].trnum = t2; + + s->is_inserted = TRUE; + return root; +} + + +/* Retun TRUE if the vertex v is to the left of line segment no. + * segnum. Takes care of the degenerate cases when both the vertices + * have the same y--cood, etc. + */ + +static int is_left_of(segnum, v) + int segnum; + point_t *v; +{ + segment_t *s = &seg[segnum]; + double area; + + if (_greater_than(&s->v1, &s->v0)) /* seg. going upwards */ + { + if (FP_EQUAL(s->v1.y, v->y)) + { + if (v->x < s->v1.x) + area = 1.0; + else + area = -1.0; + } + else if (FP_EQUAL(s->v0.y, v->y)) + { + if (v->x < s->v0.x) + area = 1.0; + else + area = -1.0; + } + else + area = CROSS(s->v0, s->v1, (*v)); + } + else /* v0 > v1 */ + { + if (FP_EQUAL(s->v1.y, v->y)) + { + if (v->x < s->v1.x) + area = 1.0; + else + area = -1.0; + } + else if (FP_EQUAL(s->v0.y, v->y)) + { + if (v->x < s->v0.x) + area = 1.0; + else + area = -1.0; + } + else + area = CROSS(s->v1, s->v0, (*v)); + } + + if (area > 0.0) + return TRUE; + else + return FALSE; +} + + + +/* Returns true if the corresponding endpoint of the given segment is */ +/* already inserted into the segment tree. Use the simple test of */ +/* whether the segment which shares this endpoint is already inserted */ + +static int inserted(segnum, whichpt) + int segnum; + int whichpt; +{ + if (whichpt == FIRSTPT) + return seg[seg[segnum].prev].is_inserted; + else + return seg[seg[segnum].next].is_inserted; +} + +/* This is query routine which determines which trapezoid does the + * point v lie in. The return value is the trapezoid number. + */ + +int locate_endpoint(v, vo, r) + point_t *v; + point_t *vo; + int r; +{ + node_t *rptr = &qs[r]; + + switch (rptr->nodetype) + { + case T_SINK: + return rptr->trnum; + + case T_Y: + if (_greater_than(v, &rptr->yval)) /* above */ + return locate_endpoint(v, vo, rptr->right); + else if (_equal_to(v, &rptr->yval)) /* the point is already */ + { /* inserted. */ + if (_greater_than(vo, &rptr->yval)) /* above */ + return locate_endpoint(v, vo, rptr->right); + else + return locate_endpoint(v, vo, rptr->left); /* below */ + } + else + return locate_endpoint(v, vo, rptr->left); /* below */ + + case T_X: + if (_equal_to(v, &seg[rptr->segnum].v0) || + _equal_to(v, &seg[rptr->segnum].v1)) + { + if (FP_EQUAL(v->y, vo->y)) /* horizontal segment */ + { + if (vo->x < v->x) + return locate_endpoint(v, vo, rptr->left); /* left */ + else + return locate_endpoint(v, vo, rptr->right); /* right */ + } + + else if (is_left_of(rptr->segnum, vo)) + return locate_endpoint(v, vo, rptr->left); /* left */ + else + return locate_endpoint(v, vo, rptr->right); /* right */ + } + else if (is_left_of(rptr->segnum, v)) + return locate_endpoint(v, vo, rptr->left); /* left */ + else + return locate_endpoint(v, vo, rptr->right); /* right */ + + default: + fprintf(stderr, "Haggu !!!!!\n"); + break; + } +} + + +/* Thread in the segment into the existing trapezoidation. The + * limiting trapezoids are given by tfirst and tlast (which are the + * trapezoids containing the two endpoints of the segment. Merges all + * possible trapezoids which flank this segment and have been recently + * divided because of its insertion + */ + +static int merge_trapezoids(segnum, tfirst, tlast, side) + int segnum; + int tfirst; + int tlast; + int side; +{ + int t, tnext, cond; + int ptnext; + + /* First merge polys on the LHS */ + t = tfirst; + while ((t > 0) && _greater_than_equal_to(&tr[t].lo, &tr[tlast].lo)) + { + if (side == S_LEFT) + cond = ((((tnext = tr[t].d0) > 0) && (tr[tnext].rseg == segnum)) || + (((tnext = tr[t].d1) > 0) && (tr[tnext].rseg == segnum))); + else + cond = ((((tnext = tr[t].d0) > 0) && (tr[tnext].lseg == segnum)) || + (((tnext = tr[t].d1) > 0) && (tr[tnext].lseg == segnum))); + + if (cond) + { + if ((tr[t].lseg == tr[tnext].lseg) && + (tr[t].rseg == tr[tnext].rseg)) /* good neighbours */ + { /* merge them */ + /* Use the upper node as the new node i.e. t */ + + ptnext = qs[tr[tnext].sink].parent; + + if (qs[ptnext].left == tr[tnext].sink) + qs[ptnext].left = tr[t].sink; + else + qs[ptnext].right = tr[t].sink; /* redirect parent */ + + + /* Change the upper neighbours of the lower trapezoids */ + + if ((tr[t].d0 = tr[tnext].d0) > 0) + if (tr[tr[t].d0].u0 == tnext) + tr[tr[t].d0].u0 = t; + else if (tr[tr[t].d0].u1 == tnext) + tr[tr[t].d0].u1 = t; + + if ((tr[t].d1 = tr[tnext].d1) > 0) + if (tr[tr[t].d1].u0 == tnext) + tr[tr[t].d1].u0 = t; + else if (tr[tr[t].d1].u1 == tnext) + tr[tr[t].d1].u1 = t; + + tr[t].lo = tr[tnext].lo; + tr[tnext].state = ST_INVALID; /* invalidate the lower */ + /* trapezium */ + } + else /* not good neighbours */ + t = tnext; + } + else /* do not satisfy the outer if */ + t = tnext; + + } /* end-while */ + + return 0; +} + + +/* Add in the new segment into the trapezoidation and update Q and T + * structures. First locate the two endpoints of the segment in the + * Q-structure. Then start from the topmost trapezoid and go down to + * the lower trapezoid dividing all the trapezoids in between . + */ + +static int add_segment(segnum) + int segnum; +{ + segment_t s; + segment_t *so = &seg[segnum]; + int tu, tl, sk, tfirst, tlast, tnext; + int tfirstr, tlastr, tfirstl, tlastl; + int i1, i2, t, t1, t2, tn; + point_t tpt; + int tritop = 0, tribot = 0, is_swapped = 0; + int tmptriseg; + + s = seg[segnum]; + if (_greater_than(&s.v1, &s.v0)) /* Get higher vertex in v0 */ + { + int tmp; + tpt = s.v0; + s.v0 = s.v1; + s.v1 = tpt; + tmp = s.root0; + s.root0 = s.root1; + s.root1 = tmp; + is_swapped = TRUE; + } + + if ((is_swapped) ? !inserted(segnum, LASTPT) : + !inserted(segnum, FIRSTPT)) /* insert v0 in the tree */ + { + int tmp_d; + + tu = locate_endpoint(&s.v0, &s.v1, s.root0); + tl = newtrap(); /* tl is the new lower trapezoid */ + tr[tl].state = ST_VALID; + tr[tl] = tr[tu]; + tr[tu].lo.y = tr[tl].hi.y = s.v0.y; + tr[tu].lo.x = tr[tl].hi.x = s.v0.x; + tr[tu].d0 = tl; + tr[tu].d1 = 0; + tr[tl].u0 = tu; + tr[tl].u1 = 0; + + if (((tmp_d = tr[tl].d0) > 0) && (tr[tmp_d].u0 == tu)) + tr[tmp_d].u0 = tl; + if (((tmp_d = tr[tl].d0) > 0) && (tr[tmp_d].u1 == tu)) + tr[tmp_d].u1 = tl; + + if (((tmp_d = tr[tl].d1) > 0) && (tr[tmp_d].u0 == tu)) + tr[tmp_d].u0 = tl; + if (((tmp_d = tr[tl].d1) > 0) && (tr[tmp_d].u1 == tu)) + tr[tmp_d].u1 = tl; + + /* Now update the query structure and obtain the sinks for the */ + /* two trapezoids */ + + i1 = newnode(); /* Upper trapezoid sink */ + i2 = newnode(); /* Lower trapezoid sink */ + sk = tr[tu].sink; + + qs[sk].nodetype = T_Y; + qs[sk].yval = s.v0; + qs[sk].segnum = segnum; /* not really reqd ... maybe later */ + qs[sk].left = i2; + qs[sk].right = i1; + + qs[i1].nodetype = T_SINK; + qs[i1].trnum = tu; + qs[i1].parent = sk; + + qs[i2].nodetype = T_SINK; + qs[i2].trnum = tl; + qs[i2].parent = sk; + + tr[tu].sink = i1; + tr[tl].sink = i2; + tfirst = tl; + } + else /* v0 already present */ + { /* Get the topmost intersecting trapezoid */ + tfirst = locate_endpoint(&s.v0, &s.v1, s.root0); + tritop = 1; + } + + + if ((is_swapped) ? !inserted(segnum, FIRSTPT) : + !inserted(segnum, LASTPT)) /* insert v1 in the tree */ + { + int tmp_d; + + tu = locate_endpoint(&s.v1, &s.v0, s.root1); + + tl = newtrap(); /* tl is the new lower trapezoid */ + tr[tl].state = ST_VALID; + tr[tl] = tr[tu]; + tr[tu].lo.y = tr[tl].hi.y = s.v1.y; + tr[tu].lo.x = tr[tl].hi.x = s.v1.x; + tr[tu].d0 = tl; + tr[tu].d1 = 0; + tr[tl].u0 = tu; + tr[tl].u1 = 0; + + if (((tmp_d = tr[tl].d0) > 0) && (tr[tmp_d].u0 == tu)) + tr[tmp_d].u0 = tl; + if (((tmp_d = tr[tl].d0) > 0) && (tr[tmp_d].u1 == tu)) + tr[tmp_d].u1 = tl; + + if (((tmp_d = tr[tl].d1) > 0) && (tr[tmp_d].u0 == tu)) + tr[tmp_d].u0 = tl; + if (((tmp_d = tr[tl].d1) > 0) && (tr[tmp_d].u1 == tu)) + tr[tmp_d].u1 = tl; + + /* Now update the query structure and obtain the sinks for the */ + /* two trapezoids */ + + i1 = newnode(); /* Upper trapezoid sink */ + i2 = newnode(); /* Lower trapezoid sink */ + sk = tr[tu].sink; + + qs[sk].nodetype = T_Y; + qs[sk].yval = s.v1; + qs[sk].segnum = segnum; /* not really reqd ... maybe later */ + qs[sk].left = i2; + qs[sk].right = i1; + + qs[i1].nodetype = T_SINK; + qs[i1].trnum = tu; + qs[i1].parent = sk; + + qs[i2].nodetype = T_SINK; + qs[i2].trnum = tl; + qs[i2].parent = sk; + + tr[tu].sink = i1; + tr[tl].sink = i2; + tlast = tu; + } + else /* v1 already present */ + { /* Get the lowermost intersecting trapezoid */ + tlast = locate_endpoint(&s.v1, &s.v0, s.root1); + tribot = 1; + } + + /* Thread the segment into the query tree creating a new X-node */ + /* First, split all the trapezoids which are intersected by s into */ + /* two */ + + t = tfirst; /* topmost trapezoid */ + + while ((t > 0) && + _greater_than_equal_to(&tr[t].lo, &tr[tlast].lo)) + /* traverse from top to bot */ + { + int t_sav, tn_sav; + sk = tr[t].sink; + i1 = newnode(); /* left trapezoid sink */ + i2 = newnode(); /* right trapezoid sink */ + + qs[sk].nodetype = T_X; + qs[sk].segnum = segnum; + qs[sk].left = i1; + qs[sk].right = i2; + + qs[i1].nodetype = T_SINK; /* left trapezoid (use existing one) */ + qs[i1].trnum = t; + qs[i1].parent = sk; + + qs[i2].nodetype = T_SINK; /* right trapezoid (allocate new) */ + qs[i2].trnum = tn = newtrap(); + tr[tn].state = ST_VALID; + qs[i2].parent = sk; + + if (t == tfirst) + tfirstr = tn; + if (_equal_to(&tr[t].lo, &tr[tlast].lo)) + tlastr = tn; + + tr[tn] = tr[t]; + tr[t].sink = i1; + tr[tn].sink = i2; + t_sav = t; + tn_sav = tn; + + /* error */ + + if ((tr[t].d0 <= 0) && (tr[t].d1 <= 0)) /* case cannot arise */ + { + fprintf(stderr, "add_segment: error\n"); + break; + } + + /* only one trapezoid below. partition t into two and make the */ + /* two resulting trapezoids t and tn as the upper neighbours of */ + /* the sole lower trapezoid */ + + else if ((tr[t].d0 > 0) && (tr[t].d1 <= 0)) + { /* Only one trapezoid below */ + if ((tr[t].u0 > 0) && (tr[t].u1 > 0)) + { /* continuation of a chain from abv. */ + if (tr[t].usave > 0) /* three upper neighbours */ + { + if (tr[t].uside == S_LEFT) + { + tr[tn].u0 = tr[t].u1; + tr[t].u1 = -1; + tr[tn].u1 = tr[t].usave; + + tr[tr[t].u0].d0 = t; + tr[tr[tn].u0].d0 = tn; + tr[tr[tn].u1].d0 = tn; + } + else /* intersects in the right */ + { + tr[tn].u1 = -1; + tr[tn].u0 = tr[t].u1; + tr[t].u1 = tr[t].u0; + tr[t].u0 = tr[t].usave; + + tr[tr[t].u0].d0 = t; + tr[tr[t].u1].d0 = t; + tr[tr[tn].u0].d0 = tn; + } + + tr[t].usave = tr[tn].usave = 0; + } + else /* No usave.... simple case */ + { + tr[tn].u0 = tr[t].u1; + tr[t].u1 = tr[tn].u1 = -1; + tr[tr[tn].u0].d0 = tn; + } + } + else + { /* fresh seg. or upward cusp */ + int tmp_u = tr[t].u0; + int td0, td1; + if (((td0 = tr[tmp_u].d0) > 0) && + ((td1 = tr[tmp_u].d1) > 0)) + { /* upward cusp */ + if ((tr[td0].rseg > 0) && + !is_left_of(tr[td0].rseg, &s.v1)) + { + tr[t].u0 = tr[t].u1 = tr[tn].u1 = -1; + tr[tr[tn].u0].d1 = tn; + } + else /* cusp going leftwards */ + { + tr[tn].u0 = tr[tn].u1 = tr[t].u1 = -1; + tr[tr[t].u0].d0 = t; + } + } + else /* fresh segment */ + { + tr[tr[t].u0].d0 = t; + tr[tr[t].u0].d1 = tn; + } + } + + if (FP_EQUAL(tr[t].lo.y, tr[tlast].lo.y) && + FP_EQUAL(tr[t].lo.x, tr[tlast].lo.x) && tribot) + { /* bottom forms a triangle */ + + if (is_swapped) + tmptriseg = seg[segnum].prev; + else + tmptriseg = seg[segnum].next; + + if ((tmptriseg > 0) && is_left_of(tmptriseg, &s.v0)) + { + /* L-R downward cusp */ + tr[tr[t].d0].u0 = t; + tr[tn].d0 = tr[tn].d1 = -1; + } + else + { + /* R-L downward cusp */ + tr[tr[tn].d0].u1 = tn; + tr[t].d0 = tr[t].d1 = -1; + } + } + else + { + if ((tr[tr[t].d0].u0 > 0) && (tr[tr[t].d0].u1 > 0)) + { + if (tr[tr[t].d0].u0 == t) /* passes thru LHS */ + { + tr[tr[t].d0].usave = tr[tr[t].d0].u1; + tr[tr[t].d0].uside = S_LEFT; + } + else + { + tr[tr[t].d0].usave = tr[tr[t].d0].u0; + tr[tr[t].d0].uside = S_RIGHT; + } + } + tr[tr[t].d0].u0 = t; + tr[tr[t].d0].u1 = tn; + } + + t = tr[t].d0; + } + + + else if ((tr[t].d0 <= 0) && (tr[t].d1 > 0)) + { /* Only one trapezoid below */ + if ((tr[t].u0 > 0) && (tr[t].u1 > 0)) + { /* continuation of a chain from abv. */ + if (tr[t].usave > 0) /* three upper neighbours */ + { + if (tr[t].uside == S_LEFT) + { + tr[tn].u0 = tr[t].u1; + tr[t].u1 = -1; + tr[tn].u1 = tr[t].usave; + + tr[tr[t].u0].d0 = t; + tr[tr[tn].u0].d0 = tn; + tr[tr[tn].u1].d0 = tn; + } + else /* intersects in the right */ + { + tr[tn].u1 = -1; + tr[tn].u0 = tr[t].u1; + tr[t].u1 = tr[t].u0; + tr[t].u0 = tr[t].usave; + + tr[tr[t].u0].d0 = t; + tr[tr[t].u1].d0 = t; + tr[tr[tn].u0].d0 = tn; + } + + tr[t].usave = tr[tn].usave = 0; + } + else /* No usave.... simple case */ + { + tr[tn].u0 = tr[t].u1; + tr[t].u1 = tr[tn].u1 = -1; + tr[tr[tn].u0].d0 = tn; + } + } + else + { /* fresh seg. or upward cusp */ + int tmp_u = tr[t].u0; + int td0, td1; + if (((td0 = tr[tmp_u].d0) > 0) && + ((td1 = tr[tmp_u].d1) > 0)) + { /* upward cusp */ + if ((tr[td0].rseg > 0) && + !is_left_of(tr[td0].rseg, &s.v1)) + { + tr[t].u0 = tr[t].u1 = tr[tn].u1 = -1; + tr[tr[tn].u0].d1 = tn; + } + else + { + tr[tn].u0 = tr[tn].u1 = tr[t].u1 = -1; + tr[tr[t].u0].d0 = t; + } + } + else /* fresh segment */ + { + tr[tr[t].u0].d0 = t; + tr[tr[t].u0].d1 = tn; + } + } + + if (FP_EQUAL(tr[t].lo.y, tr[tlast].lo.y) && + FP_EQUAL(tr[t].lo.x, tr[tlast].lo.x) && tribot) + { /* bottom forms a triangle */ + int tmpseg; + + if (is_swapped) + tmptriseg = seg[segnum].prev; + else + tmptriseg = seg[segnum].next; + + if ((tmpseg > 0) && is_left_of(tmpseg, &s.v0)) + { + /* L-R downward cusp */ + tr[tr[t].d1].u0 = t; + tr[tn].d0 = tr[tn].d1 = -1; + } + else + { + /* R-L downward cusp */ + tr[tr[tn].d1].u1 = tn; + tr[t].d0 = tr[t].d1 = -1; + } + } + else + { + if ((tr[tr[t].d1].u0 > 0) && (tr[tr[t].d1].u1 > 0)) + { + if (tr[tr[t].d1].u0 == t) /* passes thru LHS */ + { + tr[tr[t].d1].usave = tr[tr[t].d1].u1; + tr[tr[t].d1].uside = S_LEFT; + } + else + { + tr[tr[t].d1].usave = tr[tr[t].d1].u0; + tr[tr[t].d1].uside = S_RIGHT; + } + } + tr[tr[t].d1].u0 = t; + tr[tr[t].d1].u1 = tn; + } + + t = tr[t].d1; + } + + /* two trapezoids below. Find out which one is intersected by */ + /* this segment and proceed down that one */ + + else + { + int tmpseg = tr[tr[t].d0].rseg; + double y0, yt; + point_t tmppt; + int tnext, i_d0, i_d1; + + i_d0 = i_d1 = FALSE; + if (FP_EQUAL(tr[t].lo.y, s.v0.y)) + { + if (tr[t].lo.x > s.v0.x) + i_d0 = TRUE; + else + i_d1 = TRUE; + } + else + { + tmppt.y = y0 = tr[t].lo.y; + yt = (y0 - s.v0.y)/(s.v1.y - s.v0.y); + tmppt.x = s.v0.x + yt * (s.v1.x - s.v0.x); + + if (_less_than(&tmppt, &tr[t].lo)) + i_d0 = TRUE; + else + i_d1 = TRUE; + } + + /* check continuity from the top so that the lower-neighbour */ + /* values are properly filled for the upper trapezoid */ + + if ((tr[t].u0 > 0) && (tr[t].u1 > 0)) + { /* continuation of a chain from abv. */ + if (tr[t].usave > 0) /* three upper neighbours */ + { + if (tr[t].uside == S_LEFT) + { + tr[tn].u0 = tr[t].u1; + tr[t].u1 = -1; + tr[tn].u1 = tr[t].usave; + + tr[tr[t].u0].d0 = t; + tr[tr[tn].u0].d0 = tn; + tr[tr[tn].u1].d0 = tn; + } + else /* intersects in the right */ + { + tr[tn].u1 = -1; + tr[tn].u0 = tr[t].u1; + tr[t].u1 = tr[t].u0; + tr[t].u0 = tr[t].usave; + + tr[tr[t].u0].d0 = t; + tr[tr[t].u1].d0 = t; + tr[tr[tn].u0].d0 = tn; + } + + tr[t].usave = tr[tn].usave = 0; + } + else /* No usave.... simple case */ + { + tr[tn].u0 = tr[t].u1; + tr[tn].u1 = -1; + tr[t].u1 = -1; + tr[tr[tn].u0].d0 = tn; + } + } + else + { /* fresh seg. or upward cusp */ + int tmp_u = tr[t].u0; + int td0, td1; + if (((td0 = tr[tmp_u].d0) > 0) && + ((td1 = tr[tmp_u].d1) > 0)) + { /* upward cusp */ + if ((tr[td0].rseg > 0) && + !is_left_of(tr[td0].rseg, &s.v1)) + { + tr[t].u0 = tr[t].u1 = tr[tn].u1 = -1; + tr[tr[tn].u0].d1 = tn; + } + else + { + tr[tn].u0 = tr[tn].u1 = tr[t].u1 = -1; + tr[tr[t].u0].d0 = t; + } + } + else /* fresh segment */ + { + tr[tr[t].u0].d0 = t; + tr[tr[t].u0].d1 = tn; + } + } + + if (FP_EQUAL(tr[t].lo.y, tr[tlast].lo.y) && + FP_EQUAL(tr[t].lo.x, tr[tlast].lo.x) && tribot) + { + /* this case arises only at the lowest trapezoid.. i.e. + tlast, if the lower endpoint of the segment is + already inserted in the structure */ + + tr[tr[t].d0].u0 = t; + tr[tr[t].d0].u1 = -1; + tr[tr[t].d1].u0 = tn; + tr[tr[t].d1].u1 = -1; + + tr[tn].d0 = tr[t].d1; + tr[t].d1 = tr[tn].d1 = -1; + + tnext = tr[t].d1; + } + else if (i_d0) + /* intersecting d0 */ + { + tr[tr[t].d0].u0 = t; + tr[tr[t].d0].u1 = tn; + tr[tr[t].d1].u0 = tn; + tr[tr[t].d1].u1 = -1; + + /* new code to determine the bottom neighbours of the */ + /* newly partitioned trapezoid */ + + tr[t].d1 = -1; + + tnext = tr[t].d0; + } + else /* intersecting d1 */ + { + tr[tr[t].d0].u0 = t; + tr[tr[t].d0].u1 = -1; + tr[tr[t].d1].u0 = t; + tr[tr[t].d1].u1 = tn; + + /* new code to determine the bottom neighbours of the */ + /* newly partitioned trapezoid */ + + tr[tn].d0 = tr[t].d1; + tr[tn].d1 = -1; + + tnext = tr[t].d1; + } + + t = tnext; + } + + tr[t_sav].rseg = tr[tn_sav].lseg = segnum; + } /* end-while */ + + /* Now combine those trapezoids which share common segments. We can */ + /* use the pointers to the parent to connect these together. This */ + /* works only because all these new trapezoids have been formed */ + /* due to splitting by the segment, and hence have only one parent */ + + tfirstl = tfirst; + tlastl = tlast; + merge_trapezoids(segnum, tfirstl, tlastl, S_LEFT); + merge_trapezoids(segnum, tfirstr, tlastr, S_RIGHT); + + seg[segnum].is_inserted = TRUE; + return 0; +} + + +/* Update the roots stored for each of the endpoints of the segment. + * This is done to speed up the location-query for the endpoint when + * the segment is inserted into the trapezoidation subsequently + */ +static int find_new_roots(segnum) + int segnum; +{ + segment_t *s = &seg[segnum]; + + if (s->is_inserted) + return 0; + + s->root0 = locate_endpoint(&s->v0, &s->v1, s->root0); + s->root0 = tr[s->root0].sink; + + s->root1 = locate_endpoint(&s->v1, &s->v0, s->root1); + s->root1 = tr[s->root1].sink; + return 0; +} + + +/* Main routine to perform trapezoidation */ +int construct_trapezoids(nseg) + int nseg; +{ + register int i; + int root, h; + + /* Add the first segment and get the query structure and trapezoid */ + /* list initialised */ + + root = init_query_structure(choose_segment()); + + for (i = 1; i <= nseg; i++) + seg[i].root0 = seg[i].root1 = root; + + for (h = 1; h <= math_logstar_n(nseg); h++) + { + for (i = math_N(nseg, h -1) + 1; i <= math_N(nseg, h); i++) + add_segment(choose_segment()); + + /* Find a new root for each of the segment endpoints */ + for (i = 1; i <= nseg; i++) + find_new_roots(i); + } + + for (i = math_N(nseg, math_logstar_n(nseg)) + 1; i <= nseg; i++) + add_segment(choose_segment()); + + return 0; +} + + diff --git a/src/Lib/poly2tri/data_1 b/src/Lib/poly2tri/data_1 new file mode 100644 index 00000000..f405c7dc --- /dev/null +++ b/src/Lib/poly2tri/data_1 @@ -0,0 +1,24 @@ +4 + +4 +0.0 0.0 +6.0 0.0 +6.0 6.0 +0.0 6.0 + +3 +0.5 1.0 +1.0 2.0 +2.0 1.5 + +3 +0.5 4.0 +1.0 5.0 +2.0 4.5 + +3 +3.0 3.0 +5.0 3.5 +5.0 2.5 + + diff --git a/src/Lib/poly2tri/interface.h b/src/Lib/poly2tri/interface.h new file mode 100644 index 00000000..fb84ab88 --- /dev/null +++ b/src/Lib/poly2tri/interface.h @@ -0,0 +1,18 @@ +#ifndef __interface_h +#define __interface_h + +#define TRUE 1 +#define FALSE 0 + +#if defined ( __cplusplus ) +extern "C" { +#endif + +extern int triangulate_polygon(int, int *, double (*)[2], int (*)[3]); +extern int is_point_inside_polygon(double *); + +#if defined ( __cplusplus ) +} +#endif + +#endif /* __interface_h */ diff --git a/src/Lib/poly2tri/misc.c b/src/Lib/poly2tri/misc.c new file mode 100644 index 00000000..4d3c6fef --- /dev/null +++ b/src/Lib/poly2tri/misc.c @@ -0,0 +1,157 @@ +#include +#include +#include + +#ifdef __STDC__ +extern double log2(double); +#else +extern double log2(); +#endif + +static int choose_idx; +static int permute[SEGSIZE]; + + +/* Generate a random permutation of the segments 1..n */ +int generate_random_ordering(n) + int n; +{ + struct timeval tval; + struct timezone tzone; + register int i; + int m, st[SEGSIZE], *p; + + choose_idx = 1; + gettimeofday(&tval, &tzone); + srand48(tval.tv_sec); + + for (i = 0; i <= n; i++) + st[i] = i; + + p = st; + for (i = 1; i <= n; i++, p++) + { + m = lrand48() % (n + 1 - i) + 1; + permute[i] = p[m]; + if (m != 1) + p[m] = p[1]; + } + return 0; +} + + +/* Return the next segment in the generated random ordering of all the */ +/* segments in S */ +int choose_segment() +{ + int i; + +#ifdef DEBUG + fprintf(stderr, "choose_segment: %d\n", permute[choose_idx]); +#endif + return permute[choose_idx++]; +} + + +#ifdef STANDALONE + +/* Read in the list of vertices from infile */ +int read_segments(filename, genus) + char *filename; + int *genus; +{ + FILE *infile; + int ccount; + register int i; + int ncontours, npoints, first, last; + + if ((infile = fopen(filename, "r")) == NULL) + { + perror(filename); + return -1; + } + + fscanf(infile, "%d", &ncontours); + if (ncontours <= 0) + return -1; + + /* For every contour, read in all the points for the contour. The */ + /* outer-most contour is read in first (points specified in */ + /* anti-clockwise order). Next, the inner contours are input in */ + /* clockwise order */ + + ccount = 0; + i = 1; + + while (ccount < ncontours) + { + int j; + + fscanf(infile, "%d", &npoints); + first = i; + last = first + npoints - 1; + for (j = 0; j < npoints; j++, i++) + { + fscanf(infile, "%lf%lf", &seg[i].v0.x, &seg[i].v0.y); + if (i == last) + { + seg[i].next = first; + seg[i].prev = i-1; + seg[i-1].v1 = seg[i].v0; + } + else if (i == first) + { + seg[i].next = i+1; + seg[i].prev = last; + seg[last].v1 = seg[i].v0; + } + else + { + seg[i].prev = i-1; + seg[i].next = i+1; + seg[i-1].v1 = seg[i].v0; + } + + seg[i].is_inserted = FALSE; + } + + ccount++; + } + + *genus = ncontours - 1; + return i-1; +} + +#endif + + +/* Get log*n for given n */ +int math_logstar_n(n) + int n; +{ + register int i; + double v; + + for (i = 0, v = (double) n; v >= 1; i++) { + /* v = log2(v); */ + v = log(v) / log(2.0); + } + + return (i - 1); +} + + +int math_N(n, h) + int n; + int h; +{ + register int i; + double v; + + for (i = 0, v = (int) n; i < h; i++) { + /* v = log2(v); */ + v = log(v) / log(2.0); + } + + return (int) ceil((double) 1.0*n/v); +} diff --git a/src/Lib/poly2tri/monotone.c b/src/Lib/poly2tri/monotone.c new file mode 100644 index 00000000..689987c2 --- /dev/null +++ b/src/Lib/poly2tri/monotone.c @@ -0,0 +1,737 @@ +#include +#include + +#define CROSS_SINE(v0, v1) ((v0).x * (v1).y - (v1).x * (v0).y) +#define LENGTH(v0) (sqrt((v0).x * (v0).x + (v0).y * (v0).y)) + +static monchain_t mchain[TRSIZE]; /* Table to hold all the monotone */ + /* polygons . Each monotone polygon */ + /* is a circularly linked list */ + +static vertexchain_t vert[SEGSIZE]; /* chain init. information. This */ + /* is used to decide which */ + /* monotone polygon to split if */ + /* there are several other */ + /* polygons touching at the same */ + /* vertex */ + +static int mon[SEGSIZE]; /* contains position of any vertex in */ + /* the monotone chain for the polygon */ +static int visited[TRSIZE]; +static int chain_idx, op_idx, mon_idx; + + +static int triangulate_single_polygon(int, int, int, int (*)[3]); +static int traverse_polygon(int, int, int, int); + +/* Function returns TRUE if the trapezoid lies inside the polygon */ +static int inside_polygon(t) + trap_t *t; +{ + int rseg = t->rseg; + + if (t->state == ST_INVALID) + return 0; + + if ((t->lseg <= 0) || (t->rseg <= 0)) + return 0; + + if (((t->u0 <= 0) && (t->u1 <= 0)) || + ((t->d0 <= 0) && (t->d1 <= 0))) /* triangle */ + return (_greater_than(&seg[rseg].v1, &seg[rseg].v0)); + + return 0; +} + + +/* return a new mon structure from the table */ +static int newmon() +{ + return ++mon_idx; +} + + +/* return a new chain element from the table */ +static int new_chain_element() +{ + return ++chain_idx; +} + + +static double get_angle(vp0, vpnext, vp1) + point_t *vp0; + point_t *vpnext; + point_t *vp1; +{ + point_t v0, v1; + + v0.x = vpnext->x - vp0->x; + v0.y = vpnext->y - vp0->y; + + v1.x = vp1->x - vp0->x; + v1.y = vp1->y - vp0->y; + + if (CROSS_SINE(v0, v1) >= 0) /* sine is positive */ + return DOT(v0, v1)/LENGTH(v0)/LENGTH(v1); + else + return (-1.0 * DOT(v0, v1)/LENGTH(v0)/LENGTH(v1) - 2); +} + + +/* (v0, v1) is the new diagonal to be added to the polygon. Find which */ +/* chain to use and return the positions of v0 and v1 in p and q */ +static int get_vertex_positions(v0, v1, ip, iq) + int v0; + int v1; + int *ip; + int *iq; +{ + vertexchain_t *vp0, *vp1; + register int i; + double angle, temp; + int tp, tq; + + vp0 = &vert[v0]; + vp1 = &vert[v1]; + + /* p is identified as follows. Scan from (v0, v1) rightwards till */ + /* you hit the first segment starting from v0. That chain is the */ + /* chain of our interest */ + + angle = -4.0; + for (i = 0; i < 4; i++) + { + if (vp0->vnext[i] <= 0) + continue; + if ((temp = get_angle(&vp0->pt, &(vert[vp0->vnext[i]].pt), + &vp1->pt)) > angle) + { + angle = temp; + tp = i; + } + } + + *ip = tp; + + /* Do similar actions for q */ + + angle = -4.0; + for (i = 0; i < 4; i++) + { + if (vp1->vnext[i] <= 0) + continue; + if ((temp = get_angle(&vp1->pt, &(vert[vp1->vnext[i]].pt), + &vp0->pt)) > angle) + { + angle = temp; + tq = i; + } + } + + *iq = tq; + + return 0; +} + + +/* v0 and v1 are specified in anti-clockwise order with respect to + * the current monotone polygon mcur. Split the current polygon into + * two polygons using the diagonal (v0, v1) + */ +static int make_new_monotone_poly(mcur, v0, v1) + int mcur; + int v0; + int v1; +{ + int p, q, ip, iq; + int mnew = newmon(); + int i, j, nf0, nf1; + vertexchain_t *vp0, *vp1; + + vp0 = &vert[v0]; + vp1 = &vert[v1]; + + get_vertex_positions(v0, v1, &ip, &iq); + + p = vp0->vpos[ip]; + q = vp1->vpos[iq]; + + /* At this stage, we have got the positions of v0 and v1 in the */ + /* desired chain. Now modify the linked lists */ + + i = new_chain_element(); /* for the new list */ + j = new_chain_element(); + + mchain[i].vnum = v0; + mchain[j].vnum = v1; + + mchain[i].next = mchain[p].next; + mchain[mchain[p].next].prev = i; + mchain[i].prev = j; + mchain[j].next = i; + mchain[j].prev = mchain[q].prev; + mchain[mchain[q].prev].next = j; + + mchain[p].next = q; + mchain[q].prev = p; + + nf0 = vp0->nextfree; + nf1 = vp1->nextfree; + + vp0->vnext[ip] = v1; + + vp0->vpos[nf0] = i; + vp0->vnext[nf0] = mchain[mchain[i].next].vnum; + vp1->vpos[nf1] = j; + vp1->vnext[nf1] = v0; + + vp0->nextfree++; + vp1->nextfree++; + +#ifdef DEBUG + fprintf(stderr, "make_poly: mcur = %d, (v0, v1) = (%d, %d)\n", + mcur, v0, v1); + fprintf(stderr, "next posns = (p, q) = (%d, %d)\n", p, q); +#endif + + mon[mcur] = p; + mon[mnew] = i; + return mnew; +} + +/* Main routine to get monotone polygons from the trapezoidation of + * the polygon. + */ + +int monotonate_trapezoids(n) + int n; +{ + register int i; + int tr_start; + + memset((void *)vert, 0, sizeof(vert)); + memset((void *)visited, 0, sizeof(visited)); + memset((void *)mchain, 0, sizeof(mchain)); + memset((void *)mon, 0, sizeof(mon)); + + /* First locate a trapezoid which lies inside the polygon */ + /* and which is triangular */ + for (i = 0; i < TRSIZE; i++) + if (inside_polygon(&tr[i])) + break; + tr_start = i; + + /* Initialise the mon data-structure and start spanning all the */ + /* trapezoids within the polygon */ + +#if 0 + for (i = 1; i <= n; i++) + { + mchain[i].prev = i - 1; + mchain[i].next = i + 1; + mchain[i].vnum = i; + vert[i].pt = seg[i].v0; + vert[i].vnext[0] = i + 1; /* next vertex */ + vert[i].vpos[0] = i; /* locn. of next vertex */ + vert[i].nextfree = 1; + } + mchain[1].prev = n; + mchain[n].next = 1; + vert[n].vnext[0] = 1; + vert[n].vpos[0] = n; + chain_idx = n; + mon_idx = 0; + mon[0] = 1; /* position of any vertex in the first */ + /* chain */ + +#else + + for (i = 1; i <= n; i++) + { + mchain[i].prev = seg[i].prev; + mchain[i].next = seg[i].next; + mchain[i].vnum = i; + vert[i].pt = seg[i].v0; + vert[i].vnext[0] = seg[i].next; /* next vertex */ + vert[i].vpos[0] = i; /* locn. of next vertex */ + vert[i].nextfree = 1; + } + + chain_idx = n; + mon_idx = 0; + mon[0] = 1; /* position of any vertex in the first */ + /* chain */ + +#endif + + /* traverse the polygon */ + if (tr[tr_start].u0 > 0) + traverse_polygon(0, tr_start, tr[tr_start].u0, TR_FROM_UP); + else if (tr[tr_start].d0 > 0) + traverse_polygon(0, tr_start, tr[tr_start].d0, TR_FROM_DN); + + /* return the number of polygons created */ + return newmon(); +} + + +/* recursively visit all the trapezoids */ +static int traverse_polygon(mcur, trnum, from, dir) + int mcur; + int trnum; + int from; + int dir; +{ + trap_t *t = &tr[trnum]; + int howsplit, mnew; + int v0, v1, v0next, v1next; + int retval, tmp; + int do_switch = FALSE; + + if ((trnum <= 0) || visited[trnum]) + return 0; + + visited[trnum] = TRUE; + + /* We have much more information available here. */ + /* rseg: goes upwards */ + /* lseg: goes downwards */ + + /* Initially assume that dir = TR_FROM_DN (from the left) */ + /* Switch v0 and v1 if necessary afterwards */ + + + /* special cases for triangles with cusps at the opposite ends. */ + /* take care of this first */ + if ((t->u0 <= 0) && (t->u1 <= 0)) + { + if ((t->d0 > 0) && (t->d1 > 0)) /* downward opening triangle */ + { + v0 = tr[t->d1].lseg; + v1 = t->lseg; + if (from == t->d1) + { + do_switch = TRUE; + mnew = make_new_monotone_poly(mcur, v1, v0); + traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP); + } + else + { + mnew = make_new_monotone_poly(mcur, v0, v1); + traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP); + } + } + else + { + retval = SP_NOSPLIT; /* Just traverse all neighbours */ + traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP); + traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP); + } + } + + else if ((t->d0 <= 0) && (t->d1 <= 0)) + { + if ((t->u0 > 0) && (t->u1 > 0)) /* upward opening triangle */ + { + v0 = t->rseg; + v1 = tr[t->u0].rseg; + if (from == t->u1) + { + do_switch = TRUE; + mnew = make_new_monotone_poly(mcur, v1, v0); + traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN); + } + else + { + mnew = make_new_monotone_poly(mcur, v0, v1); + traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN); + } + } + else + { + retval = SP_NOSPLIT; /* Just traverse all neighbours */ + traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP); + traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP); + } + } + + else if ((t->u0 > 0) && (t->u1 > 0)) + { + if ((t->d0 > 0) && (t->d1 > 0)) /* downward + upward cusps */ + { + v0 = tr[t->d1].lseg; + v1 = tr[t->u0].rseg; + retval = SP_2UP_2DN; + if (((dir == TR_FROM_DN) && (t->d1 == from)) || + ((dir == TR_FROM_UP) && (t->u1 == from))) + { + do_switch = TRUE; + mnew = make_new_monotone_poly(mcur, v1, v0); + traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP); + } + else + { + mnew = make_new_monotone_poly(mcur, v0, v1); + traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP); + } + } + else /* only downward cusp */ + { + if (_equal_to(&t->lo, &seg[t->lseg].v1)) + { + v0 = tr[t->u0].rseg; + v1 = seg[t->lseg].next; + + retval = SP_2UP_LEFT; + if ((dir == TR_FROM_UP) && (t->u0 == from)) + { + do_switch = TRUE; + mnew = make_new_monotone_poly(mcur, v1, v0); + traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP); + } + else + { + mnew = make_new_monotone_poly(mcur, v0, v1); + traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP); + traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN); + } + } + else + { + v0 = t->rseg; + v1 = tr[t->u0].rseg; + retval = SP_2UP_RIGHT; + if ((dir == TR_FROM_UP) && (t->u1 == from)) + { + do_switch = TRUE; + mnew = make_new_monotone_poly(mcur, v1, v0); + traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN); + } + else + { + mnew = make_new_monotone_poly(mcur, v0, v1); + traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP); + traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN); + } + } + } + } + else if ((t->u0 > 0) || (t->u1 > 0)) /* no downward cusp */ + { + if ((t->d0 > 0) && (t->d1 > 0)) /* only upward cusp */ + { + if (_equal_to(&t->hi, &seg[t->lseg].v0)) + { + v0 = tr[t->d1].lseg; + v1 = t->lseg; + retval = SP_2DN_LEFT; + if (!((dir == TR_FROM_DN) && (t->d0 == from))) + { + do_switch = TRUE; + mnew = make_new_monotone_poly(mcur, v1, v0); + traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP); + traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP); + } + else + { + mnew = make_new_monotone_poly(mcur, v0, v1); + traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP); + } + } + else + { + v0 = tr[t->d1].lseg; + v1 = seg[t->rseg].next; + + retval = SP_2DN_RIGHT; + if ((dir == TR_FROM_DN) && (t->d1 == from)) + { + do_switch = TRUE; + mnew = make_new_monotone_poly(mcur, v1, v0); + traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP); + } + else + { + mnew = make_new_monotone_poly(mcur, v0, v1); + traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP); + traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP); + } + } + } + else /* no cusp */ + { + if (_equal_to(&t->hi, &seg[t->lseg].v0) && + _equal_to(&t->lo, &seg[t->rseg].v0)) + { + v0 = t->rseg; + v1 = t->lseg; + retval = SP_SIMPLE_LRDN; + if (dir == TR_FROM_UP) + { + do_switch = TRUE; + mnew = make_new_monotone_poly(mcur, v1, v0); + traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP); + } + else + { + mnew = make_new_monotone_poly(mcur, v0, v1); + traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP); + traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN); + } + } + else if (_equal_to(&t->hi, &seg[t->rseg].v1) && + _equal_to(&t->lo, &seg[t->lseg].v1)) + { + v0 = seg[t->rseg].next; + v1 = seg[t->lseg].next; + + retval = SP_SIMPLE_LRUP; + if (dir == TR_FROM_UP) + { + do_switch = TRUE; + mnew = make_new_monotone_poly(mcur, v1, v0); + traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP); + } + else + { + mnew = make_new_monotone_poly(mcur, v0, v1); + traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP); + traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP); + traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN); + } + } + else /* no split possible */ + { + retval = SP_NOSPLIT; + traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN); + traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP); + traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN); + traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP); + } + } + } + + return retval; +} + + +/* For each monotone polygon, find the ymax and ymin (to determine the */ +/* two y-monotone chains) and pass on this monotone polygon for greedy */ +/* triangulation. */ +/* Take care not to triangulate duplicate monotone polygons */ + +int triangulate_monotone_polygons(nvert, nmonpoly, op) + int nvert; + int nmonpoly; + int op[][3]; +{ + register int i; + point_t ymax, ymin; + int p, vfirst, posmax, posmin, v; + int vcount, processed; + +#ifdef DEBUG + for (i = 0; i < nmonpoly; i++) + { + fprintf(stderr, "\n\nPolygon %d: ", i); + vfirst = mchain[mon[i]].vnum; + p = mchain[mon[i]].next; + fprintf (stderr, "%d ", mchain[mon[i]].vnum); + while (mchain[p].vnum != vfirst) + { + fprintf(stderr, "%d ", mchain[p].vnum); + p = mchain[p].next; + } + } + fprintf(stderr, "\n"); +#endif + + op_idx = 0; + for (i = 0; i < nmonpoly; i++) + { + vcount = 1; + processed = FALSE; + vfirst = mchain[mon[i]].vnum; + ymax = ymin = vert[vfirst].pt; + posmax = posmin = mon[i]; + mchain[mon[i]].marked = TRUE; + p = mchain[mon[i]].next; + while ((v = mchain[p].vnum) != vfirst) + { + if (mchain[p].marked) + { + processed = TRUE; + break; /* break from while */ + } + else + mchain[p].marked = TRUE; + + if (_greater_than(&vert[v].pt, &ymax)) + { + ymax = vert[v].pt; + posmax = p; + } + if (_less_than(&vert[v].pt, &ymin)) + { + ymin = vert[v].pt; + posmin = p; + } + p = mchain[p].next; + vcount++; + } + + if (processed) /* Go to next polygon */ + continue; + + if (vcount == 3) /* already a triangle */ + { + op[op_idx][0] = mchain[p].vnum; + op[op_idx][1] = mchain[mchain[p].next].vnum; + op[op_idx][2] = mchain[mchain[p].prev].vnum; + op_idx++; + } + else /* triangulate the polygon */ + { + v = mchain[mchain[posmax].next].vnum; + if (_equal_to(&vert[v].pt, &ymin)) + { /* LHS is a single line */ + triangulate_single_polygon(nvert, posmax, TRI_LHS, op); + } + else + triangulate_single_polygon(nvert, posmax, TRI_RHS, op); + } + } + +#ifdef DEBUG + for (i = 0; i < op_idx; i++) + fprintf(stderr, "tri #%d: (%d, %d, %d)\n", i, op[i][0], op[i][1], + op[i][2]); +#endif + return op_idx; +} + + +/* A greedy corner-cutting algorithm to triangulate a y-monotone + * polygon in O(n) time. + * Joseph O-Rourke, Computational Geometry in C. + */ +static int triangulate_single_polygon(nvert, posmax, side, op) + int nvert; + int posmax; + int side; + int op[][3]; +{ + register int v; + int rc[SEGSIZE], ri = 0; /* reflex chain */ + int endv, tmp, vpos; + + if (side == TRI_RHS) /* RHS segment is a single segment */ + { + rc[0] = mchain[posmax].vnum; + tmp = mchain[posmax].next; + rc[1] = mchain[tmp].vnum; + ri = 1; + + vpos = mchain[tmp].next; + v = mchain[vpos].vnum; + + if ((endv = mchain[mchain[posmax].prev].vnum) == 0) + endv = nvert; + } + else /* LHS is a single segment */ + { + tmp = mchain[posmax].next; + rc[0] = mchain[tmp].vnum; + tmp = mchain[tmp].next; + rc[1] = mchain[tmp].vnum; + ri = 1; + + vpos = mchain[tmp].next; + v = mchain[vpos].vnum; + + endv = mchain[posmax].vnum; + } + + while ((v != endv) || (ri > 1)) + { + if (ri > 0) /* reflex chain is non-empty */ + { + if (CROSS(vert[v].pt, vert[rc[ri - 1]].pt, + vert[rc[ri]].pt) > 0) + { /* convex corner: cut if off */ + op[op_idx][0] = rc[ri - 1]; + op[op_idx][1] = rc[ri]; + op[op_idx][2] = v; + op_idx++; + ri--; + } + else /* non-convex */ + { /* add v to the chain */ + ri++; + rc[ri] = v; + vpos = mchain[vpos].next; + v = mchain[vpos].vnum; + } + } + else /* reflex-chain empty: add v to the */ + { /* reflex chain and advance it */ + rc[++ri] = v; + vpos = mchain[vpos].next; + v = mchain[vpos].vnum; + } + } /* end-while */ + + /* reached the bottom vertex. Add in the triangle formed */ + op[op_idx][0] = rc[ri - 1]; + op[op_idx][1] = rc[ri]; + op[op_idx][2] = v; + op_idx++; + ri--; + + return 0; +} + + diff --git a/src/Lib/poly2tri/tri.c b/src/Lib/poly2tri/tri.c new file mode 100644 index 00000000..1b3a64b8 --- /dev/null +++ b/src/Lib/poly2tri/tri.c @@ -0,0 +1,167 @@ +#include +#include + + +static int initialise(n) + int n; +{ + register int i; + + for (i = 1; i <= n; i++) + seg[i].is_inserted = FALSE; + + generate_random_ordering(n); + + return 0; +} + +#ifdef STANDALONE + +int main(argc, argv) + int argc; + char *argv[]; +{ + int n, nmonpoly, genus; + int op[SEGSIZE][3], i, ntriangles; + + if ((argc < 2) || ((n = read_segments(argv[1], &genus)) < 0)) + { + fprintf(stderr, "usage: triangulate \n"); + exit(1); + } + + initialise(n); + construct_trapezoids(n); + nmonpoly = monotonate_trapezoids(n); + ntriangles = triangulate_monotone_polygons(n, nmonpoly, op); + + for (i = 0; i < ntriangles; i++) + printf("triangle #%d: %d %d %d\n", i, + op[i][0], op[i][1], op[i][2]); + + return 0; +} + + +#else /* Not standalone. Use this as an interface routine */ + + +/* Input specified as contours. + * Outer contour must be anti-clockwise. + * All inner contours must be clockwise. + * + * Every contour is specified by giving all its points in order. No + * point shoud be repeated. i.e. if the outer contour is a square, + * only the four distinct endpoints shopudl be specified in order. + * + * ncontours: #contours + * cntr: An array describing the number of points in each + * contour. Thus, cntr[i] = #points in the i'th contour. + * vertices: Input array of vertices. Vertices for each contour + * immediately follow those for previous one. Array location + * vertices[0] must NOT be used (i.e. i/p starts from + * vertices[1] instead. The output triangles are + * specified w.r.t. the indices of these vertices. + * triangles: Output array to hold triangles. + * + * Enough space must be allocated for all the arrays before calling + * this routine + */ + + +int triangulate_polygon(ncontours, cntr, vertices, triangles) + int ncontours; + int cntr[]; + double (*vertices)[2]; + int (*triangles)[3]; +{ + register int i; + int nmonpoly, ccount, npoints, genus; + int n, ntriangles; + + memset((void *)seg, 0, sizeof(seg)); + ccount = 0; + i = 1; + + while (ccount < ncontours) + { + int j; + int first, last; + + npoints = cntr[ccount]; + first = i; + last = first + npoints - 1; + for (j = 0; j < npoints; j++, i++) + { + seg[i].v0.x = vertices[i][0]; + seg[i].v0.y = vertices[i][1]; + + if (i == last) + { + seg[i].next = first; + seg[i].prev = i-1; + seg[i-1].v1 = seg[i].v0; + } + else if (i == first) + { + seg[i].next = i+1; + seg[i].prev = last; + seg[last].v1 = seg[i].v0; + } + else + { + seg[i].prev = i-1; + seg[i].next = i+1; + seg[i-1].v1 = seg[i].v0; + } + + seg[i].is_inserted = FALSE; + } + + ccount++; + } + + genus = ncontours - 1; + n = i-1; + + initialise(n); + construct_trapezoids(n); + nmonpoly = monotonate_trapezoids(n); + ntriangles = triangulate_monotone_polygons(n, nmonpoly, triangles); + + return ntriangles; +} + + +/* This function returns TRUE or FALSE depending upon whether the + * vertex is inside the polygon or not. The polygon must already have + * been triangulated before this routine is called. + * This routine will always detect all the points belonging to the + * set (polygon-area - polygon-boundary). The return value for points + * on the boundary is not consistent!!! + */ + +int is_point_inside_polygon(vertex) + double vertex[2]; +{ + point_t v; + int trnum, rseg; + trap_t *t; + + v.x = vertex[0]; + v.y = vertex[1]; + + trnum = locate_endpoint(&v, &v, 1); + t = &tr[trnum]; + + if (t->state == ST_INVALID) + return FALSE; + + if ((t->lseg <= 0) || (t->rseg <= 0)) + return FALSE; + rseg = t->rseg; + return _greater_than_equal_to(&seg[rseg].v1, &seg[rseg].v0); +} + + +#endif /* STANDALONE */ diff --git a/src/Lib/poly2tri/triangulate.h b/src/Lib/poly2tri/triangulate.h new file mode 100644 index 00000000..ee323c60 --- /dev/null +++ b/src/Lib/poly2tri/triangulate.h @@ -0,0 +1,159 @@ +#ifndef _triangulate_h +#define _triangulate_h + +#include +#include +#include + +typedef struct { + double x, y; +} point_t, vector_t; + + +/* Segment attributes */ + +typedef struct { + point_t v0, v1; /* two endpoints */ + int is_inserted; /* inserted in trapezoidation yet ? */ + int root0, root1; /* root nodes in Q */ + int next; /* Next logical segment */ + int prev; /* Previous segment */ +} segment_t; + + +/* Trapezoid attributes */ + +typedef struct { + int lseg, rseg; /* two adjoining segments */ + point_t hi, lo; /* max/min y-values */ + int u0, u1; + int d0, d1; + int sink; /* pointer to corresponding in Q */ + int usave, uside; /* I forgot what this means */ + int state; +} trap_t; + + +/* Node attributes for every node in the query structure */ + +typedef struct { + int nodetype; /* Y-node or S-node */ + int segnum; + point_t yval; + int trnum; + int parent; /* doubly linked DAG */ + int left, right; /* children */ +} node_t; + + +typedef struct { + int vnum; + int next; /* Circularly linked list */ + int prev; /* describing the monotone */ + int marked; /* polygon */ +} monchain_t; + + +typedef struct { + point_t pt; + int vnext[4]; /* next vertices for the 4 chains */ + int vpos[4]; /* position of v in the 4 chains */ + int nextfree; +} vertexchain_t; + + +/* Node types */ + +#define T_X 1 +#define T_Y 2 +#define T_SINK 3 + + +#define SEGSIZE 200 /* max# of segments. Determines how */ + /* many points can be specified as */ + /* input. If your datasets have large */ + /* number of points, increase this */ + /* value accordingly. */ + +#define QSIZE 8*SEGSIZE /* maximum table sizes */ +#define TRSIZE 4*SEGSIZE /* max# trapezoids */ + + +#define TRUE 1 +#define FALSE 0 + + +#define FIRSTPT 1 /* checking whether pt. is inserted */ +#define LASTPT 2 + + +#define INFINITY 1<<30 +#define C_EPS 1.0e-7 /* tolerance value: Used for making */ + /* all decisions about collinearity or */ + /* left/right of segment. Decrease */ + /* this value if the input points are */ + /* spaced very close together */ + + +#define S_LEFT 1 /* for merge-direction */ +#define S_RIGHT 2 + + +#define ST_VALID 1 /* for trapezium state */ +#define ST_INVALID 2 + + +#define SP_SIMPLE_LRUP 1 /* for splitting trapezoids */ +#define SP_SIMPLE_LRDN 2 +#define SP_2UP_2DN 3 +#define SP_2UP_LEFT 4 +#define SP_2UP_RIGHT 5 +#define SP_2DN_LEFT 6 +#define SP_2DN_RIGHT 7 +#define SP_NOSPLIT -1 + +#define TR_FROM_UP 1 /* for traverse-direction */ +#define TR_FROM_DN 2 + +#define TRI_LHS 1 +#define TRI_RHS 2 + + +#define MAX(a, b) (((a) > (b)) ? (a) : (b)) +#define MIN(a, b) (((a) < (b)) ? (a) : (b)) + +#define CROSS(v0, v1, v2) (((v1).x - (v0).x)*((v2).y - (v0).y) - \ + ((v1).y - (v0).y)*((v2).x - (v0).x)) + +#define DOT(v0, v1) ((v0).x * (v1).x + (v0).y * (v1).y) + +#define FP_EQUAL(s, t) (fabs(s - t) <= C_EPS) + + + +/* Global variables */ + +extern node_t qs[QSIZE]; /* Query structure */ +extern trap_t tr[TRSIZE]; /* Trapezoid structure */ +extern segment_t seg[SEGSIZE]; /* Segment table */ + + +/* Functions */ + +extern int monotonate_trapezoids(int); +extern int triangulate_monotone_polygons(int, int, int (*)[3]); + +extern int _greater_than(point_t *, point_t *); +extern int _equal_to(point_t *, point_t *); +extern int _greater_than_equal_to(point_t *, point_t *); +extern int _less_than(point_t *, point_t *); +extern int locate_endpoint(point_t *, point_t *, int); +extern int construct_trapezoids(int); + +extern int generate_random_ordering(int); +extern int choose_segment(void); +extern int read_segments(char *, int *); +extern int math_logstar_n(int); +extern int math_N(int, int); + +#endif /* triangulate_h */ diff --git a/src/Lib/shapelib-1.2.5.tar.gz b/src/Lib/shapelib-1.2.5.tar.gz new file mode 100644 index 00000000..bef122f3 Binary files /dev/null and b/src/Lib/shapelib-1.2.5.tar.gz differ diff --git a/src/Lib/shapelib/ChangeLog b/src/Lib/shapelib/ChangeLog new file mode 100644 index 00000000..5b633a2d --- /dev/null +++ b/src/Lib/shapelib/ChangeLog @@ -0,0 +1,6 @@ +Tue May 4 11:04:31 1999 Frank Warmerdam + + * Prepare 1.2.5 release. + + * Added support for 'F' fields. + diff --git a/src/Lib/shapelib/Makefile.am b/src/Lib/shapelib/Makefile.am new file mode 100644 index 00000000..07805df7 --- /dev/null +++ b/src/Lib/shapelib/Makefile.am @@ -0,0 +1,37 @@ +EXTRA_DIST = ChangeLog dbf_api.html makeshape.sh shape.errata \ + shapelib.html shp_api.html stream1.sh stream2.sh + +noinst_LIBRARIES = libshape.a + +libshape_a_SOURCES = \ + dbfopen.c shpopen.c shapefil.h + +noinst_PROGRAMS = shpcreate shpadd shpdump \ + dbfcreate dbfadd dbfdump \ + shptest shputils + +shpcreate_SOURCES = shpcreate.c +shpcreate_LDADD = libshape.a + +shpadd_SOURCES = shpadd.c +shpadd_LDADD = libshape.a + +shpdump_SOURCES = shpdump.c +shpdump_LDADD = libshape.a + +dbfcreate_SOURCES = dbfcreate.c +dbfcreate_LDADD = libshape.a + +dbfadd_SOURCES = dbfadd.c +dbfadd_LDADD = libshape.a + +dbfdump_SOURCES = dbfdump.c +dbfdump_LDADD = libshape.a + +shptest_SOURCES = shptest.c +shptest_LDADD = libshape.a + +shputils_SOURCES = shputils.c +shputils_LDADD = libshape.a + +INCLUDES += -I$(top_builddir) -I$(top_builddir)/Lib diff --git a/src/Lib/shapelib/dbf_api.html b/src/Lib/shapelib/dbf_api.html new file mode 100644 index 00000000..15f85ec8 --- /dev/null +++ b/src/Lib/shapelib/dbf_api.html @@ -0,0 +1,322 @@ + +

Attribute (.DBF) API

DBFOpen()

DBFCreate()

DBFGetFieldCount()

DBFGetRecordCount()

DBFGetFieldInfo()

DBFAddField()

DBFReadIntegerAttribute()

DBFReadDoubleAttribute()

DBFReadStringAttribute()

DBFWriteIntegerAttribute

DBFWriteDoubleAttribute()

DBFWriteStringAttribute()

DBFClose()

Shapefile C Library V1.2

Purpose

Copyright

Manifest

What is a Shapefile?

Release Notes

Maintainer

Portability

Limitations

.SHP File API

Shape Types

SHPObject

SHPOpen()

SHPGetInfo()

SHPReadObject()

SHPClose()

SHPCreate()

SHPCreateSimpleObject()

SHPCreateObject()

SHPComputeExtents()

SHPWriteObject()

SHPDestroyObject()