From c01604133711d8d6a6eb0d5f563485c85b4416ff Mon Sep 17 00:00:00 2001 From: Christian Schmitt <chris@ilovelinux.de> Date: Mon, 3 Sep 2012 21:44:23 +0200 Subject: [PATCH] Remove TriangleJRS. All tesselation is now done by CGAL. --- README | 9 - TerraGear.dsp | 64 - src/Airports/GenAirports/CMakeLists.txt | 1 - src/Airports/GenAirports850/CMakeLists.txt | 1 - src/BuildTiles/Main/CMakeLists.txt | 1 - src/Lib/CMakeLists.txt | 2 - src/Lib/Geometry/poly_support.cxx | 341 - src/Lib/Geometry/poly_support.hxx | 17 +- src/Lib/TriangleJRS/.gitignore | 1 - src/Lib/TriangleJRS/CMakeLists.txt | 17 - src/Lib/TriangleJRS/README | 181 - src/Lib/TriangleJRS/showme.c | 3384 ----- src/Lib/TriangleJRS/test_triangle.c | 189 - src/Lib/TriangleJRS/tri_support.c | 173 - src/Lib/TriangleJRS/tri_support.h | 49 - src/Lib/TriangleJRS/triangle.c | 13266 ------------------- src/Lib/TriangleJRS/triangle.h | 296 - src/Prep/E00Lines/CMakeLists.txt | 2 +- src/Prep/OGRDecode/CMakeLists.txt | 2 +- src/Prep/Photo/CMakeLists.txt | 2 +- src/Prep/ShapeFile/CMakeLists.txt | 4 +- src/Prep/TGVPF/CMakeLists.txt | 2 +- src/Prep/UserDef/CMakeLists.txt | 2 +- 23 files changed, 8 insertions(+), 17998 deletions(-) delete mode 100644 src/Lib/TriangleJRS/.gitignore delete mode 100644 src/Lib/TriangleJRS/CMakeLists.txt delete mode 100644 src/Lib/TriangleJRS/README delete mode 100644 src/Lib/TriangleJRS/showme.c delete mode 100644 src/Lib/TriangleJRS/test_triangle.c delete mode 100644 src/Lib/TriangleJRS/tri_support.c delete mode 100644 src/Lib/TriangleJRS/tri_support.h delete mode 100644 src/Lib/TriangleJRS/triangle.c delete mode 100644 src/Lib/TriangleJRS/triangle.h diff --git a/README b/README index 7dae6542..f560615a 100644 --- a/README +++ b/README @@ -21,15 +21,6 @@ smaller chunks is much more doable though. Building the Tools ================== -IMPORTANT: if you are compiling with gcc, I recommend that you compile -the /Libs/TriangleJRS code without optimization (-O2). Optimization can -lead to problems for some tiles. (Different numerical stability properties -in the optimized code????) Usually I will go and remove the -O2 option (twice) -from the Makefile after it has been generated from the Makefile.am file. Be -warned that any time you change the Makefile.am, or rerun autogen.sh or -configure, you will have to go back and fix this particular Makefile. - - These tools are primarily compiled and tested under Unix with the Gnu C/C++ compilers. I believe they also build and run on windows with Cygwin. If anyone has patches for supporting other platforms, I will diff --git a/TerraGear.dsp b/TerraGear.dsp index 63bd3be3..d98972c3 100644 --- a/TerraGear.dsp +++ b/TerraGear.dsp @@ -1146,70 +1146,6 @@ SOURCE=.\src\Lib\shapelib\shapefil.h !ENDIF -# End Source File -# End Group -# Begin Group "Lib_TriangleJRS" - -# PROP Default_Filter "" -# Begin Source File - -SOURCE=.\src\Lib\TriangleJRS\triangle.c - -!IF "$(CFG)" == "TerraGear - Win32 Release" - -# PROP Intermediate_Dir "Release\Lib_TriangleJRS" - -!ELSEIF "$(CFG)" == "TerraGear - Win32 Debug" - -# PROP Intermediate_Dir "Debug\Lib_TriangleJRS" - -!ENDIF - -# End Source File -# Begin Source File - -SOURCE=.\src\Lib\TriangleJRS\triangle.h - -!IF "$(CFG)" == "TerraGear - Win32 Release" - -# PROP Intermediate_Dir "Release\Lib_TriangleJRS" - -!ELSEIF "$(CFG)" == "TerraGear - Win32 Debug" - -# PROP Intermediate_Dir "Debug\Lib_TriangleJRS" - -!ENDIF - -# End Source File -# Begin Source File - -SOURCE=.\src\Lib\TriangleJRS\tri_support.c - -!IF "$(CFG)" == "TerraGear - Win32 Release" - -# PROP Intermediate_Dir "Release\Lib_TriangleJRS" - -!ELSEIF "$(CFG)" == "TerraGear - Win32 Debug" - -# PROP Intermediate_Dir "Debug\Lib_TriangleJRS" - -!ENDIF - -# End Source File -# Begin Source File - -SOURCE=.\src\Lib\TriangleJRS\tri_support.h - -!IF "$(CFG)" == "TerraGear - Win32 Release" - -# PROP Intermediate_Dir "Release\Lib_TriangleJRS" - -!ELSEIF "$(CFG)" == "TerraGear - Win32 Debug" - -# PROP Intermediate_Dir "Debug\Lib_TriangleJRS" - -!ENDIF - # End Source File # End Group # Begin Group "Lib_vpf" diff --git a/src/Airports/GenAirports/CMakeLists.txt b/src/Airports/GenAirports/CMakeLists.txt index f7a2bd87..f64840dc 100644 --- a/src/Airports/GenAirports/CMakeLists.txt +++ b/src/Airports/GenAirports/CMakeLists.txt @@ -21,7 +21,6 @@ add_executable(genapts target_link_libraries(genapts Polygon Geometry Array Output poly2tri - TriangleJRS ${SIMGEAR_CORE_LIBRARIES} ${SIMGEAR_CORE_LIBRARY_DEPENDENCIES} ${GDAL_LIBRARY} diff --git a/src/Airports/GenAirports850/CMakeLists.txt b/src/Airports/GenAirports850/CMakeLists.txt index b987eb53..001908c8 100644 --- a/src/Airports/GenAirports850/CMakeLists.txt +++ b/src/Airports/GenAirports850/CMakeLists.txt @@ -26,7 +26,6 @@ add_executable(genapts850 target_link_libraries(genapts850 Polygon Geometry Array Output poly2tri - TriangleJRS ${POCO_FOUNDATION} ${POCO_NET} ${GDAL_LIBRARY} diff --git a/src/BuildTiles/Main/CMakeLists.txt b/src/BuildTiles/Main/CMakeLists.txt index a174ffa9..94fe3d16 100644 --- a/src/BuildTiles/Main/CMakeLists.txt +++ b/src/BuildTiles/Main/CMakeLists.txt @@ -15,7 +15,6 @@ target_link_libraries(tg-construct Match Polygon Geometry Array landcover poly2tri - TriangleJRS ${GDAL_LIBRARY} ${SIMGEAR_CORE_LIBRARIES} ${SIMGEAR_CORE_LIBRARY_DEPENDENCIES} diff --git a/src/Lib/CMakeLists.txt b/src/Lib/CMakeLists.txt index 62c44002..74a7712a 100644 --- a/src/Lib/CMakeLists.txt +++ b/src/Lib/CMakeLists.txt @@ -6,10 +6,8 @@ add_subdirectory(Geometry) add_subdirectory(HGT) add_subdirectory(Output) add_subdirectory(Polygon) -add_subdirectory(TriangleJRS) add_subdirectory(e00) add_subdirectory(landcover) add_subdirectory(poly2tri) add_subdirectory(shapelib) add_subdirectory(vpf) - diff --git a/src/Lib/Geometry/poly_support.cxx b/src/Lib/Geometry/poly_support.cxx index 75259c74..31a3cfa8 100644 --- a/src/Lib/Geometry/poly_support.cxx +++ b/src/Lib/Geometry/poly_support.cxx @@ -38,12 +38,6 @@ #include <algorithm> #include <iterator> -#define REAL double -extern "C" { -#include <TriangleJRS/triangle.h> -} -#include <TriangleJRS/tri_support.h> - #include "contour_tree.hxx" #include "poly_support.hxx" #include "trinodes.hxx" @@ -114,341 +108,6 @@ static bool intersects( Point3D p0, Point3D p1, double x, Point3D *result ) { } #endif -// basic triangulation of a polygon with out adding points or -// splitting edges, this should triangulate around interior holes. -int polygon_tesselate( const TGPolygon &p, - const point_list &extra_nodes, - triele_list &elelist, - point_list &out_pts, - string tri_flags ) -{ - struct triangulateio in, out, vorout; - int i; - int success = 0; - - // make sure all elements of these structs point to "NULL" - zero_triangulateio( &in ); - zero_triangulateio( &out ); - zero_triangulateio( &vorout ); - - int counter, start, end; - - // list of points - double max_x = p.get_pt(0,0).x(); - - int total_pts = 0; - int total_segments = 0; - - for ( i = 0; i < p.contours(); ++i ) { - total_pts += p.contour_size( i ); - } - total_segments = total_pts; - total_pts += extra_nodes.size(); - - in.numberofpoints = total_pts; - in.pointlist = (REAL *) malloc(in.numberofpoints * 2 * sizeof(REAL)); - - counter = 0; - for ( i = 0; i < p.contours(); ++i ) { - point_list contour = p.get_contour( i ); - for ( int j = 0; j < (int)contour.size(); ++j ) { - in.pointlist[2*counter] = contour[j].x(); - in.pointlist[2*counter + 1] = contour[j].y(); - /* remember largest x value of the polygon to - * easily calc outside point - */ - if ( contour[j].x() > max_x ) { - max_x = contour[j].x(); - } - ++counter; - } - } - - for ( i = 0; i < (int)extra_nodes.size(); ++i ) { - in.pointlist[2*counter] = extra_nodes[i].x(); - in.pointlist[2*counter + 1] = extra_nodes[i].y(); - ++counter; - } - - /* set the node attribute to elevation data */ - in.numberofpointattributes = 1; - in.pointattributelist = (REAL *) malloc(in.numberofpoints * - in.numberofpointattributes * - sizeof(REAL)); - counter = 0; - for ( i = 0; i < p.contours(); ++i ) { - point_list contour = p.get_contour( i ); - for ( int j = 0; j < (int)contour.size(); ++j ) { - in.pointattributelist[counter] = contour[j].z(); - ++counter; - } - } - - for ( i = 0; i < (int)extra_nodes.size(); ++i ) { - in.pointattributelist[counter] = extra_nodes[i].z(); - ++counter; - } - - in.pointmarkerlist = NULL; - - // segment list - in.numberofsegments = total_segments; - in.segmentlist = (int *) malloc(in.numberofsegments * 2 * sizeof(int)); - counter = 0; - start = 0; - end = -1; - - for ( i = 0; i < p.contours(); ++i ) { - point_list contour = p.get_contour( i ); - start = end + 1; - end = start + contour.size() - 1; - for ( int j = 0; j < (int)contour.size() - 1; ++j ) { - in.segmentlist[counter++] = j + start; - in.segmentlist[counter++] = j + start + 1; - } - in.segmentlist[counter++] = end; - in.segmentlist[counter++] = start; - } - - in.segmentmarkerlist = (int *) malloc(in.numberofsegments * sizeof(int)); - for ( i = 0; i < in.numberofsegments; ++i ) { - in.segmentmarkerlist[i] = 0; - } - - // hole list - in.numberofholes = 1; - for ( i = 0; i < p.contours(); ++i ) { - if ( p.get_hole_flag( i ) ) { - ++in.numberofholes; - } - } - in.holelist = (REAL *) malloc(in.numberofholes * 2 * sizeof(REAL)); - - // outside of polygon - counter = 0; - in.holelist[counter++] = max_x + 1.0; - in.holelist[counter++] = 0.0; - - for ( i = 0; i < (int)p.contours(); ++i ) { - if ( p.get_hole_flag( i ) ) { - in.holelist[counter++] = p.get_point_inside(i).x(); - in.holelist[counter++] = p.get_point_inside(i).y(); - } - } - - // region list - in.numberofregions = 0; - in.regionlist = NULL; - - // no triangle list - in.numberoftriangles = 0; - in.numberofcorners = 0; - in.numberoftriangleattributes = 0; - in.trianglelist = NULL; - in.triangleattributelist = NULL; - in.trianglearealist = NULL; - in.neighborlist = NULL; - - // no edge list - in.numberofedges = 0; - in.edgelist = NULL; - in.edgemarkerlist = NULL; - in.normlist = NULL; - - // dump the results to screen - // print_tri_data( &in ); - - // TEMPORARY - // write_tri_data(&in); - /* cout << "Press return to continue:"; - char junk; - cin >> junk; */ - - // Triangulate the points. Switches are chosen to read and write - // a PSLG (p), number everything from zero (z), and produce an - // edge list (e), and a triangle neighbor list (n). - // no new points on boundary (Y), no internal segment - // splitting (YY), no quality refinement (q) - // Quite (Q) - success = triangulate( (char *)tri_flags.c_str(), &in, &out, &vorout ); - - // TEMPORARY - // write_tri_data(&out); - - // now copy the results back into the corresponding TGTriangle - // structures - - if (success >= 0) { - - // triangles - elelist.clear(); - int n1, n2, n3; - double attribute; - for ( 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( TGTriEle( n1, n2, n3, attribute ) ); - } - - // output points - out_pts.clear(); - double x, y, z; - for ( i = 0; i < out.numberofpoints; ++i ) { - x = out.pointlist[i * 2 ]; - y = out.pointlist[i * 2 + 1]; - z = out.pointattributelist[i]; - out_pts.push_back( Point3D(x, y, z) ); - } - } - - // free mem allocated to the "Triangle" structures - free(in.pointlist); - free(in.pointattributelist); - free(in.pointmarkerlist); - free(in.segmentlist); - free(in.segmentmarkerlist); - free(in.holelist); - 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 success; -} - - -// Alternate basic triangulation of a polygon with out adding points -// or splitting edges and without regard for holes. Returns a polygon -// with one contour per tesselated triangle. This is mostly just a -// wrapper for the polygon_tesselate() function. Note, this routine -// will modify the points_inside list for your polygon. - -TGPolygon polygon_tesselate_alt( TGPolygon &p, bool verbose ) { - TGPolygon result; - point_list extra_nodes; - result.erase(); - int i; - - // Bail right away if polygon is empty - if ( p.contours() == 0 ) { - return result; - } - - // 1. Robustly find a point inside each contour that is not - // inside any other contour - calc_points_inside( p ); - - // 2. Do a final triangulation of the entire polygon - triele_list trieles; - point_list nodes; - string flags; - if (verbose) { - flags = "pzenXYY"; -// flags = "pzqenXY"; // allow adding interior points - } else { - flags = "pzenXYYQ"; -// flags = "pzqenXYQ"; // allow adding interior points - } - - // check the input for nan point - for (int c = 0; c < p.contours(); c++) { - point_list contour = p.get_contour( c ); - for ( int d = 0; d < (int)contour.size(); ++d ) { - if ( isnan( contour[d].x() ) || isnan( contour[d].y() ) ) { - printf("Uh-oh - got nan before tesselation\n"); - exit(0); - } - } - } - - if ( polygon_tesselate( p, extra_nodes, trieles, nodes, flags ) >= 0 ) { - // 3. Convert the tesselated output to a list of tringles. - // basically a polygon with a contour for every triangle - for ( i = 0; i < (int)trieles.size(); ++i ) { - TGTriEle t = trieles[i]; - Point3D p1 = nodes[ t.get_n1() ]; - Point3D p2 = nodes[ t.get_n2() ]; - Point3D p3 = nodes[ t.get_n3() ]; - result.add_node( i, p1 ); - result.add_node( i, p2 ); - result.add_node( i, p3 ); - } - } - - // check the result for nan point - for (int c = 0; c < result.contours(); c++) { - point_list contour = result.get_contour( c ); - for ( int d = 0; d < (int)contour.size(); ++d ) { - if ( isnan( contour[d].x() ) || isnan( contour[d].y() ) ) { - printf("Uh-oh - got nan from tesselation\n"); - exit(0); - } - } - } - - return result; -} - -TGPolygon polygon_tesselate_alt_with_extra( TGPolygon &p, const point_list& extra_nodes, bool verbose ) { - TGPolygon result; - result.erase(); - int i; - - // Bail right away if polygon is empty - if ( p.contours() == 0 ) { - return result; - } - - // 1. Robustly find a point inside each contour that is not - // inside any other contour - calc_points_inside( p ); - for ( i = 0; i < p.contours(); ++i ); - - // 2. Do a final triangulation of the entire polygon - triele_list trieles; - point_list nodes; - string flags; - if (verbose) { - flags = "VVpzenXYY"; - } else { - flags = "pzenXYYQ"; - } - - if ( polygon_tesselate( p, extra_nodes, trieles, nodes, flags ) >= 0 ) { - // 3. Convert the tesselated output to a list of tringles. - // basically a polygon with a contour for every triangle - for ( i = 0; i < (int)trieles.size(); ++i ) { - TGTriEle t = trieles[i]; - Point3D p1 = nodes[ t.get_n1() ]; - Point3D p2 = nodes[ t.get_n2() ]; - Point3D p3 = nodes[ t.get_n3() ]; - result.add_node( i, p1 ); - result.add_node( i, p2 ); - result.add_node( i, p3 ); - } - } - - return result; -} /* * Find all intersections of the given contour with the x-parallel line at diff --git a/src/Lib/Geometry/poly_support.hxx b/src/Lib/Geometry/poly_support.hxx index 675570eb..a1c35c4c 100644 --- a/src/Lib/Geometry/poly_support.hxx +++ b/src/Lib/Geometry/poly_support.hxx @@ -51,24 +51,9 @@ inline double triangle_area( const Point3D p1, } -// basic triangulation of a polygon with out adding points or -// splitting edges -int polygon_tesselate( const TGPolygon &p, - const point_list &extra_nodes, - triele_list &elelist, - point_list &out_pts, - std::string flags ); - // Alternate basic triangulation of a polygon with out adding points // or splitting edges and without regard for holes. Returns a polygon -// with one contour per tesselated triangle. This is mostly just a -// wrapper for the polygon_tesselate() function. Note, this routine -// will modify the points_inside list for your polygon. -TGPolygon polygon_tesselate_alt( TGPolygon &p, bool verbose ); - -TGPolygon polygon_tesselate_alt_with_extra( TGPolygon &p, - const point_list &extra_nodes, bool verbose ); - +// with one contour per tesselated triangle. TGPolygon polygon_tesselate_alt_with_extra_cgal( TGPolygon &p, const point_list &extra_nodes, bool verbose ); diff --git a/src/Lib/TriangleJRS/.gitignore b/src/Lib/TriangleJRS/.gitignore deleted file mode 100644 index 3e2430ee..00000000 --- a/src/Lib/TriangleJRS/.gitignore +++ /dev/null @@ -1 +0,0 @@ -test_triangle diff --git a/src/Lib/TriangleJRS/CMakeLists.txt b/src/Lib/TriangleJRS/CMakeLists.txt deleted file mode 100644 index 001c3ee0..00000000 --- a/src/Lib/TriangleJRS/CMakeLists.txt +++ /dev/null @@ -1,17 +0,0 @@ - - -add_library(TriangleJRS STATIC - tri_support.c - tri_support.h - triangle.c - triangle.h -) - -set_target_properties(TriangleJRS PROPERTIES - COMPILE_DEFINITIONS TRILIBRARY ) - -#add_executable(test_triangle test_triangle.c) - -#target_link_libraries(test_triangle -# TriangleJRS -# ) diff --git a/src/Lib/TriangleJRS/README b/src/Lib/TriangleJRS/README deleted file mode 100644 index 571d5689..00000000 --- a/src/Lib/TriangleJRS/README +++ /dev/null @@ -1,181 +0,0 @@ -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 deleted file mode 100644 index 722cba8a..00000000 --- a/src/Lib/TriangleJRS/showme.c +++ /dev/null @@ -1,3384 +0,0 @@ -/*****************************************************************************/ -/* */ -/* ,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 <stdio.h> -#include <string.h> -#include <X11/Xlib.h> -#include <X11/Xutil.h> -#include <X11/Xatom.h> - -/* 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> <dimension (must be 2)> <# of attributes>\n"); - printf( -" <# of boundary markers (0 or 1)>\n" -); - printf( -" Remaining lines: <point #> <x> <y> [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> <dimension (must be 2)> <# of attributes>\n"); - printf( -" <# of boundary markers (0 or 1)>\n" -); - printf( -" Following lines: <point #> <x> <y> [attributes] [boundary marker]\n"); - printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n"); - printf( -" Following lines: <segment #> <endpoint> <endpoint> [boundary marker]\n"); - printf(" One line: <# of holes>\n"); - printf(" Following lines: <hole #> <x> <y>\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> <points per triangle> <# of attributes>\n"); - printf( -" Remaining lines: <triangle #> <point> <point> <point> ... [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: <edge #> <endpoint> <endpoint> [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(" <edge #> <endpoint> -1 <direction x> <direction y>\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: <triangle #> <subdomain #>\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: <adjacency matrix entry>\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/test_triangle.c b/src/Lib/TriangleJRS/test_triangle.c deleted file mode 100644 index 60c0b1be..00000000 --- a/src/Lib/TriangleJRS/test_triangle.c +++ /dev/null @@ -1,189 +0,0 @@ -/* a test of the Shewchuk triangulator (lib form) */ - -#include <string.h> -#include <stdio.h> -#include <stdlib.h> - -#define REAL double -#include "triangle.h" -#include "tri_support.h" - -int main( int argc, char **argv ) { - struct triangulateio in, out, vorout; - char basename[256], nodefile[256], polyfile[256]; - FILE *fp; - int count, dim, attr, bndmrkrs, end1, end2, boundmark; - int i, counter; - double x, y, z; - char tri_options[256]; - int n1, n2, n3; - - /* make sure all elements of these structs point to "NULL" */ - zero_triangulateio( &in ); - zero_triangulateio( &out ); - zero_triangulateio( &vorout ); - - /* get base name */ - if ( argc == 2 ) { - strcpy( basename, argv[1] ); - } else { - printf( "usage: %s base_name\n", argv[0] ); - return -1; - } - - /* - * generate file names - */ - - sprintf( nodefile, "%s.node", basename ); - sprintf( polyfile, "%s.poly", basename ); - - /* - * load node file - */ - - if ( (fp = fopen( nodefile, "r" )) == NULL ) { - printf( "cannot locate file: %s\n", nodefile ); - return -1; - } - - /* read in points */ - fscanf( fp, "%d %d %d %d\n", &count, &dim, &attr, &bndmrkrs ); - printf( "loading %d points\n", count ); - in.numberofpoints = count; - in.numberofpointattributes = 1; - in.pointlist = (REAL *) malloc(in.numberofpoints * 2 * sizeof(REAL)); - in.pointattributelist = (REAL *) malloc(in.numberofpoints * - in.numberofpointattributes * - sizeof(REAL)); - in.pointmarkerlist = NULL; - - for ( i = 0; i < count; ++i ) { - fscanf( fp, "%d %lf %lf %lf\n", &counter, &x, &y, &z ); - printf( " read = %d %.2f %.2f %.2f\n", counter, x, y, z ); - in.pointlist[2*counter] = x; - in.pointlist[2*counter + 1] = y; - in.pointattributelist[counter] = z; - } - fclose( fp ); - - /* - * load poly file - */ - - if ( (fp = fopen( polyfile, "r" )) == NULL ) { - printf( "cannot locate file: %s\n", polyfile ); - return -1; - } - - /* first line is ignored, points are specified in .node file */ - fscanf( fp, "%d %d %d %d\n", &count, &dim, &attr, &bndmrkrs ); - - /* read in segments */ - fscanf( fp, "%d %d\n", &count, &bndmrkrs ); - printf( "loading %d segments\n", count ); - in.numberofsegments = count; - in.segmentlist = (int *) malloc(in.numberofsegments * 2 * sizeof(int)); - in.segmentmarkerlist = (int *) malloc(in.numberofsegments * sizeof(int)); - - for ( i = 0; i < count; ++i ) { - fscanf( fp, "%d %d %d %d\n", &counter, &end1, &end2, &boundmark ); - printf( " read = %d %d %d %d\n", counter, end1, end2, boundmark ); - in.segmentlist[2*counter] = end1; - in.segmentlist[2*counter + 1] = end2; - in.segmentmarkerlist[counter] = boundmark; - } - - /* read in holes */ - fscanf( fp, "%d\n", &count ); - printf( "loading %d holes\n", count ); - in.numberofholes = count; - in.holelist = (REAL *) malloc(in.numberofholes * 2 * sizeof(REAL)); - - for ( i = 0; i < count; ++i ) { - fscanf( fp, "%d %lf %lf %lf\n", &counter, &x, &y, &z ); - printf( " read = %d %.2f %.2f %.2f\n", counter, x, y, z ); - in.holelist[2*counter] = x; - in.holelist[2*counter + 1] = y; - } - - /* read in regions */ - /* number of regions is always zero for this example */ - fscanf( fp, "%d\n", &count ); - in.numberofregions = 0; - in.regionlist = NULL; - - fclose( fp ); - - /* no triangle list */ - in.numberoftriangles = 0; - in.numberofcorners = 0; - in.numberoftriangleattributes = 0; - in.trianglelist = NULL; - in.triangleattributelist = NULL; - in.trianglearealist = NULL; - in.neighborlist = NULL; - - /* no edge list */ - in.numberofedges = 0; - in.edgelist = NULL; - in.edgemarkerlist = NULL; - in.normlist = NULL; - - /* dump the results */ - print_tri_data( &in ); - - /* Triangulate the points. Switches are chosen to read and write - * a PSLG (p), number everything from zero (z), and produce an - * edge list (e), and a triangle neighbor list (n). no new points - * on boundary (Y), no internal segment splitting (YY), no quality - * refinement (q) and Quite (Q) - */ - - strcpy( tri_options, "VVVpzYYenQ" ); - printf( "Triangulation with options = %s\n", tri_options ); - - triangulate( tri_options, &in, &out, &vorout ); - - zero_triangulateio( &out ); - zero_triangulateio( &vorout ); - - triangulate( tri_options, &in, &out, &vorout ); - - /* print resulting triangles */ - for ( 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 ) { - z = out.triangleattributelist[i]; - } else { - z = 0.0; - } - printf( "triangle %d = %d %d %d (%.2f)\n", i, n1, n2, n3, z ); - } - - /* free mem allocated Floating point roundoff is of magnitude 1.1102230246251565e-16 -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/Lib/TriangleJRS/tri_support.c b/src/Lib/TriangleJRS/tri_support.c deleted file mode 100644 index ae0a1352..00000000 --- a/src/Lib/TriangleJRS/tri_support.c +++ /dev/null @@ -1,173 +0,0 @@ -// tri_support.c -- supporting routines for the triangulation library -// -// Written by Curtis Olson, started May 2000. -// -// Copyright (C) 2000 Curtis L. Olson - http://www.flightgear.org/~curt -// -// 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., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. -// -// $Id: tri_support.c,v 1.4 2004-11-19 22:25:50 curt Exp $ - - -#include <stdio.h> - -#include "tri_support.h" - - -void zero_triangulateio( struct triangulateio *in ) { - in->pointlist = NULL; - in->pointattributelist = NULL; - in->pointmarkerlist = NULL; - in->numberofpoints = 0; - in->numberofpointattributes = 0; - - in->trianglelist = NULL; - in->triangleattributelist = NULL; - in->trianglearealist = NULL; - in->neighborlist = NULL; - in->numberoftriangles = 0; - in->numberofcorners = 0; - in->numberoftriangleattributes = 0; - - in->segmentlist = NULL; - in->segmentmarkerlist = NULL; - in->numberofsegments = 0; - - in->holelist = NULL; - in->numberofholes = 0; - - in->regionlist = NULL; - in->numberofregions = 0; - - in->edgelist = NULL; - in->edgemarkerlist = NULL; - in->normlist = NULL; - in->numberofedges = 0; -} - - -void print_tri_data( struct triangulateio *out ) { - int i, j; - - printf( "NODES\n" ); - printf( "%d 2 %d 0\n", - out->numberofpoints, out->numberofpointattributes); - for ( i = 0; i < out->numberofpoints; ++i ) { - printf( "%d %.13f %.13f %.2f\n", - i, out->pointlist[2*i], out->pointlist[2*i + 1], 0.0); - } - - printf( "TRIANGLES\n" ); - printf( "%d %d 0\n", out->numberoftriangles, out->numberofcorners ); - for ( i = 0; i < out->numberoftriangles; ++i ) { - printf( "%d ", i ); - for ( j = 0; j < out->numberofcorners; ++j ) { - printf( "%d ", out->trianglelist[i * out->numberofcorners + j] ); - } - for ( j = 0; j < out->numberoftriangleattributes; ++j ) { - printf( "%.13f ", - out->triangleattributelist[i - * out->numberoftriangleattributes - + j] - ); - } - printf("\n"); - } - - printf( "SEGMENTS\n" ); - printf( "0 2 1 0\n" ); - printf( "%d 1\n", out->numberofsegments); - for ( i = 0; i < out->numberofsegments; ++i ) { - printf( "%d %d %d %d\n", - i, out->segmentlist[2*i], out->segmentlist[2*i + 1], - out->segmentmarkerlist[i] ); - } - printf( "HOLES\n" ); - printf( "%d\n", out->numberofholes); - for (i = 0; i < out->numberofholes; ++i) { - printf( "%d %.13f %.13f\n", - i, out->holelist[2*i], out->holelist[2*i + 1] ); - } - printf( "REGIONS\n" ); - printf( "%d\n", out->numberofregions ); - for ( i = 0; i < out->numberofregions; ++i ) { - printf( "%d %.13f %.13f %.13f\n", - i, out->regionlist[4*i], out->regionlist[4*i + 1], - out->regionlist[4*i + 2] ); - } - - printf(" EDGES\n" ); - printf( "%d 1\n", out->numberofedges ); - for ( i = 0; i < out->numberofedges; ++i ) { - printf( "%d %d %d %d\n", i, out->edgelist[2*i], out->edgelist[2*i + 1], - out->edgemarkerlist[i] ); - } -} - - -void write_tri_data( struct triangulateio *out ) { - int i, j; - FILE *node, *ele, *fp; - - node = fopen("tile.node", "w"); - fprintf(node, "%d 2 %d 0\n", - out->numberofpoints, out->numberofpointattributes); - for (i = 0; i < out->numberofpoints; ++i) { - fprintf(node, "%d %.13f %.13f %.2f\n", - i, out->pointlist[2*i], out->pointlist[2*i + 1], 0.0); - } - fclose(node); - - ele = fopen("tile.ele", "w"); - fprintf(ele, "%d 3 0\n", out->numberoftriangles); - for (i = 0; i < out->numberoftriangles; ++i) { - fprintf(ele, "%d ", i); - for (j = 0; j < out->numberofcorners; ++j) { - fprintf(ele, "%d ", out->trianglelist[i * out->numberofcorners + j]); - } - for (j = 0; j < out->numberoftriangleattributes; ++j) { - fprintf(ele, "%.13f ", - out->triangleattributelist[i - * out->numberoftriangleattributes - + j] - ); - } - fprintf(ele, "\n"); - } - fclose(ele); - - fp = fopen("tile.poly", "w"); - fprintf(fp, "0 2 1 0\n"); - fprintf(fp, "%d 1\n", out->numberofsegments); - for (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 (i = 0; i < out->numberofholes; ++i) { - fprintf(fp, "%d %.13f %.13f\n", - i, out->holelist[2*i], out->holelist[2*i + 1]); - } - fprintf(fp, "%d\n", out->numberofregions); - for (i = 0; i < out->numberofregions; ++i) { - fprintf(fp, "%d %.13f %.13f %.13f\n", - i, out->regionlist[4*i], out->regionlist[4*i + 1], - out->regionlist[4*i + 2]); - } - fclose(fp); -} - - diff --git a/src/Lib/TriangleJRS/tri_support.h b/src/Lib/TriangleJRS/tri_support.h deleted file mode 100644 index 7cec3385..00000000 --- a/src/Lib/TriangleJRS/tri_support.h +++ /dev/null @@ -1,49 +0,0 @@ -// tri_support.h -- supporting routines for the triangulation library -// -// Written by Curtis Olson, started May 2000. -// -// Copyright (C) 2000 Curtis L. Olson - http://www.flightgear.org/~curt -// -// 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., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. -// -// $Id: tri_support.h,v 1.3 2004-11-19 22:25:50 curt Exp $ - - -#ifndef _TRI_SUPPORT_H -#define _TRI_SUPPORT_H - - -#ifdef __cplusplus -extern "C" { -#endif - - -#define REAL double -#include "triangle.h" - - -void zero_triangulateio( struct triangulateio *in ); -void print_tri_data( struct triangulateio *out ); -void write_tri_data( struct triangulateio *out ); - - -#ifdef __cplusplus -} -#endif - - -#endif // _TRI_SUPPORT_H - - diff --git a/src/Lib/TriangleJRS/triangle.c b/src/Lib/TriangleJRS/triangle.c deleted file mode 100644 index 49786219..00000000 --- a/src/Lib/TriangleJRS/triangle.c +++ /dev/null @@ -1,13266 +0,0 @@ -/*****************************************************************************/ -/* */ -/* 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. */ - -/* Added CLO 11/20/2000. Explanation: this code does a lot of - malloc()'ing of space and in some cases blindly expects the results - to be zero'd out, even though this isn't gauranteed by malloc(). - So I (Curt Olson, http://www.flightgear.org/~curt) have added some code here to - map all the malloc(x) calls to calloc( 1, x). */ -#define MALLOC( x ) calloc( 1, x ) -/* CLO end */ - -/* #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 <stdio.h> -#include <stdlib.h> -#include <string.h> -#include <math.h> -#ifndef NO_TIMER -#include <sys/time.h> -#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> <dimension (must be 2)> <# of attributes>\n"); - printf( -" <# of boundary markers (0 or 1)>\n" -); - printf( -" Remaining lines: <point #> <x> <y> [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> <points per triangle> <# of attributes>\n"); - printf( -" Remaining lines: <triangle #> <point> <point> <point> ... [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> <dimension (must be 2)> <# of attributes>\n"); - printf( -" <# of boundary markers (0 or 1)>\n" -); - printf( -" Following lines: <point #> <x> <y> [attributes] [boundary marker]\n"); - printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n"); - printf( -" Following lines: <segment #> <endpoint> <endpoint> [boundary marker]\n"); - printf(" One line: <# of holes>\n"); - printf(" Following lines: <hole #> <x> <y>\n"); - printf( -" Optional line: <# of regional attributes and/or area constraints>\n"); - printf( -" Optional following lines: <constraint #> <x> <y> <attrib> <max area>\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: <triangle #> <maximum area>\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: <edge #> <endpoint> <endpoint> [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(" <edge #> <endpoint> -1 <direction x> <direction y>\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: <triangle #> <neighbor> <neighbor> <neighbor>\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) atof(workstring); - } 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; - char *ptr; /* Added CLO 11/20/2000 */ - int i; /* Added CLO 11/20/2000 */ - - /* 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++; - - /* Added CLO 11/20/2000. Explanation: this code does a lot of - malloc()'ing of space, and in some cases blindly expects the - results to be zero'd out, even though this may not be gauranteed. - So I (Curt Olson, http://www.flightgear.org/~curt) have added some code here - to explicitely zero out the space after it is malloc()'ed. */ - ptr = (char *)newitem; - for ( i = 0; i < pool->itembytes; ++i ) { - ptr[i] = 0; - } - /* End of CLO 11/20/2000 addition */ - - 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(" point2triindex = %d\n", point2triindex ); - 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 (verbose > 1) { - printf("encodedtri = %x\n", encodedtri ); - } - 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 - -int 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(); - - return 0; -} diff --git a/src/Lib/TriangleJRS/triangle.h b/src/Lib/TriangleJRS/triangle.h deleted file mode 100644 index b034113f..00000000 --- a/src/Lib/TriangleJRS/triangle.h +++ /dev/null @@ -1,296 +0,0 @@ -/*****************************************************************************/ -/* */ -/* (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. */ -/* */ -/*****************************************************************************/ - -#ifndef _SHEWCHUK_TRIANGLE_H -#define _SHEWCHUK_TRIANGLE_H - - -/* 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 -int triangulate(char *, struct triangulateio *, struct triangulateio *, - struct triangulateio *); -#else /* not ANSI_DECLARATORS */ -int triangulate(); -#endif /* not ANSI_DECLARATORS */ - - -#endif /* SHEWCHUK TRIANGLE */ diff --git a/src/Prep/E00Lines/CMakeLists.txt b/src/Prep/E00Lines/CMakeLists.txt index 37d20213..9036611a 100644 --- a/src/Prep/E00Lines/CMakeLists.txt +++ b/src/Prep/E00Lines/CMakeLists.txt @@ -4,7 +4,7 @@ add_executable(e00lines target_link_libraries(e00lines e00 - Polygon Geometry Output poly2tri TriangleJRS vpf + Polygon Geometry Output poly2tri vpf ${SIMGEAR_CORE_LIBRARIES} ${SIMGEAR_CORE_LIBRARY_DEPENDENCIES} ) diff --git a/src/Prep/OGRDecode/CMakeLists.txt b/src/Prep/OGRDecode/CMakeLists.txt index f879c4d6..0aca05c3 100644 --- a/src/Prep/OGRDecode/CMakeLists.txt +++ b/src/Prep/OGRDecode/CMakeLists.txt @@ -6,7 +6,7 @@ add_executable(ogr-decode ogr-decode.cxx) target_link_libraries(ogr-decode ${GDAL_LIBRARY} - Polygon Geometry poly2tri TriangleJRS + Polygon Geometry poly2tri ${SIMGEAR_CORE_LIBRARIES} ${SIMGEAR_CORE_LIBRARY_DEPENDENCIES} ) diff --git a/src/Prep/Photo/CMakeLists.txt b/src/Prep/Photo/CMakeLists.txt index e8d9e689..e653f40c 100644 --- a/src/Prep/Photo/CMakeLists.txt +++ b/src/Prep/Photo/CMakeLists.txt @@ -3,7 +3,7 @@ add_executable(photo photo.cxx) target_link_libraries(photo - Polygon Geometry Array Output poly2tri TriangleJRS + Polygon Geometry Array Output poly2tri ${SIMGEAR_CORE_LIBRARIES} ${SIMGEAR_CORE_LIBRARY_DEPENDENCIES} ) diff --git a/src/Prep/ShapeFile/CMakeLists.txt b/src/Prep/ShapeFile/CMakeLists.txt index 0ac57972..ec565bc9 100644 --- a/src/Prep/ShapeFile/CMakeLists.txt +++ b/src/Prep/ShapeFile/CMakeLists.txt @@ -1,7 +1,7 @@ add_executable(shape-decode shape-decode.cxx) target_link_libraries(shape-decode - shape Polygon Geometry Output poly2tri TriangleJRS vpf + shape Polygon Geometry Output poly2tri vpf ${SIMGEAR_CORE_LIBRARIES} ${SIMGEAR_CORE_LIBRARY_DEPENDENCIES} ) @@ -11,7 +11,7 @@ install(TARGETS shape-decode RUNTIME DESTINATION bin) add_executable(noaa-decode noaa-decode.cxx) target_link_libraries(noaa-decode - shape Polygon Geometry Output poly2tri TriangleJRS vpf + shape Polygon Geometry Output poly2tri vpf ${SIMGEAR_CORE_LIBRARIES} ${SIMGEAR_CORE_LIBRARY_DEPENDENCIES} ) diff --git a/src/Prep/TGVPF/CMakeLists.txt b/src/Prep/TGVPF/CMakeLists.txt index 73a786d0..02989cdd 100644 --- a/src/Prep/TGVPF/CMakeLists.txt +++ b/src/Prep/TGVPF/CMakeLists.txt @@ -2,7 +2,7 @@ add_executable(tgvpf tgvpf.cxx) target_link_libraries(tgvpf - Polygon Geometry Output poly2tri TriangleJRS vpf + Polygon Geometry Output poly2tri vpf ${SIMGEAR_CORE_LIBRARIES} ${SIMGEAR_CORE_LIBRARY_DEPENDENCIES} ${RT_LIBRARY}) diff --git a/src/Prep/UserDef/CMakeLists.txt b/src/Prep/UserDef/CMakeLists.txt index d003204b..81b5de01 100644 --- a/src/Prep/UserDef/CMakeLists.txt +++ b/src/Prep/UserDef/CMakeLists.txt @@ -2,7 +2,7 @@ add_executable(tguserdef tguserdef.cxx) target_link_libraries(tguserdef - Polygon Geometry Output poly2tri TriangleJRS + Polygon Geometry Output poly2tri ${SIMGEAR_CORE_LIBRARIES} ${SIMGEAR_CORE_LIBRARY_DEPENDENCIES} )