flightgear/src/Main/views.cxx

// views.cxx -- data structures and routines for managing and view
//               parameters.
//
// Written by Curtis Olson, started August 1997.
//
// Copyright (C) 1997  Curtis L. Olson  - curt@infoplane.com
//
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of the
// License, or (at your option) any later version.
//
// This program is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
//
// $Id$


#ifdef HAVE_CONFIG_H
#  include <config.h>
#endif

#include <ssg.h>		// plib include

#include <Aircraft/aircraft.hxx>
#include <Cockpit/panel.hxx>
#include <Debug/logstream.hxx>
#include <Include/fg_constants.h>
#include <Math/mat3.h>
#include <Math/point3d.hxx>
#include <Math/polar3d.hxx>
#include <Math/vector.hxx>
#include <Scenery/scenery.hxx>
#include <Time/fg_time.hxx>

#include "options.hxx"
#include "views.hxx"


// Define following to extract various vectors directly
// from matrices we have allready computed
// rather then performing 'textbook algebra' to rederive them
// Norman Vine -- nhv@yahoo.com
// #define FG_VIEW_INLINE_OPTIMIZATIONS

// temporary (hopefully) hack
static int panel_hist = 0;


// specify code paths ... these are done as variable rather than
// #define's because down the road we may want to choose between them
// on the fly for different flight models ... this way magic carpet
// and external modes wouldn't need to recreate the LaRCsim matrices
// themselves.

static const bool use_larcsim_local_to_body = false;


// This is a record containing current view parameters for the current
// aircraft position
FGView pilot_view;

// This is a record containing current view parameters for the current
// view position
FGView current_view;


// Constructor
FGView::FGView( void ) {
}


// Initialize a view structure
void FGView::Init( void ) {
    FG_LOG( FG_VIEW, FG_INFO, "Initializing View parameters" );

    view_offset = 0.0;
    goal_view_offset = 0.0;

    winWidth = current_options.get_xsize();
    winHeight = current_options.get_ysize();

    if ( ! current_options.get_panel_status() ) {
	current_view.set_win_ratio( (GLfloat) winWidth / (GLfloat) winHeight );
    } else {
	current_view.set_win_ratio( (GLfloat) winWidth / 
				    ((GLfloat) (winHeight)*0.4232) );
    }

    force_update_fov_math();
}


// Update the field of view coefficients
void FGView::UpdateFOV( const fgOPTIONS& o ) {
    ssgSetFOV( o.get_fov(), 0.0 );

    double fov, theta_x, theta_y;

    fov = o.get_fov();
	
    // printf("win_ratio = %.2f\n", win_ratio);
    // calculate sin() and cos() of fov / 2 in X direction;
    theta_x = (fov * win_ratio * DEG_TO_RAD) / 2.0;
    // printf("theta_x = %.2f\n", theta_x);
    sin_fov_x = sin(theta_x);
    cos_fov_x = cos(theta_x);
    slope_x =  -cos_fov_x / sin_fov_x;
    // printf("slope_x = %.2f\n", slope_x);

    // fov_x_clip and fov_y_clip convoluted algebraic simplification
    // see code executed in tilemgr.cxx when USE_FAST_FOV_CLIP not
    // defined Norman Vine -- nhv@yahoo.com
#if defined( USE_FAST_FOV_CLIP )
    fov_x_clip = slope_x*cos_fov_x - sin_fov_x;
#endif // defined( USE_FAST_FOV_CLIP )

    // calculate sin() and cos() of fov / 2 in Y direction;
    theta_y = (fov * DEG_TO_RAD) / 2.0;
    // printf("theta_y = %.2f\n", theta_y);
    sin_fov_y = sin(theta_y);
    cos_fov_y = cos(theta_y);
    slope_y = cos_fov_y / sin_fov_y;
    // printf("slope_y = %.2f\n", slope_y);

#if defined( USE_FAST_FOV_CLIP )
    fov_y_clip = -(slope_y*cos_fov_y + sin_fov_y);	
#endif // defined( USE_FAST_FOV_CLIP )
}


// Update the view volume, position, and orientation
void FGView::UpdateViewParams( const FGInterface& f ) {
    UpdateViewMath(f);
    
    if ((current_options.get_panel_status() != panel_hist) &&                          (current_options.get_panel_status()))
    {
	FGPanel::OurPanel->ReInit( 0, 0, 1024, 768);
    }

    if ( ! current_options.get_panel_status() ) {
	xglViewport(0, 0 , (GLint)(winWidth), (GLint)(winHeight) );
    } else {
	xglViewport(0, (GLint)((winHeight)*0.5768), (GLint)(winWidth), 
		    (GLint)((winHeight)*0.4232) );
    }

    panel_hist = current_options.get_panel_status();
}


void getRotMatrix(double* out, MAT3vec vec, double radians)
{
    /* This function contributed by Erich Boleyn (erich@uruk.org) */
    /* This function used from the Mesa OpenGL code (matrix.c)  */
    double s, c; // mag,
    double vx, vy, vz, xy, yz, zx, xs, ys, zs, one_c; //, xx, yy, zz
  
    MAT3identity(out);
    s = sin(radians);
    c = cos(radians);
  
    //  mag = getMagnitude();
  
    vx = vec[0];
    vy = vec[1];
    vz = vec[2];
  
#define M(row,col)  out[row*4 + col]
  
    /*
     *     Arbitrary axis rotation matrix.
     *
     *  This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
     *  like so:  Rz * Ry * T * Ry' * Rz'.  T is the final rotation
     *  (which is about the X-axis), and the two composite transforms
     *  Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
     *  from the arbitrary axis to the X-axis then back.  They are
     *  all elementary rotations.
     *
     *  Rz' is a rotation about the Z-axis, to bring the axis vector
     *  into the x-z plane.  Then Ry' is applied, rotating about the
     *  Y-axis to bring the axis vector parallel with the X-axis.  The
     *  rotation about the X-axis is then performed.  Ry and Rz are
     *  simply the respective inverse transforms to bring the arbitrary
     *  axis back to it's original orientation.  The first transforms
     *  Rz' and Ry' are considered inverses, since the data from the
     *  arbitrary axis gives you info on how to get to it, not how
     *  to get away from it, and an inverse must be applied.
     *
     *  The basic calculation used is to recognize that the arbitrary
     *  axis vector (x, y, z), since it is of unit length, actually
     *  represents the sines and cosines of the angles to rotate the
     *  X-axis to the same orientation, with theta being the angle about
     *  Z and phi the angle about Y (in the order described above)
     *  as follows:
     *
     *  cos ( theta ) = x / sqrt ( 1 - z^2 )
     *  sin ( theta ) = y / sqrt ( 1 - z^2 )
     *
     *  cos ( phi ) = sqrt ( 1 - z^2 )
     *  sin ( phi ) = z
     *
     *  Note that cos ( phi ) can further be inserted to the above
     *  formulas:
     *
     *  cos ( theta ) = x / cos ( phi )
     *  sin ( theta ) = y / cos ( phi )
     *
     *  ...etc.  Because of those relations and the standard trigonometric
     *  relations, it is pssible to reduce the transforms down to what
     *  is used below.  It may be that any primary axis chosen will give the
     *  same results (modulo a sign convention) using thie method.
     *
     *  Particularly nice is to notice that all divisions that might
     *  have caused trouble when parallel to certain planes or
     *  axis go away with care paid to reducing the expressions.
     *  After checking, it does perform correctly under all cases, since
     *  in all the cases of division where the denominator would have
     *  been zero, the numerator would have been zero as well, giving
     *  the expected result.
     */
    
    one_c = 1.0F - c;
    
    //  xx = vx * vx;
    //  yy = vy * vy;
    //  zz = vz * vz;
  
    //  xy = vx * vy;
    //  yz = vy * vz;
    //  zx = vz * vx;
  
  
    M(0,0) = (one_c * vx * vx) + c;  
    xs = vx * s;
    yz = vy * vz * one_c;
    M(1,2) = yz + xs;
    M(2,1) = yz - xs;

    M(1,1) = (one_c * vy * vy) + c;
    ys = vy * s;
    zx = vz * vx * one_c;
    M(0,2) = zx - ys;
    M(2,0) = zx + ys;
  
    M(2,2) = (one_c * vz *vz) + c;
    zs = vz * s;
    xy = vx * vy * one_c;
    M(0,1) = xy + zs;
    M(1,0) = xy - zs;
  
    //  M(0,0) = (one_c * xx) + c;
    //  M(1,0) = (one_c * xy) - zs;
    //  M(2,0) = (one_c * zx) + ys;
  
    //  M(0,1) = (one_c * xy) + zs;
    //  M(1,1) = (one_c * yy) + c;
    //  M(2,1) = (one_c * yz) - xs;
  
    //  M(0,2) = (one_c * zx) - ys;
    //  M(1,2) = (one_c * yz) + xs;
    //  M(2,2) = (one_c * zz) + c;
  
#undef M
}


// Update the view parameters
void FGView::UpdateViewMath( const FGInterface& f ) {
    Point3D p;
    MAT3vec vec, forward, v0, minus_z;
    MAT3mat R, TMP, UP, LOCAL, VIEW;
    double ntmp;

    if ( update_fov ) {
	// printf("Updating fov\n");
	UpdateFOV( current_options );
	update_fov = false;
    }
		
    scenery.center = scenery.next_center;

#if !defined(FG_VIEW_INLINE_OPTIMIZATIONS)
    // printf("scenery center = %.2f %.2f %.2f\n", scenery.center.x,
    //        scenery.center.y, scenery.center.z);

    // calculate the cartesion coords of the current lat/lon/0 elev
    p = Point3D( f.get_Longitude(), 
		 f.get_Lat_geocentric(), 
		 f.get_Sea_level_radius() * FEET_TO_METER );

    cur_zero_elev = fgPolarToCart3d(p) - scenery.center;

    // calculate view position in current FG view coordinate system
    // p.lon & p.lat are already defined earlier, p.radius was set to
    // the sea level radius, so now we add in our altitude.
    if ( f.get_Altitude() * FEET_TO_METER > 
	 (scenery.cur_elev + 0.5 * METER_TO_FEET) ) {
	p.setz( p.radius() + f.get_Altitude() * FEET_TO_METER );
    } else {
	p.setz( p.radius() + scenery.cur_elev + 0.5 * METER_TO_FEET );
    }

    abs_view_pos = fgPolarToCart3d(p);
	
#else // FG_VIEW_INLINE_OPTIMIZATIONS
	
    double tmp_radius = f.get_Sea_level_radius() * FEET_TO_METER;
    double tmp = f.get_cos_lat_geocentric() * tmp_radius;
	
    cur_zero_elev.setx(f.get_cos_longitude()*tmp - scenery.center.x());
    cur_zero_elev.sety(f.get_sin_longitude()*tmp - scenery.center.y());
    cur_zero_elev.setz(f.get_sin_lat_geocentric()*tmp_radius - scenery.center.z());

    // calculate view position in current FG view coordinate system
    // p.lon & p.lat are already defined earlier, p.radius was set to
    // the sea level radius, so now we add in our altitude.
    if ( f.get_Altitude() * FEET_TO_METER > 
	 (scenery.cur_elev + 0.5 * METER_TO_FEET) ) {
	tmp_radius += f.get_Altitude() * FEET_TO_METER;
    } else {
	tmp_radius += scenery.cur_elev + 0.5 * METER_TO_FEET ;
    }
    tmp = f.get_cos_lat_geocentric() * tmp_radius;
    abs_view_pos.setx(f.get_cos_longitude()*tmp);
    abs_view_pos.sety(f.get_sin_longitude()*tmp);
    abs_view_pos.setz(f.get_sin_lat_geocentric()*tmp_radius);
	
#endif // FG_VIEW_INLINE_OPTIMIZATIONS
	
    view_pos = abs_view_pos - scenery.center;

    FG_LOG( FG_VIEW, FG_DEBUG, "Polar view pos = " << p );
    FG_LOG( FG_VIEW, FG_DEBUG, "Absolute view pos = " << abs_view_pos );
    FG_LOG( FG_VIEW, FG_DEBUG, "Relative view pos = " << view_pos );

    // Derive the LOCAL aircraft rotation matrix (roll, pitch, yaw)
    // from FG_T_local_to_body[3][3]

    if ( use_larcsim_local_to_body ) {

	// Question: Why is the LaRCsim matrix arranged so differently
	// than the one we need???

	// Answer (I think): The LaRCsim matrix is generated in a
	// different reference frame than we've set up for our world

	LOCAL[0][0] = f.get_T_local_to_body_33();
	LOCAL[0][1] = -f.get_T_local_to_body_32();
	LOCAL[0][2] = -f.get_T_local_to_body_31();
	LOCAL[0][3] = 0.0;
	LOCAL[1][0] = -f.get_T_local_to_body_23();
	LOCAL[1][1] = f.get_T_local_to_body_22();
	LOCAL[1][2] = f.get_T_local_to_body_21();
	LOCAL[1][3] = 0.0;
	LOCAL[2][0] = -f.get_T_local_to_body_13();
	LOCAL[2][1] = f.get_T_local_to_body_12();
	LOCAL[2][2] = f.get_T_local_to_body_11();
	LOCAL[2][3] = 0.0;
	LOCAL[3][0] = LOCAL[3][1] = LOCAL[3][2] = LOCAL[3][3] = 0.0;
	LOCAL[3][3] = 1.0;

	// printf("LaRCsim LOCAL matrix\n");
	// MAT3print(LOCAL, stdout);

    } else {

	// calculate the transformation matrix to go from LaRCsim to ssg
	sgVec3 vec1;
	sgSetVec3( vec1, 0.0, 1.0, 0.0 );
	sgMat4 mat1;
	sgMakeRotMat4( mat1, 90, vec1 );

	sgVec3 vec2;
	sgSetVec3( vec2, 1.0, 0.0, 0.0 );
	sgMat4 mat2;
	sgMakeRotMat4( mat2, 90, vec2 );

	sgMultMat4( sgLARC_TO_SSG, mat1, mat2 );

	/*
	cout << "LaRCsim to SSG:" << endl;
	MAT3mat print;
	int i;
	int j;
	for ( i = 0; i < 4; i++ ) {
	    for ( j = 0; j < 4; j++ ) {
		print[i][j] = sgLARC_TO_SSG[i][j];
	    }
	}
	MAT3print( print, stdout);
	*/

	// code to calculate LOCAL matrix calculated from Phi, Theta, and
	// Psi (roll, pitch, yaw) in case we aren't running LaRCsim as our
	// flight model

	MAT3_SET_VEC(vec, 0.0, 0.0, 1.0);
	MAT3rotate(R, vec, f.get_Phi());
	// cout << "Roll matrix" << endl;
	// MAT3print(R, stdout);

	sgVec3 sgrollvec;
	sgSetVec3( sgrollvec, 0.0, 0.0, 1.0 );
	sgMat4 sgPHI;		// roll
	sgMakeRotMat4( sgPHI, f.get_Phi() * RAD_TO_DEG, sgrollvec );


	MAT3_SET_VEC(vec, 0.0, 1.0, 0.0);
	MAT3rotate(TMP, vec, f.get_Theta());
	// cout << "Pitch matrix" << endl;;
	// MAT3print(TMP, stdout);
	MAT3mult(R, R, TMP);
	// cout << "tmp rotation matrix, R:" << endl;;
	// MAT3print(R, stdout);

	sgVec3 sgpitchvec;
	sgSetVec3( sgpitchvec, 0.0, 1.0, 0.0 );
	sgMat4 sgTHETA;		// pitch
	sgMakeRotMat4( sgTHETA, f.get_Theta() * RAD_TO_DEG,
		       sgpitchvec );

	sgMat4 sgROT;
	sgMultMat4( sgROT, sgPHI, sgTHETA );


	MAT3_SET_VEC(vec, 1.0, 0.0, 0.0);
	MAT3rotate(TMP, vec, -f.get_Psi());
	// cout << "Yaw matrix" << endl;
	// MAT3print(TMP, stdout);
	MAT3mult(LOCAL, R, TMP);
	// cout << "LOCAL matrix:" << endl;
	// MAT3print(LOCAL, stdout);

	sgVec3 sgyawvec;
	sgSetVec3( sgyawvec, 1.0, 0.0, 0.0 );
	sgMat4 sgPSI;		// pitch
	sgMakeRotMat4( sgPSI, -f.get_Psi() * RAD_TO_DEG, sgyawvec );

	sgMultMat4( sgLOCAL, sgROT, sgPSI );

	/*
	MAT3mat print;
	int i;
	int j;
	for ( i = 0; i < 4; i++ ) {
	    for ( j = 0; j < 4; j++ ) {
		print[i][j] = sgLOCAL[i][j];
	    }
	}
	MAT3print( print, stdout);
	*/
    } // if ( use_larcsim_local_to_body ) 

#if !defined(FG_VIEW_INLINE_OPTIMIZATIONS)
	
    // Derive the local UP transformation matrix based on *geodetic*
    // coordinates
    MAT3_SET_VEC(vec, 0.0, 0.0, 1.0);
    MAT3rotate(R, vec, f.get_Longitude());     // R = rotate about Z axis
    // printf("Longitude matrix\n");
    // MAT3print(R, stdout);

    MAT3_SET_VEC(vec, 0.0, 1.0, 0.0);
    MAT3mult_vec(vec, vec, R);
    MAT3rotate(TMP, vec, -f.get_Latitude());  // TMP = rotate about X axis
    // printf("Latitude matrix\n");
    // MAT3print(TMP, stdout);

    MAT3mult(UP, R, TMP);
    // cout << "Local up matrix" << endl;;
    // MAT3print(UP, stdout);

    sgMakeRotMat4( sgUP, 
		   f.get_Longitude() * RAD_TO_DEG,
		   0.0,
		   -f.get_Latitude() * RAD_TO_DEG );
    /*
    cout << "FG derived UP matrix using sg routines" << endl;
    MAT3mat print;
    int i;
    int j;
    for ( i = 0; i < 4; i++ ) {
	for ( j = 0; j < 4; j++ ) {
	    print[i][j] = sgUP[i][j];
	}
    }
    MAT3print( print, stdout);
    */

    MAT3_SET_VEC(local_up, 1.0, 0.0, 0.0);
    MAT3mult_vec(local_up, local_up, UP);

    // printf( "Local Up = (%.4f, %.4f, %.4f)\n",
    //         local_up[0], local_up[1], local_up[2]);
    
    // Alternative method to Derive local up vector based on
    // *geodetic* coordinates
    // alt_up = fgPolarToCart(FG_Longitude, FG_Latitude, 1.0);
    // printf( "    Alt Up = (%.4f, %.4f, %.4f)\n", 
    //         alt_up.x, alt_up.y, alt_up.z);

    // Calculate the VIEW matrix
    MAT3mult(VIEW, LOCAL, UP);
    // cout << "VIEW matrix" << endl;;
    // MAT3print(VIEW, stdout);

    sgMat4 sgTMP, sgTMP2;
    sgMultMat4( sgTMP, sgLOCAL, sgUP );

    // generate the sg view up vector
    sgVec3 vec1;
    sgSetVec3( vec1, 1.0, 0.0, 0.0 );
    sgXformVec3( sgview_up, vec1, sgTMP );

    // generate the view offset matrix
    sgMakeRotMat4( sgVIEW_OFFSET, view_offset * RAD_TO_DEG, sgview_up );

    /*
    cout << "sg VIEW_OFFSET matrix" << endl;
    MAT3mat print;
    int i;
    int j;
    for ( i = 0; i < 4; i++ ) {
	for ( j = 0; j < 4; j++ ) {
	    print[i][j] = sgVIEW_OFFSET[i][j];
	}
    }
    MAT3print( print, stdout);
    */

    sgMultMat4( sgTMP2, sgTMP, sgVIEW_OFFSET );
    sgMultMat4( sgVIEW_ROT, sgLARC_TO_SSG, sgTMP2 );

    sgMakeTransMat4( sgTRANS, view_pos.x(), view_pos.y(), view_pos.z() );

    sgMultMat4( sgVIEW, sgVIEW_ROT, sgTRANS );

    // FGMat4Wrapper tmp;
    // sgCopyMat4( tmp.m, sgVIEW );
    // follow.push_back( tmp );

    // generate the current up, forward, and fwrd-view vectors
    MAT3_SET_VEC(vec, 1.0, 0.0, 0.0);
    MAT3mult_vec(view_up, vec, VIEW);

    /*
    cout << "FG derived VIEW matrix using sg routines" << endl;
    MAT3mat print;
    int i;
    int j;
    for ( i = 0; i < 4; i++ ) {
	for ( j = 0; j < 4; j++ ) {
	    print[i][j] = sgVIEW[i][j];
	}
    }
    MAT3print( print, stdout);
    */

    MAT3_SET_VEC(vec, 0.0, 0.0, 1.0);
    MAT3mult_vec(forward, vec, VIEW);
    // printf( "Forward vector is (%.2f,%.2f,%.2f)\n", forward[0], forward[1], 
    //         forward[2]);

    MAT3rotate(TMP, view_up, view_offset);
    MAT3mult_vec(view_forward, forward, TMP);

    // make a vector to the current view position
    MAT3_SET_VEC(v0, view_pos.x(), view_pos.y(), view_pos.z());

    // Given a vector pointing straight down (-Z), map into onto the
    // local plane representing "horizontal".  This should give us the
    // local direction for moving "south".
    MAT3_SET_VEC(minus_z, 0.0, 0.0, -1.0);
    map_vec_onto_cur_surface_plane(local_up, v0, minus_z, surface_south);
    MAT3_NORMALIZE_VEC(surface_south, ntmp);
    // printf( "Surface direction directly south %.2f %.2f %.2f\n",
    //         surface_south[0], surface_south[1], surface_south[2]);

    // now calculate the surface east vector
    MAT3rotate(TMP, view_up, FG_PI_2);
    MAT3mult_vec(surface_east, surface_south, TMP);
    // printf( "Surface direction directly east %.2f %.2f %.2f\n",
    //         surface_east[0], surface_east[1], surface_east[2]);
    // printf( "Should be close to zero = %.2f\n", 
    //         MAT3_DOT_PRODUCT(surface_south, surface_east));
	
#else // FG_VIEW_INLINE_OPTIMIZATIONS
	 
    //	// Build spherical to cartesian transform matrix directly
    double cos_lat = f.get_cos_latitude(); // cos(-f.get_Latitude());
    double sin_lat = -f.get_sin_latitude(); // sin(-f.get_Latitude());
    double cos_lon = f.get_cos_longitude(); //cos(f.get_Longitude());
    double sin_lon = f.get_sin_longitude(); //sin(f.get_Longitude());

    double *mat = (double *)UP;
	
    mat[0] =  cos_lat*cos_lon;
    mat[1] =  cos_lat*sin_lon;
    mat[2] = -sin_lat;
    mat[3] =  0.0;
    mat[4] =  -sin_lon;
    mat[5] =  cos_lon;
    mat[6] =  0.0;
    mat[7] =  0.0;
    mat[8]  =  sin_lat*cos_lon;
    mat[9]  =  sin_lat*sin_lon;
    mat[10] =  cos_lat;
    mat[11] =  mat[12] = mat[13] = mat[14] = 0.0;
    mat[15] =  1.0;

    MAT3mult(VIEW, LOCAL, UP);
	
    // THESE COULD JUST BE POINTERS !!!
    MAT3_SET_VEC(local_up, mat[0],     mat[1],     mat[2]);
    MAT3_SET_VEC(view_up,  VIEW[0][0], VIEW[0][1], VIEW[0][2]);
    MAT3_SET_VEC(forward,  VIEW[2][0], VIEW[2][1], VIEW[2][2]);

    getRotMatrix((double *)TMP, view_up, view_offset);
    MAT3mult_vec(view_forward, forward, TMP);

    // make a vector to the current view position
    MAT3_SET_VEC(v0, view_pos.x(), view_pos.y(), view_pos.z());

    // Given a vector pointing straight down (-Z), map into onto the
    // local plane representing "horizontal".  This should give us the
    // local direction for moving "south".
    MAT3_SET_VEC(minus_z, 0.0, 0.0, -1.0);
    map_vec_onto_cur_surface_plane(local_up, v0, minus_z, surface_south);

    MAT3_NORMALIZE_VEC(surface_south, ntmp);
    // printf( "Surface direction directly south %.6f %.6f %.6f\n",
    //         surface_south[0], surface_south[1], surface_south[2]);

    // now calculate the surface east vector
    getRotMatrix((double *)TMP, view_up, FG_PI_2);
    MAT3mult_vec(surface_east, surface_south, TMP);
    // printf( "Surface direction directly east %.6f %.6f %.6f\n",
    //         surface_east[0], surface_east[1], surface_east[2]);
    // printf( "Should be close to zero = %.6f\n", 
    //         MAT3_DOT_PRODUCT(surface_south, surface_east));
#endif // !defined(FG_VIEW_INLINE_OPTIMIZATIONS)
}


// Destructor
FGView::~FGView( void ) {
}