/* projectiveplane --- Shows a 4d embedding of the real projective plane that rotates in 4d or on which you can walk */ #if 0 static const char sccsid[] = "@(#)projectiveplane.c 1.1 14/01/01 xlockmore"; #endif /* Copyright (c) 2005-2014 Carsten Steger . */ /* * Permission to use, copy, modify, and distribute this software and its * documentation for any purpose and without fee is hereby granted, * provided that the above copyright notice appear in all copies and that * both that copyright notice and this permission notice appear in * supporting documentation. * * This file is provided AS IS with no warranties of any kind. The author * shall have no liability with respect to the infringement of copyrights, * trade secrets or any patents by this file or any part thereof. In no * event will the author be liable for any lost revenue or profits or * other special, indirect and consequential damages. * * REVISION HISTORY: * C. Steger - 14/01/03: Initial version * C. Steger - 14/10/03: Moved the curlicue texture to curlicue.h */ /* * This program shows a 4d embedding of the real projective plane. * You can walk on the projective plane, see it turn in 4d, or walk on * it while it turns in 4d. The fact that the surface is an embedding * of the real projective plane in 4d can be seen in the depth colors * mode: set all rotation speeds to 0 and the projection mode to 4d * orthographic projection. In its default orientation, the embedding * of the real projective plane will then project to the Roman * surface, which has three lines of self-intersection. However, at * the three lines of self-intersection the parts of the surface that * intersect have different colors, i.e., different 4d depths. * * The real projective plane is a non-orientable surface. To make * this apparent, the two-sided color mode can be used. * Alternatively, orientation markers (curling arrows) can be drawn as * a texture map on the surface of the projective plane. While * walking on the projective plane, you will notice that the * orientation of the curling arrows changes (which it must because * the projective plane is non-orientable). * * The real projective plane is a model for the projective geometry in * 2d space. One point can be singled out as the origin. A line can * be singled out as the line at infinity, i.e., a line that lies at * an infinite distance to the origin. The line at infinity is * topologically a circle. Points on the line at infinity are also * used to model directions in projective geometry. The origin can be * visualized in different manners. When using distance colors, the * origin is the point that is displayed as fully saturated red, which * is easier to see as the center of the reddish area on the * projective plane. Alternatively, when using distance bands, the * origin is the center of the only band that projects to a disc. * When using direction bands, the origin is the point where all * direction bands collapse to a point. Finally, when orientation * markers are being displayed, the origin the the point where all * orientation markers are compressed to a point. The line at * infinity can also be visualized in different ways. When using * distance colors, the line at infinity is the line that is displayed * as fully saturated magenta. When two-sided colors are used, the * line at infinity lies at the points where the red and green "sides" * of the projective plane meet (of course, the real projective plane * only has one side, so this is a design choice of the * visualization). Alternatively, when orientation markers are being * displayed, the line at infinity is the place where the orientation * markers change their orientation. * * Note that when the projective plane is displayed with bands, the * orientation markers are placed in the middle of the bands. For * distance bands, the bands are chosen in such a way that the band at * the origin is only half as wide as the remaining bands, which * results in a disc being displayed at the origin that has the same * diameter as the remaining bands. This choice, however, also * implies that the band at infinity is half as wide as the other * bands. Since the projective plane is attached to itself (in a * complicated fashion) at the line at infinity, effectively the band * at infinity is again as wide as the remaining bands. However, * since the orientation markers are displayed in the middle of the * bands, this means that only one half of the orientation markers * will be displayed twice at the line at infinity if distance bands * are used. If direction bands are used or if the projective plane * is displayed as a solid surface, the orientation markers are * displayed fully at the respective sides of the line at infinity. * * The program projects the 4d projective plane to 3d using either a * perspective or an orthographic projection. Which of the two * alternatives looks more appealing is up to you. However, two * famous surfaces are obtained if orthographic 4d projection is used: * The Roman surface and the cross cap. If the projective plane is * rotated in 4d, the result of the projection for certain rotations * is a Roman surface and for certain rotations it is a cross cap. * The easiest way to see this is to set all rotation speeds to 0 and * the rotation speed around the yz plane to a value different from 0. * However, for any 4d rotation speeds, the projections will generally * cycle between the Roman surface and the cross cap. The difference * is where the origin and the line at infinity will lie with respect * to the self-intersections in the projections to 3d. * * The projected projective plane can then be projected to the screen * either perspectively or orthographically. When using the walking * modes, perspective projection to the screen will be used. * * There are three display modes for the projective plane: mesh * (wireframe), solid, or transparent. Furthermore, the appearance of * the projective plane can be as a solid object or as a set of * see-through bands. The bands can be distance bands, i.e., bands * that lie at increasing distances from the origin, or direction * bands, i.e., bands that lie at increasing angles with respect to * the origin. * * When the projective plane is displayed with direction bands, you * will be able to see that each direction band (modulo the "pinching" * at the origin) is a Moebius strip, which also shows that the * projective plane is non-orientable. * * Finally, the colors with with the projective plane is drawn can be * set to two-sided, distance, direction, or depth. In two-sided * mode, the projective plane is drawn with red on one "side" and * green on the "other side". As described above, the projective * plane only has one side, so the color jumps from red to green along * the line at infinity. This mode enables you to see that the * projective plane is non-orientable. In distance mode, the * projective plane is displayed with fully saturated colors that * depend on the distance of the points on the projective plane to the * origin. The origin is displayed in red, the line at infinity is * displayed in magenta. If the projective plane is displayed as * distance bands, each band will be displayed with a different color. * In direction mode, the projective plane is displayed with fully * saturated colors that depend on the angle of the points on the * projective plane with respect to the origin. Angles in opposite * directions to the origin (e.g., 15 and 205 degrees) are displayed * in the same color since they are projectively equivalent. If the * projective plane is displayed as direction bands, each band will be * displayed with a different color. Finally, in depth mode the * projective plane with colors chosen depending on the 4d "depth" * (i.e., the w coordinate) of the points on the projective plane at * its default orientation in 4d. As discussed above, this mode * enables you to see that the projective plane does not intersect * itself in 4d. * * The rotation speed for each of the six planes around which the * projective plane rotates can be chosen. For the walk-and-turn * more, only the rotation speeds around the true 4d planes are used * (the xy, xz, and yz planes). * * Furthermore, in the walking modes the walking direction in the 2d * base square of the projective plane and the walking speed can be * chosen. The walking direction is measured as an angle in degrees * in the 2d square that forms the coordinate system of the surface of * the projective plane. A value of 0 or 180 means that the walk is * along a circle at a randomly chosen distance from the origin * (parallel to a distance band). A value of 90 or 270 means that the * walk is directly from the origin to the line at infinity and back * (analogous to a direction band). Any other value results in a * curved path from the origin to the line at infinity and back. * * This program is somewhat inspired by Thomas Banchoff's book "Beyond * the Third Dimension: Geometry, Computer Graphics, and Higher * Dimensions", Scientific American Library, 1990. */ #include "curlicue.h" #ifndef M_PI #define M_PI 3.14159265358979323846 #endif #define DISP_WIREFRAME 0 #define DISP_SURFACE 1 #define DISP_TRANSPARENT 2 #define NUM_DISPLAY_MODES 3 #define APPEARANCE_SOLID 0 #define APPEARANCE_DISTANCE_BANDS 1 #define APPEARANCE_DIRECTION_BANDS 2 #define NUM_APPEARANCES 3 #define COLORS_TWOSIDED 0 #define COLORS_DISTANCE 1 #define COLORS_DIRECTION 2 #define COLORS_DEPTH 3 #define NUM_COLORS 4 #define VIEW_WALK 0 #define VIEW_TURN 1 #define VIEW_WALKTURN 2 #define NUM_VIEW_MODES 3 #define DISP_3D_PERSPECTIVE 0 #define DISP_3D_ORTHOGRAPHIC 1 #define NUM_DISP_3D_MODES 2 #define DISP_4D_PERSPECTIVE 0 #define DISP_4D_ORTHOGRAPHIC 1 #define NUM_DISP_4D_MODES 2 #define DEF_DISPLAY_MODE "random" #define DEF_APPEARANCE "random" #define DEF_COLORS "random" #define DEF_VIEW_MODE "random" #define DEF_MARKS "False" #define DEF_PROJECTION_3D "random" #define DEF_PROJECTION_4D "random" #define DEF_SPEEDWX "1.1" #define DEF_SPEEDWY "1.3" #define DEF_SPEEDWZ "1.5" #define DEF_SPEEDXY "1.7" #define DEF_SPEEDXZ "1.9" #define DEF_SPEEDYZ "2.1" #define DEF_WALK_DIRECTION "83.0" #define DEF_WALK_SPEED "20.0" #ifdef STANDALONE # define DEFAULTS "*delay: 10000 \n" \ "*showFPS: False \n" \ # define release_projectiveplane 0 # include "xlockmore.h" /* from the xscreensaver distribution */ #else /* !STANDALONE */ # include "xlock.h" /* from the xlockmore distribution */ #endif /* !STANDALONE */ #ifdef USE_GL #ifndef HAVE_JWXYZ # include #endif #include "gltrackball.h" #include #ifdef USE_MODULES ModStruct projectiveplane_description = {"projectiveplane", "init_projectiveplane", "draw_projectiveplane", NULL, "draw_projectiveplane", "change_projectiveplane", NULL, &projectiveplane_opts, 25000, 1, 1, 1, 1.0, 4, "", "Rotate a 4d embedding of the real projective plane in 4d or walk on it", 0, NULL}; #endif static char *mode; static char *appear; static char *color_mode; static char *view_mode; static Bool marks; static char *proj_3d; static char *proj_4d; static float speed_wx; static float speed_wy; static float speed_wz; static float speed_xy; static float speed_xz; static float speed_yz; static float walk_direction; static float walk_speed; static XrmOptionDescRec opts[] = { {"-mode", ".displayMode", XrmoptionSepArg, 0 }, {"-wireframe", ".displayMode", XrmoptionNoArg, "wireframe" }, {"-surface", ".displayMode", XrmoptionNoArg, "surface" }, {"-transparent", ".displayMode", XrmoptionNoArg, "transparent" }, {"-appearance", ".appearance", XrmoptionSepArg, 0 }, {"-solid", ".appearance", XrmoptionNoArg, "solid" }, {"-distance-bands", ".appearance", XrmoptionNoArg, "distance-bands" }, {"-direction-bands", ".appearance", XrmoptionNoArg, "direction-bands" }, {"-colors", ".colors", XrmoptionSepArg, 0 }, {"-twosided-colors", ".colors", XrmoptionNoArg, "two-sided" }, {"-distance-colors", ".colors", XrmoptionNoArg, "distance" }, {"-direction-colors", ".colors", XrmoptionNoArg, "direction" }, {"-depth-colors", ".colors", XrmoptionNoArg, "depth" }, {"-view-mode", ".viewMode", XrmoptionSepArg, 0 }, {"-walk", ".viewMode", XrmoptionNoArg, "walk" }, {"-turn", ".viewMode", XrmoptionNoArg, "turn" }, {"-walk-turn", ".viewMode", XrmoptionNoArg, "walk-turn" }, {"-orientation-marks", ".marks", XrmoptionNoArg, "on"}, {"+orientation-marks", ".marks", XrmoptionNoArg, "off"}, {"-projection-3d", ".projection3d", XrmoptionSepArg, 0 }, {"-perspective-3d", ".projection3d", XrmoptionNoArg, "perspective" }, {"-orthographic-3d", ".projection3d", XrmoptionNoArg, "orthographic" }, {"-projection-4d", ".projection4d", XrmoptionSepArg, 0 }, {"-perspective-4d", ".projection4d", XrmoptionNoArg, "perspective" }, {"-orthographic-4d", ".projection4d", XrmoptionNoArg, "orthographic" }, {"-speed-wx", ".speedwx", XrmoptionSepArg, 0 }, {"-speed-wy", ".speedwy", XrmoptionSepArg, 0 }, {"-speed-wz", ".speedwz", XrmoptionSepArg, 0 }, {"-speed-xy", ".speedxy", XrmoptionSepArg, 0 }, {"-speed-xz", ".speedxz", XrmoptionSepArg, 0 }, {"-speed-yz", ".speedyz", XrmoptionSepArg, 0 }, {"-walk-direction", ".walkDirection", XrmoptionSepArg, 0 }, {"-walk-speed", ".walkSpeed", XrmoptionSepArg, 0 } }; static argtype vars[] = { { &mode, "displayMode", "DisplayMode", DEF_DISPLAY_MODE, t_String }, { &appear, "appearance", "Appearance", DEF_APPEARANCE, t_String }, { &color_mode, "colors", "Colors", DEF_COLORS, t_String }, { &view_mode, "viewMode", "ViewMode", DEF_VIEW_MODE, t_String }, { &marks, "marks", "Marks", DEF_MARKS, t_Bool }, { &proj_3d, "projection3d", "Projection3d", DEF_PROJECTION_3D, t_String }, { &proj_4d, "projection4d", "Projection4d", DEF_PROJECTION_4D, t_String }, { &speed_wx, "speedwx", "Speedwx", DEF_SPEEDWX, t_Float}, { &speed_wy, "speedwy", "Speedwy", DEF_SPEEDWY, t_Float}, { &speed_wz, "speedwz", "Speedwz", DEF_SPEEDWZ, t_Float}, { &speed_xy, "speedxy", "Speedxy", DEF_SPEEDXY, t_Float}, { &speed_xz, "speedxz", "Speedxz", DEF_SPEEDXZ, t_Float}, { &speed_yz, "speedyz", "Speedyz", DEF_SPEEDYZ, t_Float}, { &walk_direction, "walkDirection", "WalkDirection", DEF_WALK_DIRECTION, t_Float}, { &walk_speed, "walkSpeed", "WalkSpeed", DEF_WALK_SPEED, t_Float} }; ENTRYPOINT ModeSpecOpt projectiveplane_opts = {sizeof opts / sizeof opts[0], opts, sizeof vars / sizeof vars[0], vars, NULL}; /* Offset by which we walk above the projective plane */ #define DELTAY 0.01 /* Number of subdivisions of the projective plane */ #define NUMU 128 #define NUMV 128 /* Number of subdivisions per band */ #define NUMB 8 typedef struct { GLint WindH, WindW; GLXContext *glx_context; /* Options */ int display_mode; int appearance; int colors; int view; Bool marks; int projection_3d; int projection_4d; /* 4D rotation angles */ float alpha, beta, delta, zeta, eta, theta; /* Movement parameters */ float umove, vmove, dumove, dvmove; int side, dir; /* The viewing offset in 4d */ float offset4d[4]; /* The viewing offset in 3d */ float offset3d[4]; /* The 4d coordinates of the projective plane and their derivatives */ float x[(NUMU+1)*(NUMV+1)][4]; float xu[(NUMU+1)*(NUMV+1)][4]; float xv[(NUMU+1)*(NUMV+1)][4]; float pp[(NUMU+1)*(NUMV+1)][3]; float pn[(NUMU+1)*(NUMV+1)][3]; /* The precomputed colors of the projective plane */ float col[(NUMU+1)*(NUMV+1)][4]; /* The precomputed texture coordinates of the projective plane */ float tex[(NUMU+1)*(NUMV+1)][2]; /* The "curlicue" texture */ GLuint tex_name; /* Aspect ratio of the current window */ float aspect; /* Trackball states */ trackball_state *trackballs[2]; int current_trackball; Bool button_pressed; /* A random factor to modify the rotation speeds */ float speed_scale; } projectiveplanestruct; static projectiveplanestruct *projectiveplane = (projectiveplanestruct *) NULL; /* Add a rotation around the wx-plane to the matrix m. */ static void rotatewx(float m[4][4], float phi) { float c, s, u, v; int i; phi *= M_PI/180.0; c = cos(phi); s = sin(phi); for (i=0; i<4; i++) { u = m[i][1]; v = m[i][2]; m[i][1] = c*u+s*v; m[i][2] = -s*u+c*v; } } /* Add a rotation around the wy-plane to the matrix m. */ static void rotatewy(float m[4][4], float phi) { float c, s, u, v; int i; phi *= M_PI/180.0; c = cos(phi); s = sin(phi); for (i=0; i<4; i++) { u = m[i][0]; v = m[i][2]; m[i][0] = c*u-s*v; m[i][2] = s*u+c*v; } } /* Add a rotation around the wz-plane to the matrix m. */ static void rotatewz(float m[4][4], float phi) { float c, s, u, v; int i; phi *= M_PI/180.0; c = cos(phi); s = sin(phi); for (i=0; i<4; i++) { u = m[i][0]; v = m[i][1]; m[i][0] = c*u+s*v; m[i][1] = -s*u+c*v; } } /* Add a rotation around the xy-plane to the matrix m. */ static void rotatexy(float m[4][4], float phi) { float c, s, u, v; int i; phi *= M_PI/180.0; c = cos(phi); s = sin(phi); for (i=0; i<4; i++) { u = m[i][2]; v = m[i][3]; m[i][2] = c*u+s*v; m[i][3] = -s*u+c*v; } } /* Add a rotation around the xz-plane to the matrix m. */ static void rotatexz(float m[4][4], float phi) { float c, s, u, v; int i; phi *= M_PI/180.0; c = cos(phi); s = sin(phi); for (i=0; i<4; i++) { u = m[i][1]; v = m[i][3]; m[i][1] = c*u-s*v; m[i][3] = s*u+c*v; } } /* Add a rotation around the yz-plane to the matrix m. */ static void rotateyz(float m[4][4], float phi) { float c, s, u, v; int i; phi *= M_PI/180.0; c = cos(phi); s = sin(phi); for (i=0; i<4; i++) { u = m[i][0]; v = m[i][3]; m[i][0] = c*u-s*v; m[i][3] = s*u+c*v; } } /* Compute the rotation matrix m from the rotation angles. */ static void rotateall(float al, float be, float de, float ze, float et, float th, float m[4][4]) { int i, j; for (i=0; i<4; i++) for (j=0; j<4; j++) m[i][j] = (i==j); rotatewx(m,al); rotatewy(m,be); rotatewz(m,de); rotatexy(m,ze); rotatexz(m,et); rotateyz(m,th); } /* Compute the rotation matrix m from the 4d rotation angles. */ static void rotateall4d(float ze, float et, float th, float m[4][4]) { int i, j; for (i=0; i<4; i++) for (j=0; j<4; j++) m[i][j] = (i==j); rotatexy(m,ze); rotatexz(m,et); rotateyz(m,th); } /* Multiply two rotation matrices: o=m*n. */ static void mult_rotmat(float m[4][4], float n[4][4], float o[4][4]) { int i, j, k; for (i=0; i<4; i++) { for (j=0; j<4; j++) { o[i][j] = 0.0; for (k=0; k<4; k++) o[i][j] += m[i][k]*n[k][j]; } } } /* Compute a 4D rotation matrix from two unit quaternions. */ static void quats_to_rotmat(float p[4], float q[4], float m[4][4]) { double al, be, de, ze, et, th; double r00, r01, r02, r12, r22; r00 = 1.0-2.0*(p[1]*p[1]+p[2]*p[2]); r01 = 2.0*(p[0]*p[1]+p[2]*p[3]); r02 = 2.0*(p[2]*p[0]-p[1]*p[3]); r12 = 2.0*(p[1]*p[2]+p[0]*p[3]); r22 = 1.0-2.0*(p[1]*p[1]+p[0]*p[0]); al = atan2(-r12,r22)*180.0/M_PI; be = atan2(r02,sqrt(r00*r00+r01*r01))*180.0/M_PI; de = atan2(-r01,r00)*180.0/M_PI; r00 = 1.0-2.0*(q[1]*q[1]+q[2]*q[2]); r01 = 2.0*(q[0]*q[1]+q[2]*q[3]); r02 = 2.0*(q[2]*q[0]-q[1]*q[3]); r12 = 2.0*(q[1]*q[2]+q[0]*q[3]); r22 = 1.0-2.0*(q[1]*q[1]+q[0]*q[0]); et = atan2(-r12,r22)*180.0/M_PI; th = atan2(r02,sqrt(r00*r00+r01*r01))*180.0/M_PI; ze = atan2(-r01,r00)*180.0/M_PI; rotateall(al,be,de,ze,et,-th,m); } /* Compute a fully saturated and bright color based on an angle. */ static void color(projectiveplanestruct *pp, double angle, float col[4]) { int s; double t; if (pp->colors == COLORS_TWOSIDED) return; if (angle >= 0.0) angle = fmod(angle,2.0*M_PI); else angle = fmod(angle,-2.0*M_PI); s = floor(angle/(M_PI/3)); t = angle/(M_PI/3)-s; if (s >= 6) s = 0; switch (s) { case 0: col[0] = 1.0; col[1] = t; col[2] = 0.0; break; case 1: col[0] = 1.0-t; col[1] = 1.0; col[2] = 0.0; break; case 2: col[0] = 0.0; col[1] = 1.0; col[2] = t; break; case 3: col[0] = 0.0; col[1] = 1.0-t; col[2] = 1.0; break; case 4: col[0] = t; col[1] = 0.0; col[2] = 1.0; break; case 5: col[0] = 1.0; col[1] = 0.0; col[2] = 1.0-t; break; } if (pp->display_mode == DISP_TRANSPARENT) col[3] = 0.7; else col[3] = 1.0; } /* Set up the projective plane coordinates, colors, and texture. */ static void setup_projective_plane(ModeInfo *mi, double umin, double umax, double vmin, double vmax) { int i, j, k; double u, v, ur, vr; double cu, su, cv2, sv2, cv4, sv4, c2u, s2u; projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)]; ur = umax-umin; vr = vmax-vmin; for (i=0; i<=NUMV; i++) { for (j=0; j<=NUMU; j++) { k = i*(NUMU+1)+j; if (pp->appearance != APPEARANCE_DIRECTION_BANDS) u = -ur*j/NUMU+umin; else u = ur*j/NUMU+umin; v = vr*i/NUMV+vmin; cu = cos(u); su = sin(u); c2u = cos(2.0*u); s2u = sin(2.0*u); sv2 = sin(0.5*v); cv4 = cos(0.25*v); sv4 = sin(0.25*v); if (pp->colors == COLORS_DEPTH) color(pp,((su*su*sv4*sv4-cv4*cv4)+1.0)*M_PI*2.0/3.0,pp->col[k]); else if (pp->colors == COLORS_DIRECTION) color(pp,2.0*M_PI+fmod(2.0*u,2.0*M_PI),pp->col[k]); else /* pp->colors == COLORS_DISTANCE */ color(pp,v*(5.0/6.0),pp->col[k]); pp->tex[k][0] = -32*u/(2.0*M_PI); if (pp->appearance != APPEARANCE_DISTANCE_BANDS) pp->tex[k][1] = 32*v/(2.0*M_PI); else pp->tex[k][1] = 32*v/(2.0*M_PI)-0.5; pp->x[k][0] = 0.5*s2u*sv4*sv4; pp->x[k][1] = 0.5*su*sv2; pp->x[k][2] = 0.5*cu*sv2; pp->x[k][3] = 0.5*(su*su*sv4*sv4-cv4*cv4); /* Avoid degenerate tangential plane basis vectors. */ if (v < FLT_EPSILON) v = FLT_EPSILON; cv2 = cos(0.5*v); sv2 = sin(0.5*v); sv4 = sin(0.25*v); pp->xu[k][0] = c2u*sv4*sv4; pp->xu[k][1] = 0.5*cu*sv2; pp->xu[k][2] = -0.5*su*sv2; pp->xu[k][3] = 0.5*s2u*sv4*sv4; pp->xv[k][0] = 0.125*s2u*sv2; pp->xv[k][1] = 0.25*su*cv2; pp->xv[k][2] = 0.25*cu*cv2; pp->xv[k][3] = 0.125*(su*su+1.0)*sv2; } } } /* Draw a 4d embedding of the projective plane projected into 3D. */ static int projective_plane(ModeInfo *mi, double umin, double umax, double vmin, double vmax) { int polys = 0; static const GLfloat mat_diff_red[] = { 1.0, 0.0, 0.0, 1.0 }; static const GLfloat mat_diff_green[] = { 0.0, 1.0, 0.0, 1.0 }; static const GLfloat mat_diff_trans_red[] = { 1.0, 0.0, 0.0, 0.7 }; static const GLfloat mat_diff_trans_green[] = { 0.0, 1.0, 0.0, 0.7 }; float p[3], pu[3], pv[3], pm[3], n[3], b[3], mat[4][4]; int i, j, k, l, m, o; double u, v; double xx[4], xxu[4], xxv[4], y[4], yu[4], yv[4]; double q, r, s, t; double cu, su, cv2, sv2, cv4, sv4, c2u, s2u; float q1[4], q2[4], r1[4][4], r2[4][4]; projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)]; if (pp->view == VIEW_WALK || pp->view == VIEW_WALKTURN) { /* Compute the rotation that rotates the projective plane in 4D without the trackball rotations. */ rotateall4d(pp->zeta,pp->eta,pp->theta,mat); u = pp->umove; v = pp->vmove; cu = cos(u); su = sin(u); c2u = cos(2.0*u); s2u = sin(2.0*u); sv2 = sin(0.5*v); cv4 = cos(0.25*v); sv4 = sin(0.25*v); xx[0] = 0.5*s2u*sv4*sv4; xx[1] = 0.5*su*sv2; xx[2] = 0.5*cu*sv2; xx[3] = 0.5*(su*su*sv4*sv4-cv4*cv4); /* Avoid degenerate tangential plane basis vectors. */ if (v < FLT_EPSILON) v = FLT_EPSILON; cv2 = cos(0.5*v); sv2 = sin(0.5*v); sv4 = sin(0.25*v); xxu[0] = c2u*sv4*sv4; xxu[1] = 0.5*cu*sv2; xxu[2] = -0.5*su*sv2; xxu[3] = 0.5*s2u*sv4*sv4; xxv[0] = 0.125*s2u*sv2; xxv[1] = 0.25*su*cv2; xxv[2] = 0.25*cu*cv2; xxv[3] = 0.125*(su*su+1.0)*sv2; for (l=0; l<4; l++) { y[l] = (mat[l][0]*xx[0]+mat[l][1]*xx[1]+ mat[l][2]*xx[2]+mat[l][3]*xx[3]); yu[l] = (mat[l][0]*xxu[0]+mat[l][1]*xxu[1]+ mat[l][2]*xxu[2]+mat[l][3]*xxu[3]); yv[l] = (mat[l][0]*xxv[0]+mat[l][1]*xxv[1]+ mat[l][2]*xxv[2]+mat[l][3]*xxv[3]); } if (pp->projection_4d == DISP_4D_ORTHOGRAPHIC) { for (l=0; l<3; l++) { p[l] = y[l]+pp->offset4d[l]; pu[l] = yu[l]; pv[l] = yv[l]; } } else { s = y[3]+pp->offset4d[3]; q = 1.0/s; t = q*q; for (l=0; l<3; l++) { r = y[l]+pp->offset4d[l]; p[l] = r*q; pu[l] = (yu[l]*s-r*yu[3])*t; pv[l] = (yv[l]*s-r*yv[3])*t; } } n[0] = pu[1]*pv[2]-pu[2]*pv[1]; n[1] = pu[2]*pv[0]-pu[0]*pv[2]; n[2] = pu[0]*pv[1]-pu[1]*pv[0]; t = 1.0/(pp->side*4.0*sqrt(n[0]*n[0]+n[1]*n[1]+n[2]*n[2])); n[0] *= t; n[1] *= t; n[2] *= t; pm[0] = pu[0]*pp->dumove+pv[0]*pp->dvmove; pm[1] = pu[1]*pp->dumove+pv[1]*pp->dvmove; pm[2] = pu[2]*pp->dumove+pv[2]*pp->dvmove; t = 1.0/(4.0*sqrt(pm[0]*pm[0]+pm[1]*pm[1]+pm[2]*pm[2])); pm[0] *= t; pm[1] *= t; pm[2] *= t; b[0] = n[1]*pm[2]-n[2]*pm[1]; b[1] = n[2]*pm[0]-n[0]*pm[2]; b[2] = n[0]*pm[1]-n[1]*pm[0]; t = 1.0/(4.0*sqrt(b[0]*b[0]+b[1]*b[1]+b[2]*b[2])); b[0] *= t; b[1] *= t; b[2] *= t; /* Compute alpha, beta, delta from the three basis vectors. | -b[0] -b[1] -b[2] | m = | n[0] n[1] n[2] | | -pm[0] -pm[1] -pm[2] | */ pp->alpha = atan2(-n[2],-pm[2])*180/M_PI; pp->beta = atan2(-b[2],sqrt(b[0]*b[0]+b[1]*b[1]))*180/M_PI; pp->delta = atan2(b[1],-b[0])*180/M_PI; /* Compute the rotation that rotates the projective plane in 4D. */ rotateall(pp->alpha,pp->beta,pp->delta,pp->zeta,pp->eta,pp->theta,mat); u = pp->umove; v = pp->vmove; cu = cos(u); su = sin(u); s2u = sin(2.0*u); sv2 = sin(0.5*v); cv4 = cos(0.25*v); sv4 = sin(0.25*v); xx[0] = 0.5*s2u*sv4*sv4; xx[1] = 0.5*su*sv2; xx[2] = 0.5*cu*sv2; xx[3] = 0.5*(su*su*sv4*sv4-cv4*cv4); for (l=0; l<4; l++) { r = 0.0; for (m=0; m<4; m++) r += mat[l][m]*xx[m]; y[l] = r; } if (pp->projection_4d == DISP_4D_ORTHOGRAPHIC) { for (l=0; l<3; l++) p[l] = y[l]+pp->offset4d[l]; } else { s = y[3]+pp->offset4d[3]; for (l=0; l<3; l++) p[l] = (y[l]+pp->offset4d[l])/s; } pp->offset3d[0] = -p[0]; pp->offset3d[1] = -p[1]-DELTAY; pp->offset3d[2] = -p[2]; } else { /* Compute the rotation that rotates the projective plane in 4D, including the trackball rotations. */ rotateall(pp->alpha,pp->beta,pp->delta,pp->zeta,pp->eta,pp->theta,r1); gltrackball_get_quaternion(pp->trackballs[0],q1); gltrackball_get_quaternion(pp->trackballs[1],q2); quats_to_rotmat(q1,q2,r2); mult_rotmat(r2,r1,mat); } /* Project the points from 4D to 3D. */ for (i=0; i<=NUMV; i++) { for (j=0; j<=NUMU; j++) { o = i*(NUMU+1)+j; for (l=0; l<4; l++) { y[l] = (mat[l][0]*pp->x[o][0]+mat[l][1]*pp->x[o][1]+ mat[l][2]*pp->x[o][2]+mat[l][3]*pp->x[o][3]); yu[l] = (mat[l][0]*pp->xu[o][0]+mat[l][1]*pp->xu[o][1]+ mat[l][2]*pp->xu[o][2]+mat[l][3]*pp->xu[o][3]); yv[l] = (mat[l][0]*pp->xv[o][0]+mat[l][1]*pp->xv[o][1]+ mat[l][2]*pp->xv[o][2]+mat[l][3]*pp->xv[o][3]); } if (pp->projection_4d == DISP_4D_ORTHOGRAPHIC) { for (l=0; l<3; l++) { pp->pp[o][l] = (y[l]+pp->offset4d[l])+pp->offset3d[l]; pu[l] = yu[l]; pv[l] = yv[l]; } } else { s = y[3]+pp->offset4d[3]; q = 1.0/s; t = q*q; for (l=0; l<3; l++) { r = y[l]+pp->offset4d[l]; pp->pp[o][l] = r*q+pp->offset3d[l]; pu[l] = (yu[l]*s-r*yu[3])*t; pv[l] = (yv[l]*s-r*yv[3])*t; } } pp->pn[o][0] = pu[1]*pv[2]-pu[2]*pv[1]; pp->pn[o][1] = pu[2]*pv[0]-pu[0]*pv[2]; pp->pn[o][2] = pu[0]*pv[1]-pu[1]*pv[0]; t = 1.0/sqrt(pp->pn[o][0]*pp->pn[o][0]+pp->pn[o][1]*pp->pn[o][1]+ pp->pn[o][2]*pp->pn[o][2]); pp->pn[o][0] *= t; pp->pn[o][1] *= t; pp->pn[o][2] *= t; } } if (pp->colors == COLORS_TWOSIDED) { glColor3fv(mat_diff_red); if (pp->display_mode == DISP_TRANSPARENT) { glMaterialfv(GL_FRONT,GL_AMBIENT_AND_DIFFUSE,mat_diff_trans_red); glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,mat_diff_trans_green); } else { glMaterialfv(GL_FRONT,GL_AMBIENT_AND_DIFFUSE,mat_diff_red); glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,mat_diff_green); } } glBindTexture(GL_TEXTURE_2D,pp->tex_name); if (pp->appearance != APPEARANCE_DIRECTION_BANDS) { for (i=0; iappearance == APPEARANCE_DISTANCE_BANDS && ((i & (NUMB-1)) >= NUMB/4) && ((i & (NUMB-1)) < 3*NUMB/4)) continue; if (pp->display_mode == DISP_WIREFRAME) glBegin(GL_QUAD_STRIP); else glBegin(GL_TRIANGLE_STRIP); for (j=0; j<=NUMU; j++) { for (k=0; k<=1; k++) { l = (i+k); m = j; o = l*(NUMU+1)+m; glNormal3fv(pp->pn[o]); glTexCoord2fv(pp->tex[o]); if (pp->colors != COLORS_TWOSIDED) { glColor3fv(pp->col[o]); glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,pp->col[o]); } glVertex3fv(pp->pp[o]); polys++; } } glEnd(); } } else /* pp->appearance == APPEARANCE_DIRECTION_BANDS */ { for (j=0; j= NUMB/2) continue; if (pp->display_mode == DISP_WIREFRAME) glBegin(GL_QUAD_STRIP); else glBegin(GL_TRIANGLE_STRIP); for (i=0; i<=NUMV; i++) { for (k=0; k<=1; k++) { l = i; m = (j+k); o = l*(NUMU+1)+m; glNormal3fv(pp->pn[o]); glTexCoord2fv(pp->tex[o]); if (pp->colors != COLORS_TWOSIDED) { glColor3fv(pp->col[o]); glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,pp->col[o]); } glVertex3fv(pp->pp[o]); polys++; } } glEnd(); } } polys /= 2; return polys; } /* Generate a texture image that shows the orientation reversal. */ static void gen_texture(ModeInfo *mi) { projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)]; glGenTextures(1,&pp->tex_name); glBindTexture(GL_TEXTURE_2D,pp->tex_name); glPixelStorei(GL_UNPACK_ALIGNMENT,1); glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_WRAP_S,GL_REPEAT); glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_WRAP_T,GL_REPEAT); glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_MAG_FILTER,GL_LINEAR); glTexParameterf(GL_TEXTURE_2D,GL_TEXTURE_MIN_FILTER,GL_LINEAR); glTexEnvf(GL_TEXTURE_ENV,GL_TEXTURE_ENV_MODE,GL_MODULATE); glTexImage2D(GL_TEXTURE_2D,0,GL_RGB,TEX_DIMENSION,TEX_DIMENSION,0, GL_LUMINANCE,GL_UNSIGNED_BYTE,texture); } static void init(ModeInfo *mi) { static const GLfloat light_ambient[] = { 0.0, 0.0, 0.0, 1.0 }; static const GLfloat light_diffuse[] = { 1.0, 1.0, 1.0, 1.0 }; static const GLfloat light_specular[] = { 1.0, 1.0, 1.0, 1.0 }; static const GLfloat light_position[] = { 1.0, 1.0, 1.0, 0.0 }; static const GLfloat mat_specular[] = { 1.0, 1.0, 1.0, 1.0 }; projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)]; if (walk_speed == 0.0) walk_speed = 20.0; if (pp->view == VIEW_TURN) { pp->alpha = frand(360.0); pp->beta = frand(360.0); pp->delta = frand(360.0); pp->zeta = 0.0; pp->eta = 0.0; pp->theta = 0.0; } else { pp->alpha = 0.0; pp->beta = 0.0; pp->delta = 0.0; pp->zeta = 120.0; pp->eta = 180.0; pp->theta = 90.0; } pp->umove = frand(2.0*M_PI); pp->vmove = frand(2.0*M_PI); pp->dumove = 0.0; pp->dvmove = 0.0; pp->side = 1; if (sin(walk_direction*M_PI/180.0) >= 0.0) pp->dir = 1; else pp->dir = -1; pp->offset4d[0] = 0.0; pp->offset4d[1] = 0.0; pp->offset4d[2] = 0.0; pp->offset4d[3] = 1.2; pp->offset3d[0] = 0.0; pp->offset3d[1] = 0.0; pp->offset3d[2] = -1.2; pp->offset3d[3] = 0.0; gen_texture(mi); setup_projective_plane(mi,0.0,2.0*M_PI,0.0,2.0*M_PI); if (pp->marks) glEnable(GL_TEXTURE_2D); else glDisable(GL_TEXTURE_2D); glMatrixMode(GL_PROJECTION); glLoadIdentity(); if (pp->projection_3d == DISP_3D_PERSPECTIVE || pp->view == VIEW_WALK || pp->view == VIEW_WALKTURN) { if (pp->view == VIEW_WALK || pp->view == VIEW_WALKTURN) gluPerspective(60.0,1.0,0.01,10.0); else gluPerspective(60.0,1.0,0.1,10.0); } else { glOrtho(-0.6,0.6,-0.6,0.6,0.1,10.0); } glMatrixMode(GL_MODELVIEW); glLoadIdentity(); # ifdef HAVE_JWZGLES /* #### glPolygonMode other than GL_FILL unimplemented */ if (pp->display_mode == DISP_WIREFRAME) pp->display_mode = DISP_SURFACE; # endif if (pp->display_mode == DISP_SURFACE) { glEnable(GL_DEPTH_TEST); glDepthFunc(GL_LESS); glShadeModel(GL_SMOOTH); glPolygonMode(GL_FRONT_AND_BACK,GL_FILL); glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,GL_TRUE); glEnable(GL_LIGHTING); glEnable(GL_LIGHT0); glLightfv(GL_LIGHT0,GL_AMBIENT,light_ambient); glLightfv(GL_LIGHT0,GL_DIFFUSE,light_diffuse); glLightfv(GL_LIGHT0,GL_SPECULAR,light_specular); glLightfv(GL_LIGHT0,GL_POSITION,light_position); glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,mat_specular); glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,50.0); glDepthMask(GL_TRUE); glDisable(GL_BLEND); } else if (pp->display_mode == DISP_TRANSPARENT) { glDisable(GL_DEPTH_TEST); glShadeModel(GL_SMOOTH); glPolygonMode(GL_FRONT_AND_BACK,GL_FILL); glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,GL_TRUE); glEnable(GL_LIGHTING); glEnable(GL_LIGHT0); glLightfv(GL_LIGHT0,GL_AMBIENT,light_ambient); glLightfv(GL_LIGHT0,GL_DIFFUSE,light_diffuse); glLightfv(GL_LIGHT0,GL_SPECULAR,light_specular); glLightfv(GL_LIGHT0,GL_POSITION,light_position); glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,mat_specular); glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,50.0); glDepthMask(GL_FALSE); glEnable(GL_BLEND); glBlendFunc(GL_SRC_ALPHA,GL_ONE); } else /* pp->display_mode == DISP_WIREFRAME */ { glDisable(GL_DEPTH_TEST); glShadeModel(GL_FLAT); glPolygonMode(GL_FRONT_AND_BACK,GL_LINE); glDisable(GL_LIGHTING); glDisable(GL_LIGHT0); glDisable(GL_BLEND); } } /* Redisplay the Klein bottle. */ static void display_projectiveplane(ModeInfo *mi) { projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)]; if (!pp->button_pressed) { if (pp->view == VIEW_TURN) { pp->alpha += speed_wx * pp->speed_scale; if (pp->alpha >= 360.0) pp->alpha -= 360.0; pp->beta += speed_wy * pp->speed_scale; if (pp->beta >= 360.0) pp->beta -= 360.0; pp->delta += speed_wz * pp->speed_scale; if (pp->delta >= 360.0) pp->delta -= 360.0; pp->zeta += speed_xy * pp->speed_scale; if (pp->zeta >= 360.0) pp->zeta -= 360.0; pp->eta += speed_xz * pp->speed_scale; if (pp->eta >= 360.0) pp->eta -= 360.0; pp->theta += speed_yz * pp->speed_scale; if (pp->theta >= 360.0) pp->theta -= 360.0; } if (pp->view == VIEW_WALKTURN) { pp->zeta += speed_xy * pp->speed_scale; if (pp->zeta >= 360.0) pp->zeta -= 360.0; pp->eta += speed_xz * pp->speed_scale; if (pp->eta >= 360.0) pp->eta -= 360.0; pp->theta += speed_yz * pp->speed_scale; if (pp->theta >= 360.0) pp->theta -= 360.0; } if (pp->view == VIEW_WALK || pp->view == VIEW_WALKTURN) { pp->dvmove = (pp->dir*sin(walk_direction*M_PI/180.0)* walk_speed*M_PI/4096.0); pp->vmove += pp->dvmove; if (pp->vmove > 2.0*M_PI) { pp->vmove = 4.0*M_PI-pp->vmove; pp->umove = pp->umove-M_PI; if (pp->umove < 0.0) pp->umove += 2.0*M_PI; pp->side = -pp->side; pp->dir = -pp->dir; pp->dvmove = -pp->dvmove; } if (pp->vmove < 0.0) { pp->vmove = -pp->vmove; pp->umove = pp->umove-M_PI; if (pp->umove < 0.0) pp->umove += 2.0*M_PI; pp->dir = -pp->dir; pp->dvmove = -pp->dvmove; } pp->dumove = cos(walk_direction*M_PI/180.0)*walk_speed*M_PI/4096.0; pp->umove += pp->dumove; if (pp->umove >= 2.0*M_PI) pp->umove -= 2.0*M_PI; if (pp->umove < 0.0) pp->umove += 2.0*M_PI; } } glMatrixMode(GL_PROJECTION); glLoadIdentity(); if (pp->projection_3d == DISP_3D_PERSPECTIVE || pp->view == VIEW_WALK || pp->view == VIEW_WALKTURN) { if (pp->view == VIEW_WALK || pp->view == VIEW_WALKTURN) gluPerspective(60.0,pp->aspect,0.01,10.0); else gluPerspective(60.0,pp->aspect,0.1,10.0); } else { if (pp->aspect >= 1.0) glOrtho(-0.6*pp->aspect,0.6*pp->aspect,-0.6,0.6,0.1,10.0); else glOrtho(-0.6,0.6,-0.6/pp->aspect,0.6/pp->aspect,0.1,10.0); } glMatrixMode(GL_MODELVIEW); glLoadIdentity(); mi->polygon_count = projective_plane(mi,0.0,2.0*M_PI,0.0,2.0*M_PI); } ENTRYPOINT void reshape_projectiveplane(ModeInfo *mi, int width, int height) { projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)]; pp->WindW = (GLint)width; pp->WindH = (GLint)height; glViewport(0,0,width,height); pp->aspect = (GLfloat)width/(GLfloat)height; } ENTRYPOINT Bool projectiveplane_handle_event(ModeInfo *mi, XEvent *event) { projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)]; KeySym sym = 0; char c = 0; if (event->xany.type == KeyPress || event->xany.type == KeyRelease) XLookupString (&event->xkey, &c, 1, &sym, 0); if (event->xany.type == ButtonPress && event->xbutton.button == Button1) { pp->button_pressed = True; gltrackball_start(pp->trackballs[pp->current_trackball], event->xbutton.x, event->xbutton.y, MI_WIDTH(mi), MI_HEIGHT(mi)); return True; } else if (event->xany.type == ButtonRelease && event->xbutton.button == Button1) { pp->button_pressed = False; return True; } else if (event->xany.type == KeyPress) { if (sym == XK_Shift_L || sym == XK_Shift_R) { pp->current_trackball = 1; if (pp->button_pressed) gltrackball_start(pp->trackballs[pp->current_trackball], event->xbutton.x, event->xbutton.y, MI_WIDTH(mi), MI_HEIGHT(mi)); return True; } } else if (event->xany.type == KeyRelease) { if (sym == XK_Shift_L || sym == XK_Shift_R) { pp->current_trackball = 0; if (pp->button_pressed) gltrackball_start(pp->trackballs[pp->current_trackball], event->xbutton.x, event->xbutton.y, MI_WIDTH(mi), MI_HEIGHT(mi)); return True; } } else if (event->xany.type == MotionNotify && pp->button_pressed) { gltrackball_track(pp->trackballs[pp->current_trackball], event->xmotion.x, event->xmotion.y, MI_WIDTH(mi), MI_HEIGHT(mi)); return True; } return False; } /* *----------------------------------------------------------------------------- *----------------------------------------------------------------------------- * Xlock hooks. *----------------------------------------------------------------------------- *----------------------------------------------------------------------------- */ /* *----------------------------------------------------------------------------- * Initialize projectiveplane. Called each time the window changes. *----------------------------------------------------------------------------- */ ENTRYPOINT void init_projectiveplane(ModeInfo *mi) { projectiveplanestruct *pp; MI_INIT(mi, projectiveplane); pp = &projectiveplane[MI_SCREEN(mi)]; pp->trackballs[0] = gltrackball_init(True); pp->trackballs[1] = gltrackball_init(True); pp->current_trackball = 0; pp->button_pressed = False; /* Set the display mode. */ if (!strcasecmp(mode,"random")) { pp->display_mode = random() % NUM_DISPLAY_MODES; } else if (!strcasecmp(mode,"wireframe")) { pp->display_mode = DISP_WIREFRAME; } else if (!strcasecmp(mode,"surface")) { pp->display_mode = DISP_SURFACE; } else if (!strcasecmp(mode,"transparent")) { pp->display_mode = DISP_TRANSPARENT; } else { pp->display_mode = random() % NUM_DISPLAY_MODES; } /* Orientation marks don't make sense in wireframe mode. */ pp->marks = marks; if (pp->display_mode == DISP_WIREFRAME) pp->marks = False; /* Set the appearance. */ if (!strcasecmp(appear,"random")) { pp->appearance = random() % NUM_APPEARANCES; } else if (!strcasecmp(appear,"solid")) { pp->appearance = APPEARANCE_SOLID; } else if (!strcasecmp(appear,"distance-bands")) { pp->appearance = APPEARANCE_DISTANCE_BANDS; } else if (!strcasecmp(appear,"direction-bands")) { pp->appearance = APPEARANCE_DIRECTION_BANDS; } else { pp->appearance = random() % NUM_APPEARANCES; } /* Set the color mode. */ if (!strcasecmp(color_mode,"random")) { pp->colors = random() % NUM_COLORS; } else if (!strcasecmp(color_mode,"two-sided")) { pp->colors = COLORS_TWOSIDED; } else if (!strcasecmp(color_mode,"distance")) { pp->colors = COLORS_DISTANCE; } else if (!strcasecmp(color_mode,"direction")) { pp->colors = COLORS_DIRECTION; } else if (!strcasecmp(color_mode,"depth")) { pp->colors = COLORS_DEPTH; } else { pp->colors = random() % NUM_COLORS; } /* Set the view mode. */ if (!strcasecmp(view_mode,"random")) { pp->view = random() % NUM_VIEW_MODES; } else if (!strcasecmp(view_mode,"walk")) { pp->view = VIEW_WALK; } else if (!strcasecmp(view_mode,"turn")) { pp->view = VIEW_TURN; } else if (!strcasecmp(view_mode,"walk-turn")) { pp->view = VIEW_WALKTURN; } else { pp->view = random() % NUM_VIEW_MODES; } /* Set the 3d projection mode. */ if (!strcasecmp(proj_3d,"random")) { /* Orthographic projection only makes sense in turn mode. */ if (pp->view == VIEW_TURN) pp->projection_3d = random() % NUM_DISP_3D_MODES; else pp->projection_3d = DISP_3D_PERSPECTIVE; } else if (!strcasecmp(proj_3d,"perspective")) { pp->projection_3d = DISP_3D_PERSPECTIVE; } else if (!strcasecmp(proj_3d,"orthographic")) { pp->projection_3d = DISP_3D_ORTHOGRAPHIC; } else { /* Orthographic projection only makes sense in turn mode. */ if (pp->view == VIEW_TURN) pp->projection_3d = random() % NUM_DISP_3D_MODES; else pp->projection_3d = DISP_3D_PERSPECTIVE; } /* Set the 4d projection mode. */ if (!strcasecmp(proj_4d,"random")) { pp->projection_4d = random() % NUM_DISP_4D_MODES; } else if (!strcasecmp(proj_4d,"perspective")) { pp->projection_4d = DISP_4D_PERSPECTIVE; } else if (!strcasecmp(proj_4d,"orthographic")) { pp->projection_4d = DISP_4D_ORTHOGRAPHIC; } else { pp->projection_4d = random() % NUM_DISP_4D_MODES; } /* Modify the speeds to a useful range in walk-and-turn mode. */ if (pp->view == VIEW_WALKTURN) { speed_wx *= 0.2; speed_wy *= 0.2; speed_wz *= 0.2; speed_xy *= 0.2; speed_xz *= 0.2; speed_yz *= 0.2; } /* make multiple screens rotate at slightly different rates. */ pp->speed_scale = 0.9 + frand(0.3); if ((pp->glx_context = init_GL(mi)) != NULL) { reshape_projectiveplane(mi,MI_WIDTH(mi),MI_HEIGHT(mi)); glDrawBuffer(GL_BACK); init(mi); } else { MI_CLEARWINDOW(mi); } } /* *----------------------------------------------------------------------------- * Called by the mainline code periodically to update the display. *----------------------------------------------------------------------------- */ ENTRYPOINT void draw_projectiveplane(ModeInfo *mi) { Display *display = MI_DISPLAY(mi); Window window = MI_WINDOW(mi); projectiveplanestruct *pp; if (projectiveplane == NULL) return; pp = &projectiveplane[MI_SCREEN(mi)]; MI_IS_DRAWN(mi) = True; if (!pp->glx_context) return; glXMakeCurrent(display, window, *pp->glx_context); glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT); glLoadIdentity(); display_projectiveplane(mi); if (MI_IS_FPS(mi)) do_fps (mi); glFlush(); glXSwapBuffers(display,window); } #ifndef STANDALONE ENTRYPOINT void change_projectiveplane(ModeInfo *mi) { projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)]; if (!pp->glx_context) return; glXMakeCurrent(MI_DISPLAY(mi), MI_WINDOW(mi), *pp->glx_context); init(mi); } #endif /* !STANDALONE */ ENTRYPOINT void free_projectiveplane(ModeInfo *mi) { projectiveplanestruct *pp = &projectiveplane[MI_SCREEN(mi)]; if (!pp->glx_context) return; glXMakeCurrent (MI_DISPLAY(mi), MI_WINDOW(mi), *pp->glx_context); gltrackball_free (pp->trackballs[0]); gltrackball_free (pp->trackballs[1]); if (pp->tex_name) glDeleteTextures (1, &pp->tex_name); } XSCREENSAVER_MODULE ("ProjectivePlane", projectiveplane) #endif /* USE_GL */