/* klein --- Shows a Klein bottle that rotates in 4d or on which you can walk */ #if 0 static const char sccsid[] = "@(#)klein.c 1.1 08/10/04 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 - 08/10/04: Initial version * C. Steger - 09/08/03: Changes to the parameter handling * C. Steger - 13/12/25: Added the squeezed torus Klein bottle * C. Steger - 14/10/03: Moved the curlicue texture to curlicue.h */ /* * This program shows three different Klein bottles in 4d: the figure-8 Klein * bottle, the squeezed torus Klein bottle, or the Lawson Klein bottle. You * can walk on the Klein bottle, see it turn in 4d, or walk on it while it * turns in 4d. The figure-8 Klein bottle is well known in its 3d form. The * 4d form used in this program is an extension of the 3d form to 4d that * does not intersect itself in 4d (which can be seen in the depth colors * mode). The squeezed torus Klein bottle also does not intersect itself in * 4d (which can be seen in the depth colors mode). The Lawson Klein bottle, * on the other hand, does intersect itself in 4d. Its primary use is that * it has a nice appearance for walking and for turning in 3d. The Klein * bottle 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 Klein bottle. * While walking on the Klein bottle, you will notice that the orientation * of the curling arrows changes (which it must because the Klein bottle is * non-orientable). The program projects the 4d Klein bottle to 3d using * either a perspective or an orthographic projection. Which of the two * alternatives looks more appealing depends on the viewing mode and the * Klein bottle. For example, the Lawson Klein bottle looks nicest when * projected perspectively. The figure-8 Klein bottle, on the other * hand, looks nicer while walking when projected orthographically from 4d. * For the squeezed torus Klein bottle, both projection modes give equally * acceptable projections. The projected Klein bottle can then be projected * to the screen either perspectively or orthographically. When using the * walking modes, perspective projection to the screen should be used. There * are three display modes for the Klein bottle: mesh (wireframe), solid, or * transparent. Furthermore, the appearance of the Klein bottle can be as * a solid object or as a set of see-through bands. Finally, the colors * with with the Klein bottle is drawn can be set to two-sided, rainbow, or * depth. In the first case, the Klein bottle is drawn with red on one * "side" and green on the "other side". Of course, the Klein bottle only * has one side, so the color jumps from red to green along a curve on the * surface of the Klein bottle. This mode enables you to see that the Klein * bottle is non-orientable. The second mode draws the Klein bottle with * fully saturated rainbow colors. This gives a very nice effect when * combined with the see-through bands mode or with the orientation markers * drawn. The third mode draws the Klein bottle with colors that are chosen * according to the 4d "depth" of the points. This mode enables you to see * that the figure-8 and squeezed torus Klein bottles do not intersect * themselves in 4d, while the Lawson Klein bottle does intersect itself. * The rotation speed for each of the six planes around which the Klein * bottle 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 Klein bottle and the walking speed can be chosen. * 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 KLEIN_BOTTLE_FIGURE_8 0 #define KLEIN_BOTTLE_SQUEEZED_TORUS 1 #define KLEIN_BOTTLE_LAWSON 2 #define NUM_KLEIN_BOTTLES 3 #define DISP_WIREFRAME 0 #define DISP_SURFACE 1 #define DISP_TRANSPARENT 2 #define NUM_DISPLAY_MODES 3 #define APPEARANCE_SOLID 0 #define APPEARANCE_BANDS 1 #define NUM_APPEARANCES 2 #define COLORS_TWOSIDED 0 #define COLORS_RAINBOW 1 #define COLORS_DEPTH 2 #define NUM_COLORS 3 #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_KLEIN_BOTTLE "random" #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 "7.0" #define DEF_WALK_SPEED "20.0" #ifdef STANDALONE # define DEFAULTS "*delay: 10000 \n" \ "*showFPS: False \n" \ # define release_klein 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" #ifdef USE_MODULES ModStruct klein_description = {"klein", "init_klein", "draw_klein", NULL, "draw_klein", "change_klein", NULL, &klein_opts, 25000, 1, 1, 1, 1.0, 4, "", "Rotate a Klein bottle in 4d or walk on it", 0, NULL}; #endif static char *klein_bottle; 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[] = { {"-klein-bottle", ".kleinBottle", XrmoptionSepArg, 0 }, {"-figure-8", ".kleinBottle", XrmoptionNoArg, "figure-8" }, {"-squeezed-torus", ".kleinBottle", XrmoptionNoArg, "squeezed-torus" }, {"-lawson", ".kleinBottle", XrmoptionNoArg, "lawson" }, {"-mode", ".displayMode", XrmoptionSepArg, 0 }, {"-wireframe", ".displayMode", XrmoptionNoArg, "wireframe" }, {"-surface", ".displayMode", XrmoptionNoArg, "surface" }, {"-transparent", ".displayMode", XrmoptionNoArg, "transparent" }, {"-appearance", ".appearance", XrmoptionSepArg, 0 }, {"-solid", ".appearance", XrmoptionNoArg, "solid" }, {"-bands", ".appearance", XrmoptionNoArg, "bands" }, {"-colors", ".colors", XrmoptionSepArg, 0 }, {"-twosided", ".colors", XrmoptionNoArg, "two-sided" }, {"-rainbow", ".colors", XrmoptionNoArg, "rainbow" }, {"-depth", ".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[] = { { &klein_bottle, "kleinBottle", "KleinBottle", DEF_KLEIN_BOTTLE, t_String }, { &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 klein_opts = {sizeof opts / sizeof opts[0], opts, sizeof vars / sizeof vars[0], vars, NULL}; /* Radius of the figure-8 Klein bottle */ #define FIGURE_8_RADIUS 2.0 /* Radius of the squeezed torus Klein bottle */ #define SQUEEZED_TORUS_RADIUS 2.0 /* Offset by which we walk above the Klein bottle */ #define DELTAY 0.02 /* Number of subdivisions of the Klein bottle */ #define NUMU 128 #define NUMV 128 /* Number of subdivisions per band */ #define NUMB 8 typedef struct { GLint WindH, WindW; GLXContext *glx_context; /* Options */ int bottle_type; int display_mode; int appearance; int colors; int view; 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; /* The viewing offset in 4d */ float offset4d[4]; /* The viewing offset in 3d */ float offset3d[4]; /* The 4d coordinates of the Klein bottle 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 Klein bottle */ float col[(NUMU+1)*(NUMV+1)][4]; /* The precomputed texture coordinates of the Klein bottle */ 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; } kleinstruct; static kleinstruct *klein = (kleinstruct *) 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(kleinstruct *kb, double angle, float col[4]) { int s; double t; if (kb->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 (kb->display_mode == DISP_TRANSPARENT) col[3] = 0.7; else col[3] = 1.0; } /* Set up the figure-8 Klein bottle coordinates, colors, and texture. */ static void setup_figure8(ModeInfo *mi, double umin, double umax, double vmin, double vmax) { int i, j, k, l; double u, v, ur, vr; double cu, su, cv, sv, cv2, sv2, c2u, s2u; kleinstruct *kb = &klein[MI_SCREEN(mi)]; ur = umax-umin; vr = vmax-vmin; for (i=0; i<=NUMU; i++) { for (j=0; j<=NUMV; j++) { k = i*(NUMV+1)+j; u = -ur*j/NUMU+umin; v = vr*i/NUMV+vmin; if (kb->colors == COLORS_DEPTH) color(kb,(cos(u)+1.0)*M_PI*2.0/3.0,kb->col[k]); else color(kb,v,kb->col[k]); kb->tex[k][0] = -32*u/(2.0*M_PI); kb->tex[k][1] = 32*v/(2.0*M_PI); cu = cos(u); su = sin(u); cv = cos(v); sv = sin(v); cv2 = cos(0.5*v); sv2 = sin(0.5*v); c2u = cos(2.0*u); s2u = sin(2.0*u); kb->x[k][0] = (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*cv; kb->x[k][1] = (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*sv; kb->x[k][2] = su*sv2+s2u*cv2; kb->x[k][3] = cu; kb->xu[k][0] = (cu*cv2-2.0*c2u*sv2)*cv; kb->xu[k][1] = (cu*cv2-2.0*c2u*sv2)*sv; kb->xu[k][2] = cu*sv2+2.0*c2u*cv2; kb->xu[k][3] = -su; kb->xv[k][0] = ((-0.5*su*sv2-0.5*s2u*cv2)*cv- (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*sv); kb->xv[k][1] = ((-0.5*su*sv2-0.5*s2u*cv2)*sv+ (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*cv); kb->xv[k][2] = 0.5*su*cv2-0.5*s2u*sv2; kb->xv[k][3] = 0.0; for (l=0; l<4; l++) { kb->x[k][l] /= FIGURE_8_RADIUS+1.25; kb->xu[k][l] /= FIGURE_8_RADIUS+1.25; kb->xv[k][l] /= FIGURE_8_RADIUS+1.25; } } } } /* Set up the squeezed torus Klein bottle coordinates, colors, and texture. */ static void setup_squeezed_torus(ModeInfo *mi, double umin, double umax, double vmin, double vmax) { int i, j, k, l; double u, v, ur, vr; double cu, su, cv, sv, cv2, sv2; kleinstruct *kb = &klein[MI_SCREEN(mi)]; ur = umax-umin; vr = vmax-vmin; for (i=0; i<=NUMU; i++) { for (j=0; j<=NUMV; j++) { k = i*(NUMV+1)+j; u = -ur*j/NUMU+umin; v = vr*i/NUMV+vmin; if (kb->colors == COLORS_DEPTH) color(kb,(sin(u)*sin(0.5*v)+1.0)*M_PI*2.0/3.0,kb->col[k]); else color(kb,v,kb->col[k]); kb->tex[k][0] = -32*u/(2.0*M_PI); kb->tex[k][1] = 32*v/(2.0*M_PI); cu = cos(u); su = sin(u); cv = cos(v); sv = sin(v); cv2 = cos(0.5*v); sv2 = sin(0.5*v); kb->x[k][0] = (SQUEEZED_TORUS_RADIUS+cu)*cv; kb->x[k][1] = (SQUEEZED_TORUS_RADIUS+cu)*sv; kb->x[k][2] = su*cv2; kb->x[k][3] = su*sv2; kb->xu[k][0] = -su*cv; kb->xu[k][1] = -su*sv; kb->xu[k][2] = cu*cv2; kb->xu[k][3] = cu*sv2; kb->xv[k][0] = -(SQUEEZED_TORUS_RADIUS+cu)*sv; kb->xv[k][1] = (SQUEEZED_TORUS_RADIUS+cu)*cv; kb->xv[k][2] = -0.5*su*sv2; kb->xv[k][3] = 0.5*su*cv2; for (l=0; l<4; l++) { kb->x[k][l] /= SQUEEZED_TORUS_RADIUS+1.25; kb->xu[k][l] /= SQUEEZED_TORUS_RADIUS+1.25; kb->xv[k][l] /= SQUEEZED_TORUS_RADIUS+1.25; } } } } /* Set up the Lawson Klein bottle coordinates, colors, and texture. */ static void setup_lawson(ModeInfo *mi, double umin, double umax, double vmin, double vmax) { int i, j, k; double u, v, ur, vr; double cu, su, cv, sv, cv2, sv2; kleinstruct *kb = &klein[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; u = -ur*j/NUMU+umin; v = vr*i/NUMV+vmin; if (kb->colors == COLORS_DEPTH) color(kb,(sin(u)*cos(0.5*v)+1.0)*M_PI*2.0/3.0,kb->col[k]); else color(kb,v,kb->col[k]); kb->tex[k][0] = -32*u/(2.0*M_PI); kb->tex[k][1] = 32*v/(2.0*M_PI); cu = cos(u); su = sin(u); cv = cos(v); sv = sin(v); cv2 = cos(0.5*v); sv2 = sin(0.5*v); kb->x[k][0] = cu*cv; kb->x[k][1] = cu*sv; kb->x[k][2] = su*sv2; kb->x[k][3] = su*cv2; kb->xu[k][0] = -su*cv; kb->xu[k][1] = -su*sv; kb->xu[k][2] = cu*sv2; kb->xu[k][3] = cu*cv2; kb->xv[k][0] = -cu*sv; kb->xv[k][1] = cu*cv; kb->xv[k][2] = su*cv2*0.5; kb->xv[k][3] = -su*sv2*0.5; } } } /* Draw a figure-8 Klein bottle projected into 3D. */ static int figure8(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, cv, sv, cv2, sv2, c2u, s2u; float q1[4], q2[4], r1[4][4], r2[4][4]; kleinstruct *kb = &klein[MI_SCREEN(mi)]; if (kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN) { /* Compute the rotation that rotates the Klein bottle in 4D without the trackball rotations. */ rotateall4d(kb->zeta,kb->eta,kb->theta,mat); u = kb->umove; v = kb->vmove; cu = cos(u); su = sin(u); cv = cos(v); sv = sin(v); cv2 = cos(0.5*v); sv2 = sin(0.5*v); c2u = cos(2.0*u); s2u = sin(2.0*u); xx[0] = (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*cv; xx[1] = (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*sv; xx[2] = su*sv2+s2u*cv2; xx[3] = cu; xxu[0] = (cu*cv2-2.0*c2u*sv2)*cv; xxu[1] = (cu*cv2-2.0*c2u*sv2)*sv; xxu[2] = cu*sv2+2.0*c2u*cv2; xxu[3] = -su; xxv[0] = ((-0.5*su*sv2-0.5*s2u*cv2)*cv- (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*sv); xxv[1] = ((-0.5*su*sv2-0.5*s2u*cv2)*sv+ (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*cv); xxv[2] = 0.5*su*cv2-0.5*s2u*sv2; xxv[3] = 0.0; for (l=0; l<4; l++) { xx[l] /= FIGURE_8_RADIUS+1.25; xxu[l] /= FIGURE_8_RADIUS+1.25; xxv[l] /= FIGURE_8_RADIUS+1.25; } 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 (kb->projection_4d == DISP_4D_ORTHOGRAPHIC) { for (l=0; l<3; l++) { p[l] = y[l]+kb->offset4d[l]; pu[l] = yu[l]; pv[l] = yv[l]; } } else { s = y[3]+kb->offset4d[3]; q = 1.0/s; t = q*q; for (l=0; l<3; l++) { r = y[l]+kb->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/(kb->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]*kb->dumove+pv[0]*kb->dvmove; pm[1] = pu[1]*kb->dumove+pv[1]*kb->dvmove; pm[2] = pu[2]*kb->dumove+pv[2]*kb->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] | */ kb->alpha = atan2(-n[2],-pm[2])*180/M_PI; kb->beta = atan2(-b[2],sqrt(b[0]*b[0]+b[1]*b[1]))*180/M_PI; kb->delta = atan2(b[1],-b[0])*180/M_PI; /* Compute the rotation that rotates the Klein bottle in 4D. */ rotateall(kb->alpha,kb->beta,kb->delta,kb->zeta,kb->eta,kb->theta,mat); u = kb->umove; v = kb->vmove; cu = cos(u); su = sin(u); cv = cos(v); sv = sin(v); cv2 = cos(0.5*v); sv2 = sin(0.5*v); /*c2u = cos(2.0*u);*/ s2u = sin(2.0*u); xx[0] = (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*cv; xx[1] = (su*cv2-s2u*sv2+FIGURE_8_RADIUS)*sv; xx[2] = su*sv2+s2u*cv2; xx[3] = cu; for (l=0; l<4; l++) xx[l] /= FIGURE_8_RADIUS+1.25; 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 (kb->projection_4d == DISP_4D_ORTHOGRAPHIC) { for (l=0; l<3; l++) p[l] = y[l]+kb->offset4d[l]; } else { s = y[3]+kb->offset4d[3]; for (l=0; l<3; l++) p[l] = (y[l]+kb->offset4d[l])/s; } kb->offset3d[0] = -p[0]; kb->offset3d[1] = -p[1]-DELTAY; kb->offset3d[2] = -p[2]; } else { /* Compute the rotation that rotates the Klein bottle in 4D, including the trackball rotations. */ rotateall(kb->alpha,kb->beta,kb->delta,kb->zeta,kb->eta,kb->theta,r1); gltrackball_get_quaternion(kb->trackballs[0],q1); gltrackball_get_quaternion(kb->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<=NUMU; i++) { for (j=0; j<=NUMV; j++) { o = i*(NUMV+1)+j; for (l=0; l<4; l++) { y[l] = (mat[l][0]*kb->x[o][0]+mat[l][1]*kb->x[o][1]+ mat[l][2]*kb->x[o][2]+mat[l][3]*kb->x[o][3]); yu[l] = (mat[l][0]*kb->xu[o][0]+mat[l][1]*kb->xu[o][1]+ mat[l][2]*kb->xu[o][2]+mat[l][3]*kb->xu[o][3]); yv[l] = (mat[l][0]*kb->xv[o][0]+mat[l][1]*kb->xv[o][1]+ mat[l][2]*kb->xv[o][2]+mat[l][3]*kb->xv[o][3]); } if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC) { for (l=0; l<3; l++) { kb->pp[o][l] = (y[l]+kb->offset4d[l])+kb->offset3d[l]; pu[l] = yu[l]; pv[l] = yv[l]; } } else { s = y[3]+kb->offset4d[3]; q = 1.0/s; t = q*q; for (l=0; l<3; l++) { r = y[l]+kb->offset4d[l]; kb->pp[o][l] = r*q+kb->offset3d[l]; pu[l] = (yu[l]*s-r*yu[3])*t; pv[l] = (yv[l]*s-r*yv[3])*t; } } kb->pn[o][0] = pu[1]*pv[2]-pu[2]*pv[1]; kb->pn[o][1] = pu[2]*pv[0]-pu[0]*pv[2]; kb->pn[o][2] = pu[0]*pv[1]-pu[1]*pv[0]; t = 1.0/sqrt(kb->pn[o][0]*kb->pn[o][0]+kb->pn[o][1]*kb->pn[o][1]+ kb->pn[o][2]*kb->pn[o][2]); kb->pn[o][0] *= t; kb->pn[o][1] *= t; kb->pn[o][2] *= t; } } if (kb->colors == COLORS_TWOSIDED) { glColor3fv(mat_diff_red); if (kb->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,kb->tex_name); for (i=0; iappearance == APPEARANCE_BANDS && ((i & (NUMB-1)) >= NUMB/2)) continue; if (kb->display_mode == DISP_WIREFRAME) glBegin(GL_QUAD_STRIP); else glBegin(GL_TRIANGLE_STRIP); for (j=0; j<=NUMV; j++) { for (k=0; k<=1; k++) { l = (i+k); m = j; o = l*(NUMV+1)+m; glNormal3fv(kb->pn[o]); glTexCoord2fv(kb->tex[o]); if (kb->colors != COLORS_TWOSIDED) { glColor3fv(kb->col[o]); glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,kb->col[o]); } glVertex3fv(kb->pp[o]); polys++; } } glEnd(); } polys /= 2; return polys; } /* Draw a squeezed torus Klein bottle projected into 3D. */ static int squeezed_torus(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, cv, sv, cv2, sv2; float q1[4], q2[4], r1[4][4], r2[4][4]; kleinstruct *kb = &klein[MI_SCREEN(mi)]; if (kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN) { /* Compute the rotation that rotates the Klein bottle in 4D without the trackball rotations. */ rotateall4d(kb->zeta,kb->eta,kb->theta,mat); u = kb->umove; v = kb->vmove; cu = cos(u); su = sin(u); cv = cos(v); sv = sin(v); cv2 = cos(0.5*v); sv2 = sin(0.5*v); xx[0] = (SQUEEZED_TORUS_RADIUS+cu)*cv; xx[1] = (SQUEEZED_TORUS_RADIUS+cu)*sv; xx[2] = su*cv2; xx[3] = su*sv2; xxu[0] = -su*cv; xxu[1] = -su*sv; xxu[2] = cu*cv2; xxu[3] = cu*sv2; xxv[0] = -(SQUEEZED_TORUS_RADIUS+cu)*sv; xxv[1] = (SQUEEZED_TORUS_RADIUS+cu)*cv; xxv[2] = -0.5*su*sv2; xxv[3] = 0.5*su*cv2; for (l=0; l<4; l++) { xx[l] /= SQUEEZED_TORUS_RADIUS+1.25; xxu[l] /= SQUEEZED_TORUS_RADIUS+1.25; xxv[l] /= SQUEEZED_TORUS_RADIUS+1.25; } 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 (kb->projection_4d == DISP_4D_ORTHOGRAPHIC) { for (l=0; l<3; l++) { p[l] = y[l]+kb->offset4d[l]; pu[l] = yu[l]; pv[l] = yv[l]; } } else { s = y[3]+kb->offset4d[3]; q = 1.0/s; t = q*q; for (l=0; l<3; l++) { r = y[l]+kb->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/(kb->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]*kb->dumove+pv[0]*kb->dvmove; pm[1] = pu[1]*kb->dumove+pv[1]*kb->dvmove; pm[2] = pu[2]*kb->dumove+pv[2]*kb->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] | */ kb->alpha = atan2(-n[2],-pm[2])*180/M_PI; kb->beta = atan2(-b[2],sqrt(b[0]*b[0]+b[1]*b[1]))*180/M_PI; kb->delta = atan2(b[1],-b[0])*180/M_PI; /* Compute the rotation that rotates the Klein bottle in 4D. */ rotateall(kb->alpha,kb->beta,kb->delta,kb->zeta,kb->eta,kb->theta,mat); u = kb->umove; v = kb->vmove; cu = cos(u); su = sin(u); cv = cos(v); sv = sin(v); cv2 = cos(0.5*v); sv2 = sin(0.5*v); xx[0] = (SQUEEZED_TORUS_RADIUS+cu)*cv; xx[1] = (SQUEEZED_TORUS_RADIUS+cu)*sv; xx[2] = su*cv2; xx[3] = su*sv2; for (l=0; l<4; l++) xx[l] /= SQUEEZED_TORUS_RADIUS+1.25; 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 (kb->projection_4d == DISP_4D_ORTHOGRAPHIC) { for (l=0; l<3; l++) p[l] = y[l]+kb->offset4d[l]; } else { s = y[3]+kb->offset4d[3]; for (l=0; l<3; l++) p[l] = (y[l]+kb->offset4d[l])/s; } kb->offset3d[0] = -p[0]; kb->offset3d[1] = -p[1]-DELTAY; kb->offset3d[2] = -p[2]; } else { /* Compute the rotation that rotates the Klein bottle in 4D, including the trackball rotations. */ rotateall(kb->alpha,kb->beta,kb->delta,kb->zeta,kb->eta,kb->theta,r1); gltrackball_get_quaternion(kb->trackballs[0],q1); gltrackball_get_quaternion(kb->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<=NUMU; i++) { for (j=0; j<=NUMV; j++) { o = i*(NUMV+1)+j; for (l=0; l<4; l++) { y[l] = (mat[l][0]*kb->x[o][0]+mat[l][1]*kb->x[o][1]+ mat[l][2]*kb->x[o][2]+mat[l][3]*kb->x[o][3]); yu[l] = (mat[l][0]*kb->xu[o][0]+mat[l][1]*kb->xu[o][1]+ mat[l][2]*kb->xu[o][2]+mat[l][3]*kb->xu[o][3]); yv[l] = (mat[l][0]*kb->xv[o][0]+mat[l][1]*kb->xv[o][1]+ mat[l][2]*kb->xv[o][2]+mat[l][3]*kb->xv[o][3]); } if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC) { for (l=0; l<3; l++) { kb->pp[o][l] = (y[l]+kb->offset4d[l])+kb->offset3d[l]; pu[l] = yu[l]; pv[l] = yv[l]; } } else { s = y[3]+kb->offset4d[3]; q = 1.0/s; t = q*q; for (l=0; l<3; l++) { r = y[l]+kb->offset4d[l]; kb->pp[o][l] = r*q+kb->offset3d[l]; pu[l] = (yu[l]*s-r*yu[3])*t; pv[l] = (yv[l]*s-r*yv[3])*t; } } kb->pn[o][0] = pu[1]*pv[2]-pu[2]*pv[1]; kb->pn[o][1] = pu[2]*pv[0]-pu[0]*pv[2]; kb->pn[o][2] = pu[0]*pv[1]-pu[1]*pv[0]; t = 1.0/sqrt(kb->pn[o][0]*kb->pn[o][0]+kb->pn[o][1]*kb->pn[o][1]+ kb->pn[o][2]*kb->pn[o][2]); kb->pn[o][0] *= t; kb->pn[o][1] *= t; kb->pn[o][2] *= t; } } if (kb->colors == COLORS_TWOSIDED) { glColor3fv(mat_diff_red); if (kb->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,kb->tex_name); for (i=0; iappearance == APPEARANCE_BANDS && ((i & (NUMB-1)) >= NUMB/2)) continue; if (kb->display_mode == DISP_WIREFRAME) glBegin(GL_QUAD_STRIP); else glBegin(GL_TRIANGLE_STRIP); for (j=0; j<=NUMV; j++) { for (k=0; k<=1; k++) { l = (i+k); m = j; o = l*(NUMV+1)+m; glNormal3fv(kb->pn[o]); glTexCoord2fv(kb->tex[o]); if (kb->colors != COLORS_TWOSIDED) { glColor3fv(kb->col[o]); glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,kb->col[o]); } glVertex3fv(kb->pp[o]); polys++; } } glEnd(); } polys /= 2; return polys; } /* Draw a Lawson Klein bottle projected into 3D. */ static int lawson(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 cu, su, cv, sv, cv2, sv2; double xx[4], xxu[4], xxv[4], y[4], yu[4], yv[4]; double q, r, s, t; float q1[4], q2[4], r1[4][4], r2[4][4]; kleinstruct *kb = &klein[MI_SCREEN(mi)]; if (kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN) { /* Compute the rotation that rotates the Klein bottle in 4D without the trackball rotations. */ rotateall4d(kb->zeta,kb->eta,kb->theta,mat); u = kb->umove; v = kb->vmove; cu = cos(u); su = sin(u); cv = cos(v); sv = sin(v); cv2 = cos(0.5*v); sv2 = sin(0.5*v); xx[0] = cu*cv; xx[1] = cu*sv; xx[2] = su*sv2; xx[3] = su*cv2; xxu[0] = -su*cv; xxu[1] = -su*sv; xxu[2] = cu*sv2; xxu[3] = cu*cv2; xxv[0] = -cu*sv; xxv[1] = cu*cv; xxv[2] = su*cv2*0.5; xxv[3] = -su*sv2*0.5; 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 (kb->projection_4d == DISP_4D_ORTHOGRAPHIC) { for (l=0; l<3; l++) { p[l] = y[l]+kb->offset4d[l]; pu[l] = yu[l]; pv[l] = yv[l]; } } else { s = y[3]+kb->offset4d[3]; q = 1.0/s; t = q*q; for (l=0; l<3; l++) { r = y[l]+kb->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/(kb->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]*kb->dumove+pv[0]*kb->dvmove; pm[1] = pu[1]*kb->dumove+pv[1]*kb->dvmove; pm[2] = pu[2]*kb->dumove+pv[2]*kb->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] | */ kb->alpha = atan2(-n[2],-pm[2])*180/M_PI; kb->beta = atan2(-b[2],sqrt(b[0]*b[0]+b[1]*b[1]))*180/M_PI; kb->delta = atan2(b[1],-b[0])*180/M_PI; /* Compute the rotation that rotates the Klein bottle in 4D. */ rotateall(kb->alpha,kb->beta,kb->delta,kb->zeta,kb->eta,kb->theta,mat); u = kb->umove; v = kb->vmove; cu = cos(u); su = sin(u); cv = cos(v); sv = sin(v); cv2 = cos(0.5*v); sv2 = sin(0.5*v); xx[0] = cu*cv; xx[1] = cu*sv; xx[2] = su*sv2; xx[3] = su*cv2; 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 (kb->projection_4d == DISP_4D_ORTHOGRAPHIC) { for (l=0; l<3; l++) p[l] = y[l]+kb->offset4d[l]; } else { s = y[3]+kb->offset4d[3]; for (l=0; l<3; l++) p[l] = (y[l]+kb->offset4d[l])/s; } kb->offset3d[0] = -p[0]; kb->offset3d[1] = -p[1]-DELTAY; kb->offset3d[2] = -p[2]; } else { /* Compute the rotation that rotates the Klein bottle in 4D, including the trackball rotations. */ rotateall(kb->alpha,kb->beta,kb->delta,kb->zeta,kb->eta,kb->theta,r1); gltrackball_get_quaternion(kb->trackballs[0],q1); gltrackball_get_quaternion(kb->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]*kb->x[o][0]+mat[l][1]*kb->x[o][1]+ mat[l][2]*kb->x[o][2]+mat[l][3]*kb->x[o][3]); yu[l] = (mat[l][0]*kb->xu[o][0]+mat[l][1]*kb->xu[o][1]+ mat[l][2]*kb->xu[o][2]+mat[l][3]*kb->xu[o][3]); yv[l] = (mat[l][0]*kb->xv[o][0]+mat[l][1]*kb->xv[o][1]+ mat[l][2]*kb->xv[o][2]+mat[l][3]*kb->xv[o][3]); } if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC) { for (l=0; l<3; l++) { kb->pp[o][l] = (y[l]+kb->offset4d[l])+kb->offset3d[l]; pu[l] = yu[l]; pv[l] = yv[l]; } } else { s = y[3]+kb->offset4d[3]; q = 1.0/s; t = q*q; for (l=0; l<3; l++) { r = y[l]+kb->offset4d[l]; kb->pp[o][l] = r*q+kb->offset3d[l]; pu[l] = (yu[l]*s-r*yu[3])*t; pv[l] = (yv[l]*s-r*yv[3])*t; } } kb->pn[o][0] = pu[1]*pv[2]-pu[2]*pv[1]; kb->pn[o][1] = pu[2]*pv[0]-pu[0]*pv[2]; kb->pn[o][2] = pu[0]*pv[1]-pu[1]*pv[0]; t = 1.0/sqrt(kb->pn[o][0]*kb->pn[o][0]+kb->pn[o][1]*kb->pn[o][1]+ kb->pn[o][2]*kb->pn[o][2]); kb->pn[o][0] *= t; kb->pn[o][1] *= t; kb->pn[o][2] *= t; } } if (kb->colors == COLORS_TWOSIDED) { glColor3fv(mat_diff_red); if (kb->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,kb->tex_name); for (i=0; iappearance == APPEARANCE_BANDS && ((i & (NUMB-1)) >= NUMB/2)) continue; if (kb->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(kb->pn[o]); glTexCoord2fv(kb->tex[o]); if (kb->colors != COLORS_TWOSIDED) { glColor3fv(kb->col[o]); glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,kb->col[o]); } glVertex3fv(kb->pp[o]); polys++; } } glEnd(); } polys /= 2; return polys; } /* Generate a texture image that shows the orientation reversal. */ static void gen_texture(ModeInfo *mi) { kleinstruct *kb = &klein[MI_SCREEN(mi)]; glGenTextures(1,&kb->tex_name); glBindTexture(GL_TEXTURE_2D,kb->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 }; kleinstruct *kb = &klein[MI_SCREEN(mi)]; if (walk_speed == 0.0) walk_speed = 20.0; if (kb->view == VIEW_TURN) { kb->alpha = frand(360.0); kb->beta = frand(360.0); kb->delta = frand(360.0); } else { kb->alpha = 0.0; kb->beta = 0.0; kb->delta = 0.0; } kb->zeta = 0.0; if (kb->bottle_type == KLEIN_BOTTLE_FIGURE_8 || kb->bottle_type == KLEIN_BOTTLE_SQUEEZED_TORUS) kb->eta = 0.0; else kb->eta = 45.0; kb->theta = 0.0; kb->umove = frand(2.0*M_PI); kb->vmove = frand(2.0*M_PI); kb->dumove = 0.0; kb->dvmove = 0.0; kb->side = 1; if (kb->bottle_type == KLEIN_BOTTLE_FIGURE_8) { kb->offset4d[0] = 0.0; kb->offset4d[1] = 0.0; kb->offset4d[2] = 0.0; kb->offset4d[3] = 1.5; kb->offset3d[0] = 0.0; kb->offset3d[1] = 0.0; if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC) kb->offset3d[2] = -2.1; else kb->offset3d[2] = -1.9; kb->offset3d[3] = 0.0; } else if (kb->bottle_type == KLEIN_BOTTLE_SQUEEZED_TORUS) { kb->offset4d[0] = 0.0; kb->offset4d[1] = 0.0; kb->offset4d[2] = 0.0; kb->offset4d[3] = 1.4; kb->offset3d[0] = 0.0; kb->offset3d[1] = 0.0; kb->offset3d[2] = -2.0; kb->offset3d[3] = 0.0; } else /* kb->bottle_type == KLEIN_BOTTLE_LAWSON */ { kb->offset4d[0] = 0.0; kb->offset4d[1] = 0.0; kb->offset4d[2] = 0.0; if (kb->projection_4d == DISP_4D_PERSPECTIVE && kb->projection_3d == DISP_3D_ORTHOGRAPHIC) kb->offset4d[3] = 1.5; else kb->offset4d[3] = 1.1; kb->offset3d[0] = 0.0; kb->offset3d[1] = 0.0; if (kb->projection_4d == DISP_4D_ORTHOGRAPHIC) kb->offset3d[2] = -2.0; else kb->offset3d[2] = -5.0; kb->offset3d[3] = 0.0; } gen_texture(mi); if (kb->bottle_type == KLEIN_BOTTLE_FIGURE_8) setup_figure8(mi,0.0,2.0*M_PI,0.0,2.0*M_PI); else if (kb->bottle_type == KLEIN_BOTTLE_SQUEEZED_TORUS) setup_squeezed_torus(mi,0.0,2.0*M_PI,0.0,2.0*M_PI); else /* kb->bottle_type == KLEIN_BOTTLE_LAWSON */ setup_lawson(mi,0.0,2.0*M_PI,0.0,2.0*M_PI); if (marks) glEnable(GL_TEXTURE_2D); else glDisable(GL_TEXTURE_2D); glMatrixMode(GL_PROJECTION); glLoadIdentity(); if (kb->projection_3d == DISP_3D_PERSPECTIVE || kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN) { if (kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN) gluPerspective(60.0,1.0,0.01,10.0); else gluPerspective(60.0,1.0,0.1,10.0); } else { glOrtho(-1.0,1.0,-1.0,1.0,0.1,10.0); } glMatrixMode(GL_MODELVIEW); glLoadIdentity(); # ifdef HAVE_JWZGLES /* #### glPolygonMode other than GL_FILL unimplemented */ if (kb->display_mode == DISP_WIREFRAME) kb->display_mode = DISP_SURFACE; # endif if (kb->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 (kb->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 /* kb->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_klein(ModeInfo *mi) { kleinstruct *kb = &klein[MI_SCREEN(mi)]; if (!kb->button_pressed) { if (kb->view == VIEW_TURN) { kb->alpha += speed_wx * kb->speed_scale; if (kb->alpha >= 360.0) kb->alpha -= 360.0; kb->beta += speed_wy * kb->speed_scale; if (kb->beta >= 360.0) kb->beta -= 360.0; kb->delta += speed_wz * kb->speed_scale; if (kb->delta >= 360.0) kb->delta -= 360.0; kb->zeta += speed_xy * kb->speed_scale; if (kb->zeta >= 360.0) kb->zeta -= 360.0; kb->eta += speed_xz * kb->speed_scale; if (kb->eta >= 360.0) kb->eta -= 360.0; kb->theta += speed_yz * kb->speed_scale; if (kb->theta >= 360.0) kb->theta -= 360.0; } if (kb->view == VIEW_WALKTURN) { kb->zeta += speed_xy * kb->speed_scale; if (kb->zeta >= 360.0) kb->zeta -= 360.0; kb->eta += speed_xz * kb->speed_scale; if (kb->eta >= 360.0) kb->eta -= 360.0; kb->theta += speed_yz * kb->speed_scale; if (kb->theta >= 360.0) kb->theta -= 360.0; } if (kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN) { kb->dvmove = cos(walk_direction*M_PI/180.0)*walk_speed*M_PI/4096.0; kb->vmove += kb->dvmove; if (kb->vmove >= 2.0*M_PI) { kb->vmove -= 2.0*M_PI; kb->umove = 2.0*M_PI-kb->umove; kb->side = -kb->side; } kb->dumove = (kb->side*sin(walk_direction*M_PI/180.0)* walk_speed*M_PI/4096.0); kb->umove += kb->dumove; if (kb->umove >= 2.0*M_PI) kb->umove -= 2.0*M_PI; if (kb->umove < 0.0) kb->umove += 2.0*M_PI; } } glMatrixMode(GL_PROJECTION); glLoadIdentity(); if (kb->projection_3d == DISP_3D_PERSPECTIVE || kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN) { if (kb->view == VIEW_WALK || kb->view == VIEW_WALKTURN) gluPerspective(60.0,kb->aspect,0.01,10.0); else gluPerspective(60.0,kb->aspect,0.1,10.0); } else { if (kb->aspect >= 1.0) glOrtho(-kb->aspect,kb->aspect,-1.0,1.0,0.1,10.0); else glOrtho(-1.0,1.0,-1.0/kb->aspect,1.0/kb->aspect,0.1,10.0); } glMatrixMode(GL_MODELVIEW); glLoadIdentity(); if (kb->bottle_type == KLEIN_BOTTLE_FIGURE_8) mi->polygon_count = figure8(mi,0.0,2.0*M_PI,0.0,2.0*M_PI); else if (kb->bottle_type == KLEIN_BOTTLE_SQUEEZED_TORUS) mi->polygon_count = squeezed_torus(mi,0.0,2.0*M_PI,0.0,2.0*M_PI); else /* kb->bottle_type == KLEIN_BOTTLE_LAWSON */ mi->polygon_count = lawson(mi,0.0,2.0*M_PI,0.0,2.0*M_PI); } ENTRYPOINT void reshape_klein(ModeInfo *mi, int width, int height) { kleinstruct *kb = &klein[MI_SCREEN(mi)]; kb->WindW = (GLint)width; kb->WindH = (GLint)height; glViewport(0,0,width,height); kb->aspect = (GLfloat)width/(GLfloat)height; } ENTRYPOINT Bool klein_handle_event(ModeInfo *mi, XEvent *event) { kleinstruct *kb = &klein[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) { kb->button_pressed = True; gltrackball_start(kb->trackballs[kb->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) { kb->button_pressed = False; return True; } else if (event->xany.type == KeyPress) { if (sym == XK_Shift_L || sym == XK_Shift_R) { kb->current_trackball = 1; if (kb->button_pressed) gltrackball_start(kb->trackballs[kb->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) { kb->current_trackball = 0; if (kb->button_pressed) gltrackball_start(kb->trackballs[kb->current_trackball], event->xbutton.x, event->xbutton.y, MI_WIDTH(mi), MI_HEIGHT(mi)); return True; } } else if (event->xany.type == MotionNotify && kb->button_pressed) { gltrackball_track(kb->trackballs[kb->current_trackball], event->xmotion.x, event->xmotion.y, MI_WIDTH(mi), MI_HEIGHT(mi)); return True; } return False; } /* *----------------------------------------------------------------------------- *----------------------------------------------------------------------------- * Xlock hooks. *----------------------------------------------------------------------------- *----------------------------------------------------------------------------- */ /* *----------------------------------------------------------------------------- * Initialize klein. Called each time the window changes. *----------------------------------------------------------------------------- */ ENTRYPOINT void init_klein(ModeInfo *mi) { kleinstruct *kb; MI_INIT(mi, klein); kb = &klein[MI_SCREEN(mi)]; kb->trackballs[0] = gltrackball_init(True); kb->trackballs[1] = gltrackball_init(True); kb->current_trackball = 0; kb->button_pressed = False; /* Set the Klein bottle. */ if (!strcasecmp(klein_bottle,"random")) { kb->bottle_type = random() % NUM_KLEIN_BOTTLES; } else if (!strcasecmp(klein_bottle,"figure-8")) { kb->bottle_type = KLEIN_BOTTLE_FIGURE_8; } else if (!strcasecmp(klein_bottle,"squeezed-torus")) { kb->bottle_type = KLEIN_BOTTLE_SQUEEZED_TORUS; } else if (!strcasecmp(klein_bottle,"lawson")) { kb->bottle_type = KLEIN_BOTTLE_LAWSON; } else { kb->bottle_type = random() % NUM_KLEIN_BOTTLES; } /* Set the display mode. */ if (!strcasecmp(mode,"random")) { kb->display_mode = random() % NUM_DISPLAY_MODES; } else if (!strcasecmp(mode,"wireframe")) { kb->display_mode = DISP_WIREFRAME; } else if (!strcasecmp(mode,"surface")) { kb->display_mode = DISP_SURFACE; } else if (!strcasecmp(mode,"transparent")) { kb->display_mode = DISP_TRANSPARENT; } else { kb->display_mode = random() % NUM_DISPLAY_MODES; } /* Orientation marks don't make sense in wireframe mode. */ if (kb->display_mode == DISP_WIREFRAME) marks = False; /* Set the appearance. */ if (!strcasecmp(appear,"random")) { kb->appearance = random() % NUM_APPEARANCES; } else if (!strcasecmp(appear,"solid")) { kb->appearance = APPEARANCE_SOLID; } else if (!strcasecmp(appear,"bands")) { kb->appearance = APPEARANCE_BANDS; } else { kb->appearance = random() % NUM_APPEARANCES; } /* Set the color mode. */ if (!strcasecmp(color_mode,"random")) { kb->colors = random() % NUM_COLORS; } else if (!strcasecmp(color_mode,"two-sided")) { kb->colors = COLORS_TWOSIDED; } else if (!strcasecmp(color_mode,"rainbow")) { kb->colors = COLORS_RAINBOW; } else if (!strcasecmp(color_mode,"depth")) { kb->colors = COLORS_DEPTH; } else { kb->colors = random() % NUM_COLORS; } /* Set the view mode. */ if (!strcasecmp(view_mode,"random")) { kb->view = random() % NUM_VIEW_MODES; } else if (!strcasecmp(view_mode,"walk")) { kb->view = VIEW_WALK; } else if (!strcasecmp(view_mode,"turn")) { kb->view = VIEW_TURN; } else if (!strcasecmp(view_mode,"walk-turn")) { kb->view = VIEW_WALKTURN; } else { kb->view = random() % NUM_VIEW_MODES; } /* Set the 3d projection mode. */ if (!strcasecmp(proj_3d,"random")) { /* Orthographic projection only makes sense in turn mode. */ if (kb->view == VIEW_TURN) kb->projection_3d = random() % NUM_DISP_3D_MODES; else kb->projection_3d = DISP_3D_PERSPECTIVE; } else if (!strcasecmp(proj_3d,"perspective")) { kb->projection_3d = DISP_3D_PERSPECTIVE; } else if (!strcasecmp(proj_3d,"orthographic")) { kb->projection_3d = DISP_3D_ORTHOGRAPHIC; } else { /* Orthographic projection only makes sense in turn mode. */ if (kb->view == VIEW_TURN) kb->projection_3d = random() % NUM_DISP_3D_MODES; else kb->projection_3d = DISP_3D_PERSPECTIVE; } /* Set the 4d projection mode. */ if (!strcasecmp(proj_4d,"random")) { kb->projection_4d = random() % NUM_DISP_4D_MODES; } else if (!strcasecmp(proj_4d,"perspective")) { kb->projection_4d = DISP_4D_PERSPECTIVE; } else if (!strcasecmp(proj_4d,"orthographic")) { kb->projection_4d = DISP_4D_ORTHOGRAPHIC; } else { kb->projection_4d = random() % NUM_DISP_4D_MODES; } /* Modify the speeds to a useful range in walk-and-turn mode. */ if (kb->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. */ kb->speed_scale = 0.9 + frand(0.3); if ((kb->glx_context = init_GL(mi)) != NULL) { reshape_klein(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_klein(ModeInfo *mi) { Display *display = MI_DISPLAY(mi); Window window = MI_WINDOW(mi); kleinstruct *kb; if (klein == NULL) return; kb = &klein[MI_SCREEN(mi)]; MI_IS_DRAWN(mi) = True; if (!kb->glx_context) return; glXMakeCurrent(display, window, *kb->glx_context); glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT); glLoadIdentity(); display_klein(mi); if (MI_IS_FPS(mi)) do_fps (mi); glFlush(); glXSwapBuffers(display,window); } #ifndef STANDALONE ENTRYPOINT void change_klein(ModeInfo *mi) { kleinstruct *kb = &klein[MI_SCREEN(mi)]; if (!kb->glx_context) return; glXMakeCurrent(MI_DISPLAY(mi), MI_WINDOW(mi), *kb->glx_context); init(mi); } #endif /* !STANDALONE */ ENTRYPOINT void free_klein(ModeInfo *mi) { kleinstruct *kb = &klein[MI_SCREEN(mi)]; if (!kb->glx_context) return; glXMakeCurrent (MI_DISPLAY(mi), MI_WINDOW(mi), *kb->glx_context); gltrackball_free (kb->trackballs[0]); gltrackball_free (kb->trackballs[1]); if (kb->tex_name) glDeleteTextures (1, &kb->tex_name); } XSCREENSAVER_MODULE ("Klein", klein) #endif /* USE_GL */