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Diffstat (limited to 'hacks/glx/klein.c')
| -rw-r--r-- | hacks/glx/klein.c | 2099 |
1 files changed, 2099 insertions, 0 deletions
diff --git a/hacks/glx/klein.c b/hacks/glx/klein.c new file mode 100644 index 0000000..1c042da --- /dev/null +++ b/hacks/glx/klein.c @@ -0,0 +1,2099 @@ +/* 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 <carsten@mirsanmir.org>. */ + +/* + * 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 free_klein 0 +# 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 <X11/keysym.h> +#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; i<NUMU; i++) + { + if (kb->appearance == 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; i<NUMU; i++) + { + if (kb->appearance == 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; i<NUMV; i++) + { + if (kb->appearance == 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 */ + +XSCREENSAVER_MODULE ("Klein", klein) + +#endif /* USE_GL */ |