1 /* hypertorus --- Shows a hypertorus that rotates in 4d */
4 static const char sccsid[] = "@(#)hypertorus.c 1.1 03/05/18 xlockmore";
7 /* Copyright (c) 2003 Carsten Steger <carsten@mirsanmir.org>. */
10 * Permission to use, copy, modify, and distribute this software and its
11 * documentation for any purpose and without fee is hereby granted,
12 * provided that the above copyright notice appear in all copies and that
13 * both that copyright notice and this permission notice appear in
14 * supporting documentation.
16 * This file is provided AS IS with no warranties of any kind. The author
17 * shall have no liability with respect to the infringement of copyrights,
18 * trade secrets or any patents by this file or any part thereof. In no
19 * event will the author be liable for any lost revenue or profits or
20 * other special, indirect and consequential damages.
23 * C. Steger - 03/05/18: Initial version
27 * This program shows the Clifford torus as it rotates in 4d. The Clifford
28 * torus is a torus lies on the "surface" of the hypersphere in 4d. The
29 * program projects the 4d torus to 3d using either a perspective or an
30 * orthographic projection. Of the two alternatives, the perspecitve
31 * projection looks much more appealing. In orthographic projections the
32 * torus degenerates into a doubly covered cylinder for some angles. The
33 * projected 3d torus can then be projected to the screen either perspectively
34 * or orthographically. There are three display modes for the torus: mesh
35 * (wireframe), solid, or transparent. Furthermore, the appearance of the
36 * torus can be as a solid object or as a set of see-through bands. Finally,
37 * the colors with with the torus is drawn can be set to either two-sided or
38 * to colorwheel. In the first case, the torus is drawn with red on the
39 * outside and green on the inside. This mode enables you to see that the
40 * torus turns inside-out as it rotates in 4d. The second mode draws the
41 * torus in a fully saturated color wheel. This gives a very nice effect
42 * when combined with the see-through bands mode. The rotation speed for
43 * each of the six planes around which the torus rotates can be chosen.
44 * This program is very much inspired by Thomas Banchoff's book "Beyond the
45 * Third Dimension: Geometry, Computer Graphics, and Higher Dimensions",
46 * Scientific American Library, 1990.
50 #define M_PI 3.14159265358979323846
53 #define DISP_WIREFRAME 0
54 #define DISP_WIREFRAME_STR "0"
55 #define DISP_SURFACE 1
56 #define DISP_SURFACE_STR "1"
57 #define DISP_TRANSPARENT 2
58 #define DISP_TRANSPARENT_STR "2"
60 #define APPEARANCE_SOLID 0
61 #define APPEARANCE_SOLID_STR "0"
62 #define APPEARANCE_BANDS 1
63 #define APPEARANCE_BANDS_STR "1"
65 #define COLORS_TWOSIDED 0
66 #define COLORS_TWOSIDED_STR "0"
67 #define COLORS_COLORWHEEL 1
68 #define COLORS_COLORWHEEL_STR "1"
70 #define DISP_3D_PERSPECTIVE 0
71 #define DISP_3D_PERSPECTIVE_STR "0"
72 #define DISP_3D_ORTHOGRAPHIC 1
73 #define DISP_3D_ORTHOGRAPHIC_STR "1"
75 #define DISP_4D_PERSPECTIVE 0
76 #define DISP_4D_PERSPECTIVE_STR "0"
77 #define DISP_4D_ORTHOGRAPHIC 1
78 #define DISP_4D_ORTHOGRAPHIC_STR "1"
81 #define DALPHA_STR "1.1"
83 #define DBETA_STR "1.3"
85 #define DDELTA_STR "1.5"
87 #define DZETA_STR "1.7"
89 #define DETA_STR "1.9"
91 #define DTHETA_STR "2.1"
93 #define DEF_DISPLAY_MODE DISP_SURFACE_STR
94 #define DEF_APPEARANCE APPEARANCE_BANDS_STR
95 #define DEF_COLORS COLORS_COLORWHEEL_STR
96 #define DEF_3D_PROJECTION DISP_3D_PERSPECTIVE_STR
97 #define DEF_4D_PROJECTION DISP_4D_PERSPECTIVE_STR
98 #define DEF_DALPHA DALPHA_STR
99 #define DEF_DBETA DBETA_STR
100 #define DEF_DDELTA DDELTA_STR
101 #define DEF_DZETA DZETA_STR
102 #define DEF_DETA DETA_STR
103 #define DEF_DTHETA DTHETA_STR
106 # define PROGCLASS "Hypertorus"
107 # define HACK_INIT init_hypertorus
108 # define HACK_DRAW draw_hypertorus
109 # define HACK_RESHAPE reshape_hypertorus
110 # define hypertorus_opts xlockmore_opts
111 # define DEFAULTS "*delay: 25000 \n" \
112 "*showFPS: False \n" \
113 "*wireframe: False \n" \
114 "*displayMode: " DEF_DISPLAY_MODE " \n" \
115 "*appearance: " DEF_APPEARANCE " \n" \
116 "*colors: " DEF_COLORS " \n" \
117 "*projection3d: " DEF_3D_PROJECTION " \n" \
118 "*projection4d: " DEF_4D_PROJECTION " \n" \
119 "speedwx: " DEF_DALPHA " \n" \
120 "speedwy: " DEF_DBETA " \n" \
121 "speedwz: " DEF_DDELTA " \n" \
122 "speedxy: " DEF_DZETA " \n" \
123 "speedxz: " DEF_DETA " \n" \
124 "speedyz: " DEF_DTHETA " \n"
125 # include "xlockmore.h" /* from the xscreensaver distribution */
126 #else /* !STANDALONE */
127 # include "xlock.h" /* from the xlockmore distribution */
128 #endif /* !STANDALONE */
137 ModStruct hypertorus_description =
138 {"hypertorus", "init_hypertorus", "draw_hypertorus", "release_hypertorus",
139 "draw_hypertorus", "change_hypertorus", NULL, &hypertorus_opts,
140 25000, 1, 1, 1, 1.0, 4, "",
141 "Shows a hypertorus rotating in 4d", 0, NULL};
146 static int display_mode;
147 static int appearance;
149 static int projection_3d;
150 static int projection_4d;
151 static float speed_wx;
152 static float speed_wy;
153 static float speed_wz;
154 static float speed_xy;
155 static float speed_xz;
156 static float speed_yz;
158 /* 4D rotation angles */
159 static float alpha, beta, delta, zeta, eta, theta;
162 static const float offset4d[4] = {
166 static const float offset3d[4] = {
171 static XrmOptionDescRec opts[] =
173 {"-mesh", ".hypertorus.displayMode", XrmoptionNoArg,
174 DISP_WIREFRAME_STR },
175 {"-surface", ".hypertorus.displayMode", XrmoptionNoArg,
177 {"-transparent", ".hypertorus.displayMode", XrmoptionNoArg,
178 DISP_TRANSPARENT_STR },
179 {"-solid", ".hypertorus.appearance", XrmoptionNoArg,
180 APPEARANCE_SOLID_STR },
181 {"-bands", ".hypertorus.appearance", XrmoptionNoArg,
182 APPEARANCE_BANDS_STR },
183 {"-twosided", ".hypertorus.colors", XrmoptionNoArg,
184 COLORS_TWOSIDED_STR },
185 {"-colorwheel", ".hypertorus.colors", XrmoptionNoArg,
186 COLORS_COLORWHEEL_STR },
187 {"-perspective-3d", ".hypertorus.projection3d", XrmoptionNoArg,
188 DISP_3D_PERSPECTIVE_STR },
189 {"-orthographic-3d", ".hypertorus.projection3d", XrmoptionNoArg,
190 DISP_3D_ORTHOGRAPHIC_STR },
191 {"-perspective-4d", ".hypertorus.projection4d", XrmoptionNoArg,
192 DISP_4D_PERSPECTIVE_STR },
193 {"-orthographic-4d", ".hypertorus.projection4d", XrmoptionNoArg,
194 DISP_4D_ORTHOGRAPHIC_STR },
195 {"-speed-wx", ".hypertorus.speedwx", XrmoptionSepArg, 0 },
196 {"-speed-wy", ".hypertorus.speedwy", XrmoptionSepArg, 0 },
197 {"-speed-wz", ".hypertorus.speedwz", XrmoptionSepArg, 0 },
198 {"-speed-xy", ".hypertorus.speedxy", XrmoptionSepArg, 0 },
199 {"-speed-xz", ".hypertorus.speedxz", XrmoptionSepArg, 0 },
200 {"-speed-yz", ".hypertorus.speedyz", XrmoptionSepArg, 0 }
203 static argtype vars[] =
205 { &display_mode, "displayMode", "DisplayMode",
206 DEF_DISPLAY_MODE, t_Int },
207 { &appearance, "appearance", "Appearance",
208 DEF_APPEARANCE, t_Int },
209 { &colors, "colors", "Colors",
211 { &projection_3d, "projection3d", "Projection3d",
212 DEF_3D_PROJECTION, t_Int },
213 { &projection_4d, "projection4d", "Projection4d",
214 DEF_4D_PROJECTION, t_Int },
215 { &speed_wx, "speedwx", "Speedwx",
216 DEF_DALPHA, t_Float},
217 { &speed_wy, "speedwy", "Speedwy",
219 { &speed_wz, "speedwz", "Speedwz",
220 DEF_DDELTA, t_Float},
221 { &speed_xy, "speedxy", "Speedxy",
223 { &speed_xz, "speedxz", "Speedxz",
225 { &speed_yz, "speedyz", "Speedyz",
229 static OptionStruct desc[] =
231 { "-mesh", "display the torus as a wireframe mesh" },
232 { "-surface", "display the torus as a solid surface" },
233 { "-transparent", "display the torus as a transparent surface" },
234 { "-solid", "display the torus as a solid object" },
235 { "-bands", "display the torus as see-through bands" },
236 { "-twosided", "display the torus with two colors" },
237 { "-colorwheel", "display the torus with a smooth color wheel" },
238 { "-perspective-3d", "project the torus perspectively from 3d to 2d" },
239 { "-orthographic-3d", "project the torus orthographically from 3d to 2d" },
240 { "-perspective-4d", "project the torus perspectively from 4d to 3d" },
241 { "-orthographic-4d", "project the torus orthographically from 4d to 3d" },
242 { "-speed-wx <arg>", "rotation speed around the wx plane" },
243 { "-speed-wy <arg>", "rotation speed around the wy plane" },
244 { "-speed-wz <arg>", "rotation speed around the wz plane" },
245 { "-speed-xy <arg>", "rotation speed around the xy plane" },
246 { "-speed-xz <arg>", "rotation speed around the xz plane" },
247 { "-speed-yz <arg>", "rotation speed around the yz plane" }
250 ModeSpecOpt hypertorus_opts =
251 {sizeof opts / sizeof opts[0], opts, sizeof vars / sizeof vars[0], vars, desc};
256 GLXContext *glx_context;
259 static hypertorusstruct *hyper = (hypertorusstruct *) NULL;
262 /* Add a rotation around the wx-plane to the matrix m. */
263 static void rotatewx(float m[4][4], float phi)
281 /* Add a rotation around the wy-plane to the matrix m. */
282 static void rotatewy(float m[4][4], float phi)
300 /* Add a rotation around the wz-plane to the matrix m. */
301 static void rotatewz(float m[4][4], float phi)
319 /* Add a rotation around the xy-plane to the matrix m. */
320 static void rotatexy(float m[4][4], float phi)
338 /* Add a rotation around the xz-plane to the matrix m. */
339 static void rotatexz(float m[4][4], float phi)
357 /* Add a rotation around the yz-plane to the matrix m. */
358 static void rotateyz(float m[4][4], float phi)
376 /* Compute a fully saturated and bright color based on an angle. */
377 static void color(double angle)
383 if (colors != COLORS_COLORWHEEL)
387 angle = fmod(angle,2*M_PI);
389 angle = fmod(angle,-2*M_PI);
390 s = floor(angle/(M_PI/3));
391 t = angle/(M_PI/3)-s;
427 if (display_mode == DISP_TRANSPARENT)
432 glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT_AND_DIFFUSE,color);
436 /* Draw a hyperturus projected into 3D. */
437 static void hypertorus(double umin, double umax, double vmin, double vmax,
440 static GLfloat mat_diff_red[] = { 1.0, 0.0, 0.0, 1.0 };
441 static GLfloat mat_diff_green[] = { 0.0, 1.0, 0.0, 1.0 };
442 static GLfloat mat_diff_trans_red[] = { 1.0, 0.0, 0.0, 0.5 };
443 static GLfloat mat_diff_trans_green[] = { 0.0, 1.0, 0.0, 0.5 };
444 float p[3], pu[3], pv[3], n[3], mat[4][4];
447 double cu, su, cv, sv;
448 double xx[4], xxu[4], xxv[4], x[4], xu[4], xv[4];
451 /* Compute the rotation that rotates the hypercube in 4D. */
462 if (colors != COLORS_COLORWHEEL)
464 glColor3fv(mat_diff_red);
465 if (display_mode == DISP_TRANSPARENT)
467 glMaterialfv(GL_FRONT,GL_AMBIENT_AND_DIFFUSE,mat_diff_trans_red);
468 glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,mat_diff_trans_green);
472 glMaterialfv(GL_FRONT,GL_AMBIENT_AND_DIFFUSE,mat_diff_red);
473 glMaterialfv(GL_BACK,GL_AMBIENT_AND_DIFFUSE,mat_diff_green);
479 for (i=0; i<numu; i++)
481 if (appearance == APPEARANCE_BANDS && ((i & 3) >= 2))
483 if (display_mode == DISP_WIREFRAME)
484 glBegin(GL_QUAD_STRIP);
486 glBegin(GL_TRIANGLE_STRIP);
487 for (j=0; j<=numv; j++)
519 r += mat[l][m]*xx[m];
520 s += mat[l][m]*xxu[m];
521 t += mat[l][m]*xxv[m];
527 if (projection_4d == DISP_4D_ORTHOGRAPHIC)
531 p[l] = (x[l]+offset4d[l])/1.5+offset3d[l];
538 s = x[3]+offset4d[3];
542 r = x[l]+offset4d[l];
543 p[l] = r/s+offset3d[l];
544 pu[l] = (xu[l]*s-r*xu[3])/t;
545 pv[l] = (xv[l]*s-r*xv[3])/t;
548 n[0] = pu[1]*pv[2]-pu[2]*pv[1];
549 n[1] = pu[2]*pv[0]-pu[0]*pv[2];
550 n[2] = pu[0]*pv[1]-pu[1]*pv[0];
551 t = sqrt(n[0]*n[0]+n[1]*n[1]+n[2]*n[2]);
564 static void init(ModeInfo *mi)
566 static GLfloat light_ambient[] = { 0.0, 0.0, 0.0, 1.0 };
567 static GLfloat light_diffuse[] = { 1.0, 1.0, 1.0, 1.0 };
568 static GLfloat light_specular[] = { 1.0, 1.0, 1.0, 1.0 };
569 static GLfloat light_position[] = { 1.0, 1.0, 1.0, 0.0 };
570 static GLfloat mat_specular[] = { 1.0, 1.0, 1.0, 1.0 };
579 glMatrixMode(GL_PROJECTION);
581 if (projection_3d == DISP_3D_PERSPECTIVE)
582 gluPerspective(60.0,1.0,0.1,100.0);
584 glOrtho(-1.0,1.0,-1.0,1.0,0.1,100.0);;
585 glMatrixMode(GL_MODELVIEW);
588 if (display_mode == DISP_WIREFRAME)
590 glDisable(GL_DEPTH_TEST);
591 glShadeModel(GL_FLAT);
592 glPolygonMode(GL_FRONT_AND_BACK,GL_LINE);
593 glDisable(GL_LIGHTING);
594 glDisable(GL_LIGHT0);
597 else if (display_mode == DISP_SURFACE)
599 glEnable(GL_DEPTH_TEST);
600 glDepthFunc(GL_LESS);
601 glShadeModel(GL_SMOOTH);
602 glPolygonMode(GL_FRONT_AND_BACK,GL_FILL);
603 glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,GL_TRUE);
604 glEnable(GL_LIGHTING);
606 glLightfv(GL_LIGHT0,GL_AMBIENT,light_ambient);
607 glLightfv(GL_LIGHT0,GL_DIFFUSE,light_diffuse);
608 glLightfv(GL_LIGHT0,GL_SPECULAR,light_specular);
609 glLightfv(GL_LIGHT0,GL_POSITION,light_position);
610 glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,mat_specular);
611 glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,50.0);
612 glDepthMask(GL_TRUE);
615 else if (display_mode == DISP_TRANSPARENT)
617 glDisable(GL_DEPTH_TEST);
618 glShadeModel(GL_SMOOTH);
619 glPolygonMode(GL_FRONT_AND_BACK,GL_FILL);
620 glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,GL_TRUE);
621 glEnable(GL_LIGHTING);
623 glLightfv(GL_LIGHT0,GL_AMBIENT,light_ambient);
624 glLightfv(GL_LIGHT0,GL_DIFFUSE,light_diffuse);
625 glLightfv(GL_LIGHT0,GL_SPECULAR,light_specular);
626 glLightfv(GL_LIGHT0,GL_POSITION,light_position);
627 glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,mat_specular);
628 glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,50.0);
629 glDepthMask(GL_FALSE);
631 glBlendFunc(GL_SRC_ALPHA,GL_ONE);
635 glDisable(GL_DEPTH_TEST);
636 glShadeModel(GL_FLAT);
637 glPolygonMode(GL_FRONT_AND_BACK,GL_LINE);
638 glDisable(GL_LIGHTING);
639 glDisable(GL_LIGHT0);
645 /* Redisplay the hypertorus. */
646 static void display_hypertorus(void)
667 glMatrixMode(GL_PROJECTION);
669 if (projection_3d == DISP_3D_ORTHOGRAPHIC)
672 glOrtho(-aspect,aspect,-1.0,1.0,0.1,100.0);
674 glOrtho(-1.0,1.0,-1.0/aspect,1.0/aspect,0.1,100.0);
678 gluPerspective(60.0,aspect,0.1,100.0);
680 glMatrixMode(GL_MODELVIEW);
683 if (display_mode == DISP_WIREFRAME)
684 hypertorus(0.0,2.0*M_PI,0.0,2.0*M_PI,40,40);
686 hypertorus(0.0,2.0*M_PI,0.0,2.0*M_PI,60,60);
690 void reshape_hypertorus(ModeInfo * mi, int width, int height)
692 hypertorusstruct *hp = &hyper[MI_SCREEN(mi)];
694 hp->WindW = (GLint)width;
695 hp->WindH = (GLint)height;
696 glViewport(0,0,width,height);
697 aspect = (GLfloat)width/(GLfloat)height;
702 *-----------------------------------------------------------------------------
703 *-----------------------------------------------------------------------------
705 *-----------------------------------------------------------------------------
706 *-----------------------------------------------------------------------------
710 *-----------------------------------------------------------------------------
711 * Initialize hypertorus. Called each time the window changes.
712 *-----------------------------------------------------------------------------
715 void init_hypertorus(ModeInfo * mi)
717 hypertorusstruct *hp;
721 hyper = (hypertorusstruct *)calloc(MI_NUM_SCREENS(mi),
722 sizeof(hypertorusstruct));
726 hp = &hyper[MI_SCREEN(mi)];
728 if ((hp->glx_context = init_GL(mi)) != NULL)
730 reshape_hypertorus(mi,MI_WIDTH(mi),MI_HEIGHT(mi));
731 glDrawBuffer(GL_BACK);
741 *-----------------------------------------------------------------------------
742 * Called by the mainline code periodically to update the display.
743 *-----------------------------------------------------------------------------
745 void draw_hypertorus(ModeInfo * mi)
747 Display *display = MI_DISPLAY(mi);
748 Window window = MI_WINDOW(mi);
749 hypertorusstruct *hp;
753 hp = &hyper[MI_SCREEN(mi)];
755 MI_IS_DRAWN(mi) = True;
756 if (!hp->glx_context)
759 glXMakeCurrent(display,window,*(hp->glx_context));
761 glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
764 display_hypertorus();
771 glXSwapBuffers(display,window);
776 *-----------------------------------------------------------------------------
777 * The display is being taken away from us. Free up malloc'ed
778 * memory and X resources that we've alloc'ed. Only called
779 * once, we must zap everything for every screen.
780 *-----------------------------------------------------------------------------
783 void release_hypertorus(ModeInfo * mi)
789 for (screen = 0; screen < MI_NUM_SCREENS(mi); screen++)
791 hypertorusstruct *hp = &hyper[screen];
794 hp->glx_context = (GLXContext *)NULL;
796 (void) free((void *)hyper);
797 hyper = (hypertorusstruct *)NULL;
802 void change_hypertorus(ModeInfo * mi)
804 hypertorusstruct *hp = &hyper[MI_SCREEN(mi)];
806 if (!hp->glx_context)
809 glXMakeCurrent(MI_DISPLAY(mi),MI_WINDOW(mi),*(hp->glx_context));