1 /* -*- Mode: C; tab-width: 4 -*- */
2 /* superquadrics --- 3D mathematical shapes */
4 #if !defined( lint ) && !defined( SABER )
5 static const char sccsid[] = "@(#)superquadrics.c 4.07 97/11/24 xlockmore";
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.
22 * Superquadrics were invented by Dr. Alan Barr of Caltech University.
23 * They were first published in "Computer Graphics and Applications",
24 * volume 1, number 1, 1981, in the article "Superquadrics and Angle-
25 * Preserving Transformations." Dr. Barr based the Superquadrics on
26 * Piet Hein's "super ellipses." Super ellipses are like 2D ellipses,
27 * except that the formula includes an exponent, raising its X and Y
28 * values to a (fractional) power, and allowing them to gradually
29 * change from round to square edges. Superquadrics extend this
30 * idea into 3 dimensions, using two exponents to modify a
31 * quadric surface in a similar fashion.
34 * 30-Mar-97: Turned into a module for xlockmore 4.02 alpha. The code
35 * is almost unrecognizable now from the first revision, except for
36 * a few remaining two-letter variable names. I still don't have
37 * the normal vectors working right (I wrote the buggy normal vector
38 * code myself, can you tell?)
39 * 07-Jan-97: A legend reborn; Superquadrics make an appearance as a
40 * real OpenGL program written in C. I can even render them with
41 * proper lighting and specular highlights. Gee, they look almost
42 * as good now as the original color plates of them that my uncle
43 * showed me as a child in 1981. I don't know what computer hardware
44 * he was using at the time, but it's taken a couple decades for the
45 * PC clone hardware to catch up to it.
46 * 05-Jan-97: After almost a decade, Superquadrics had almost faded away
47 * into the myths and folklore of all the things my brother and I played
48 * with on computers when we were kids with too much time on our hands.
49 * I had since gotten involved in Unix, OpenGL, and other things.
50 * A sudden flash of inspiration caused me to dig out the old Pascal
51 * source code, run it through p2c, and start ripping away the old
52 * wireframe rendering code, to be replaced by OpenGL.
53 * Late 1989 or early 1990: Around this time I did the Turbo Pascal
54 * port of the Superquadrics. Unfortunately, many of the original variable
55 * names remained the same from the C= 64 original. This was unfortunate
56 * because BASIC on the c64 only allowed 2-letter, global variable names.
57 * But the speed improvement over BASIC was very impressive at the time.
58 * Thanksgiving, 1987: Written. My uncle Al, who invented Superquadrics some
59 * years earlier, came to visit us. I was a high school kid at the time,
60 * with nothing more than a Commodore 64. Somehow we wrote this program,
61 * (he did the math obviously, I just coded it into BASIC for the c64).
62 * Yeah, 320x200 resolution, colorless white wireframe, and half an hour
63 * rendering time per superquadric. PLOT x,y. THOSE were the days.
64 * In the following years I would port Superquadrics to AppleBASIC,
65 * AmigaBASIC, and then Turbo Pascal for IBM clones. 5 minutes on a 286!
66 * Talk about fast rendering! But these days, when my Pentium 166 runs
67 * the same program, the superquadric will already be waiting on the
68 * screen before my monitor can change frequency from text to graphics
69 * mode. Can't time the number of minutes that way! Darn ;)
75 * due to a Bug/feature in VMS X11/Intrinsic.h has to be placed before xlock.
76 * otherwise caddr_t is not defined correctly
79 #include <X11/Intrinsic.h>
82 # define PROGCLASS "Superquadrics"
83 # define HACK_INIT init_superquadrics
84 # define HACK_DRAW draw_superquadrics
85 # define superquadrics_opts xlockmore_opts
86 # define DEFAULTS "*delay: 40000 \n" \
89 "*wireframe: False \n"
90 # include "xlockmore.h" /* from the xscreensaver distribution */
91 #else /* !STANDALONE */
92 # include "xlock.h" /* from the xlockmore distribution */
93 #endif /* !STANDALONE */
98 * Note for low-CPU-speed machines: If your frame rate is so low that
99 * attempts at animation appear futile, try using "-cycles 1", which puts
100 * Superquadrics into kind of a slide-show mode. It will still use up
101 * all of your CPU power, but it may look nicer.
104 #define DEF_SPINSPEED "5.0"
106 static float spinspeed;
108 static XrmOptionDescRec opts[] =
110 {"-spinspeed", ".superquadrics.spinspeed", XrmoptionSepArg, (caddr_t) NULL}
112 static argtype vars[] =
114 {(caddr_t *) & spinspeed, "spinspeed", "Spinspeed", DEF_SPINSPEED, t_Float}
116 static OptionStruct desc[] =
118 {"-spinspeed num", "speed of rotation, in degrees per frame"}
121 ModeSpecOpt superquadrics_opts =
122 {sizeof opts / sizeof opts[0], opts, sizeof vars / sizeof vars[0], vars, desc};
125 ModStruct superquadrics_description =
126 {"superquadrics", "init_superquadrics", "draw_superquadrics", "release_superquadrics",
127 "refresh_superquadrics", "init_superquadrics", NULL, &superquadrics_opts,
128 1000, 25, 40, 1, 4, 1.0, "",
129 "Shows 3D mathematical shapes", 0, NULL};
138 typedef double dimi[MaxRes + 1];
141 double xExponent, yExponent;
142 GLfloat r[4], g[4], b[4];
148 GLXContext *glx_context;
149 int dist, wireframe, flatshade, shownorms, maxcount, maxwait;
150 int counter, viewcount, viewwait, mono;
151 GLfloat curmat[4][4], rotx, roty, rotz, spinspeed;
152 /* In dimi: the first letter stands for cosine/sine, the second
153 * stands for North, South, East, or West. I think.
155 dimi cs, se, sw, sn, ss, ce, cw, cn, Prevxx, Prevyy, Prevzz,
156 Prevxn, Prevyn, Prevzn;
157 double xExponent, yExponent, Mode;
160 } superquadricsstruct;
162 static superquadricsstruct *superquadrics = NULL;
164 #define CLIP_NORMALS 10000.0
166 static void ReshapeSuperquadrics(int w, int h);
171 return ((int) (((float) range) * LRAND() / (MAXRAND)));
177 return (LRAND() / (MAXRAND));
180 /* Some old, old, OLD code follows. Ahh this takes me back..... */
182 /* Output from p2c, the Pascal-to-C translator */
183 /* From input file "squad.pas" */
186 XtoY(double x, double y)
190 /* This is NOT your typical raise-X-to-the-Y-power function. Do not attempt
191 * to replace this with a standard exponent function. If you must, just
192 * replace the "a = exp(y * log(z));" line with something faster.
201 if (a > CLIP_NORMALS)
210 Sine(double x, double e)
212 /* This is just the sine wave raised to the exponent. BUT, you can't
213 * raise negative numbers to fractional exponents. So we have a special
214 * XtoY routune which handles it in a way useful to superquadrics.
217 return (XtoY(sin(x), e));
222 Cosine(double x, double e)
224 return (XtoY(cos(x), e));
229 MakeUpStuff(int allstuff, superquadricsstruct * sp)
231 static int pats[4][4] =
241 GLfloat r, g, b, r2, g2, b2;
245 if (sp->maxcount < 2)
247 dostuff = allstuff * 15;
249 dostuff = myrand(3) + 1;
250 if (myrand(2) || (dostuff & 1))
256 sp->later.xExponent = (((long) floor(myrandreal() * 250 + 0.5)) / 100.0) + 0.1;
257 sp->later.yExponent = (((long) floor(myrandreal() * 250 + 0.5)) / 100.0) + 0.1;
259 /* Increase the 2.0 .. 2.5 range to 2.0 .. 3.0 */
260 if (sp->later.xExponent > 2.0)
261 sp->later.xExponent = (sp->later.xExponent * 2.0) - 2.0;
262 if (sp->later.yExponent > 2.0)
263 sp->later.yExponent = (sp->later.yExponent * 2.0) - 2.0;
267 sp->later.Mode = myrand(3L) + 1;
268 } while (!allstuff && (sp->later.Mode == sp->now.Mode));
269 /* On init: make sure it can stay in mode 1 if it feels like it. */
277 b = g = r = (GLfloat) (140 + myrand(100)) / 255.0;
278 b2 = g2 = r2 = ((r > 0.69) ? (1.0 - r) : r);
281 r = (GLfloat) (40 + myrand(200)) / 255.0;
282 g = (GLfloat) (40 + myrand(200)) / 255.0;
283 b = (GLfloat) (40 + myrand(200)) / 255.0;
285 r2 = ((myrand(4) && ((r < 0.31) || (r > 0.69))) ? (1.0 - r) : r);
286 g2 = ((myrand(4) && ((g < 0.31) || (g > 0.69))) ? (1.0 - g) : g);
287 b2 = ((myrand(4) && ((b < 0.31) || (b > 0.69))) ? (1.0 - b) : b);
291 for (t = 0; t < 4; ++t) {
292 sp->later.r[t] = pats[pat][t] ? r : r2;
293 sp->later.g[t] = pats[pat][t] ? g : g2;
294 sp->later.b[t] = pats[pat][t] ? b : b2;
298 sp->later.rotx = myrand(360) - 180;
299 sp->later.rotz = myrand(160) - 80;
304 inputs(superquadricsstruct * sp)
307 double u, v, mode3, cn3, inverter2, flatu, flatv;
309 if (sp->Mode < 1.000001) {
313 } else if (sp->Mode < 2.000001) {
315 cn3 = (sp->Mode - 1.0) * 1.5;
316 inverter2 = (sp->Mode - 1.0) * -2.0 + 1.0;
318 mode3 = (sp->Mode - 1.0);
319 cn3 = (sp->Mode - 2.0) / 2.0 + 1.5;
324 flatu = M_PI / (sp->resolution - 1);
325 flatv = mode3 * M_PI / ((sp->resolution - 1) * 2);
330 /* (void) printf("Calculating....\n"); */
331 for (iv = 1; iv <= sp->resolution; iv++) {
333 /* u ranges from PI down to -PI */
334 u = (1 - iv) * 2 * M_PI / (sp->resolution - 1) + M_PI;
336 /* v ranges from PI/2 down to -PI/2 */
337 v = (1 - iv) * mode3 * M_PI / (sp->resolution - 1) + M_PI * (mode3 / 2.0);
339 /* Use of xExponent */
340 sp->se[iv] = Sine(u, sp->xExponent);
341 sp->ce[iv] = Cosine(u, sp->xExponent);
342 sp->sn[iv] = Sine(v, sp->yExponent);
343 sp->cn[iv] = Cosine(v, sp->yExponent) * inverter2 + cn3;
345 /* Normal vector computations only */
346 sp->sw[iv] = Sine(u + flatu, 2 - sp->xExponent);
347 sp->cw[iv] = Cosine(u + flatu, 2 - sp->xExponent);
348 sp->ss[iv] = Sine(v + flatv, 2 - sp->yExponent) * inverter2;
349 sp->cs[iv] = Cosine(v + flatv, 2 - sp->yExponent);
352 /* Now fix up the endpoints */
353 sp->se[sp->resolution] = sp->se[1];
354 sp->ce[sp->resolution] = sp->ce[1];
356 if (sp->Mode > 2.999999) {
357 sp->sn[sp->resolution] = sp->sn[1];
358 sp->cn[sp->resolution] = sp->cn[1];
364 DoneScale(superquadricsstruct * sp)
366 double xx, yy, zz, xp = 0, yp = 0, zp = 0, xn, yn, zn, xnp = 0,
370 /* Hey don't knock my 2-letter variable names. Simon's BASIC rules, man! ;-> */
371 /* Just kidding..... */
374 for (ih = 1; ih <= sp->resolution; ih++) {
376 for (iv = 1; iv <= sp->resolution; iv++) {
379 glColor3f(sp->curmat[toggle][0], sp->curmat[toggle][1], sp->curmat[toggle][2]);
381 glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE, sp->curmat[toggle]);
383 xx = sp->cn[iv] * sp->ce[ih];
384 zz = sp->cn[iv] * sp->se[ih];
388 if ((ih > 1) || (iv > 1)) {
391 glVertex3f(xx, yy, zz);
392 glVertex3f(sp->Prevxx[iv], sp->Prevyy[iv], sp->Prevzz[iv]);
395 glVertex3f(xx, yy, zz);
396 glVertex3f(sp->Prevxx[iv - 1], sp->Prevyy[iv - 1], sp->Prevzz[iv - 1]);
398 /* PURIFY 4.0.1 reports an unitialized memory read on the next line when using
399 * MesaGL 2.2 and -mono. This has been fixed in MesaGL 2.3 and later. */
403 if ((sp->cs[iv] > 1e+10) || (sp->cs[iv] < -1e+10)) {
408 xn = sp->cs[iv] * sp->cw[ih];
409 zn = sp->cs[iv] * sp->sw[ih];
412 if ((ih > 1) && (iv > 1)) {
413 glNormal3f(xn, yn, zn);
415 glVertex3f(xx, yy, zz);
417 glNormal3f(sp->Prevxn[iv], sp->Prevyn[iv], sp->Prevzn[iv]);
418 glVertex3f(sp->Prevxx[iv], sp->Prevyy[iv], sp->Prevzz[iv]);
420 glNormal3f(xnp, ynp, znp);
421 glVertex3f(xp, yp, zp);
423 glNormal3f(sp->Prevxn[iv - 1], sp->Prevyn[iv - 1], sp->Prevzn[iv - 1]);
424 glVertex3f(sp->Prevxx[iv - 1], sp->Prevyy[iv - 1], sp->Prevzz[iv - 1]);
429 glShadeModel(GL_FLAT);
430 glDisable(GL_LIGHTING);
432 glVertex3f(xx, yy, zz);
433 glVertex3f(xx + xn, yy + yn, zz + zn);
436 glShadeModel(GL_SMOOTH);
437 glEnable(GL_LIGHTING);
439 xnp = sp->Prevxn[iv];
440 ynp = sp->Prevyn[iv];
441 znp = sp->Prevzn[iv];
458 /**** End of really old code ****/
461 SetCull(int init, superquadricsstruct * sp)
469 if (sp->Mode < 1.0001) {
471 glEnable(GL_CULL_FACE);
475 } else if (sp->Mode > 2.9999) {
477 glEnable(GL_CULL_FACE);
478 glCullFace(GL_FRONT);
483 glDisable(GL_CULL_FACE);
490 SetCurrentShape(superquadricsstruct * sp)
494 sp->xExponent = sp->now.xExponent = sp->later.xExponent;
495 sp->yExponent = sp->now.yExponent = sp->later.yExponent;
497 for (t = 0; t < 4; ++t) {
498 sp->curmat[t][0] = sp->now.r[t] = sp->later.r[t];
499 sp->curmat[t][1] = sp->now.g[t] = sp->later.g[t];
500 sp->curmat[t][2] = sp->now.b[t] = sp->later.b[t];
503 sp->Mode = (double) (sp->now.Mode = sp->later.Mode);
504 sp->rotx = sp->now.rotx = sp->later.rotx;
505 sp->rotz = sp->now.rotz = sp->later.rotz;
507 sp->counter = -sp->maxwait;
513 NextSuperquadric(superquadricsstruct * sp)
518 sp->roty -= sp->spinspeed;
519 while (sp->roty >= 360.0)
521 while (sp->roty < 0.0)
526 if (sp->counter > 0) {
527 if (--sp->counter == 0) {
529 if (sp->counter == 0) { /* Happens if sp->maxwait == 0 */
531 sp->counter = sp->maxcount;
534 fnow = (double) sp->counter / (double) sp->maxcount;
535 flater = (double) (sp->maxcount - sp->counter) / (double) sp->maxcount;
536 sp->xExponent = sp->now.xExponent * fnow + sp->later.xExponent * flater;
537 sp->yExponent = sp->now.yExponent * fnow + sp->later.yExponent * flater;
539 for (t = 0; t < 4; ++t) {
540 sp->curmat[t][0] = sp->now.r[t] * fnow + sp->later.r[t] * flater;
541 sp->curmat[t][1] = sp->now.g[t] * fnow + sp->later.g[t] * flater;
542 sp->curmat[t][2] = sp->now.b[t] * fnow + sp->later.b[t] * flater;
545 sp->Mode = (double) sp->now.Mode * fnow + (double) sp->later.Mode * flater;
546 sp->rotx = (double) sp->now.rotx * fnow + (double) sp->later.rotx * flater;
547 sp->rotz = (double) sp->now.rotz * fnow + (double) sp->later.rotz * flater;
552 if (++sp->counter >= 0) {
554 sp->counter = sp->maxcount;
560 DisplaySuperquadrics(superquadricsstruct * sp)
562 glDrawBuffer(GL_BACK);
564 glClear(GL_COLOR_BUFFER_BIT);
566 glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
568 if (sp->viewcount < 1) {
569 sp->viewcount = sp->viewwait;
570 ReshapeSuperquadrics(-1, -1);
573 glTranslatef(0.0, 0.0, -((GLfloat) (sp->dist) / 16.0) - (sp->Mode * 3.0 - 1.0)); /* viewing transform */
574 glRotatef(sp->rotx, 1.0, 0.0, 0.0); /* pitch */
575 glRotatef(sp->rotz, 0.0, 0.0, 1.0); /* bank */
576 glRotatef(sp->roty, 0.0, 1.0, 0.0); /* "spin", like heading but comes after P & B */
584 /* Remember to flush & swap the buffers after calling this function! */
588 NextSuperquadricDisplay(superquadricsstruct * sp)
590 NextSuperquadric(sp);
591 DisplaySuperquadrics(sp);
596 ReshapeSuperquadrics(int w, int h)
598 static int last_w = 0, last_h = 0;
599 int maxsize, cursize;
608 maxsize = (w < h) ? w : h;
609 if (maxsize <= MINSIZE) {
612 cursize = myrand(maxsize - MINSIZE) + MINSIZE;
614 if ((w > cursize) && (h > cursize)) {
615 glViewport(myrand(w - cursize), myrand(h - cursize), cursize, cursize);
618 glViewport(0, 0, w, h);
620 glMatrixMode(GL_PROJECTION);
622 gluPerspective(30.0, (GLfloat) w / (GLfloat) h, 0.1, 200.0);
623 glMatrixMode(GL_MODELVIEW);
628 InitSuperquadrics(int wfmode, int snorm, int res, int count, float speed, superquadricsstruct * sp)
631 {0.4, 0.4, 0.4, 1.0};
633 {10.0, 1.0, 1.0, 10.0};
634 GLfloat mat_diffuse[] =
635 {1.0, 0.5, 0.5, 1.0};
636 GLfloat mat_specular[] =
637 {0.8, 0.8, 0.8, 1.0};
638 GLfloat mat_shininess[] =
643 for (t = 0; t < 4; ++t)
644 sp->curmat[t][3] = 1.0;
649 sp->dist = (16 << 3);
650 sp->wireframe = sp->flatshade = sp->shownorms = 0;
651 sp->maxcount = count;
652 if (sp->maxcount < 1)
654 sp->maxwait = sp->maxcount >> 1;
657 sp->spinspeed = speed;
658 sp->viewcount = sp->viewwait = (sp->maxcount < 2) ? 1 : (sp->maxcount << 3);
664 sp->resolution = res;
675 glShadeModel(GL_FLAT);
676 glDisable(GL_LIGHTING);
677 glColor3f(mat_diffuse[0], mat_diffuse[1], mat_diffuse[2]);
680 glShadeModel(GL_FLAT);
684 glEnable(GL_LIGHTING);
686 glDepthFunc(GL_LEQUAL);
687 glEnable(GL_DEPTH_TEST);
689 glLightfv(GL_LIGHT0, GL_AMBIENT, ambient);
690 glLightfv(GL_LIGHT0, GL_POSITION, position);
692 /*glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE, mat_diffuse); */
693 glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, mat_specular);
694 glMaterialfv(GL_FRONT_AND_BACK, GL_SHININESS, mat_shininess);
696 glLightModeli(GL_LIGHT_MODEL_TWO_SIDE, GL_TRUE);
699 glEnable(GL_NORMALIZE);
704 MakeUpStuff(1, sp); /* Initialize it */
705 sp->counter = sp->maxcount;
708 /* End of superquadrics main functions */
711 init_superquadrics(ModeInfo * mi)
713 Display *display = MI_DISPLAY(mi);
714 Window window = MI_WINDOW(mi);
715 int screen = MI_SCREEN(mi);
717 superquadricsstruct *sp;
719 if (superquadrics == NULL) {
720 if ((superquadrics = (superquadricsstruct *) calloc(MI_NUM_SCREENS(mi),
721 sizeof (superquadricsstruct))) == NULL)
724 sp = &superquadrics[screen];
725 sp->mono = (MI_IS_MONO(mi) ? 1 : 0);
727 if ((sp->glx_context = init_GL(mi)) != NULL) {
729 InitSuperquadrics(MI_IS_WIREFRAME(mi), 0,
730 MI_COUNT(mi), MI_CYCLES(mi), spinspeed, sp);
731 ReshapeSuperquadrics(MI_WIDTH(mi), MI_HEIGHT(mi));
733 DisplaySuperquadrics(sp);
735 glXSwapBuffers(display, window);
742 draw_superquadrics(ModeInfo * mi)
744 superquadricsstruct *sp = &superquadrics[MI_SCREEN(mi)];
745 Display *display = MI_DISPLAY(mi);
746 Window window = MI_WINDOW(mi);
748 if (!sp->glx_context)
751 glXMakeCurrent(display, window, *(sp->glx_context));
753 NextSuperquadricDisplay(sp);
756 glXSwapBuffers(display, window);
760 refresh_superquadrics(ModeInfo * mi)
762 /* Nothing happens here */
766 release_superquadrics(ModeInfo * mi)
768 if (superquadrics != NULL) {
769 (void) free((void *) superquadrics);
770 superquadrics = NULL;
778 /* End of superquadrics.c */