1 /* -*- Mode: C; tab-width: 4 -*- */
2 /* superquadrics --- 3D mathematical shapes */
5 static const char sccsid[] = "@(#)superquadrics.c 4.07 97/11/24 xlockmore";
9 * Permission to use, copy, modify, and distribute this software and its
10 * documentation for any purpose and without fee is hereby granted,
11 * provided that the above copyright notice appear in all copies and that
12 * both that copyright notice and this permission notice appear in
13 * supporting documentation.
15 * This file is provided AS IS with no warranties of any kind. The author
16 * shall have no liability with respect to the infringement of copyrights,
17 * trade secrets or any patents by this file or any part thereof. In no
18 * event will the author be liable for any lost revenue or profits or
19 * other special, indirect and consequential damages.
21 * Superquadrics were invented by Dr. Alan Barr of Caltech University.
22 * They were first published in "Computer Graphics and Applications",
23 * volume 1, number 1, 1981, in the article "Superquadrics and Angle-
24 * Preserving Transformations." Dr. Barr based the Superquadrics on
25 * Piet Hein's "super ellipses." Super ellipses are like 2D ellipses,
26 * except that the formula includes an exponent, raising its X and Y
27 * values to a (fractional) power, and allowing them to gradually
28 * change from round to square edges. Superquadrics extend this
29 * idea into 3 dimensions, using two exponents to modify a
30 * quadric surface in a similar fashion.
33 * 30-Mar-97: Turned into a module for xlockmore 4.02 alpha. The code
34 * is almost unrecognizable now from the first revision, except for
35 * a few remaining two-letter variable names. I still don't have
36 * the normal vectors working right (I wrote the buggy normal vector
37 * code myself, can you tell?)
38 * 07-Jan-97: A legend reborn; Superquadrics make an appearance as a
39 * real OpenGL program written in C. I can even render them with
40 * proper lighting and specular highlights. Gee, they look almost
41 * as good now as the original color plates of them that my uncle
42 * showed me as a child in 1981. I don't know what computer hardware
43 * he was using at the time, but it's taken a couple decades for the
44 * PC clone hardware to catch up to it.
45 * 05-Jan-97: After almost a decade, Superquadrics had almost faded away
46 * into the myths and folklore of all the things my brother and I played
47 * with on computers when we were kids with too much time on our hands.
48 * I had since gotten involved in Unix, OpenGL, and other things.
49 * A sudden flash of inspiration caused me to dig out the old Pascal
50 * source code, run it through p2c, and start ripping away the old
51 * wireframe rendering code, to be replaced by OpenGL.
52 * Late 1989 or early 1990: Around this time I did the Turbo Pascal
53 * port of the Superquadrics. Unfortunately, many of the original variable
54 * names remained the same from the C= 64 original. This was unfortunate
55 * because BASIC on the c64 only allowed 2-letter, global variable names.
56 * But the speed improvement over BASIC was very impressive at the time.
57 * Thanksgiving, 1987: Written. My uncle Al, who invented Superquadrics some
58 * years earlier, came to visit us. I was a high school kid at the time,
59 * with nothing more than a Commodore 64. Somehow we wrote this program,
60 * (he did the math obviously, I just coded it into BASIC for the c64).
61 * Yeah, 320x200 resolution, colorless white wireframe, and half an hour
62 * rendering time per superquadric. PLOT x,y. THOSE were the days.
63 * In the following years I would port Superquadrics to AppleBASIC,
64 * AmigaBASIC, and then Turbo Pascal for IBM clones. 5 minutes on a 286!
65 * Talk about fast rendering! But these days, when my Pentium 166 runs
66 * the same program, the superquadric will already be waiting on the
67 * screen before my monitor can change frequency from text to graphics
68 * mode. Can't time the number of minutes that way! Darn ;)
74 # define DEFAULTS "*delay: 40000 \n" \
77 "*showFPS: False \n" \
78 "*wireframe: False \n" \
79 "*suppressRotationAnimation: True\n" \
81 # define release_superquadrics 0
82 # define superquadrics_handle_event 0
83 # include "xlockmore.h" /* from the xscreensaver distribution */
84 #else /* !STANDALONE */
85 # include "xlock.h" /* from the xlockmore distribution */
86 #endif /* !STANDALONE */
91 * Note for low-CPU-speed machines: If your frame rate is so low that
92 * attempts at animation appear futile, try using "-cycles 1", which puts
93 * Superquadrics into kind of a slide-show mode. It will still use up
94 * all of your CPU power, but it may look nicer.
97 #define DEF_SPINSPEED "5.0"
99 static float spinspeed;
101 static XrmOptionDescRec opts[] =
103 {"-spinspeed", ".superquadrics.spinspeed", XrmoptionSepArg, 0}
105 static argtype vars[] =
107 {&spinspeed, "spinspeed", "Spinspeed", DEF_SPINSPEED, t_Float}
109 static OptionStruct desc[] =
111 {"-spinspeed num", "speed of rotation, in degrees per frame"}
114 ENTRYPOINT ModeSpecOpt superquadrics_opts =
115 {sizeof opts / sizeof opts[0], opts, sizeof vars / sizeof vars[0], vars, desc};
118 ModStruct superquadrics_description =
119 {"superquadrics", "init_superquadrics", "draw_superquadrics", NULL,
120 "refresh_superquadrics", "init_superquadrics", NULL, &superquadrics_opts,
121 1000, 25, 40, 1, 4, 1.0, "",
122 "Shows 3D mathematical shapes", 0, NULL};
129 typedef double dimi[MaxRes + 1];
132 double xExponent, yExponent;
133 GLfloat r[4], g[4], b[4];
139 GLXContext *glx_context;
140 int dist, wireframe, flatshade, shownorms, maxcount, maxwait;
141 int counter, viewcount, viewwait, mono;
142 GLfloat curmat[4][4], rotx, roty, rotz, spinspeed;
143 /* In dimi: the first letter stands for cosine/sine, the second
144 * stands for North, South, East, or West. I think.
146 dimi cs, se, sw, sn, ss, ce, cw, cn, Prevxx, Prevyy, Prevzz,
147 Prevxn, Prevyn, Prevzn;
148 double xExponent, yExponent, Mode;
155 } superquadricsstruct;
157 static superquadricsstruct *superquadrics = NULL;
159 #define CLIP_NORMALS 10000.0
161 static void ReshapeSuperquadrics(int w, int h);
166 return ((int) (((float) range) * LRAND() / (MAXRAND)));
172 return (LRAND() / (MAXRAND));
175 /* Some old, old, OLD code follows. Ahh this takes me back..... */
177 /* Output from p2c, the Pascal-to-C translator */
178 /* From input file "squad.pas" */
181 XtoY(double x, double y)
185 /* This is NOT your typical raise-X-to-the-Y-power function. Do not attempt
186 * to replace this with a standard exponent function. If you must, just
187 * replace the "a = exp(y * log(z));" line with something faster.
196 if (a > CLIP_NORMALS)
205 Sine(double x, double e)
207 /* This is just the sine wave raised to the exponent. BUT, you can't
208 * raise negative numbers to fractional exponents. So we have a special
209 * XtoY routune which handles it in a way useful to superquadrics.
212 return (XtoY(sin(x), e));
217 Cosine(double x, double e)
219 return (XtoY(cos(x), e));
224 MakeUpStuff(int allstuff, superquadricsstruct * sp)
228 GLfloat r, g, b, r2, g2, b2;
232 if (sp->maxcount < 2)
234 dostuff = allstuff * 15;
236 dostuff = myrand(3) + 1;
237 if (myrand(2) || (dostuff & 1))
243 sp->later.xExponent = (((long) floor(myrandreal() * 250 + 0.5)) / 100.0) + 0.1;
244 sp->later.yExponent = (((long) floor(myrandreal() * 250 + 0.5)) / 100.0) + 0.1;
246 /* Increase the 2.0 .. 2.5 range to 2.0 .. 3.0 */
247 if (sp->later.xExponent > 2.0)
248 sp->later.xExponent = (sp->later.xExponent * 2.0) - 2.0;
249 if (sp->later.yExponent > 2.0)
250 sp->later.yExponent = (sp->later.yExponent * 2.0) - 2.0;
254 sp->later.Mode = myrand(3L) + 1;
255 } while (!allstuff && (sp->later.Mode == sp->now.Mode));
256 /* On init: make sure it can stay in mode 1 if it feels like it. */
264 b = g = r = (GLfloat) (140 + myrand(100)) / 255.0;
265 b2 = g2 = r2 = ((r > 0.69) ? (1.0 - r) : r);
268 r = (GLfloat) (40 + myrand(200)) / 255.0;
269 g = (GLfloat) (40 + myrand(200)) / 255.0;
270 b = (GLfloat) (40 + myrand(200)) / 255.0;
272 r2 = ((myrand(4) && ((r < 0.31) || (r > 0.69))) ? (1.0 - r) : r);
273 g2 = ((myrand(4) && ((g < 0.31) || (g > 0.69))) ? (1.0 - g) : g);
274 b2 = ((myrand(4) && ((b < 0.31) || (b > 0.69))) ? (1.0 - b) : b);
278 for (t = 0; t < 4; ++t) {
279 sp->later.r[t] = sp->pats[pat][t] ? r : r2;
280 sp->later.g[t] = sp->pats[pat][t] ? g : g2;
281 sp->later.b[t] = sp->pats[pat][t] ? b : b2;
285 sp->later.rotx = myrand(360) - 180;
286 sp->later.rotz = myrand(160) - 80;
291 inputs(superquadricsstruct * sp)
294 double u, v, mode3, cn3, inverter2, flatu, flatv;
296 if (sp->Mode < 1.000001) {
300 } else if (sp->Mode < 2.000001) {
302 cn3 = (sp->Mode - 1.0) * 1.5;
303 inverter2 = (sp->Mode - 1.0) * -2.0 + 1.0;
305 mode3 = (sp->Mode - 1.0);
306 cn3 = (sp->Mode - 2.0) / 2.0 + 1.5;
311 flatu = M_PI / (sp->resolution - 1);
312 flatv = mode3 * M_PI / ((sp->resolution - 1) * 2);
317 /* (void) printf("Calculating....\n"); */
318 for (iv = 1; iv <= sp->resolution; iv++) {
320 /* u ranges from PI down to -PI */
321 u = (1 - iv) * 2 * M_PI / (sp->resolution - 1) + M_PI;
323 /* v ranges from PI/2 down to -PI/2 */
324 v = (1 - iv) * mode3 * M_PI / (sp->resolution - 1) + M_PI * (mode3 / 2.0);
326 /* Use of xExponent */
327 sp->se[iv] = Sine(u, sp->xExponent);
328 sp->ce[iv] = Cosine(u, sp->xExponent);
329 sp->sn[iv] = Sine(v, sp->yExponent);
330 sp->cn[iv] = Cosine(v, sp->yExponent) * inverter2 + cn3;
332 /* Normal vector computations only */
333 sp->sw[iv] = Sine(u + flatu, 2 - sp->xExponent);
334 sp->cw[iv] = Cosine(u + flatu, 2 - sp->xExponent);
335 sp->ss[iv] = Sine(v + flatv, 2 - sp->yExponent) * inverter2;
336 sp->cs[iv] = Cosine(v + flatv, 2 - sp->yExponent);
339 /* Now fix up the endpoints */
340 sp->se[sp->resolution] = sp->se[1];
341 sp->ce[sp->resolution] = sp->ce[1];
343 if (sp->Mode > 2.999999) {
344 sp->sn[sp->resolution] = sp->sn[1];
345 sp->cn[sp->resolution] = sp->cn[1];
351 DoneScale(superquadricsstruct * sp)
353 double xx, yy, zz, xp = 0, yp = 0, zp = 0, xn, yn, zn, xnp = 0,
358 /* Hey don't knock my 2-letter variable names. Simon's BASIC rules, man! ;-> */
359 /* Just kidding..... */
362 for (ih = 1; ih <= sp->resolution; ih++) {
364 for (iv = 1; iv <= sp->resolution; iv++) {
367 glColor3f(sp->curmat[toggle][0], sp->curmat[toggle][1], sp->curmat[toggle][2]);
369 glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE, sp->curmat[toggle]);
371 xx = sp->cn[iv] * sp->ce[ih];
372 zz = sp->cn[iv] * sp->se[ih];
376 if ((ih > 1) || (iv > 1)) {
379 glVertex3f(xx, yy, zz);
380 glVertex3f(sp->Prevxx[iv], sp->Prevyy[iv], sp->Prevzz[iv]);
384 glVertex3f(xx, yy, zz);
385 glVertex3f(sp->Prevxx[iv - 1], sp->Prevyy[iv - 1], sp->Prevzz[iv - 1]);
388 /* PURIFY 4.0.1 reports an unitialized memory read on the next line when using
389 * MesaGL 2.2 and -mono. This has been fixed in MesaGL 2.3 and later. */
393 if ((sp->cs[iv] > 1e+10) || (sp->cs[iv] < -1e+10)) {
398 xn = sp->cs[iv] * sp->cw[ih];
399 zn = sp->cs[iv] * sp->sw[ih];
402 if ((ih > 1) && (iv > 1)) {
403 glNormal3f(xn, yn, zn);
405 glVertex3f(xx, yy, zz);
407 glNormal3f(sp->Prevxn[iv], sp->Prevyn[iv], sp->Prevzn[iv]);
408 glVertex3f(sp->Prevxx[iv], sp->Prevyy[iv], sp->Prevzz[iv]);
410 glNormal3f(xnp, ynp, znp);
411 glVertex3f(xp, yp, zp);
413 glNormal3f(sp->Prevxn[iv - 1], sp->Prevyn[iv - 1], sp->Prevzn[iv - 1]);
414 glVertex3f(sp->Prevxx[iv - 1], sp->Prevyy[iv - 1], sp->Prevzz[iv - 1]);
420 glShadeModel(GL_FLAT);
421 glDisable(GL_LIGHTING);
423 glVertex3f(xx, yy, zz);
424 glVertex3f(xx + xn, yy + yn, zz + zn);
428 glShadeModel(GL_SMOOTH);
429 glEnable(GL_LIGHTING);
431 xnp = sp->Prevxn[iv];
432 ynp = sp->Prevyn[iv];
433 znp = sp->Prevzn[iv];
451 /**** End of really old code ****/
454 SetCull(int init, superquadricsstruct * sp)
457 glDisable(GL_CULL_FACE);
461 if (sp->Mode < 1.0001) {
462 if (sp->cullmode != 1) {
463 glEnable(GL_CULL_FACE);
467 } else if (sp->Mode > 2.9999) {
468 if (sp->cullmode != 2) {
469 glEnable(GL_CULL_FACE);
470 glCullFace(GL_FRONT);
475 glDisable(GL_CULL_FACE);
482 SetCurrentShape(superquadricsstruct * sp)
486 sp->xExponent = sp->now.xExponent = sp->later.xExponent;
487 sp->yExponent = sp->now.yExponent = sp->later.yExponent;
489 for (t = 0; t < 4; ++t) {
490 sp->curmat[t][0] = sp->now.r[t] = sp->later.r[t];
491 sp->curmat[t][1] = sp->now.g[t] = sp->later.g[t];
492 sp->curmat[t][2] = sp->now.b[t] = sp->later.b[t];
495 sp->Mode = (double) (sp->now.Mode = sp->later.Mode);
496 sp->rotx = sp->now.rotx = sp->later.rotx;
497 sp->rotz = sp->now.rotz = sp->later.rotz;
499 sp->counter = -sp->maxwait;
505 NextSuperquadric(superquadricsstruct * sp)
510 sp->roty -= sp->spinspeed;
511 while (sp->roty >= 360.0)
513 while (sp->roty < 0.0)
518 if (sp->counter > 0) {
519 if (--sp->counter == 0) {
521 if (sp->counter == 0) { /* Happens if sp->maxwait == 0 */
523 sp->counter = sp->maxcount;
526 fnow = (double) sp->counter / (double) sp->maxcount;
527 flater = (double) (sp->maxcount - sp->counter) / (double) sp->maxcount;
528 sp->xExponent = sp->now.xExponent * fnow + sp->later.xExponent * flater;
529 sp->yExponent = sp->now.yExponent * fnow + sp->later.yExponent * flater;
531 for (t = 0; t < 4; ++t) {
532 sp->curmat[t][0] = sp->now.r[t] * fnow + sp->later.r[t] * flater;
533 sp->curmat[t][1] = sp->now.g[t] * fnow + sp->later.g[t] * flater;
534 sp->curmat[t][2] = sp->now.b[t] * fnow + sp->later.b[t] * flater;
537 sp->Mode = (double) sp->now.Mode * fnow + (double) sp->later.Mode * flater;
538 sp->rotx = (double) sp->now.rotx * fnow + (double) sp->later.rotx * flater;
539 sp->rotz = (double) sp->now.rotz * fnow + (double) sp->later.rotz * flater;
544 if (++sp->counter >= 0) {
546 sp->counter = sp->maxcount;
552 DisplaySuperquadrics(ModeInfo *mi)
554 superquadricsstruct *sp = &superquadrics[MI_SCREEN(mi)];
556 glDrawBuffer(GL_BACK);
558 glClear(GL_COLOR_BUFFER_BIT);
560 glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
562 if (sp->viewcount < 1) {
563 sp->viewcount = sp->viewwait;
564 /* ReshapeSuperquadrics(-1, -1);*/
567 glTranslatef(0.0, 0.0, -((GLfloat) (sp->dist) / 16.0) - (sp->Mode * 3.0 - 1.0)); /* viewing transform */
568 glRotatef(sp->rotx, 1.0, 0.0, 0.0); /* pitch */
569 glRotatef(sp->rotz, 0.0, 0.0, 1.0); /* bank */
570 glRotatef(sp->roty, 0.0, 1.0, 0.0); /* "spin", like heading but comes after P & B */
574 glScalef(0.7, 0.7, 0.7); /* jwz: scale it down a bit */
576 # ifdef HAVE_MOBILE /* Keep it the same relative size when rotated. */
578 GLfloat h = MI_HEIGHT(mi) / (GLfloat) MI_WIDTH(mi);
579 int o = (int) current_device_rotation();
580 if (o != 0 && o != 180 && o != -180)
581 glScalef (1/h, 1/h, 1/h);
585 polys = DoneScale(sp);
589 /* Remember to flush & swap the buffers after calling this function! */
594 NextSuperquadricDisplay(ModeInfo *mi)
596 superquadricsstruct *sp = &superquadrics[MI_SCREEN(mi)];
597 NextSuperquadric(sp);
598 return DisplaySuperquadrics(mi);
603 ReshapeSuperquadrics(int w, int h)
606 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);
621 glViewport(0, 0, w, h);
624 glMatrixMode(GL_PROJECTION);
626 gluPerspective(15.0, (GLfloat) w / (GLfloat) h, 0.1, 200.0);
627 glMatrixMode(GL_MODELVIEW);
632 InitSuperquadrics(int wfmode, int snorm, int res, int count, float speed, superquadricsstruct * sp)
635 {0.4, 0.4, 0.4, 1.0};
637 {10.0, 1.0, 1.0, 10.0};
638 GLfloat mat_diffuse[] =
639 {1.0, 0.5, 0.5, 1.0};
640 GLfloat mat_specular[] =
641 {0.8, 0.8, 0.8, 1.0};
642 GLfloat mat_shininess[] =
647 for (t = 0; t < 4; ++t) {
648 sp->curmat[t][0] = 0.0;
649 sp->curmat[t][1] = 0.0;
650 sp->curmat[t][2] = 0.0;
651 sp->curmat[t][3] = 1.0;
657 sp->dist = (16 << 3);
658 sp->wireframe = sp->flatshade = sp->shownorms = 0;
659 sp->maxcount = count;
660 if (sp->maxcount < 1)
662 sp->maxwait = sp->maxcount >> 1;
666 sp->spinspeed = speed;
667 sp->viewcount = sp->viewwait = (sp->maxcount < 2) ? 1 : (sp->maxcount << 3);
673 sp->resolution = res;
686 glShadeModel(GL_FLAT);
687 glDisable(GL_LIGHTING);
688 glColor3f(mat_diffuse[0], mat_diffuse[1], mat_diffuse[2]);
691 glShadeModel(GL_FLAT);
695 glEnable(GL_LIGHTING);
697 glDepthFunc(GL_LEQUAL);
698 glEnable(GL_DEPTH_TEST);
700 glLightfv(GL_LIGHT0, GL_AMBIENT, ambient);
701 glLightfv(GL_LIGHT0, GL_POSITION, position);
703 /*glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE, mat_diffuse); */
704 glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, mat_specular);
705 glMaterialfv(GL_FRONT_AND_BACK, GL_SHININESS, mat_shininess);
707 glLightModeli(GL_LIGHT_MODEL_TWO_SIDE, GL_TRUE);
710 glEnable(GL_NORMALIZE);
715 MakeUpStuff(1, sp); /* Initialize it */
716 sp->counter = sp->maxcount;
719 /* End of superquadrics main functions */
722 init_superquadrics(ModeInfo * mi)
724 Display *display = MI_DISPLAY(mi);
725 Window window = MI_WINDOW(mi);
726 int screen = MI_SCREEN(mi);
728 superquadricsstruct *sp;
730 MI_INIT (mi, superquadrics, NULL);
731 sp = &superquadrics[screen];
732 sp->mono = (MI_IS_MONO(mi) ? 1 : 0);
747 if ((sp->glx_context = init_GL(mi)) != NULL) {
749 InitSuperquadrics(MI_IS_WIREFRAME(mi), 0,
750 MI_COUNT(mi), MI_CYCLES(mi), spinspeed, sp);
751 ReshapeSuperquadrics(MI_WIDTH(mi), MI_HEIGHT(mi));
753 DisplaySuperquadrics(mi);
755 glXSwapBuffers(display, window);
762 draw_superquadrics(ModeInfo * mi)
764 superquadricsstruct *sp = &superquadrics[MI_SCREEN(mi)];
765 Display *display = MI_DISPLAY(mi);
766 Window window = MI_WINDOW(mi);
768 if (!sp->glx_context)
771 glXMakeCurrent(display, window, *(sp->glx_context));
773 mi->polygon_count = NextSuperquadricDisplay(mi);
775 if (mi->fps_p) do_fps (mi);
777 glXSwapBuffers(display, window);
781 refresh_superquadrics(ModeInfo * mi)
783 /* Nothing happens here */
787 reshape_superquadrics(ModeInfo * mi, int width, int height)
789 ReshapeSuperquadrics(MI_WIDTH(mi), MI_HEIGHT(mi));
795 /* End of superquadrics.c */
797 XSCREENSAVER_MODULE ("Superquadrics", superquadrics)