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 # define superquadrics_handle_event 0
80 # include "xlockmore.h" /* from the xscreensaver distribution */
81 #else /* !STANDALONE */
82 # include "xlock.h" /* from the xlockmore distribution */
83 #endif /* !STANDALONE */
88 * Note for low-CPU-speed machines: If your frame rate is so low that
89 * attempts at animation appear futile, try using "-cycles 1", which puts
90 * Superquadrics into kind of a slide-show mode. It will still use up
91 * all of your CPU power, but it may look nicer.
94 #define DEF_SPINSPEED "5.0"
96 static float spinspeed;
98 static XrmOptionDescRec opts[] =
100 {"-spinspeed", ".superquadrics.spinspeed", XrmoptionSepArg, 0}
102 static argtype vars[] =
104 {&spinspeed, "spinspeed", "Spinspeed", DEF_SPINSPEED, t_Float}
106 static OptionStruct desc[] =
108 {"-spinspeed num", "speed of rotation, in degrees per frame"}
111 ENTRYPOINT ModeSpecOpt superquadrics_opts =
112 {sizeof opts / sizeof opts[0], opts, sizeof vars / sizeof vars[0], vars, desc};
115 ModStruct superquadrics_description =
116 {"superquadrics", "init_superquadrics", "draw_superquadrics", "release_superquadrics",
117 "refresh_superquadrics", "init_superquadrics", NULL, &superquadrics_opts,
118 1000, 25, 40, 1, 4, 1.0, "",
119 "Shows 3D mathematical shapes", 0, NULL};
126 typedef double dimi[MaxRes + 1];
129 double xExponent, yExponent;
130 GLfloat r[4], g[4], b[4];
136 GLXContext *glx_context;
137 int dist, wireframe, flatshade, shownorms, maxcount, maxwait;
138 int counter, viewcount, viewwait, mono;
139 GLfloat curmat[4][4], rotx, roty, rotz, spinspeed;
140 /* In dimi: the first letter stands for cosine/sine, the second
141 * stands for North, South, East, or West. I think.
143 dimi cs, se, sw, sn, ss, ce, cw, cn, Prevxx, Prevyy, Prevzz,
144 Prevxn, Prevyn, Prevzn;
145 double xExponent, yExponent, Mode;
152 } superquadricsstruct;
154 static superquadricsstruct *superquadrics = NULL;
156 #define CLIP_NORMALS 10000.0
158 static void ReshapeSuperquadrics(int w, int h);
163 return ((int) (((float) range) * LRAND() / (MAXRAND)));
169 return (LRAND() / (MAXRAND));
172 /* Some old, old, OLD code follows. Ahh this takes me back..... */
174 /* Output from p2c, the Pascal-to-C translator */
175 /* From input file "squad.pas" */
178 XtoY(double x, double y)
182 /* This is NOT your typical raise-X-to-the-Y-power function. Do not attempt
183 * to replace this with a standard exponent function. If you must, just
184 * replace the "a = exp(y * log(z));" line with something faster.
193 if (a > CLIP_NORMALS)
202 Sine(double x, double e)
204 /* This is just the sine wave raised to the exponent. BUT, you can't
205 * raise negative numbers to fractional exponents. So we have a special
206 * XtoY routune which handles it in a way useful to superquadrics.
209 return (XtoY(sin(x), e));
214 Cosine(double x, double e)
216 return (XtoY(cos(x), e));
221 MakeUpStuff(int allstuff, superquadricsstruct * sp)
225 GLfloat r, g, b, r2, g2, b2;
229 if (sp->maxcount < 2)
231 dostuff = allstuff * 15;
233 dostuff = myrand(3) + 1;
234 if (myrand(2) || (dostuff & 1))
240 sp->later.xExponent = (((long) floor(myrandreal() * 250 + 0.5)) / 100.0) + 0.1;
241 sp->later.yExponent = (((long) floor(myrandreal() * 250 + 0.5)) / 100.0) + 0.1;
243 /* Increase the 2.0 .. 2.5 range to 2.0 .. 3.0 */
244 if (sp->later.xExponent > 2.0)
245 sp->later.xExponent = (sp->later.xExponent * 2.0) - 2.0;
246 if (sp->later.yExponent > 2.0)
247 sp->later.yExponent = (sp->later.yExponent * 2.0) - 2.0;
251 sp->later.Mode = myrand(3L) + 1;
252 } while (!allstuff && (sp->later.Mode == sp->now.Mode));
253 /* On init: make sure it can stay in mode 1 if it feels like it. */
261 b = g = r = (GLfloat) (140 + myrand(100)) / 255.0;
262 b2 = g2 = r2 = ((r > 0.69) ? (1.0 - r) : r);
265 r = (GLfloat) (40 + myrand(200)) / 255.0;
266 g = (GLfloat) (40 + myrand(200)) / 255.0;
267 b = (GLfloat) (40 + myrand(200)) / 255.0;
269 r2 = ((myrand(4) && ((r < 0.31) || (r > 0.69))) ? (1.0 - r) : r);
270 g2 = ((myrand(4) && ((g < 0.31) || (g > 0.69))) ? (1.0 - g) : g);
271 b2 = ((myrand(4) && ((b < 0.31) || (b > 0.69))) ? (1.0 - b) : b);
275 for (t = 0; t < 4; ++t) {
276 sp->later.r[t] = sp->pats[pat][t] ? r : r2;
277 sp->later.g[t] = sp->pats[pat][t] ? g : g2;
278 sp->later.b[t] = sp->pats[pat][t] ? b : b2;
282 sp->later.rotx = myrand(360) - 180;
283 sp->later.rotz = myrand(160) - 80;
288 inputs(superquadricsstruct * sp)
291 double u, v, mode3, cn3, inverter2, flatu, flatv;
293 if (sp->Mode < 1.000001) {
297 } else if (sp->Mode < 2.000001) {
299 cn3 = (sp->Mode - 1.0) * 1.5;
300 inverter2 = (sp->Mode - 1.0) * -2.0 + 1.0;
302 mode3 = (sp->Mode - 1.0);
303 cn3 = (sp->Mode - 2.0) / 2.0 + 1.5;
308 flatu = M_PI / (sp->resolution - 1);
309 flatv = mode3 * M_PI / ((sp->resolution - 1) * 2);
314 /* (void) printf("Calculating....\n"); */
315 for (iv = 1; iv <= sp->resolution; iv++) {
317 /* u ranges from PI down to -PI */
318 u = (1 - iv) * 2 * M_PI / (sp->resolution - 1) + M_PI;
320 /* v ranges from PI/2 down to -PI/2 */
321 v = (1 - iv) * mode3 * M_PI / (sp->resolution - 1) + M_PI * (mode3 / 2.0);
323 /* Use of xExponent */
324 sp->se[iv] = Sine(u, sp->xExponent);
325 sp->ce[iv] = Cosine(u, sp->xExponent);
326 sp->sn[iv] = Sine(v, sp->yExponent);
327 sp->cn[iv] = Cosine(v, sp->yExponent) * inverter2 + cn3;
329 /* Normal vector computations only */
330 sp->sw[iv] = Sine(u + flatu, 2 - sp->xExponent);
331 sp->cw[iv] = Cosine(u + flatu, 2 - sp->xExponent);
332 sp->ss[iv] = Sine(v + flatv, 2 - sp->yExponent) * inverter2;
333 sp->cs[iv] = Cosine(v + flatv, 2 - sp->yExponent);
336 /* Now fix up the endpoints */
337 sp->se[sp->resolution] = sp->se[1];
338 sp->ce[sp->resolution] = sp->ce[1];
340 if (sp->Mode > 2.999999) {
341 sp->sn[sp->resolution] = sp->sn[1];
342 sp->cn[sp->resolution] = sp->cn[1];
348 DoneScale(superquadricsstruct * sp)
350 double xx, yy, zz, xp = 0, yp = 0, zp = 0, xn, yn, zn, xnp = 0,
354 /* Hey don't knock my 2-letter variable names. Simon's BASIC rules, man! ;-> */
355 /* Just kidding..... */
358 for (ih = 1; ih <= sp->resolution; ih++) {
360 for (iv = 1; iv <= sp->resolution; iv++) {
363 glColor3f(sp->curmat[toggle][0], sp->curmat[toggle][1], sp->curmat[toggle][2]);
365 glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE, sp->curmat[toggle]);
367 xx = sp->cn[iv] * sp->ce[ih];
368 zz = sp->cn[iv] * sp->se[ih];
372 if ((ih > 1) || (iv > 1)) {
375 glVertex3f(xx, yy, zz);
376 glVertex3f(sp->Prevxx[iv], sp->Prevyy[iv], sp->Prevzz[iv]);
379 glVertex3f(xx, yy, zz);
380 glVertex3f(sp->Prevxx[iv - 1], sp->Prevyy[iv - 1], sp->Prevzz[iv - 1]);
382 /* PURIFY 4.0.1 reports an unitialized memory read on the next line when using
383 * MesaGL 2.2 and -mono. This has been fixed in MesaGL 2.3 and later. */
387 if ((sp->cs[iv] > 1e+10) || (sp->cs[iv] < -1e+10)) {
392 xn = sp->cs[iv] * sp->cw[ih];
393 zn = sp->cs[iv] * sp->sw[ih];
396 if ((ih > 1) && (iv > 1)) {
397 glNormal3f(xn, yn, zn);
399 glVertex3f(xx, yy, zz);
401 glNormal3f(sp->Prevxn[iv], sp->Prevyn[iv], sp->Prevzn[iv]);
402 glVertex3f(sp->Prevxx[iv], sp->Prevyy[iv], sp->Prevzz[iv]);
404 glNormal3f(xnp, ynp, znp);
405 glVertex3f(xp, yp, zp);
407 glNormal3f(sp->Prevxn[iv - 1], sp->Prevyn[iv - 1], sp->Prevzn[iv - 1]);
408 glVertex3f(sp->Prevxx[iv - 1], sp->Prevyy[iv - 1], sp->Prevzz[iv - 1]);
413 glShadeModel(GL_FLAT);
414 glDisable(GL_LIGHTING);
416 glVertex3f(xx, yy, zz);
417 glVertex3f(xx + xn, yy + yn, zz + zn);
420 glShadeModel(GL_SMOOTH);
421 glEnable(GL_LIGHTING);
423 xnp = sp->Prevxn[iv];
424 ynp = sp->Prevyn[iv];
425 znp = sp->Prevzn[iv];
442 /**** End of really old code ****/
445 SetCull(int init, superquadricsstruct * sp)
448 glDisable(GL_CULL_FACE);
452 if (sp->Mode < 1.0001) {
453 if (sp->cullmode != 1) {
454 glEnable(GL_CULL_FACE);
458 } else if (sp->Mode > 2.9999) {
459 if (sp->cullmode != 2) {
460 glEnable(GL_CULL_FACE);
461 glCullFace(GL_FRONT);
466 glDisable(GL_CULL_FACE);
473 SetCurrentShape(superquadricsstruct * sp)
477 sp->xExponent = sp->now.xExponent = sp->later.xExponent;
478 sp->yExponent = sp->now.yExponent = sp->later.yExponent;
480 for (t = 0; t < 4; ++t) {
481 sp->curmat[t][0] = sp->now.r[t] = sp->later.r[t];
482 sp->curmat[t][1] = sp->now.g[t] = sp->later.g[t];
483 sp->curmat[t][2] = sp->now.b[t] = sp->later.b[t];
486 sp->Mode = (double) (sp->now.Mode = sp->later.Mode);
487 sp->rotx = sp->now.rotx = sp->later.rotx;
488 sp->rotz = sp->now.rotz = sp->later.rotz;
490 sp->counter = -sp->maxwait;
496 NextSuperquadric(superquadricsstruct * sp)
501 sp->roty -= sp->spinspeed;
502 while (sp->roty >= 360.0)
504 while (sp->roty < 0.0)
509 if (sp->counter > 0) {
510 if (--sp->counter == 0) {
512 if (sp->counter == 0) { /* Happens if sp->maxwait == 0 */
514 sp->counter = sp->maxcount;
517 fnow = (double) sp->counter / (double) sp->maxcount;
518 flater = (double) (sp->maxcount - sp->counter) / (double) sp->maxcount;
519 sp->xExponent = sp->now.xExponent * fnow + sp->later.xExponent * flater;
520 sp->yExponent = sp->now.yExponent * fnow + sp->later.yExponent * flater;
522 for (t = 0; t < 4; ++t) {
523 sp->curmat[t][0] = sp->now.r[t] * fnow + sp->later.r[t] * flater;
524 sp->curmat[t][1] = sp->now.g[t] * fnow + sp->later.g[t] * flater;
525 sp->curmat[t][2] = sp->now.b[t] * fnow + sp->later.b[t] * flater;
528 sp->Mode = (double) sp->now.Mode * fnow + (double) sp->later.Mode * flater;
529 sp->rotx = (double) sp->now.rotx * fnow + (double) sp->later.rotx * flater;
530 sp->rotz = (double) sp->now.rotz * fnow + (double) sp->later.rotz * flater;
535 if (++sp->counter >= 0) {
537 sp->counter = sp->maxcount;
543 DisplaySuperquadrics(superquadricsstruct * sp)
545 glDrawBuffer(GL_BACK);
547 glClear(GL_COLOR_BUFFER_BIT);
549 glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
551 if (sp->viewcount < 1) {
552 sp->viewcount = sp->viewwait;
553 /* ReshapeSuperquadrics(-1, -1);*/
556 glTranslatef(0.0, 0.0, -((GLfloat) (sp->dist) / 16.0) - (sp->Mode * 3.0 - 1.0)); /* viewing transform */
557 glRotatef(sp->rotx, 1.0, 0.0, 0.0); /* pitch */
558 glRotatef(sp->rotz, 0.0, 0.0, 1.0); /* bank */
559 glRotatef(sp->roty, 0.0, 1.0, 0.0); /* "spin", like heading but comes after P & B */
567 /* Remember to flush & swap the buffers after calling this function! */
571 NextSuperquadricDisplay(superquadricsstruct * sp)
573 NextSuperquadric(sp);
574 DisplaySuperquadrics(sp);
579 ReshapeSuperquadrics(int w, int h)
582 int maxsize, cursize;
584 maxsize = (w < h) ? w : h;
585 if (maxsize <= MINSIZE) {
588 cursize = myrand(maxsize - MINSIZE) + MINSIZE;
590 if ((w > cursize) && (h > cursize)) {
591 glViewport(myrand(w - cursize), myrand(h - cursize), cursize, cursize);
594 glViewport(0, 0, w, h);
597 glViewport(0, 0, w, h);
600 glMatrixMode(GL_PROJECTION);
602 gluPerspective(15.0, (GLfloat) w / (GLfloat) h, 0.1, 200.0);
603 glMatrixMode(GL_MODELVIEW);
608 InitSuperquadrics(int wfmode, int snorm, int res, int count, float speed, superquadricsstruct * sp)
611 {0.4, 0.4, 0.4, 1.0};
613 {10.0, 1.0, 1.0, 10.0};
614 GLfloat mat_diffuse[] =
615 {1.0, 0.5, 0.5, 1.0};
616 GLfloat mat_specular[] =
617 {0.8, 0.8, 0.8, 1.0};
618 GLfloat mat_shininess[] =
623 for (t = 0; t < 4; ++t) {
624 sp->curmat[t][0] = 0.0;
625 sp->curmat[t][1] = 0.0;
626 sp->curmat[t][2] = 0.0;
627 sp->curmat[t][3] = 1.0;
633 sp->dist = (16 << 3);
634 sp->wireframe = sp->flatshade = sp->shownorms = 0;
635 sp->maxcount = count;
636 if (sp->maxcount < 1)
638 sp->maxwait = sp->maxcount >> 1;
642 sp->spinspeed = speed;
643 sp->viewcount = sp->viewwait = (sp->maxcount < 2) ? 1 : (sp->maxcount << 3);
649 sp->resolution = res;
659 glClearColor(0.0,0.0,0.0,1.0);
663 glShadeModel(GL_FLAT);
664 glDisable(GL_LIGHTING);
665 glColor3f(mat_diffuse[0], mat_diffuse[1], mat_diffuse[2]);
668 glShadeModel(GL_FLAT);
672 glEnable(GL_LIGHTING);
674 glDepthFunc(GL_LEQUAL);
675 glEnable(GL_DEPTH_TEST);
677 glLightfv(GL_LIGHT0, GL_AMBIENT, ambient);
678 glLightfv(GL_LIGHT0, GL_POSITION, position);
680 /*glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE, mat_diffuse); */
681 glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, mat_specular);
682 glMaterialfv(GL_FRONT_AND_BACK, GL_SHININESS, mat_shininess);
684 glLightModeli(GL_LIGHT_MODEL_TWO_SIDE, GL_TRUE);
687 glEnable(GL_NORMALIZE);
692 MakeUpStuff(1, sp); /* Initialize it */
693 sp->counter = sp->maxcount;
696 /* End of superquadrics main functions */
699 init_superquadrics(ModeInfo * mi)
701 Display *display = MI_DISPLAY(mi);
702 Window window = MI_WINDOW(mi);
703 int screen = MI_SCREEN(mi);
705 superquadricsstruct *sp;
707 if (superquadrics == NULL) {
708 if ((superquadrics = (superquadricsstruct *) calloc(MI_NUM_SCREENS(mi),
709 sizeof (superquadricsstruct))) == NULL)
712 sp = &superquadrics[screen];
713 sp->mono = (MI_IS_MONO(mi) ? 1 : 0);
728 if ((sp->glx_context = init_GL(mi)) != NULL) {
730 InitSuperquadrics(MI_IS_WIREFRAME(mi), 0,
731 MI_COUNT(mi), MI_CYCLES(mi), spinspeed, sp);
732 ReshapeSuperquadrics(MI_WIDTH(mi), MI_HEIGHT(mi));
734 DisplaySuperquadrics(sp);
736 glXSwapBuffers(display, window);
743 draw_superquadrics(ModeInfo * mi)
745 superquadricsstruct *sp = &superquadrics[MI_SCREEN(mi)];
746 Display *display = MI_DISPLAY(mi);
747 Window window = MI_WINDOW(mi);
749 if (!sp->glx_context)
752 glXMakeCurrent(display, window, *(sp->glx_context));
754 NextSuperquadricDisplay(sp);
756 if (mi->fps_p) do_fps (mi);
758 glXSwapBuffers(display, window);
762 refresh_superquadrics(ModeInfo * mi)
764 /* Nothing happens here */
768 reshape_superquadrics(ModeInfo * mi, int width, int height)
770 ReshapeSuperquadrics(MI_WIDTH(mi), MI_HEIGHT(mi));
774 release_superquadrics(ModeInfo * mi)
776 if (superquadrics != NULL) {
777 (void) free((void *) superquadrics);
778 superquadrics = NULL;
786 /* End of superquadrics.c */
788 XSCREENSAVER_MODULE ("Superquadrics", superquadrics)