1 /* xscreensaver, Copyright (c) 2002-2014 Jamie Zawinski <jwz@jwz.org>
3 * Permission to use, copy, modify, distribute, and sell this software and its
4 * documentation for any purpose is hereby granted without fee, provided that
5 * the above copyright notice appear in all copies and that both that
6 * copyright notice and this permission notice appear in supporting
7 * documentation. No representations are made about the suitability of this
8 * software for any purpose. It is provided "as is" without express or
11 * Algorithm by Paul Bourke <pbourke@swin.edu.au>
12 * http://astronomy.swin.edu.au/~pbourke/geometry/sphericalh/
13 * Screensaver veneer and parameter selection by jwz.
17 * These closed objects are commonly called spherical harmonics,
18 * although they are only remotely related to the mathematical
19 * definition found in the solution to certain wave functions, most
20 * notable the eigenfunctions of angular momentum operators.
22 * The formula is quite simple: the form used here is based upon
23 * spherical (polar) coordinates (radius, theta, phi).
25 * r = sin(m0 phi) ^ m1 +
27 * sin(m4 theta) ^ m5 +
30 * Where phi ranges from 0 to pi (lines of latitude), and theta ranges
31 * from 0 to 2 pi (lines of longitude), and r is the radius. The
32 * parameters m0, m1, m2, m3, m4, m5, m6, and m7 are all integers
33 * greater than or equal to 0.
35 * As the degree increases, the objects become increasingly "pointed"
36 * and a large number of polygons are required to represent the surface
41 * The eight parameters live in the `cc->m' array.
42 * Each time we permute the image, we alter *one* of those eight parameters.
43 * Each time we alter a parameter, we move it in the same direction (either
44 * toward larger or smaller values) in the range [0, 3].
46 * By altering only one parameter at a time, and only by small amounts,
47 * we tend to produce successive objects that are pretty similar to each
48 * other, so you can see a progression.
50 * It'd be nice if they were even closer together, so that it looked more
51 * like a morph, but, well, that's not how it works.
53 * There tends to be a dark stripe in the colormaps. I don't know why.
54 * Perhaps utils/colors.c is at fault?
56 * Note that this equation sometimes generates faces that are inside out:
57 * -parameters 01210111
58 * To make this work, we need to render back-faces with two-sided lighting:
59 * figuring out how to correct the winding and normals on those inside out
60 * surfaces would be too hard.
63 #define DEFAULTS "*delay: 30000 \n" \
64 "*showFPS: False \n" \
65 "*wireframe: False \n" \
66 "*suppressRotationAnimation: True\n" \
67 "*labelfont: -*-helvetica-medium-r-normal-*-*-180-*-*-*-*-*-*\n"
69 # define free_spheremonics 0
70 # define release_spheremonics 0
72 #define countof(x) (sizeof((x))/sizeof((*x)))
74 #include "xlockmore.h"
79 #include "gltrackball.h"
82 #ifdef USE_GL /* whole file */
84 #define DEF_DURATION "100"
85 #define DEF_SPIN "XYZ"
86 #define DEF_WANDER "False"
87 #define DEF_RESOLUTION "64"
88 #define DEF_BBOX "False"
89 #define DEF_GRID "True"
90 #define DEF_SMOOTH "True"
91 #define DEF_PARMS "(default)"
94 GLXContext *glx_context;
96 trackball_state *trackball;
113 int polys1, polys2; /* polygon counts */
115 texture_font_data *font_data;
120 } spheremonics_configuration;
122 static spheremonics_configuration *ccs = NULL;
124 static char *do_spin;
125 static Bool do_wander;
129 static char *static_parms;
133 static XrmOptionDescRec opts[] = {
134 { "-spin", ".spin", XrmoptionSepArg, 0 },
135 { "+spin", ".spin", XrmoptionNoArg, "" },
136 { "-wander", ".wander", XrmoptionNoArg, "True" },
137 { "+wander", ".wander", XrmoptionNoArg, "False" },
138 { "-resolution", ".resolution", XrmoptionSepArg, 0 },
139 { "-duration", ".duration", XrmoptionSepArg, 0 },
140 { "-bbox", ".bbox", XrmoptionNoArg, "True" },
141 { "+bbox", ".bbox", XrmoptionNoArg, "False" },
142 { "-grid", ".grid", XrmoptionNoArg, "True" },
143 { "+grid", ".grid", XrmoptionNoArg, "False" },
144 {"-smooth", ".smooth", XrmoptionNoArg, "True" },
145 {"+smooth", ".smooth", XrmoptionNoArg, "False" },
146 { "-parameters", ".parameters", XrmoptionSepArg, 0 },
149 static argtype vars[] = {
150 {&do_spin, "spin", "Spin", DEF_SPIN, t_String},
151 {&do_wander, "wander", "Wander", DEF_WANDER, t_Bool},
152 {&res, "resolution", "Resolution", DEF_RESOLUTION, t_Int},
153 {&duration, "duration", "Duration", DEF_DURATION, t_Int},
154 {&do_bbox, "bbox", "BBox", DEF_BBOX, t_Bool},
155 {&do_grid, "grid", "Grid", DEF_GRID, t_Bool},
156 {&smooth_p, "smooth", "Smooth", DEF_SMOOTH, t_Bool},
157 {&static_parms, "parameters", "Parameters", DEF_PARMS, t_String},
160 ENTRYPOINT ModeSpecOpt spheremonics_opts = {countof(opts), opts, countof(vars), vars, NULL};
163 /* Window management, etc
166 reshape_spheremonics (ModeInfo *mi, int width, int height)
168 GLfloat h = (GLfloat) height / (GLfloat) width;
171 if (width > height * 5) { /* tiny window: show middle */
172 height = width * 9/16;
174 h = height / (GLfloat) width;
177 glViewport (0, y, (GLint) width, (GLint) height);
179 glMatrixMode(GL_PROJECTION);
181 gluPerspective (30.0, 1/h, 1.0, 100.0);
183 glMatrixMode(GL_MODELVIEW);
185 gluLookAt( 0.0, 0.0, 30.0,
189 # ifdef HAVE_MOBILE /* Keep it the same relative size when rotated. */
191 int o = (int) current_device_rotation();
192 if (o != 0 && o != 180 && o != -180)
193 glScalef (1/h, 1/h, 1/h);
197 glClear(GL_COLOR_BUFFER_BIT);
202 gl_init (ModeInfo *mi)
204 /* spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)]; */
205 int wire = MI_IS_WIREFRAME(mi);
207 static const GLfloat pos[4] = {5.0, 5.0, 10.0, 1.0};
209 glEnable(GL_NORMALIZE);
213 glLightfv(GL_LIGHT0, GL_POSITION, pos);
214 glEnable(GL_LIGHTING);
216 glEnable(GL_DEPTH_TEST);
218 /* With objects that have proper winding and normals set up on all
219 their faces, one can cull back-faces; however, these equations
220 generate objects that are sometimes "inside out", and determining
221 whether a facet has been inverted like that is really hard.
222 So we render both front and back faces, at a probable performance
223 penalty on non-accelerated systems.
225 When rendering back faces, we also need to do two-sided lighting,
226 or the fact that the normals are flipped gives us too-dark surfaces
227 on the inside-out surfaces.
229 This isn't generally something you'd want, because you end up
230 with half the lighting dynamic range (kind of.) So if you had
231 a sphere with correctly pointing normals, and a single light
232 source, it would be illuminated from two sides. In this case,
233 though, it saves us from a difficult and time consuming
234 inside/outside test. And we don't really care about a precise
237 glDisable(GL_CULL_FACE);
238 glLightModeli (GL_LIGHT_MODEL_TWO_SIDE, True);
243 glEnable (GL_LINE_SMOOTH);
244 glHint (GL_LINE_SMOOTH_HINT, GL_NICEST);
245 glBlendFunc (GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
252 /* generate the object */
255 sphere_eval (double theta, double phi, int *m)
260 r += pow (sin(m[0] * phi), (double)m[1]);
261 r += pow (cos(m[2] * phi), (double)m[3]);
262 r += pow (sin(m[4] * theta),(double)m[5]);
263 r += pow (cos(m[6] * theta),(double)m[7]);
265 p.x = r * sin(phi) * cos(theta);
267 p.z = r * sin(phi) * sin(theta);
274 do_color (int i, XColor *colors)
277 c[0] = colors[i].red / 65535.0;
278 c[1] = colors[i].green / 65535.0;
279 c[2] = colors[i].blue / 65535.0;
281 glMaterialfv (GL_FRONT, GL_AMBIENT_AND_DIFFUSE, c);
282 glColor3f (c[0], c[1], c[2]);
287 draw_circle (ModeInfo *mi, Bool teeth_p)
292 GLfloat step = (M_PI / 180);
294 glBegin(GL_LINE_LOOP);
295 for (th = 0; th < M_PI*2; th += step*5)
300 glVertex3f(x*r1, y*r1, 0);
304 if (!teeth_p) return;
307 for (th = 0; th < M_PI*2; th += step)
310 GLfloat r2 = r1 - 0.01;
313 else if (! (tick % 5))
319 glVertex3f(x*r1, y*r1, 0);
320 glVertex3f(x*r2, y*r2, 0);
327 draw_bounding_box (ModeInfo *mi)
329 /* spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)]; */
331 static const GLfloat c1[4] = { 0.2, 0.2, 0.6, 1.0 };
332 static const GLfloat c2[4] = { 1.0, 0.0, 0.0, 1.0 };
333 int wire = MI_IS_WIREFRAME(mi);
335 GLfloat x1,y1,z1,x2,y2,z2;
349 if (do_bbox && !wire)
351 glMaterialfv (GL_FRONT, GL_AMBIENT_AND_DIFFUSE, c1);
353 glEnable(GL_CULL_FACE);
355 glBegin(wire ? GL_LINE_LOOP : GL_QUADS);
357 glVertex3f(x1, y1, z1); glVertex3f(x1, y1, z2);
358 glVertex3f(x2, y1, z2); glVertex3f(x2, y1, z1);
360 glBegin(wire ? GL_LINE_LOOP : GL_QUADS);
361 glNormal3f(0, -1, 0);
362 glVertex3f(x2, y2, z1); glVertex3f(x2, y2, z2);
363 glVertex3f(x1, y2, z2); glVertex3f(x1, y2, z1);
365 glBegin(wire ? GL_LINE_LOOP : GL_QUADS);
367 glVertex3f(x1, y1, z1); glVertex3f(x2, y1, z1);
368 glVertex3f(x2, y2, z1); glVertex3f(x1, y2, z1);
370 glBegin(wire ? GL_LINE_LOOP : GL_QUADS);
371 glNormal3f(0, 0, -1);
372 glVertex3f(x1, y2, z2); glVertex3f(x2, y2, z2);
373 glVertex3f(x2, y1, z2); glVertex3f(x1, y1, z2);
375 glBegin(wire ? GL_LINE_LOOP : GL_QUADS);
377 glVertex3f(x1, y2, z1); glVertex3f(x1, y2, z2);
378 glVertex3f(x1, y1, z2); glVertex3f(x1, y1, z1);
380 glBegin(wire ? GL_LINE_LOOP : GL_QUADS);
381 glNormal3f(-1, 0, 0);
382 glVertex3f(x2, y1, z1); glVertex3f(x2, y1, z2);
383 glVertex3f(x2, y2, z2); glVertex3f(x2, y2, z1);
385 glDisable(GL_CULL_FACE);
390 glDisable (GL_LIGHTING);
391 glColor3f (c2[0], c2[1], c2[2]);
394 glVertex3f(0, -0.66, 0);
395 glVertex3f(0, 0.66, 0);
397 draw_circle (mi, True);
398 glRotatef(90, 1, 0, 0);
399 draw_circle (mi, True);
400 glRotatef(90, 0, 1, 0);
401 draw_circle (mi, True);
408 if (x1 > 0) x1 = 0; if (x2 < 0) x2 = 0;
409 if (y1 > 0) y1 = 0; if (y2 < 0) y2 = 0;
410 if (z1 > 0) z1 = 0; if (z2 < 0) z2 = 0;
411 glVertex3f(x1, 0, 0); glVertex3f(x2, 0, 0);
412 glVertex3f(0 , y1, 0); glVertex3f(0, y2, 0);
413 glVertex3f(0, 0, z1); glVertex3f(0, 0, z2);
421 do_tracer (ModeInfo *mi)
423 spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)];
425 if (cc->tracer == -1 &&
427 !(random() % (duration * 4)))
430 cc->tracer = ((random() & 1) ? 0 : 180);
432 cc->mesher = ((random() % ((duration / 3) + 1)) +
433 (random() % ((duration / 3) + 1)));
438 int d = (90 - cc->tracer);
439 GLfloat th = d * (M_PI / 180);
440 GLfloat x = cos (th);
441 GLfloat y = sin (th);
442 GLfloat s = 1.5 / cc->scale;
446 static const GLfloat c[4] = { 0.6, 0.5, 1.0, 1.0 };
448 glDisable (GL_LIGHTING);
451 glRotatef (90, 1, 0, 0);
452 glTranslatef (0, 0, y*s/2);
455 glColor3f (c[0], c[1], c[2]);
456 draw_circle (mi, False);
459 if (! MI_IS_WIREFRAME(mi)) glEnable (GL_LIGHTING);
463 if (cc->tracer == 180 || cc->tracer == 360)
470 unit_spheremonics (ModeInfo *mi,
471 int resolution, Bool wire, int *m, XColor *colors)
473 spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)];
483 cc->bbox[0].x = cc->bbox[0].y = cc->bbox[0].z = 0;
484 cc->bbox[1].x = cc->bbox[1].y = cc->bbox[1].z = 0;
486 du = (M_PI+M_PI) / (double)res; /* Theta */
487 dv = M_PI / (double)res; /* Phi */
492 glBegin (wire ? GL_LINE_LOOP : GL_QUADS);
494 for (i = 0; i < res; i++) {
496 for (j = 0; j < res; j++) {
498 q[0] = sphere_eval (u, v, m);
499 n[0] = calc_normal(q[0],
500 sphere_eval (u+du/10, v, m),
501 sphere_eval (u, v+dv/10, m));
502 glNormal3f(n[0].x,n[0].y,n[0].z);
503 if (!wire) do_color (i, colors);
504 glVertex3f(q[0].x,q[0].y,q[0].z);
506 q[1] = sphere_eval (u+du, v, m);
507 n[1] = calc_normal(q[1],
508 sphere_eval (u+du+du/10, v, m),
509 sphere_eval (u+du, v+dv/10, m));
510 glNormal3f(n[1].x,n[1].y,n[1].z);
511 if (!wire) do_color ((i+1)%res, colors);
512 glVertex3f(q[1].x,q[1].y,q[1].z);
514 q[2] = sphere_eval (u+du, v+dv, m);
515 n[2] = calc_normal(q[2],
516 sphere_eval (u+du+du/10, v+dv, m),
517 sphere_eval (u+du, v+dv+dv/10, m));
518 glNormal3f(n[2].x,n[2].y,n[2].z);
519 if (!wire) do_color ((i+1)%res, colors);
520 glVertex3f(q[2].x,q[2].y,q[2].z);
522 q[3] = sphere_eval (u,v+dv, m);
523 n[3] = calc_normal(q[3],
524 sphere_eval (u+du/10, v+dv, m),
525 sphere_eval (u, v+dv+dv/10, m));
526 glNormal3f(n[3].x,n[3].y,n[3].z);
527 if (!wire) do_color (i, colors);
528 glVertex3f(q[3].x,q[3].y,q[3].z);
532 # define CHECK_BBOX(N) \
533 if (q[(N)].x < cc->bbox[0].x) cc->bbox[0].x = q[(N)].x; \
534 if (q[(N)].y < cc->bbox[0].y) cc->bbox[0].y = q[(N)].y; \
535 if (q[(N)].z < cc->bbox[0].z) cc->bbox[0].z = q[(N)].z; \
536 if (q[(N)].x > cc->bbox[1].x) cc->bbox[1].x = q[(N)].x; \
537 if (q[(N)].y > cc->bbox[1].y) cc->bbox[1].y = q[(N)].y; \
538 if (q[(N)].z > cc->bbox[1].z) cc->bbox[1].z = q[(N)].z
550 GLfloat w = cc->bbox[1].x - cc->bbox[0].x;
551 GLfloat h = cc->bbox[1].y - cc->bbox[0].y;
552 GLfloat d = cc->bbox[1].z - cc->bbox[0].z;
553 GLfloat wh = (w > h ? w : h);
554 GLfloat hd = (h > d ? h : d);
555 GLfloat scale = (wh > hd ? wh : hd);
559 if (wire < 2 && (do_bbox || do_grid))
561 GLfloat s = scale * 1.5;
564 draw_bounding_box (mi);
573 init_colors (ModeInfo *mi)
575 spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)];
577 cc->ncolors = cc->resolution;
578 cc->colors = (XColor *) calloc(cc->ncolors, sizeof(XColor));
579 make_smooth_colormap (0, 0, 0,
580 cc->colors, &cc->ncolors,
583 /* brighter colors, please... */
584 for (i = 0; i < cc->ncolors; i++)
586 cc->colors[i].red = (cc->colors[i].red / 2) + 32767;
587 cc->colors[i].green = (cc->colors[i].green / 2) + 32767;
588 cc->colors[i].blue = (cc->colors[i].blue / 2) + 32767;
593 /* Pick one of the parameters to the function and tweak it up or down.
596 tweak_parameters (ModeInfo *mi)
598 spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)];
600 /* If the -parameters command line option was specified, just use that
605 !!strcasecmp (static_parms, "(default)"))
609 if (8 == sscanf (static_parms, "%d %d %d %d %d %d %d %d %c",
610 &cc->m[0], &cc->m[1], &cc->m[2], &cc->m[3],
611 &cc->m[4], &cc->m[5], &cc->m[6], &cc->m[7],
614 else if (strlen (static_parms) == 8 &&
615 1 == sscanf (static_parms, "%lu %c", &n, &dummy))
617 const char *s = static_parms;
620 cc->m[i++] = (*s++)-'0';
624 "%s: -parameters must be a string of 8 ints (not \"%s\")\n",
625 progname, static_parms);
632 # define SHIFT(N) do { \
634 cc->m[n] += cc->dm[n]; \
636 cc->m[n] = 0, cc->dm[n] = -cc->dm[n]; \
637 else if (cc->m[n] >= cc->m_max) \
638 cc->m[n] = cc->m_max, cc->dm[n] = -cc->dm[n]; \
641 /* else if (cc->m[n] >= cc->m_max/2 && (! (random() % 3))) \
642 cc->m[n] = cc->m_max/2, cc->dm[n] = -cc->dm[n]; \
647 case 0: SHIFT(0); break;
648 case 1: SHIFT(1); break;
649 case 2: SHIFT(2); break;
650 case 3: SHIFT(3); break;
651 case 4: SHIFT(4); break;
652 case 5: SHIFT(5); break;
653 case 6: SHIFT(6); break;
654 case 7: SHIFT(7); break;
655 default: abort(); break;
660 printf ("%s: state: %d %d %d %d %d %d %d %d\n",
662 cc->m[0], cc->m[1], cc->m[2], cc->m[3],
663 cc->m[4], cc->m[5], cc->m[6], cc->m[7]);
670 generate_spheremonics (ModeInfo *mi)
672 spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)];
673 int wire = MI_IS_WIREFRAME(mi);
675 tweak_parameters (mi);
677 if (!cc->done_once || (0 == (random() % 20)))
680 cc->done_once = True;
684 glNewList(cc->dlist, GL_COMPILE);
685 cc->polys1 = unit_spheremonics (mi, cc->resolution, wire,cc->m,cc->colors);
688 glNewList(cc->dlist2, GL_COMPILE);
690 glScalef (1.05, 1.05, 1.05);
691 cc->polys2 = unit_spheremonics (mi, cc->resolution, 2, cc->m, cc->colors);
701 init_spheremonics (ModeInfo *mi)
703 spheremonics_configuration *cc;
707 cc = &ccs[MI_SCREEN(mi)];
709 if ((cc->glx_context = init_GL(mi)) != NULL) {
711 reshape_spheremonics (mi, MI_WIDTH(mi), MI_HEIGHT(mi));
715 Bool spinx=False, spiny=False, spinz=False;
716 double spin_speed = 1.0;
717 double wander_speed = 0.03;
722 if (*s == 'x' || *s == 'X') spinx = True;
723 else if (*s == 'y' || *s == 'Y') spiny = True;
724 else if (*s == 'z' || *s == 'Z') spinz = True;
725 else if (*s == '0') ;
729 "%s: spin must contain only the characters X, Y, or Z (not \"%s\")\n",
736 cc->rot = make_rotator (spinx ? spin_speed : 0,
737 spinz ? spin_speed : 0,
738 spiny ? spin_speed : 0,
740 do_wander ? wander_speed : 0,
741 (spinx && spiny && spinz));
742 cc->trackball = gltrackball_init (True);
748 cc->resolution = res;
750 cc->font_data = load_texture_font (mi->dpy, "labelfont");
752 cc->dlist = glGenLists(1);
753 cc->dlist2 = glGenLists(1);
755 cc->m_max = 4; /* 9? */
758 for (i = 0; i < countof(cc->dm); i++)
759 cc->dm[i] = 1; /* going up! */
761 /* Generate a few more times so we don't always start off with a sphere */
762 for (i = 0; i < 5; i++)
763 tweak_parameters (mi);
766 generate_spheremonics(mi);
771 spheremonics_handle_event (ModeInfo *mi, XEvent *event)
773 spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)];
775 if (gltrackball_event_handler (event, cc->trackball,
776 MI_WIDTH (mi), MI_HEIGHT (mi),
779 else if (screenhack_event_helper (MI_DISPLAY(mi), MI_WINDOW(mi), event))
781 cc->change_tick = duration;
790 draw_spheremonics (ModeInfo *mi)
792 spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)];
793 Display *dpy = MI_DISPLAY(mi);
794 Window window = MI_WINDOW(mi);
796 if (!cc->glx_context)
799 glXMakeCurrent(MI_DISPLAY(mi), MI_WINDOW(mi), *(cc->glx_context));
803 glShadeModel(GL_SMOOTH);
805 glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
809 glScalef(1.1, 1.1, 1.1);
813 get_position (cc->rot, &x, &y, &z, !cc->button_down_p);
814 glTranslatef((x - 0.5) * 8,
818 gltrackball_rotate (cc->trackball);
820 get_rotation (cc->rot, &x, &y, &z, !cc->button_down_p);
821 glRotatef (x * 360, 1.0, 0.0, 0.0);
822 glRotatef (y * 360, 0.0, 1.0, 0.0);
823 glRotatef (z * 360, 0.0, 0.0, 1.0);
828 mi->polygon_count = 0;
830 glScalef (cc->scale, cc->scale, cc->scale);
831 glCallList (cc->dlist);
832 mi->polygon_count += cc->polys1;
834 if (cc->mesher >= 0 /* || cc->button_down_p */)
836 glDisable (GL_LIGHTING);
837 glCallList (cc->dlist2);
838 mi->polygon_count += cc->polys2;
845 if (cc->button_down_p)
849 ((cc->m[0]<10 && cc->m[1]<10 && cc->m[2]<10 && cc->m[3]<10 &&
850 cc->m[4]<10 && cc->m[5]<10 && cc->m[6]<10 && cc->m[7]<10)
852 : "%d %d %d %d %d %d %d %d"),
853 cc->m[0], cc->m[1], cc->m[2], cc->m[3],
854 cc->m[4], cc->m[5], cc->m[6], cc->m[7]);
856 glColor3f(1.0, 1.0, 0.0);
857 print_texture_label (mi->dpy, cc->font_data,
858 mi->xgwa.width, mi->xgwa.height,
864 if (cc->change_tick++ >= duration && !cc->button_down_p)
866 generate_spheremonics(mi);
868 cc->mesher = -1; /* turn off the mesh when switching objects */
874 if (mi->fps_p) do_fps (mi);
877 glXSwapBuffers(dpy, window);
880 XSCREENSAVER_MODULE ("Spheremonics", spheremonics)