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 "*labelfont: -*-helvetica-medium-r-normal-*-180-*\n"
68 # define refresh_spheremonics 0
69 # define release_spheremonics 0
71 #define countof(x) (sizeof((x))/sizeof((*x)))
73 #include "xlockmore.h"
78 #include "gltrackball.h"
81 #ifdef USE_GL /* whole file */
83 #define DEF_DURATION "100"
84 #define DEF_SPIN "XYZ"
85 #define DEF_WANDER "False"
86 #define DEF_RESOLUTION "64"
87 #define DEF_BBOX "False"
88 #define DEF_GRID "True"
89 #define DEF_SMOOTH "True"
90 #define DEF_PARMS "(default)"
93 GLXContext *glx_context;
95 trackball_state *trackball;
112 int polys1, polys2; /* polygon counts */
114 texture_font_data *font_data;
119 } spheremonics_configuration;
121 static spheremonics_configuration *ccs = NULL;
123 static char *do_spin;
124 static Bool do_wander;
128 static char *static_parms;
132 static XrmOptionDescRec opts[] = {
133 { "-spin", ".spin", XrmoptionSepArg, 0 },
134 { "+spin", ".spin", XrmoptionNoArg, "" },
135 { "-wander", ".wander", XrmoptionNoArg, "True" },
136 { "+wander", ".wander", XrmoptionNoArg, "False" },
137 { "-resolution", ".resolution", XrmoptionSepArg, 0 },
138 { "-duration", ".duration", XrmoptionSepArg, 0 },
139 { "-bbox", ".bbox", XrmoptionNoArg, "True" },
140 { "+bbox", ".bbox", XrmoptionNoArg, "False" },
141 { "-grid", ".grid", XrmoptionNoArg, "True" },
142 { "+grid", ".grid", XrmoptionNoArg, "False" },
143 {"-smooth", ".smooth", XrmoptionNoArg, "True" },
144 {"+smooth", ".smooth", XrmoptionNoArg, "False" },
145 { "-parameters", ".parameters", XrmoptionSepArg, 0 },
148 static argtype vars[] = {
149 {&do_spin, "spin", "Spin", DEF_SPIN, t_String},
150 {&do_wander, "wander", "Wander", DEF_WANDER, t_Bool},
151 {&res, "resolution", "Resolution", DEF_RESOLUTION, t_Int},
152 {&duration, "duration", "Duration", DEF_DURATION, t_Int},
153 {&do_bbox, "bbox", "BBox", DEF_BBOX, t_Bool},
154 {&do_grid, "grid", "Grid", DEF_GRID, t_Bool},
155 {&smooth_p, "smooth", "Smooth", DEF_SMOOTH, t_Bool},
156 {&static_parms, "parameters", "Parameters", DEF_PARMS, t_String},
159 ENTRYPOINT ModeSpecOpt spheremonics_opts = {countof(opts), opts, countof(vars), vars, NULL};
162 /* Window management, etc
165 reshape_spheremonics (ModeInfo *mi, int width, int height)
167 GLfloat h = (GLfloat) height / (GLfloat) width;
169 glViewport (0, 0, (GLint) width, (GLint) height);
171 glMatrixMode(GL_PROJECTION);
173 gluPerspective (30.0, 1/h, 1.0, 100.0);
175 glMatrixMode(GL_MODELVIEW);
177 gluLookAt( 0.0, 0.0, 30.0,
181 glClear(GL_COLOR_BUFFER_BIT);
186 gl_init (ModeInfo *mi)
188 /* spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)]; */
189 int wire = MI_IS_WIREFRAME(mi);
191 static const GLfloat pos[4] = {5.0, 5.0, 10.0, 1.0};
193 glEnable(GL_NORMALIZE);
197 glLightfv(GL_LIGHT0, GL_POSITION, pos);
198 glEnable(GL_LIGHTING);
200 glEnable(GL_DEPTH_TEST);
202 /* With objects that have proper winding and normals set up on all
203 their faces, one can cull back-faces; however, these equations
204 generate objects that are sometimes "inside out", and determining
205 whether a facet has been inverted like that is really hard.
206 So we render both front and back faces, at a probable performance
207 penalty on non-accelerated systems.
209 When rendering back faces, we also need to do two-sided lighting,
210 or the fact that the normals are flipped gives us too-dark surfaces
211 on the inside-out surfaces.
213 This isn't generally something you'd want, because you end up
214 with half the lighting dynamic range (kind of.) So if you had
215 a sphere with correctly pointing normals, and a single light
216 source, it would be illuminated from two sides. In this case,
217 though, it saves us from a difficult and time consuming
218 inside/outside test. And we don't really care about a precise
221 glDisable(GL_CULL_FACE);
222 glLightModeli (GL_LIGHT_MODEL_TWO_SIDE, True);
227 glEnable (GL_LINE_SMOOTH);
228 glHint (GL_LINE_SMOOTH_HINT, GL_NICEST);
229 glBlendFunc (GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
236 /* generate the object */
239 sphere_eval (double theta, double phi, int *m)
244 r += pow (sin(m[0] * phi), (double)m[1]);
245 r += pow (cos(m[2] * phi), (double)m[3]);
246 r += pow (sin(m[4] * theta),(double)m[5]);
247 r += pow (cos(m[6] * theta),(double)m[7]);
249 p.x = r * sin(phi) * cos(theta);
251 p.z = r * sin(phi) * sin(theta);
258 do_color (int i, XColor *colors)
261 c[0] = colors[i].red / 65535.0;
262 c[1] = colors[i].green / 65535.0;
263 c[2] = colors[i].blue / 65535.0;
265 glMaterialfv (GL_FRONT, GL_AMBIENT_AND_DIFFUSE, c);
266 glColor3f (c[0], c[1], c[2]);
271 draw_circle (ModeInfo *mi, Bool teeth_p)
276 GLfloat step = (M_PI / 180);
278 glBegin(GL_LINE_LOOP);
279 for (th = 0; th < M_PI*2; th += step*5)
284 glVertex3f(x*r1, y*r1, 0);
288 if (!teeth_p) return;
291 for (th = 0; th < M_PI*2; th += step)
294 GLfloat r2 = r1 - 0.01;
297 else if (! (tick % 5))
303 glVertex3f(x*r1, y*r1, 0);
304 glVertex3f(x*r2, y*r2, 0);
311 draw_bounding_box (ModeInfo *mi)
313 /* spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)]; */
315 static const GLfloat c1[4] = { 0.2, 0.2, 0.6, 1.0 };
316 static const GLfloat c2[4] = { 1.0, 0.0, 0.0, 1.0 };
317 int wire = MI_IS_WIREFRAME(mi);
319 GLfloat x1,y1,z1,x2,y2,z2;
333 if (do_bbox && !wire)
335 glMaterialfv (GL_FRONT, GL_AMBIENT_AND_DIFFUSE, c1);
337 glEnable(GL_CULL_FACE);
339 glBegin(wire ? GL_LINE_LOOP : GL_QUADS);
341 glVertex3f(x1, y1, z1); glVertex3f(x1, y1, z2);
342 glVertex3f(x2, y1, z2); glVertex3f(x2, y1, z1);
344 glBegin(wire ? GL_LINE_LOOP : GL_QUADS);
345 glNormal3f(0, -1, 0);
346 glVertex3f(x2, y2, z1); glVertex3f(x2, y2, z2);
347 glVertex3f(x1, y2, z2); glVertex3f(x1, y2, z1);
349 glBegin(wire ? GL_LINE_LOOP : GL_QUADS);
351 glVertex3f(x1, y1, z1); glVertex3f(x2, y1, z1);
352 glVertex3f(x2, y2, z1); glVertex3f(x1, y2, z1);
354 glBegin(wire ? GL_LINE_LOOP : GL_QUADS);
355 glNormal3f(0, 0, -1);
356 glVertex3f(x1, y2, z2); glVertex3f(x2, y2, z2);
357 glVertex3f(x2, y1, z2); glVertex3f(x1, y1, z2);
359 glBegin(wire ? GL_LINE_LOOP : GL_QUADS);
361 glVertex3f(x1, y2, z1); glVertex3f(x1, y2, z2);
362 glVertex3f(x1, y1, z2); glVertex3f(x1, y1, z1);
364 glBegin(wire ? GL_LINE_LOOP : GL_QUADS);
365 glNormal3f(-1, 0, 0);
366 glVertex3f(x2, y1, z1); glVertex3f(x2, y1, z2);
367 glVertex3f(x2, y2, z2); glVertex3f(x2, y2, z1);
369 glDisable(GL_CULL_FACE);
374 glDisable (GL_LIGHTING);
375 glColor3f (c2[0], c2[1], c2[2]);
378 glVertex3f(0, -0.66, 0);
379 glVertex3f(0, 0.66, 0);
381 draw_circle (mi, True);
382 glRotatef(90, 1, 0, 0);
383 draw_circle (mi, True);
384 glRotatef(90, 0, 1, 0);
385 draw_circle (mi, True);
392 if (x1 > 0) x1 = 0; if (x2 < 0) x2 = 0;
393 if (y1 > 0) y1 = 0; if (y2 < 0) y2 = 0;
394 if (z1 > 0) z1 = 0; if (z2 < 0) z2 = 0;
395 glVertex3f(x1, 0, 0); glVertex3f(x2, 0, 0);
396 glVertex3f(0 , y1, 0); glVertex3f(0, y2, 0);
397 glVertex3f(0, 0, z1); glVertex3f(0, 0, z2);
405 do_tracer (ModeInfo *mi)
407 spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)];
409 if (cc->tracer == -1 &&
411 !(random() % (duration * 4)))
414 cc->tracer = ((random() & 1) ? 0 : 180);
416 cc->mesher = ((random() % ((duration / 3) + 1)) +
417 (random() % ((duration / 3) + 1)));
422 int d = (90 - cc->tracer);
423 GLfloat th = d * (M_PI / 180);
424 GLfloat x = cos (th);
425 GLfloat y = sin (th);
426 GLfloat s = 1.5 / cc->scale;
430 static const GLfloat c[4] = { 0.6, 0.5, 1.0, 1.0 };
432 glDisable (GL_LIGHTING);
435 glRotatef (90, 1, 0, 0);
436 glTranslatef (0, 0, y*s/2);
439 glColor3f (c[0], c[1], c[2]);
440 draw_circle (mi, False);
443 if (! MI_IS_WIREFRAME(mi)) glEnable (GL_LIGHTING);
447 if (cc->tracer == 180 || cc->tracer == 360)
454 unit_spheremonics (ModeInfo *mi,
455 int resolution, Bool wire, int *m, XColor *colors)
457 spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)];
467 cc->bbox[0].x = cc->bbox[0].y = cc->bbox[0].z = 0;
468 cc->bbox[1].x = cc->bbox[1].y = cc->bbox[1].z = 0;
470 du = (M_PI+M_PI) / (double)res; /* Theta */
471 dv = M_PI / (double)res; /* Phi */
476 glBegin (wire ? GL_LINE_LOOP : GL_QUADS);
478 for (i = 0; i < res; i++) {
480 for (j = 0; j < res; j++) {
482 q[0] = sphere_eval (u, v, m);
483 n[0] = calc_normal(q[0],
484 sphere_eval (u+du/10, v, m),
485 sphere_eval (u, v+dv/10, m));
486 glNormal3f(n[0].x,n[0].y,n[0].z);
487 if (!wire) do_color (i, colors);
488 glVertex3f(q[0].x,q[0].y,q[0].z);
490 q[1] = sphere_eval (u+du, v, m);
491 n[1] = calc_normal(q[1],
492 sphere_eval (u+du+du/10, v, m),
493 sphere_eval (u+du, v+dv/10, m));
494 glNormal3f(n[1].x,n[1].y,n[1].z);
495 if (!wire) do_color ((i+1)%res, colors);
496 glVertex3f(q[1].x,q[1].y,q[1].z);
498 q[2] = sphere_eval (u+du, v+dv, m);
499 n[2] = calc_normal(q[2],
500 sphere_eval (u+du+du/10, v+dv, m),
501 sphere_eval (u+du, v+dv+dv/10, m));
502 glNormal3f(n[2].x,n[2].y,n[2].z);
503 if (!wire) do_color ((i+1)%res, colors);
504 glVertex3f(q[2].x,q[2].y,q[2].z);
506 q[3] = sphere_eval (u,v+dv, m);
507 n[3] = calc_normal(q[3],
508 sphere_eval (u+du/10, v+dv, m),
509 sphere_eval (u, v+dv+dv/10, m));
510 glNormal3f(n[3].x,n[3].y,n[3].z);
511 if (!wire) do_color (i, colors);
512 glVertex3f(q[3].x,q[3].y,q[3].z);
516 # define CHECK_BBOX(N) \
517 if (q[(N)].x < cc->bbox[0].x) cc->bbox[0].x = q[(N)].x; \
518 if (q[(N)].y < cc->bbox[0].y) cc->bbox[0].y = q[(N)].y; \
519 if (q[(N)].z < cc->bbox[0].z) cc->bbox[0].z = q[(N)].z; \
520 if (q[(N)].x > cc->bbox[1].x) cc->bbox[1].x = q[(N)].x; \
521 if (q[(N)].y > cc->bbox[1].y) cc->bbox[1].y = q[(N)].y; \
522 if (q[(N)].z > cc->bbox[1].z) cc->bbox[1].z = q[(N)].z
534 GLfloat w = cc->bbox[1].x - cc->bbox[0].x;
535 GLfloat h = cc->bbox[1].y - cc->bbox[0].y;
536 GLfloat d = cc->bbox[1].z - cc->bbox[0].z;
537 GLfloat wh = (w > h ? w : h);
538 GLfloat hd = (h > d ? h : d);
539 GLfloat scale = (wh > hd ? wh : hd);
543 if (wire < 2 && (do_bbox || do_grid))
545 GLfloat s = scale * 1.5;
548 draw_bounding_box (mi);
557 init_colors (ModeInfo *mi)
559 spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)];
561 cc->ncolors = cc->resolution;
562 cc->colors = (XColor *) calloc(cc->ncolors, sizeof(XColor));
563 make_smooth_colormap (0, 0, 0,
564 cc->colors, &cc->ncolors,
567 /* brighter colors, please... */
568 for (i = 0; i < cc->ncolors; i++)
570 cc->colors[i].red = (cc->colors[i].red / 2) + 32767;
571 cc->colors[i].green = (cc->colors[i].green / 2) + 32767;
572 cc->colors[i].blue = (cc->colors[i].blue / 2) + 32767;
577 /* Pick one of the parameters to the function and tweak it up or down.
580 tweak_parameters (ModeInfo *mi)
582 spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)];
584 /* If the -parameters command line option was specified, just use that
589 !!strcasecmp (static_parms, "(default)"))
593 if (8 == sscanf (static_parms, "%d %d %d %d %d %d %d %d %c",
594 &cc->m[0], &cc->m[1], &cc->m[2], &cc->m[3],
595 &cc->m[4], &cc->m[5], &cc->m[6], &cc->m[7],
598 else if (strlen (static_parms) == 8 &&
599 1 == sscanf (static_parms, "%lu %c", &n, &dummy))
601 const char *s = static_parms;
604 cc->m[i++] = (*s++)-'0';
608 "%s: -parameters must be a string of 8 ints (not \"%s\")\n",
609 progname, static_parms);
616 # define SHIFT(N) do { \
618 cc->m[n] += cc->dm[n]; \
620 cc->m[n] = 0, cc->dm[n] = -cc->dm[n]; \
621 else if (cc->m[n] >= cc->m_max) \
622 cc->m[n] = cc->m_max, cc->dm[n] = -cc->dm[n]; \
625 /* else if (cc->m[n] >= cc->m_max/2 && (! (random() % 3))) \
626 cc->m[n] = cc->m_max/2, cc->dm[n] = -cc->dm[n]; \
631 case 0: SHIFT(0); break;
632 case 1: SHIFT(1); break;
633 case 2: SHIFT(2); break;
634 case 3: SHIFT(3); break;
635 case 4: SHIFT(4); break;
636 case 5: SHIFT(5); break;
637 case 6: SHIFT(6); break;
638 case 7: SHIFT(7); break;
639 default: abort(); break;
644 printf ("%s: state: %d %d %d %d %d %d %d %d\n",
646 cc->m[0], cc->m[1], cc->m[2], cc->m[3],
647 cc->m[4], cc->m[5], cc->m[6], cc->m[7]);
654 generate_spheremonics (ModeInfo *mi)
656 spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)];
657 int wire = MI_IS_WIREFRAME(mi);
659 tweak_parameters (mi);
661 if (!cc->done_once || (0 == (random() % 20)))
664 cc->done_once = True;
668 glNewList(cc->dlist, GL_COMPILE);
669 cc->polys1 = unit_spheremonics (mi, cc->resolution, wire,cc->m,cc->colors);
672 glNewList(cc->dlist2, GL_COMPILE);
674 glScalef (1.05, 1.05, 1.05);
675 cc->polys2 = unit_spheremonics (mi, cc->resolution, 2, cc->m, cc->colors);
685 init_spheremonics (ModeInfo *mi)
687 spheremonics_configuration *cc;
690 ccs = (spheremonics_configuration *)
691 calloc (MI_NUM_SCREENS(mi), sizeof (spheremonics_configuration));
693 fprintf(stderr, "%s: out of memory\n", progname);
698 cc = &ccs[MI_SCREEN(mi)];
700 if ((cc->glx_context = init_GL(mi)) != NULL) {
702 reshape_spheremonics (mi, MI_WIDTH(mi), MI_HEIGHT(mi));
706 Bool spinx=False, spiny=False, spinz=False;
707 double spin_speed = 1.0;
708 double wander_speed = 0.03;
713 if (*s == 'x' || *s == 'X') spinx = True;
714 else if (*s == 'y' || *s == 'Y') spiny = True;
715 else if (*s == 'z' || *s == 'Z') spinz = True;
716 else if (*s == '0') ;
720 "%s: spin must contain only the characters X, Y, or Z (not \"%s\")\n",
727 cc->rot = make_rotator (spinx ? spin_speed : 0,
728 spinz ? spin_speed : 0,
729 spiny ? spin_speed : 0,
731 do_wander ? wander_speed : 0,
732 (spinx && spiny && spinz));
733 cc->trackball = gltrackball_init (True);
739 cc->resolution = res;
741 cc->font_data = load_texture_font (mi->dpy, "labelfont");
743 cc->dlist = glGenLists(1);
744 cc->dlist2 = glGenLists(1);
746 cc->m_max = 4; /* 9? */
749 for (i = 0; i < countof(cc->dm); i++)
750 cc->dm[i] = 1; /* going up! */
752 /* Generate a few more times so we don't always start off with a sphere */
753 for (i = 0; i < 5; i++)
754 tweak_parameters (mi);
757 generate_spheremonics(mi);
762 spheremonics_handle_event (ModeInfo *mi, XEvent *event)
764 spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)];
766 if (gltrackball_event_handler (event, cc->trackball,
767 MI_WIDTH (mi), MI_HEIGHT (mi),
770 else if (screenhack_event_helper (MI_DISPLAY(mi), MI_WINDOW(mi), event))
772 cc->change_tick = duration;
781 draw_spheremonics (ModeInfo *mi)
783 spheremonics_configuration *cc = &ccs[MI_SCREEN(mi)];
784 Display *dpy = MI_DISPLAY(mi);
785 Window window = MI_WINDOW(mi);
787 if (!cc->glx_context)
790 glXMakeCurrent(MI_DISPLAY(mi), MI_WINDOW(mi), *(cc->glx_context));
794 glShadeModel(GL_SMOOTH);
796 glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
800 glScalef(1.1, 1.1, 1.1);
804 get_position (cc->rot, &x, &y, &z, !cc->button_down_p);
805 glTranslatef((x - 0.5) * 8,
809 gltrackball_rotate (cc->trackball);
811 get_rotation (cc->rot, &x, &y, &z, !cc->button_down_p);
812 glRotatef (x * 360, 1.0, 0.0, 0.0);
813 glRotatef (y * 360, 0.0, 1.0, 0.0);
814 glRotatef (z * 360, 0.0, 0.0, 1.0);
819 mi->polygon_count = 0;
821 glScalef (cc->scale, cc->scale, cc->scale);
822 glCallList (cc->dlist);
823 mi->polygon_count += cc->polys1;
825 if (cc->mesher >= 0 /* || cc->button_down_p */)
827 glDisable (GL_LIGHTING);
828 glCallList (cc->dlist2);
829 mi->polygon_count += cc->polys2;
836 if (cc->button_down_p)
840 ((cc->m[0]<10 && cc->m[1]<10 && cc->m[2]<10 && cc->m[3]<10 &&
841 cc->m[4]<10 && cc->m[5]<10 && cc->m[6]<10 && cc->m[7]<10)
843 : "%d %d %d %d %d %d %d %d"),
844 cc->m[0], cc->m[1], cc->m[2], cc->m[3],
845 cc->m[4], cc->m[5], cc->m[6], cc->m[7]);
847 glColor3f(1.0, 1.0, 0.0);
848 print_gl_string (mi->dpy, cc->font_data,
849 mi->xgwa.width, mi->xgwa.height,
850 10, mi->xgwa.height - 10,
856 if (cc->change_tick++ >= duration && !cc->button_down_p)
858 generate_spheremonics(mi);
860 cc->mesher = -1; /* turn off the mesh when switching objects */
866 if (mi->fps_p) do_fps (mi);
869 glXSwapBuffers(dpy, window);
872 XSCREENSAVER_MODULE ("Spheremonics", spheremonics)