1 /* -*- Mode: C; tab-width: 4 -*- */
2 /* penrose --- quasiperiodic tilings */
4 /* As reported in News of the Weird:
6 In April, Sir Roger Penrose, a British math professor who has worked
7 with Stephen Hawking on such topics as relativity, black holes, and
8 whether time has a beginning, filed a copyright-infringement lawsuit
9 against the Kimberly-Clark Corporation, which Penrose said copied a
10 pattern he created (a pattern demonstrating that "a nonrepeating
11 pattern could exist in nature") for its Kleenex quilted toilet paper.
12 Penrose said he doesn't like litigation but, "When it comes to the
13 population of Great Britain being invited by a multinational to wipe
14 their bottoms on what appears to be the work of a Knight of the
15 Realm, then a last stand must be taken."
17 NOTW #491, 4-jul-1997, by Chuck Shepherd.
18 http://www.nine.org/notw/notw.html
22 static const char sccsid[] = "@(#)penrose.c 5.00 2000/11/01 xlockmore";
26 * Copyright (c) 1996 by Timo Korvola <tkorvola@dopey.hut.fi>
28 * Permission to use, copy, modify, and distribute this software and its
29 * documentation for any purpose and without fee is hereby granted,
30 * provided that the above copyright notice appear in all copies and that
31 * both that copyright notice and this permission notice appear in
32 * supporting documentation.
34 * This file is provided AS IS with no warranties of any kind. The author
35 * shall have no liability with respect to the infringement of copyrights,
36 * trade secrets or any patents by this file or any part thereof. In no
37 * event will the author be liable for any lost revenue or profits or
38 * other special, indirect and consequential damages.
41 * 01-Nov-2000: Allocation checks
42 * 10-May-1997: Jamie Zawinski <jwz@jwz.org> compatible with xscreensaver
43 * 09-Sep-1996: Written.
47 Be careful, this probably still has a few bugs (many of which may only
48 appear with a very low probability). These are seen with -verbose .
49 If one of these are hit penrose will reinitialize.
53 * See Onoda, Steinhardt, DiVincenzo and Socolar in
54 * Phys. Rev. Lett. 60, #25, 1988 or
55 * Strandburg in Computers in Physics, Sep/Oct 1991.
57 * This implementation uses the simpler version of the growth
58 * algorithm, i.e., if there are no forced vertices, a randomly chosen
59 * tile is added to a randomly chosen vertex (no preference for those
62 * There are two essential differences to the algorithm presented in
63 * the literature: First, we do not allow the tiling to enclose an
64 * untiled area. Whenever this is in danger of happening, we just
65 * do not add the tile, hoping for a better random choice the next
66 * time. Second, when choosing a vertex randomly, we will take
67 * one that lies within the viewport if available. If this seems to
68 * cause enclosures in the forced rule case, we will allow invisible
69 * vertices to be chosen.
71 * Tiling is restarted whenever one of the following happens: there
72 * are no incomplete vertices within the viewport or the tiling has
73 * extended a window's length beyond the edge of the window
74 * horizontally or vertically or forced rule choice has failed 100
75 * times due to areas about to become enclosed.
78 * Science News March 23 1985 Vol 127, No. 12
79 * Science News July 16 1988 Vol 134, No. 3
80 * The Economist Sept 17 1988 pg. 100
86 #define DEFAULTS "*delay: 10000 \n" \
89 "*fpsSolid: true \n" \
91 # define refresh_penrose 0
92 # define reshape_penrose 0
93 # define penrose_handle_event 0
94 # include "xlockmore.h" /* from the xscreensaver distribution */
95 #else /* !STANDALONE */
96 # include "xlock.h" /* from the xlockmore distribution */
97 #endif /* !STANDALONE */
101 #define DEF_AMMANN "False"
105 static XrmOptionDescRec opts[] =
107 {"-ammann", ".penrose.ammann", XrmoptionNoArg, "on"},
108 {"+ammann", ".penrose.ammann", XrmoptionNoArg, "off"}
110 static argtype vars[] =
112 {&ammann, "ammann", "Ammann", DEF_AMMANN, t_Bool}
114 static OptionStruct desc[] =
116 {"-/+ammann", "turn on/off Ammann lines"}
119 ENTRYPOINT ModeSpecOpt penrose_opts =
120 {sizeof opts / sizeof opts[0], opts, sizeof vars / sizeof vars[0], vars, desc};
123 ModStruct penrose_description =
124 {"penrose", "init_penrose", "draw_penrose", "release_penrose",
125 "init_penrose", "init_penrose", (char *) NULL, &penrose_opts,
126 10000, 1, 1, -40, 64, 1.0, "",
127 "Shows Penrose's quasiperiodic tilings", 0, NULL};
132 * Annoyingly the ANSI C library people have reserved all identifiers
133 * ending with _t for future use. Hence we use _c as a suffix for
134 * typedefs (c for class, although this is not C++).
140 * In theory one could fit 10 tiles to a single vertex. However, the
141 * vertex rules only allow at most seven tiles to meet at a vertex.
144 #define CELEBRATE 31415 /* This causes a pause, an error occurred. */
145 #define COMPLETION 3141 /* This causes a pause, tiles filled up screen. */
147 #define MAX_TILES_PER_VERTEX 7
148 #define N_VERTEX_RULES 8
149 #define ALLOC_NODE(type) (type *)malloc(sizeof (type))
152 * These are used to specify directions. They can also be used in bit
153 * masks to specify a combination of directions.
160 * We do not actually maintain objects corresponding to the tiles since
161 * we do not really need them and they would only consume memory and
162 * cause additional bookkeeping. Instead we only have vertices, and
163 * each vertex lists the type of each adjacent tile as well as the
164 * position of the vertex on the tile (hereafter refered to as
165 * "corner"). These positions are numbered in counterclockwise order
166 * so that 0 is where two double arrows meet (see one of the
167 * articles). The tile type and vertex number are stored in a single
168 * integer (we use char, and even most of it remains unused).
170 * The primary use of tile objects would be draw traversal, but we do
171 * not currently do redraws at all (we just start over).
173 #define VT_CORNER_MASK 0x3
174 #define VT_TYPE_MASK 0x4
178 #define VT_TOTAL_MASK 0x7
180 typedef unsigned char vertex_type_c;
183 * These allow one to compute the types of the other corners of the tile. If
184 * you are standing at a vertex of type vt looking towards the middle of the
185 * tile, VT_LEFT( vt) is the vertex on your left etc.
187 #define VT_LEFT( vt) ((((vt) - 1) & VT_CORNER_MASK) | (((vt) & VT_TYPE_MASK)))
188 #define VT_RIGHT( vt) ((((vt) + 1) & VT_CORNER_MASK) | (((vt) & VT_TYPE_MASK)))
189 #define VT_FAR( vt) ((vt) ^ 2)
193 * Since we do not do redraws, we only store the vertices we need. These are
194 * the ones with still some empty space around them for the growth algorithm
197 * Here we use a doubly chained ring-like structure as vertices often need
198 * to be removed or inserted (they are kept in geometrical order
199 * circling the tiled area counterclockwise). The ring is refered to by
200 * a pointer to one more or less random node. When deleting nodes one
201 * must make sure that this pointer continues to refer to a valid
202 * node. A vertex count is maintained to make it easier to pick
205 typedef struct forced_node forced_node_c;
207 typedef struct fringe_node {
208 struct fringe_node *prev;
209 struct fringe_node *next;
210 /* These are numbered counterclockwise. The gap, if any, lies
211 between the last and first tiles. */
212 vertex_type_c tiles[MAX_TILES_PER_VERTEX];
214 /* A bit mask used to indicate vertex rules that are still applicable for
215 completing this vertex. Initialize this to (1 << N_VERTEX_RULES) - 1,
216 i.e., all ones, and the rule matching functions will automatically mask
217 out rules that no longer match. */
218 unsigned char rule_mask;
219 /* If the vertex is on the forced vertex list, this points to the
220 pointer to the appropriate node in the list. To remove the
221 vertex from the list just set *list_ptr to the next node,
222 deallocate and decrement node count. */
223 struct forced_node **list_ptr;
224 /* Screen coordinates. */
226 /* We also keep track of 5D coordinates to avoid rounding errors.
227 These are in units of edge length. */
229 /* This is used to quickly check if a vertex is visible. */
230 unsigned char off_screen;
234 fringe_node_c *nodes;
235 /* This does not count off-screen nodes. */
241 * The forced vertex pool contains vertices where at least one
242 * side of the tiled region can only be extended in one way. Note
243 * that this does not necessarily mean that there would only be one
244 * applicable rule. forced_sides are specified using S_LEFT and
245 * S_RIGHT as if looking at the untiled region from the vertex.
248 fringe_node_c *vertex;
249 unsigned forced_sides;
250 struct forced_node *next;
254 forced_node_c *first;
255 int n_nodes, n_visible;
259 /* The tiles are listed in counterclockwise order. */
261 vertex_type_c tiles[MAX_TILES_PER_VERTEX];
265 static vertex_rule_c vertex_rules[N_VERTEX_RULES] =
268 {VT_THICK | 2, VT_THICK | 2, VT_THICK | 2, VT_THICK | 2, VT_THICK | 2}, 5},
270 {VT_THICK | 0, VT_THICK | 0, VT_THICK | 0, VT_THICK | 0, VT_THICK | 0}, 5},
272 {VT_THICK | 0, VT_THICK | 0, VT_THICK | 0, VT_THIN | 0}, 4},
274 {VT_THICK | 2, VT_THICK | 2, VT_THIN | 1, VT_THIN | 3, VT_THICK | 2,
275 VT_THIN | 1, VT_THIN | 3}, 7},
277 {VT_THICK | 2, VT_THICK | 2, VT_THICK | 2, VT_THICK | 2,
278 VT_THIN | 1, VT_THIN | 3}, 6},
280 {VT_THICK | 1, VT_THICK | 3, VT_THIN | 2}, 3},
282 {VT_THICK | 0, VT_THIN | 0, VT_THIN | 0}, 3},
284 {VT_THICK | 2, VT_THIN | 1, VT_THICK | 3, VT_THICK | 1, VT_THIN | 3}, 5}
288 /* Match information returned by match_rules. */
295 /* Occasionally floating point coordinates are needed. */
301 /* All angles are measured in multiples of 36 degrees. */
304 static angle_c vtype_angles[] =
305 {4, 1, 4, 1, 2, 3, 2, 3};
307 #define vtype_angle( v) (vtype_angles[ v])
310 /* This is the data related to the tiling of one screen. */
316 forced_pool_c forced;
318 unsigned long thick_color, thin_color;
322 fcoord_c fived_table[5];
325 static tiling_c *tilings = (tiling_c *) NULL;
329 /* Direction angle of an edge. */
331 vertex_dir(ModeInfo * mi, fringe_node_c * vertex, unsigned side)
333 tiling_c *tp = &tilings[MI_SCREEN(mi)];
335 (side == S_LEFT ? vertex->next : vertex->prev);
338 for (i = 0; i < 5; i++)
339 switch (v2->fived[i] - vertex->fived[i]) {
343 return (2 * i + 5) % 10;
346 if (MI_IS_VERBOSE(mi)) {
347 (void) fprintf(stderr,
348 "Weirdness in vertex_dir (this has been reported)\n");
349 for (i = 0; i < 5; i++)
350 (void) fprintf(stderr, "v2->fived[%d]=%d, vertex->fived[%d]=%d\n",
351 i, v2->fived[i], i, vertex->fived[i]);
353 tp->busyLoop = CELEBRATE;
358 /* Move one step to a given direction. */
360 add_unit_vec(angle_c dir, int *fived)
362 static const int dir2i[] = {0, 3, 1, 4, 2};
366 fived[dir2i[dir % 5]] += (dir % 2 ? -1 : 1);
370 /* For comparing coordinates. */
371 #define fived_equal( f1, f2) (!memcmp( (f1), (f2), 5 * sizeof( int)))
375 * This computes screen coordinates from 5D representation. Note that X
376 * uses left-handed coordinates (y increases downwards).
379 fived_to_loc(int fived[], tiling_c * tp, XPoint *pt)
381 float fifth = 8 * atan(1.) / 5;
384 register fcoord_c offset;
389 if (tp->fived_table[0].x == .0)
390 for (i = 0; i < 5; i++) {
391 tp->fived_table[i].x = cos(fifth * i);
392 tp->fived_table[i].y = sin(fifth * i);
394 for (i = 0; i < 5; i++) {
395 r = fived[i] * tp->edge_length;
396 offset.x += r * tp->fived_table[i].x;
397 offset.y -= r * tp->fived_table[i].y;
399 (*pt).x += (int) (offset.x + .5);
400 (*pt).y += (int) (offset.y + .5);
404 /* Mop up dynamic data for one screen. */
406 free_penrose(tiling_c * tp)
408 register fringe_node_c *fp1, *fp2;
409 register forced_node_c *lp1, *lp2;
411 if (tp->fringe.nodes == NULL)
413 fp1 = tp->fringe.nodes;
417 (void) free((void *) fp2);
418 } while (fp1 != tp->fringe.nodes);
419 tp->fringe.nodes = (fringe_node_c *) NULL;
420 for (lp1 = tp->forced.first; lp1 != 0;) {
423 (void) free((void *) lp2);
425 tp->forced.first = 0;
429 /* Called to init the mode. */
431 init_penrose(ModeInfo * mi)
437 if (tilings == NULL) {
438 if ((tilings = (tiling_c *) calloc(MI_NUM_SCREENS(mi),
439 sizeof (tiling_c))) == NULL)
442 tp = &tilings[MI_SCREEN(mi)];
444 #if 0 /* if you do this, then the -ammann and -no-ammann options don't work.
446 if (MI_IS_FULLRANDOM(mi))
447 tp->ammann = (Bool) (LRAND() & 1);
455 tp->width = MI_WIDTH(mi);
456 tp->height = MI_HEIGHT(mi);
457 if (MI_NPIXELS(mi) > 2) {
458 tp->thick_color = NRAND(MI_NPIXELS(mi));
459 /* Insure good contrast */
460 tp->thin_color = (NRAND(2 * MI_NPIXELS(mi) / 3) + tp->thick_color +
461 MI_NPIXELS(mi) / 6) % MI_NPIXELS(mi);
465 tp->edge_length = NRAND(MIN(-size, MAX(MINSIZE,
466 MIN(tp->width, tp->height) / 2)) - MINSIZE + 1) + MINSIZE;
467 else if (size < MINSIZE) {
469 tp->edge_length = MAX(MINSIZE, MIN(tp->width, tp->height) / 2);
471 tp->edge_length = MINSIZE;
473 tp->edge_length = MIN(size, MAX(MINSIZE,
474 MIN(tp->width, tp->height) / 2));
475 tp->origin.x = (tp->width / 2 + NRAND(tp->width)) / 2;
476 tp->origin.y = (tp->height / 2 + NRAND(tp->height)) / 2;
477 tp->fringe.n_nodes = 2;
478 if (tp->fringe.nodes != NULL)
480 if (tp->fringe.nodes != NULL || tp->forced.first != 0) {
481 if (MI_IS_VERBOSE(mi)) {
482 (void) fprintf(stderr, "Weirdness in init_penrose()\n");
483 (void) fprintf(stderr, "tp->fringe.nodes = NULL && tp->forced.first = 0\n");
485 free_penrose(tp); /* Try again */
488 tp->forced.n_nodes = tp->forced.n_visible = 0;
489 if ((fp = tp->fringe.nodes = ALLOC_NODE(fringe_node_c)) == NULL) {
494 if (MI_IS_VERBOSE(mi)) {
495 (void) fprintf(stderr, "Weirdness in init_penrose()\n");
496 (void) fprintf(stderr, "fp = 0\n");
498 if ((fp = tp->fringe.nodes = ALLOC_NODE(fringe_node_c)) == NULL) {
505 fp->rule_mask = (1 << N_VERTEX_RULES) - 1;
507 if ((fp->prev = fp->next = ALLOC_NODE(fringe_node_c)) == NULL) {
512 if (MI_IS_VERBOSE(mi)) {
513 (void) fprintf(stderr, "Weirdness in init_penrose()\n");
514 (void) fprintf(stderr, "fp->next = 0\n");
516 if ((fp->prev = fp->next = ALLOC_NODE(fringe_node_c)) == NULL) {
523 fp->loc = tp->origin;
524 fp->off_screen = False;
525 for (i = 0; i < 5; i++)
530 fp->next->prev = fp->next->next = fp;
533 fp->fived[i] = 2 * NRAND(2) - 1;
534 fived_to_loc(fp->fived, tp, &(fp->loc));
535 /* That's it! We have created our first edge. */
539 * This attempts to match the configuration of vertex with the vertex
540 * rules. The return value is a total match count. If matches is
541 * non-null, it will be used to store information about the matches
542 * and must be large enough to contain it. To play it absolutely
543 * safe, allocate room for MAX_TILES_PER_VERTEX * N_VERTEX_RULES
544 * entries when searching all matches. The rule mask of vertex will
545 * be applied and rules masked out will not be searched. Only strict
546 * subsequences match. If first_only is true, the search stops when
547 * the first match is found. Otherwise all matches will be found and
548 * the rule_mask of vertex will be updated, which also happens in
549 * single-match mode if no match is found.
552 match_rules(fringe_node_c * vertex, rule_match_c * matches, int first_only)
554 /* I will assume that I can fit all the relevant bits in vertex->tiles
555 into one unsigned long. With 3 bits per element and at most 7
556 elements this means 21 bits, which should leave plenty of room.
557 After packing the bits the rest is just integer comparisons and
558 some bit shuffling. This is essentially Rabin-Karp without
559 congruence arithmetic. */
561 int hits = 0, good_rules[N_VERTEX_RULES], n_good = 0;
563 vertex_hash = 0, lower_bits_mask = ~(VT_TOTAL_MASK << VT_BITS * (vertex->n_tiles - 1));
564 unsigned new_rule_mask = 0;
566 for (i = 0; i < N_VERTEX_RULES; i++)
567 if (vertex->n_tiles >= vertex_rules[i].n_tiles)
568 vertex->rule_mask &= ~(1 << i);
569 else if (vertex->rule_mask & 1 << i)
570 good_rules[n_good++] = i;
571 for (i = 0; i < vertex->n_tiles; i++)
572 vertex_hash |= (unsigned long) vertex->tiles[i] << (VT_BITS * i);
574 for (j = 0; j < n_good; j++) {
575 unsigned long rule_hash = 0;
576 vertex_rule_c *vr = vertex_rules + good_rules[j];
578 for (i = 0; i < vertex->n_tiles; i++)
579 rule_hash |= (unsigned long) vr->tiles[i] << (VT_BITS * i);
580 if (rule_hash == vertex_hash) {
582 matches[hits].rule = good_rules[j];
583 matches[hits].pos = 0;
589 new_rule_mask |= 1 << good_rules[j];
591 for (i = vr->n_tiles - 1; i > 0; i--) {
592 rule_hash = vr->tiles[i] | (rule_hash & lower_bits_mask) << VT_BITS;
593 if (vertex_hash == rule_hash) {
595 matches[hits].rule = good_rules[j];
596 matches[hits].pos = i;
602 new_rule_mask |= 1 << good_rules[j];
606 vertex->rule_mask = new_rule_mask;
612 * find_completions finds the possible ways to add a tile to a vertex.
613 * The return values is the number of such possibilities. You must
614 * first call match_rules to produce matches and n_matches. sides
615 * specifies which side of the vertex to extend and can be S_LEFT or
616 * S_RIGHT. If results is non-null, it should point to an array large
617 * enough to contain the results, which will be stored there.
618 * MAX_COMPL elements will always suffice. If first_only is true we
619 * stop as soon as we find one possibility (NOT USED).
624 find_completions(fringe_node_c * vertex, rule_match_c * matches, int n_matches,
625 unsigned side, vertex_type_c * results /*, int first_only */ )
629 vertex_type_c buf[MAX_COMPL];
635 for (i = 0; i < n_matches; i++) {
636 vertex_rule_c *rule = vertex_rules + matches[i].rule;
637 int pos = (matches[i].pos
638 + (side == S_RIGHT ? vertex->n_tiles : rule->n_tiles - 1))
640 vertex_type_c vtype = rule->tiles[pos];
643 for (j = 0; j < n_res; j++)
644 if (vtype == results[j]) {
649 results[n_res++] = vtype;
656 * Draw a tile on the display. Vertices must be given in a
657 * counterclockwise order. vtype is the vertex type of v1 (and thus
658 * also gives the tile type).
661 draw_tile(fringe_node_c * v1, fringe_node_c * v2,
662 fringe_node_c * v3, fringe_node_c * v4,
663 vertex_type_c vtype, ModeInfo * mi)
665 Display *display = MI_DISPLAY(mi);
666 Window window = MI_WINDOW(mi);
668 tiling_c *tp = &tilings[MI_SCREEN(mi)];
670 vertex_type_c corner = vtype & VT_CORNER_MASK;
672 if (v1->off_screen && v2->off_screen && v3->off_screen && v4->off_screen)
674 pts[corner] = v1->loc;
675 pts[VT_RIGHT(corner)] = v2->loc;
676 pts[VT_FAR(corner)] = v3->loc;
677 pts[VT_LEFT(corner)] = v4->loc;
679 if (MI_NPIXELS(mi) > 2) {
680 if ((vtype & VT_TYPE_MASK) == VT_THICK)
681 XSetForeground(display, gc, MI_PIXEL(mi, tp->thick_color));
683 XSetForeground(display, gc, MI_PIXEL(mi, tp->thin_color));
685 XSetForeground(display, gc, MI_WHITE_PIXEL(mi));
686 XFillPolygon(display, window, gc, pts, 4, Convex, CoordModeOrigin);
687 XSetForeground(display, gc, MI_BLACK_PIXEL(mi));
688 XDrawLines(display, window, gc, pts, 5, CoordModeOrigin);
691 /* Draw some Ammann lines for debugging purposes. This will probably
692 fail miserably on a b&w display. */
694 if ((vtype & VT_TYPE_MASK) == VT_THICK) {
696 if (tp->ammann_r == .0) {
697 float pi10 = 2 * atan(1.) / 5;
699 tp->ammann_r = 1 - sin(pi10) / (2 * sin(3 * pi10));
701 if (MI_NPIXELS(mi) > 2)
702 XSetForeground(display, gc, MI_PIXEL(mi, tp->thin_color));
704 XSetForeground(display, gc, MI_BLACK_PIXEL(mi));
705 XSetLineAttributes(display, gc, 1, LineOnOffDash, CapNotLast, JoinMiter);
707 XDrawLine(display, window, gc,
708 (int) (tp->ammann_r * pts[3].x + (1 - tp->ammann_r) * pts[0].x + .5),
709 (int) (tp->ammann_r * pts[3].y + (1 - tp->ammann_r) * pts[0].y + .5),
710 (int) (tp->ammann_r * pts[1].x + (1 - tp->ammann_r) * pts[0].x + .5),
711 (int) (tp->ammann_r * pts[1].y + (1 - tp->ammann_r) * pts[0].y + .5));
712 if (MI_NPIXELS(mi) <= 2)
713 XSetLineAttributes(display, gc, 1, LineSolid, CapNotLast, JoinMiter);
715 if (MI_NPIXELS(mi) > 2)
716 XSetForeground(display, gc, MI_PIXEL(mi, tp->thick_color));
718 XSetForeground(display, gc, MI_BLACK_PIXEL(mi));
719 XSetLineAttributes(display, gc, 1, LineOnOffDash, CapNotLast, JoinMiter);
721 XDrawLine(display, window, gc,
722 (int) ((pts[3].x + pts[2].x) / 2 + .5),
723 (int) ((pts[3].y + pts[2].y) / 2 + .5),
724 (int) ((pts[1].x + pts[2].x) / 2 + .5),
725 (int) ((pts[1].y + pts[2].y) / 2 + .5));
726 if (MI_NPIXELS(mi) <= 2)
727 XSetLineAttributes(display, gc, 1, LineSolid, CapNotLast, JoinMiter);
733 * Update the status of this vertex on the forced vertex queue. If
734 * the vertex has become untileable set tp->done. This is supposed
735 * to detect dislocations -- never call this routine with a completely
738 * Check for untileable vertices in check_vertex and stop tiling as
739 * soon as one finds one. I don't know if it is possible to run out
740 * of forced vertices while untileable vertices exist (or will
741 * cavities inevitably appear). If this can happen, add_random_tile
742 * might get called with an untileable vertex, causing ( n <= 1).
743 * (This is what the tp->done checks for).
745 * A delayLoop celebrates the dislocation.
748 check_vertex(ModeInfo * mi, fringe_node_c * vertex, tiling_c * tp)
750 rule_match_c hits[MAX_TILES_PER_VERTEX * N_VERTEX_RULES];
751 int n_hits = match_rules(vertex, hits, False);
752 unsigned forced_sides = 0;
754 if (vertex->rule_mask == 0) {
756 if (MI_IS_VERBOSE(mi)) {
757 (void) fprintf(stderr, "Dislocation occurred!\n");
759 tp->busyLoop = CELEBRATE; /* Should be able to recover */
761 if (1 == find_completions(vertex, hits, n_hits, S_LEFT, 0 /*, False */ ))
762 forced_sides |= S_LEFT;
763 if (1 == find_completions(vertex, hits, n_hits, S_RIGHT, 0 /*, False */ ))
764 forced_sides |= S_RIGHT;
765 if (forced_sides == 0) {
766 if (vertex->list_ptr != 0) {
767 forced_node_c *node = *vertex->list_ptr;
769 *vertex->list_ptr = node->next;
771 node->next->vertex->list_ptr = vertex->list_ptr;
772 (void) free((void *) node);
773 tp->forced.n_nodes--;
774 if (!vertex->off_screen)
775 tp->forced.n_visible--;
776 vertex->list_ptr = 0;
781 if (vertex->list_ptr == 0) {
782 if ((node = ALLOC_NODE(forced_node_c)) == NULL)
784 node->vertex = vertex;
785 node->next = tp->forced.first;
786 if (tp->forced.first != 0)
787 tp->forced.first->vertex->list_ptr = &(node->next);
788 tp->forced.first = node;
789 vertex->list_ptr = &(tp->forced.first);
790 tp->forced.n_nodes++;
791 if (!vertex->off_screen)
792 tp->forced.n_visible++;
794 node = *vertex->list_ptr;
795 node->forced_sides = forced_sides;
801 * Delete this vertex. If the vertex is a member of the forced vertex queue,
802 * also remove that entry. We assume that the vertex is no longer
803 * connected to the fringe. Note that tp->fringe.nodes must not point to
804 * the vertex being deleted.
807 delete_vertex(ModeInfo * mi, fringe_node_c * vertex, tiling_c * tp)
809 if (tp->fringe.nodes == vertex) {
811 if (MI_IS_VERBOSE(mi)) {
812 (void) fprintf(stderr, "Weirdness in delete_penrose()\n");
813 (void) fprintf(stderr, "tp->fringe.nodes == vertex\n");
815 tp->busyLoop = CELEBRATE;
817 if (vertex->list_ptr != 0) {
818 forced_node_c *node = *vertex->list_ptr;
820 *vertex->list_ptr = node->next;
822 node->next->vertex->list_ptr = vertex->list_ptr;
823 (void) free((void *) node);
824 tp->forced.n_nodes--;
825 if (!vertex->off_screen)
826 tp->forced.n_visible--;
828 if (!vertex->off_screen)
829 tp->fringe.n_nodes--;
830 (void) free((void *) vertex);
835 * Check whether the addition of a tile of type vtype would completely fill
836 * the space available at vertex.
839 fills_vertex(ModeInfo * mi, vertex_type_c vtype, fringe_node_c * vertex)
842 (vertex_dir(mi, vertex, S_LEFT) - vertex_dir(mi, vertex, S_RIGHT)
843 - vtype_angle(vtype)) % 10 == 0;
848 * If you were to add a tile of type vtype to a specified side of
849 * vertex, fringe_changes tells you which other vertices it would
850 * attach to. The addresses of these vertices will be stored in the
851 * last three arguments. Null is stored if the corresponding vertex
852 * would need to be allocated.
854 * The function also analyzes which vertices would be swallowed by the tiling
855 * and thus cut off from the fringe. The result is returned as a bit pattern.
857 #define FC_BAG 1 /* Total enclosure. Should never occur. */
858 #define FC_NEW_RIGHT 2
860 #define FC_NEW_LEFT 8
861 #define FC_NEW_MASK 0xe
862 #define FC_CUT_THIS 0x10
863 #define FC_CUT_RIGHT 0x20
864 #define FC_CUT_FAR 0x40
865 #define FC_CUT_LEFT 0x80
866 #define FC_CUT_MASK 0xf0
867 #define FC_TOTAL_MASK 0xff
870 fringe_changes(ModeInfo * mi, fringe_node_c * vertex,
871 unsigned side, vertex_type_c vtype,
872 fringe_node_c ** right, fringe_node_c ** far,
873 fringe_node_c ** left)
875 fringe_node_c *v, *f = (fringe_node_c *) NULL;
876 unsigned result = FC_NEW_FAR; /* We clear this later if necessary. */
880 if (fills_vertex(mi, vtype, vertex)) {
881 result |= FC_CUT_THIS;
882 } else if (side == S_LEFT) {
883 result |= FC_NEW_RIGHT;
887 result |= FC_NEW_LEFT;
892 if (!(result & FC_NEW_LEFT)) {
896 if (fills_vertex(mi, VT_LEFT(vtype), v)) {
897 result = (result & ~FC_NEW_FAR) | FC_CUT_LEFT;
903 if (!(result & FC_NEW_RIGHT)) {
907 if (fills_vertex(mi, VT_RIGHT(vtype), v)) {
908 result = (result & ~FC_NEW_FAR) | FC_CUT_RIGHT;
914 if (!(result & FC_NEW_FAR)
915 && fills_vertex(mi, VT_FAR(vtype), f)) {
916 result |= FC_CUT_FAR;
917 result &= (~FC_NEW_LEFT & ~FC_NEW_RIGHT);
918 if (right && (result & FC_CUT_LEFT))
920 if (left && (result & FC_CUT_RIGHT))
923 if (((result & FC_CUT_LEFT) && (result & FC_CUT_RIGHT))
924 || ((result & FC_CUT_THIS) && (result & FC_CUT_FAR)))
930 /* A couple of lesser helper functions for add_tile. */
932 add_vtype(fringe_node_c * vertex, unsigned side, vertex_type_c vtype)
935 vertex->tiles[vertex->n_tiles++] = vtype;
939 for (i = vertex->n_tiles; i > 0; i--)
940 vertex->tiles[i] = vertex->tiles[i - 1];
941 vertex->tiles[0] = vtype;
946 static fringe_node_c *
947 alloc_vertex(ModeInfo * mi, angle_c dir, fringe_node_c * from, tiling_c * tp)
951 if ((v = ALLOC_NODE(fringe_node_c)) == NULL) {
953 if (MI_IS_VERBOSE(mi)) {
954 (void) fprintf(stderr, "No memory in alloc_vertex()\n");
956 tp->busyLoop = CELEBRATE;
960 add_unit_vec(dir, v->fived);
961 fived_to_loc(v->fived, tp, &(v->loc));
962 if (v->loc.x < 0 || v->loc.y < 0
963 || v->loc.x >= tp->width || v->loc.y >= tp->height) {
964 v->off_screen = True;
965 if (v->loc.x < -tp->width || v->loc.y < -tp->height
966 || v->loc.x >= 2 * tp->width || v->loc.y >= 2 * tp->height)
969 v->off_screen = False;
970 tp->fringe.n_nodes++;
973 v->rule_mask = (1 << N_VERTEX_RULES) - 1;
979 * Add a tile described by vtype to the side of vertex. This must be
980 * allowed by the rules -- we do not check it here. New vertices are
981 * allocated as necessary. The fringe and the forced vertex pool are updated.
982 * The new tile is drawn on the display.
984 * One thing we do check here is whether the new tile causes an untiled
985 * area to become enclosed by the tiling. If this would happen, the tile
986 * is not added. The return value is true iff a tile was added.
989 add_tile(ModeInfo * mi,
990 fringe_node_c * vertex, unsigned side, vertex_type_c vtype)
992 tiling_c *tp = &tilings[MI_SCREEN(mi)];
995 *left = (fringe_node_c *) NULL,
996 *right = (fringe_node_c *) NULL,
997 *far = (fringe_node_c *) NULL,
999 unsigned fc = fringe_changes(mi, vertex, side, vtype, &right, &far, &left);
1002 ltype = VT_LEFT(vtype),
1003 rtype = VT_RIGHT(vtype),
1004 ftype = VT_FAR(vtype);
1006 /* By our conventions vertex->next lies to the left of vertex and
1007 vertex->prev to the right. */
1009 /* This should never occur. */
1012 if (MI_IS_VERBOSE(mi)) {
1013 (void) fprintf(stderr, "Weirdness in add_tile()\n");
1014 (void) fprintf(stderr, "fc = %d, FC_BAG = %d\n", fc, FC_BAG);
1017 if (side == S_LEFT) {
1019 if ((right = alloc_vertex(mi, vertex_dir(mi, vertex, S_LEFT) -
1020 vtype_angle(vtype), vertex, tp)) == NULL)
1023 if ((far = alloc_vertex(mi, vertex_dir(mi, left, S_RIGHT) +
1024 vtype_angle(ltype), left, tp)) == NULL)
1028 if ((left = alloc_vertex(mi, vertex_dir(mi, vertex, S_RIGHT) +
1029 vtype_angle(vtype), vertex, tp)) == NULL)
1032 if ((far = alloc_vertex(mi, vertex_dir(mi, right, S_LEFT) -
1033 vtype_angle(rtype), right, tp)) == NULL)
1037 /* Having allocated the new vertices, but before joining them with
1038 the rest of the fringe, check if vertices with same coordinates
1039 already exist. If any such are found, give up. */
1040 node = tp->fringe.nodes;
1042 if (((fc & FC_NEW_LEFT) && fived_equal(node->fived, left->fived))
1043 || ((fc & FC_NEW_RIGHT) && fived_equal(node->fived, right->fived))
1044 || ((fc & FC_NEW_FAR) && fived_equal(node->fived, far->fived))) {
1045 /* Better luck next time. */
1046 if (fc & FC_NEW_LEFT)
1047 delete_vertex(mi, left, tp);
1048 if (fc & FC_NEW_RIGHT)
1049 delete_vertex(mi, right, tp);
1050 if (fc & FC_NEW_FAR)
1051 delete_vertex(mi, far, tp);
1055 } while (node != tp->fringe.nodes);
1058 if (!(fc & FC_CUT_THIS)) {
1059 if (side == S_LEFT) {
1060 vertex->next = right;
1061 right->prev = vertex;
1063 vertex->prev = left;
1064 left->next = vertex;
1067 if (!(fc & FC_CUT_FAR)) {
1068 if (!(fc & FC_CUT_LEFT)) {
1072 if (!(fc & FC_CUT_RIGHT)) {
1077 draw_tile(vertex, right, far, left, vtype, mi);
1079 /* Delete vertices that are no longer on the fringe. Check the others. */
1080 if (fc & FC_CUT_THIS) {
1081 tp->fringe.nodes = far;
1082 delete_vertex(mi, vertex, tp);
1084 add_vtype(vertex, side, vtype);
1085 check_vertex(mi, vertex, tp);
1086 tp->fringe.nodes = vertex;
1088 if (fc & FC_CUT_FAR)
1089 delete_vertex(mi, far, tp);
1091 add_vtype(far, fc & FC_CUT_RIGHT ? S_LEFT : S_RIGHT, ftype);
1092 check_vertex(mi, far, tp);
1094 if (fc & FC_CUT_LEFT)
1095 delete_vertex(mi, left, tp);
1097 add_vtype(left, fc & FC_CUT_FAR ? S_LEFT : S_RIGHT, ltype);
1098 check_vertex(mi, left, tp);
1100 if (fc & FC_CUT_RIGHT)
1101 delete_vertex(mi, right, tp);
1103 add_vtype(right, fc & FC_CUT_FAR ? S_RIGHT : S_LEFT, rtype);
1104 check_vertex(mi, right, tp);
1111 * Add a forced tile to a given forced vertex. Basically an easy job,
1112 * since we know what to add. But it might fail if adding the tile
1113 * would cause some untiled area to become enclosed. There is also another
1114 * more exotic culprit: we might have a dislocation. Fortunately, they
1115 * are very rare (the PRL article reported that perfect tilings of over
1116 * 2^50 tiles had been generated). There is a version of the algorithm
1117 * that doesn't produce dislocations, but it's a lot hairier than the
1118 * simpler version I used.
1121 add_forced_tile(ModeInfo * mi, forced_node_c * node)
1123 tiling_c *tp = &tilings[MI_SCREEN(mi)];
1125 vertex_type_c vtype;
1126 rule_match_c hits[MAX_TILES_PER_VERTEX * N_VERTEX_RULES];
1129 if (node->forced_sides == (S_LEFT | S_RIGHT))
1130 side = NRAND(2) ? S_LEFT : S_RIGHT;
1132 side = node->forced_sides;
1133 n = match_rules(node->vertex, hits, True);
1134 n = find_completions(node->vertex, hits, n, side, &vtype /*, True */ );
1137 if (MI_IS_VERBOSE(mi)) {
1138 (void) fprintf(stderr, "Weirdness in add_forced_tile()\n");
1139 (void) fprintf(stderr, "n = %d\n", n);
1142 return add_tile(mi, node->vertex, side, vtype);
1147 * Whether the addition of a tile of vtype on the given side of vertex
1148 * would conform to the rules. The efficient way to do this would be
1149 * to add the new tile and then use the same type of search as in
1150 * match_rules. However, this function is not a performance
1151 * bottleneck (only needed for random tile additions, which are
1152 * relatively infrequent), so I will settle for a simpler implementation.
1155 legal_move(fringe_node_c * vertex, unsigned side, vertex_type_c vtype)
1157 rule_match_c hits[MAX_TILES_PER_VERTEX * N_VERTEX_RULES];
1158 vertex_type_c legal_vt[MAX_COMPL];
1159 int n_hits, n_legal, i;
1161 n_hits = match_rules(vertex, hits, False);
1162 n_legal = find_completions(vertex, hits, n_hits, side, legal_vt /*, False */ );
1163 for (i = 0; i < n_legal; i++)
1164 if (legal_vt[i] == vtype)
1171 * Add a randomly chosen tile to a given vertex. This requires more checking
1172 * as we must make sure the new tile conforms to the vertex rules at every
1173 * vertex it touches. */
1175 add_random_tile(fringe_node_c * vertex, ModeInfo * mi)
1177 fringe_node_c *right, *left, *far;
1178 int i, j, n, n_hits, n_good;
1179 unsigned side, fc, no_good, s;
1180 vertex_type_c vtypes[MAX_COMPL];
1181 rule_match_c hits[MAX_TILES_PER_VERTEX * N_VERTEX_RULES];
1182 tiling_c *tp = &tilings[MI_SCREEN(mi)];
1184 if (MI_NPIXELS(mi) > 2) {
1185 tp->thick_color = NRAND(MI_NPIXELS(mi));
1186 /* Insure good contrast */
1187 tp->thin_color = (NRAND(2 * MI_NPIXELS(mi) / 3) + tp->thick_color +
1188 MI_NPIXELS(mi) / 6) % MI_NPIXELS(mi);
1190 tp->thick_color = tp->thin_color = MI_WHITE_PIXEL(mi);
1191 n_hits = match_rules(vertex, hits, False);
1192 side = NRAND(2) ? S_LEFT : S_RIGHT;
1193 n = find_completions(vertex, hits, n_hits, side, vtypes /*, False */ );
1194 /* One answer would mean a forced tile. */
1197 if (MI_IS_VERBOSE(mi)) {
1198 (void) fprintf(stderr, "Weirdness in add_random_tile()\n");
1199 (void) fprintf(stderr, "n = %d\n", n);
1204 for (i = 0; i < n; i++) {
1205 fc = fringe_changes(mi, vertex, side, vtypes[i], &right, &far, &left);
1208 if (MI_IS_VERBOSE(mi)) {
1209 (void) fprintf(stderr, "Weirdness in add_random_tile()\n");
1210 (void) fprintf(stderr, "fc = %d, FC_BAG = %d\n", fc, FC_BAG);
1214 s = (((fc & FC_CUT_FAR) && (fc & FC_CUT_LEFT)) ? S_RIGHT : S_LEFT);
1215 if (!legal_move(right, s, VT_RIGHT(vtypes[i]))) {
1216 no_good |= (1 << i);
1222 s = (((fc & FC_CUT_FAR) && (fc & FC_CUT_RIGHT)) ? S_LEFT : S_RIGHT);
1223 if (!legal_move(left, s, VT_LEFT(vtypes[i]))) {
1224 no_good |= (1 << i);
1230 s = ((fc & FC_CUT_LEFT) ? S_RIGHT : S_LEFT);
1231 if (!legal_move(far, s, VT_FAR(vtypes[i]))) {
1232 no_good |= (1 << i);
1239 if (MI_IS_VERBOSE(mi)) {
1240 (void) fprintf(stderr, "Weirdness in add_random_tile()\n");
1241 (void) fprintf(stderr, "n_good = %d\n", n_good);
1245 for (i = j = 0; i <= n; i++, j++)
1246 while (no_good & (1 << j))
1249 if (!add_tile(mi, vertex, side, vtypes[j - 1])) {
1251 if (MI_IS_VERBOSE(mi)) {
1252 (void) fprintf(stderr, "Weirdness in add_random_tile()\n");
1258 /* One step of the growth algorithm. */
1260 draw_penrose(ModeInfo * mi)
1266 if (tilings == NULL)
1268 tp = &tilings[MI_SCREEN(mi)];
1269 if (tp->fringe.nodes == NULL)
1272 MI_IS_DRAWN(mi) = True;
1273 p = tp->forced.first;
1274 if (tp->busyLoop > 0) {
1278 if (tp->done || tp->failures >= 100) {
1282 /* Check for the initial "2-gon". */
1283 if (tp->fringe.nodes->prev == tp->fringe.nodes->next) {
1284 vertex_type_c vtype = (unsigned char) (VT_TOTAL_MASK & LRAND());
1288 if (!add_tile(mi, tp->fringe.nodes, S_LEFT, vtype))
1292 /* No visible nodes left. */
1293 if (tp->fringe.n_nodes == 0) {
1295 tp->busyLoop = COMPLETION; /* Just finished drawing */
1298 if (tp->forced.n_visible > 0 && tp->failures < 10) {
1299 n = NRAND(tp->forced.n_visible);
1301 while (p->vertex->off_screen)
1308 } else if (tp->forced.n_nodes > 0) {
1309 n = NRAND(tp->forced.n_nodes);
1313 fringe_node_c *fringe_p = tp->fringe.nodes;
1315 n = NRAND(tp->fringe.n_nodes);
1319 fringe_p = fringe_p->next;
1320 } while (fringe_p->off_screen);
1321 add_random_tile(fringe_p, mi);
1325 if (add_forced_tile(mi, p))
1332 /* Total clean-up. */
1334 release_penrose(ModeInfo * mi)
1336 if (tilings != NULL) {
1339 for (screen = 0; screen < MI_NUM_SCREENS(mi); screen++)
1340 free_penrose(&tilings[screen]);
1341 (void) free((void *) tilings);
1342 tilings = (tiling_c *) NULL;
1346 XSCREENSAVER_MODULE ("Penrose", penrose)
1348 #endif /* MODE_penrose */