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" \
90 "*ignoreRotation: True \n" \
92 # define release_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", (char *) NULL,
125 "init_penrose", "init_penrose", "free_penrose", &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(ModeInfo * mi)
408 tiling_c * tp = &tilings[MI_SCREEN(mi)];
409 register fringe_node_c *fp1, *fp2;
410 register forced_node_c *lp1, *lp2;
412 if (tp->fringe.nodes == NULL)
414 fp1 = tp->fringe.nodes;
418 (void) free((void *) fp2);
419 } while (fp1 != tp->fringe.nodes);
420 tp->fringe.nodes = (fringe_node_c *) NULL;
421 for (lp1 = tp->forced.first; lp1 != 0;) {
424 (void) free((void *) lp2);
426 tp->forced.first = 0;
430 /* Called to init the mode. */
432 init_penrose(ModeInfo * mi)
438 MI_INIT (mi, tilings);
439 tp = &tilings[MI_SCREEN(mi)];
441 #if 0 /* if you do this, then the -ammann and -no-ammann options don't work.
443 if (MI_IS_FULLRANDOM(mi))
444 tp->ammann = (Bool) (LRAND() & 1);
452 tp->width = MI_WIDTH(mi);
453 tp->height = MI_HEIGHT(mi);
454 if (MI_NPIXELS(mi) > 2) {
455 tp->thick_color = NRAND(MI_NPIXELS(mi));
456 /* Insure good contrast */
457 tp->thin_color = (NRAND(2 * MI_NPIXELS(mi) / 3) + tp->thick_color +
458 MI_NPIXELS(mi) / 6) % MI_NPIXELS(mi);
462 tp->edge_length = NRAND(MIN(-size, MAX(MINSIZE,
463 MIN(tp->width, tp->height) / 2)) - MINSIZE + 1) + MINSIZE;
464 else if (size < MINSIZE) {
466 tp->edge_length = MAX(MINSIZE, MIN(tp->width, tp->height) / 2);
468 tp->edge_length = MINSIZE;
470 tp->edge_length = MIN(size, MAX(MINSIZE,
471 MIN(tp->width, tp->height) / 2));
472 tp->origin.x = (tp->width / 2 + NRAND(tp->width)) / 2;
473 tp->origin.y = (tp->height / 2 + NRAND(tp->height)) / 2;
474 tp->fringe.n_nodes = 2;
475 if (tp->fringe.nodes != NULL)
477 if (tp->fringe.nodes != NULL || tp->forced.first != 0) {
478 if (MI_IS_VERBOSE(mi)) {
479 (void) fprintf(stderr, "Weirdness in init_penrose()\n");
480 (void) fprintf(stderr, "tp->fringe.nodes = NULL && tp->forced.first = 0\n");
482 free_penrose(mi); /* Try again */
485 tp->forced.n_nodes = tp->forced.n_visible = 0;
486 if ((fp = tp->fringe.nodes = ALLOC_NODE(fringe_node_c)) == NULL) {
491 if (MI_IS_VERBOSE(mi)) {
492 (void) fprintf(stderr, "Weirdness in init_penrose()\n");
493 (void) fprintf(stderr, "fp = 0\n");
495 if ((fp = tp->fringe.nodes = ALLOC_NODE(fringe_node_c)) == NULL) {
502 fp->rule_mask = (1 << N_VERTEX_RULES) - 1;
504 if ((fp->prev = fp->next = ALLOC_NODE(fringe_node_c)) == NULL) {
509 if (MI_IS_VERBOSE(mi)) {
510 (void) fprintf(stderr, "Weirdness in init_penrose()\n");
511 (void) fprintf(stderr, "fp->next = 0\n");
513 if ((fp->prev = fp->next = ALLOC_NODE(fringe_node_c)) == NULL) {
520 fp->loc = tp->origin;
521 fp->off_screen = False;
522 for (i = 0; i < 5; i++)
527 fp->next->prev = fp->next->next = fp;
530 fp->fived[i] = 2 * NRAND(2) - 1;
531 fived_to_loc(fp->fived, tp, &(fp->loc));
532 /* That's it! We have created our first edge. */
538 * This attempts to match the configuration of vertex with the vertex
539 * rules. The return value is a total match count. If matches is
540 * non-null, it will be used to store information about the matches
541 * and must be large enough to contain it. To play it absolutely
542 * safe, allocate room for MAX_TILES_PER_VERTEX * N_VERTEX_RULES
543 * entries when searching all matches. The rule mask of vertex will
544 * be applied and rules masked out will not be searched. Only strict
545 * subsequences match. If first_only is true, the search stops when
546 * the first match is found. Otherwise all matches will be found and
547 * the rule_mask of vertex will be updated, which also happens in
548 * single-match mode if no match is found.
551 match_rules(fringe_node_c * vertex, rule_match_c * matches, int first_only)
553 /* I will assume that I can fit all the relevant bits in vertex->tiles
554 into one unsigned long. With 3 bits per element and at most 7
555 elements this means 21 bits, which should leave plenty of room.
556 After packing the bits the rest is just integer comparisons and
557 some bit shuffling. This is essentially Rabin-Karp without
558 congruence arithmetic. */
560 int hits = 0, good_rules[N_VERTEX_RULES], n_good = 0;
562 vertex_hash = 0, lower_bits_mask = ~(VT_TOTAL_MASK << VT_BITS * (vertex->n_tiles - 1));
563 unsigned new_rule_mask = 0;
565 for (i = 0; i < N_VERTEX_RULES; i++)
566 if (vertex->n_tiles >= vertex_rules[i].n_tiles)
567 vertex->rule_mask &= ~(1 << i);
568 else if (vertex->rule_mask & 1 << i)
569 good_rules[n_good++] = i;
570 for (i = 0; i < vertex->n_tiles; i++)
571 vertex_hash |= (unsigned long) vertex->tiles[i] << (VT_BITS * i);
573 for (j = 0; j < n_good; j++) {
574 unsigned long rule_hash = 0;
575 vertex_rule_c *vr = vertex_rules + good_rules[j];
577 for (i = 0; i < vertex->n_tiles; i++)
578 rule_hash |= (unsigned long) vr->tiles[i] << (VT_BITS * i);
579 if (rule_hash == vertex_hash) {
581 matches[hits].rule = good_rules[j];
582 matches[hits].pos = 0;
588 new_rule_mask |= 1 << good_rules[j];
590 for (i = vr->n_tiles - 1; i > 0; i--) {
591 rule_hash = vr->tiles[i] | (rule_hash & lower_bits_mask) << VT_BITS;
592 if (vertex_hash == rule_hash) {
594 matches[hits].rule = good_rules[j];
595 matches[hits].pos = i;
601 new_rule_mask |= 1 << good_rules[j];
605 vertex->rule_mask = new_rule_mask;
611 * find_completions finds the possible ways to add a tile to a vertex.
612 * The return values is the number of such possibilities. You must
613 * first call match_rules to produce matches and n_matches. sides
614 * specifies which side of the vertex to extend and can be S_LEFT or
615 * S_RIGHT. If results is non-null, it should point to an array large
616 * enough to contain the results, which will be stored there.
617 * MAX_COMPL elements will always suffice. If first_only is true we
618 * stop as soon as we find one possibility (NOT USED).
623 find_completions(fringe_node_c * vertex, rule_match_c * matches, int n_matches,
624 unsigned side, vertex_type_c * results /*, int first_only */ )
628 vertex_type_c buf[MAX_COMPL];
634 for (i = 0; i < n_matches; i++) {
635 vertex_rule_c *rule = vertex_rules + matches[i].rule;
636 int pos = (matches[i].pos
637 + (side == S_RIGHT ? vertex->n_tiles : rule->n_tiles - 1))
639 vertex_type_c vtype = rule->tiles[pos];
642 for (j = 0; j < n_res; j++)
643 if (vtype == results[j]) {
648 results[n_res++] = vtype;
655 * Draw a tile on the display. Vertices must be given in a
656 * counterclockwise order. vtype is the vertex type of v1 (and thus
657 * also gives the tile type).
660 draw_tile(fringe_node_c * v1, fringe_node_c * v2,
661 fringe_node_c * v3, fringe_node_c * v4,
662 vertex_type_c vtype, ModeInfo * mi)
664 Display *display = MI_DISPLAY(mi);
665 Window window = MI_WINDOW(mi);
667 tiling_c *tp = &tilings[MI_SCREEN(mi)];
669 vertex_type_c corner = vtype & VT_CORNER_MASK;
671 if (v1->off_screen && v2->off_screen && v3->off_screen && v4->off_screen)
673 pts[corner] = v1->loc;
674 pts[VT_RIGHT(corner)] = v2->loc;
675 pts[VT_FAR(corner)] = v3->loc;
676 pts[VT_LEFT(corner)] = v4->loc;
678 if (MI_NPIXELS(mi) > 2) {
679 if ((vtype & VT_TYPE_MASK) == VT_THICK)
680 XSetForeground(display, gc, MI_PIXEL(mi, tp->thick_color));
682 XSetForeground(display, gc, MI_PIXEL(mi, tp->thin_color));
684 XSetForeground(display, gc, MI_WHITE_PIXEL(mi));
685 XFillPolygon(display, window, gc, pts, 4, Convex, CoordModeOrigin);
686 XSetForeground(display, gc, MI_BLACK_PIXEL(mi));
687 XDrawLines(display, window, gc, pts, 5, CoordModeOrigin);
690 /* Draw some Ammann lines for debugging purposes. This will probably
691 fail miserably on a b&w display. */
693 if ((vtype & VT_TYPE_MASK) == VT_THICK) {
695 if (tp->ammann_r == .0) {
696 float pi10 = 2 * atan(1.) / 5;
698 tp->ammann_r = 1 - sin(pi10) / (2 * sin(3 * pi10));
700 if (MI_NPIXELS(mi) > 2)
701 XSetForeground(display, gc, MI_PIXEL(mi, tp->thin_color));
703 XSetForeground(display, gc, MI_BLACK_PIXEL(mi));
704 XSetLineAttributes(display, gc, 1, LineOnOffDash, CapNotLast, JoinMiter);
706 XDrawLine(display, window, gc,
707 (int) (tp->ammann_r * pts[3].x + (1 - tp->ammann_r) * pts[0].x + .5),
708 (int) (tp->ammann_r * pts[3].y + (1 - tp->ammann_r) * pts[0].y + .5),
709 (int) (tp->ammann_r * pts[1].x + (1 - tp->ammann_r) * pts[0].x + .5),
710 (int) (tp->ammann_r * pts[1].y + (1 - tp->ammann_r) * pts[0].y + .5));
711 if (MI_NPIXELS(mi) <= 2)
712 XSetLineAttributes(display, gc, 1, LineSolid, CapNotLast, JoinMiter);
714 if (MI_NPIXELS(mi) > 2)
715 XSetForeground(display, gc, MI_PIXEL(mi, tp->thick_color));
717 XSetForeground(display, gc, MI_BLACK_PIXEL(mi));
718 XSetLineAttributes(display, gc, 1, LineOnOffDash, CapNotLast, JoinMiter);
720 XDrawLine(display, window, gc,
721 (int) ((pts[3].x + pts[2].x) / 2 + .5),
722 (int) ((pts[3].y + pts[2].y) / 2 + .5),
723 (int) ((pts[1].x + pts[2].x) / 2 + .5),
724 (int) ((pts[1].y + pts[2].y) / 2 + .5));
725 if (MI_NPIXELS(mi) <= 2)
726 XSetLineAttributes(display, gc, 1, LineSolid, CapNotLast, JoinMiter);
732 * Update the status of this vertex on the forced vertex queue. If
733 * the vertex has become untileable set tp->done. This is supposed
734 * to detect dislocations -- never call this routine with a completely
737 * Check for untileable vertices in check_vertex and stop tiling as
738 * soon as one finds one. I don't know if it is possible to run out
739 * of forced vertices while untileable vertices exist (or will
740 * cavities inevitably appear). If this can happen, add_random_tile
741 * might get called with an untileable vertex, causing ( n <= 1).
742 * (This is what the tp->done checks for).
744 * A delayLoop celebrates the dislocation.
747 check_vertex(ModeInfo * mi, fringe_node_c * vertex, tiling_c * tp)
749 rule_match_c hits[MAX_TILES_PER_VERTEX * N_VERTEX_RULES];
750 int n_hits = match_rules(vertex, hits, False);
751 unsigned forced_sides = 0;
753 if (vertex->rule_mask == 0) {
755 if (MI_IS_VERBOSE(mi)) {
756 (void) fprintf(stderr, "Dislocation occurred!\n");
758 tp->busyLoop = CELEBRATE; /* Should be able to recover */
760 if (1 == find_completions(vertex, hits, n_hits, S_LEFT, 0 /*, False */ ))
761 forced_sides |= S_LEFT;
762 if (1 == find_completions(vertex, hits, n_hits, S_RIGHT, 0 /*, False */ ))
763 forced_sides |= S_RIGHT;
764 if (forced_sides == 0) {
765 if (vertex->list_ptr != 0) {
766 forced_node_c *node = *vertex->list_ptr;
768 *vertex->list_ptr = node->next;
770 node->next->vertex->list_ptr = vertex->list_ptr;
771 (void) free((void *) node);
772 tp->forced.n_nodes--;
773 if (!vertex->off_screen)
774 tp->forced.n_visible--;
775 vertex->list_ptr = 0;
780 if (vertex->list_ptr == 0) {
781 if ((node = ALLOC_NODE(forced_node_c)) == NULL)
783 node->vertex = vertex;
784 node->next = tp->forced.first;
785 if (tp->forced.first != 0)
786 tp->forced.first->vertex->list_ptr = &(node->next);
787 tp->forced.first = node;
788 vertex->list_ptr = &(tp->forced.first);
789 tp->forced.n_nodes++;
790 if (!vertex->off_screen)
791 tp->forced.n_visible++;
793 node = *vertex->list_ptr;
794 node->forced_sides = forced_sides;
800 * Delete this vertex. If the vertex is a member of the forced vertex queue,
801 * also remove that entry. We assume that the vertex is no longer
802 * connected to the fringe. Note that tp->fringe.nodes must not point to
803 * the vertex being deleted.
806 delete_vertex(ModeInfo * mi, fringe_node_c * vertex, tiling_c * tp)
808 if (tp->fringe.nodes == vertex) {
810 if (MI_IS_VERBOSE(mi)) {
811 (void) fprintf(stderr, "Weirdness in delete_penrose()\n");
812 (void) fprintf(stderr, "tp->fringe.nodes == vertex\n");
814 tp->busyLoop = CELEBRATE;
816 if (vertex->list_ptr != 0) {
817 forced_node_c *node = *vertex->list_ptr;
819 *vertex->list_ptr = node->next;
821 node->next->vertex->list_ptr = vertex->list_ptr;
822 (void) free((void *) node);
823 tp->forced.n_nodes--;
824 if (!vertex->off_screen)
825 tp->forced.n_visible--;
827 if (!vertex->off_screen)
828 tp->fringe.n_nodes--;
829 (void) free((void *) vertex);
834 * Check whether the addition of a tile of type vtype would completely fill
835 * the space available at vertex.
838 fills_vertex(ModeInfo * mi, vertex_type_c vtype, fringe_node_c * vertex)
841 (vertex_dir(mi, vertex, S_LEFT) - vertex_dir(mi, vertex, S_RIGHT)
842 - vtype_angle(vtype)) % 10 == 0;
847 * If you were to add a tile of type vtype to a specified side of
848 * vertex, fringe_changes tells you which other vertices it would
849 * attach to. The addresses of these vertices will be stored in the
850 * last three arguments. Null is stored if the corresponding vertex
851 * would need to be allocated.
853 * The function also analyzes which vertices would be swallowed by the tiling
854 * and thus cut off from the fringe. The result is returned as a bit pattern.
856 #define FC_BAG 1 /* Total enclosure. Should never occur. */
857 #define FC_NEW_RIGHT 2
859 #define FC_NEW_LEFT 8
860 #define FC_NEW_MASK 0xe
861 #define FC_CUT_THIS 0x10
862 #define FC_CUT_RIGHT 0x20
863 #define FC_CUT_FAR 0x40
864 #define FC_CUT_LEFT 0x80
865 #define FC_CUT_MASK 0xf0
866 #define FC_TOTAL_MASK 0xff
869 fringe_changes(ModeInfo * mi, fringe_node_c * vertex,
870 unsigned side, vertex_type_c vtype,
871 fringe_node_c ** right, fringe_node_c ** far,
872 fringe_node_c ** left)
874 fringe_node_c *v, *f = (fringe_node_c *) NULL;
875 unsigned result = FC_NEW_FAR; /* We clear this later if necessary. */
879 if (fills_vertex(mi, vtype, vertex)) {
880 result |= FC_CUT_THIS;
881 } else if (side == S_LEFT) {
882 result |= FC_NEW_RIGHT;
886 result |= FC_NEW_LEFT;
891 if (!(result & FC_NEW_LEFT)) {
895 if (fills_vertex(mi, VT_LEFT(vtype), v)) {
896 result = (result & ~FC_NEW_FAR) | FC_CUT_LEFT;
902 if (!(result & FC_NEW_RIGHT)) {
906 if (fills_vertex(mi, VT_RIGHT(vtype), v)) {
907 result = (result & ~FC_NEW_FAR) | FC_CUT_RIGHT;
913 if (!(result & FC_NEW_FAR)
914 && fills_vertex(mi, VT_FAR(vtype), f)) {
915 result |= FC_CUT_FAR;
916 result &= (~FC_NEW_LEFT & ~FC_NEW_RIGHT);
917 if (right && (result & FC_CUT_LEFT))
919 if (left && (result & FC_CUT_RIGHT))
922 if (((result & FC_CUT_LEFT) && (result & FC_CUT_RIGHT))
923 || ((result & FC_CUT_THIS) && (result & FC_CUT_FAR)))
929 /* A couple of lesser helper functions for add_tile. */
931 add_vtype(fringe_node_c * vertex, unsigned side, vertex_type_c vtype)
934 vertex->tiles[vertex->n_tiles++] = vtype;
938 for (i = vertex->n_tiles; i > 0; i--)
939 vertex->tiles[i] = vertex->tiles[i - 1];
940 vertex->tiles[0] = vtype;
945 static fringe_node_c *
946 alloc_vertex(ModeInfo * mi, angle_c dir, fringe_node_c * from, tiling_c * tp)
950 if ((v = ALLOC_NODE(fringe_node_c)) == NULL) {
952 if (MI_IS_VERBOSE(mi)) {
953 (void) fprintf(stderr, "No memory in alloc_vertex()\n");
955 tp->busyLoop = CELEBRATE;
959 add_unit_vec(dir, v->fived);
960 fived_to_loc(v->fived, tp, &(v->loc));
961 if (v->loc.x < 0 || v->loc.y < 0
962 || v->loc.x >= tp->width || v->loc.y >= tp->height) {
965 if (ww < 200) ww = 200; /* tiny window */
966 if (hh < 200) hh = 200;
967 v->off_screen = True;
968 if (v->loc.x < -ww || v->loc.y < -hh ||
969 v->loc.x >= 2 * ww || v->loc.y >= 2 * hh)
972 v->off_screen = False;
973 tp->fringe.n_nodes++;
976 v->rule_mask = (1 << N_VERTEX_RULES) - 1;
982 * Add a tile described by vtype to the side of vertex. This must be
983 * allowed by the rules -- we do not check it here. New vertices are
984 * allocated as necessary. The fringe and the forced vertex pool are updated.
985 * The new tile is drawn on the display.
987 * One thing we do check here is whether the new tile causes an untiled
988 * area to become enclosed by the tiling. If this would happen, the tile
989 * is not added. The return value is true iff a tile was added.
992 add_tile(ModeInfo * mi,
993 fringe_node_c * vertex, unsigned side, vertex_type_c vtype)
995 tiling_c *tp = &tilings[MI_SCREEN(mi)];
998 *left = (fringe_node_c *) NULL,
999 *right = (fringe_node_c *) NULL,
1000 *far = (fringe_node_c *) NULL,
1002 unsigned fc = fringe_changes(mi, vertex, side, vtype, &right, &far, &left);
1005 ltype = VT_LEFT(vtype),
1006 rtype = VT_RIGHT(vtype),
1007 ftype = VT_FAR(vtype);
1009 /* By our conventions vertex->next lies to the left of vertex and
1010 vertex->prev to the right. */
1012 /* This should never occur. */
1015 if (MI_IS_VERBOSE(mi)) {
1016 (void) fprintf(stderr, "Weirdness in add_tile()\n");
1017 (void) fprintf(stderr, "fc = %d, FC_BAG = %d\n", fc, FC_BAG);
1020 if (side == S_LEFT) {
1022 if ((right = alloc_vertex(mi, vertex_dir(mi, vertex, S_LEFT) -
1023 vtype_angle(vtype), vertex, tp)) == NULL)
1026 if ((far = alloc_vertex(mi, vertex_dir(mi, left, S_RIGHT) +
1027 vtype_angle(ltype), left, tp)) == NULL)
1031 if ((left = alloc_vertex(mi, vertex_dir(mi, vertex, S_RIGHT) +
1032 vtype_angle(vtype), vertex, tp)) == NULL)
1035 if ((far = alloc_vertex(mi, vertex_dir(mi, right, S_LEFT) -
1036 vtype_angle(rtype), right, tp)) == NULL)
1040 /* Having allocated the new vertices, but before joining them with
1041 the rest of the fringe, check if vertices with same coordinates
1042 already exist. If any such are found, give up. */
1043 node = tp->fringe.nodes;
1045 if (((fc & FC_NEW_LEFT) && fived_equal(node->fived, left->fived))
1046 || ((fc & FC_NEW_RIGHT) && fived_equal(node->fived, right->fived))
1047 || ((fc & FC_NEW_FAR) && fived_equal(node->fived, far->fived))) {
1048 /* Better luck next time. */
1049 if (fc & FC_NEW_LEFT)
1050 delete_vertex(mi, left, tp);
1051 if (fc & FC_NEW_RIGHT)
1052 delete_vertex(mi, right, tp);
1053 if (fc & FC_NEW_FAR)
1054 delete_vertex(mi, far, tp);
1058 } while (node != tp->fringe.nodes);
1061 if (!(fc & FC_CUT_THIS)) {
1062 if (side == S_LEFT) {
1063 vertex->next = right;
1064 right->prev = vertex;
1066 vertex->prev = left;
1067 left->next = vertex;
1070 if (!(fc & FC_CUT_FAR)) {
1071 if (!(fc & FC_CUT_LEFT)) {
1075 if (!(fc & FC_CUT_RIGHT)) {
1080 draw_tile(vertex, right, far, left, vtype, mi);
1082 /* Delete vertices that are no longer on the fringe. Check the others. */
1083 if (fc & FC_CUT_THIS) {
1084 tp->fringe.nodes = far;
1085 delete_vertex(mi, vertex, tp);
1087 add_vtype(vertex, side, vtype);
1088 check_vertex(mi, vertex, tp);
1089 tp->fringe.nodes = vertex;
1091 if (fc & FC_CUT_FAR)
1092 delete_vertex(mi, far, tp);
1094 add_vtype(far, fc & FC_CUT_RIGHT ? S_LEFT : S_RIGHT, ftype);
1095 check_vertex(mi, far, tp);
1097 if (fc & FC_CUT_LEFT)
1098 delete_vertex(mi, left, tp);
1100 add_vtype(left, fc & FC_CUT_FAR ? S_LEFT : S_RIGHT, ltype);
1101 check_vertex(mi, left, tp);
1103 if (fc & FC_CUT_RIGHT)
1104 delete_vertex(mi, right, tp);
1106 add_vtype(right, fc & FC_CUT_FAR ? S_RIGHT : S_LEFT, rtype);
1107 check_vertex(mi, right, tp);
1114 * Add a forced tile to a given forced vertex. Basically an easy job,
1115 * since we know what to add. But it might fail if adding the tile
1116 * would cause some untiled area to become enclosed. There is also another
1117 * more exotic culprit: we might have a dislocation. Fortunately, they
1118 * are very rare (the PRL article reported that perfect tilings of over
1119 * 2^50 tiles had been generated). There is a version of the algorithm
1120 * that doesn't produce dislocations, but it's a lot hairier than the
1121 * simpler version I used.
1124 add_forced_tile(ModeInfo * mi, forced_node_c * node)
1126 tiling_c *tp = &tilings[MI_SCREEN(mi)];
1128 vertex_type_c vtype = 0;
1129 rule_match_c hits[MAX_TILES_PER_VERTEX * N_VERTEX_RULES];
1132 if (node->forced_sides == (S_LEFT | S_RIGHT))
1133 side = NRAND(2) ? S_LEFT : S_RIGHT;
1135 side = node->forced_sides;
1136 n = match_rules(node->vertex, hits, True);
1137 n = find_completions(node->vertex, hits, n, side, &vtype /*, True */ );
1140 if (MI_IS_VERBOSE(mi)) {
1141 (void) fprintf(stderr, "Weirdness in add_forced_tile()\n");
1142 (void) fprintf(stderr, "n = %d\n", n);
1145 return add_tile(mi, node->vertex, side, vtype);
1150 * Whether the addition of a tile of vtype on the given side of vertex
1151 * would conform to the rules. The efficient way to do this would be
1152 * to add the new tile and then use the same type of search as in
1153 * match_rules. However, this function is not a performance
1154 * bottleneck (only needed for random tile additions, which are
1155 * relatively infrequent), so I will settle for a simpler implementation.
1158 legal_move(fringe_node_c * vertex, unsigned side, vertex_type_c vtype)
1160 rule_match_c hits[MAX_TILES_PER_VERTEX * N_VERTEX_RULES];
1161 vertex_type_c legal_vt[MAX_COMPL];
1162 int n_hits, n_legal, i;
1164 n_hits = match_rules(vertex, hits, False);
1165 n_legal = find_completions(vertex, hits, n_hits, side, legal_vt /*, False */ );
1166 for (i = 0; i < n_legal; i++)
1167 if (legal_vt[i] == vtype)
1174 * Add a randomly chosen tile to a given vertex. This requires more checking
1175 * as we must make sure the new tile conforms to the vertex rules at every
1176 * vertex it touches. */
1178 add_random_tile(fringe_node_c * vertex, ModeInfo * mi)
1180 fringe_node_c *right, *left, *far;
1181 int i, j, n, n_hits, n_good;
1182 unsigned side, fc, no_good, s;
1183 vertex_type_c vtypes[MAX_COMPL];
1184 rule_match_c hits[MAX_TILES_PER_VERTEX * N_VERTEX_RULES];
1185 tiling_c *tp = &tilings[MI_SCREEN(mi)];
1187 if (MI_NPIXELS(mi) > 2) {
1188 tp->thick_color = NRAND(MI_NPIXELS(mi));
1189 /* Insure good contrast */
1190 tp->thin_color = (NRAND(2 * MI_NPIXELS(mi) / 3) + tp->thick_color +
1191 MI_NPIXELS(mi) / 6) % MI_NPIXELS(mi);
1193 tp->thick_color = tp->thin_color = MI_WHITE_PIXEL(mi);
1194 n_hits = match_rules(vertex, hits, False);
1195 side = NRAND(2) ? S_LEFT : S_RIGHT;
1196 n = find_completions(vertex, hits, n_hits, side, vtypes /*, False */ );
1197 /* One answer would mean a forced tile. */
1200 if (MI_IS_VERBOSE(mi)) {
1201 (void) fprintf(stderr, "Weirdness in add_random_tile()\n");
1202 (void) fprintf(stderr, "n = %d\n", n);
1207 for (i = 0; i < n; i++) {
1208 fc = fringe_changes(mi, vertex, side, vtypes[i], &right, &far, &left);
1211 if (MI_IS_VERBOSE(mi)) {
1212 (void) fprintf(stderr, "Weirdness in add_random_tile()\n");
1213 (void) fprintf(stderr, "fc = %d, FC_BAG = %d\n", fc, FC_BAG);
1217 s = (((fc & FC_CUT_FAR) && (fc & FC_CUT_LEFT)) ? S_RIGHT : S_LEFT);
1218 if (!legal_move(right, s, VT_RIGHT(vtypes[i]))) {
1219 no_good |= (1 << i);
1225 s = (((fc & FC_CUT_FAR) && (fc & FC_CUT_RIGHT)) ? S_LEFT : S_RIGHT);
1226 if (!legal_move(left, s, VT_LEFT(vtypes[i]))) {
1227 no_good |= (1 << i);
1233 s = ((fc & FC_CUT_LEFT) ? S_RIGHT : S_LEFT);
1234 if (!legal_move(far, s, VT_FAR(vtypes[i]))) {
1235 no_good |= (1 << i);
1242 if (MI_IS_VERBOSE(mi)) {
1243 (void) fprintf(stderr, "Weirdness in add_random_tile()\n");
1244 (void) fprintf(stderr, "n_good = %d\n", n_good);
1248 for (i = j = 0; i <= n; i++, j++)
1249 while (no_good & (1 << j))
1252 if (!add_tile(mi, vertex, side, vtypes[j - 1])) {
1254 if (MI_IS_VERBOSE(mi)) {
1255 (void) fprintf(stderr, "Weirdness in add_random_tile()\n");
1261 /* One step of the growth algorithm. */
1263 draw_penrose(ModeInfo * mi)
1269 if (tilings == NULL)
1271 tp = &tilings[MI_SCREEN(mi)];
1272 if (tp->fringe.nodes == NULL)
1275 MI_IS_DRAWN(mi) = True;
1276 p = tp->forced.first;
1277 if (tp->busyLoop > 0) {
1281 if (tp->done || tp->failures >= 100) {
1285 /* Check for the initial "2-gon". */
1286 if (tp->fringe.nodes->prev == tp->fringe.nodes->next) {
1287 vertex_type_c vtype = (unsigned char) (VT_TOTAL_MASK & LRAND());
1289 if (!add_tile(mi, tp->fringe.nodes, S_LEFT, vtype))
1293 /* No visible nodes left. */
1294 if (tp->fringe.n_nodes == 0) {
1296 tp->busyLoop = COMPLETION; /* Just finished drawing */
1299 if (tp->forced.n_visible > 0 && tp->failures < 10) {
1300 n = NRAND(tp->forced.n_visible);
1302 while (p->vertex->off_screen)
1309 } else if (tp->forced.n_nodes > 0) {
1310 n = NRAND(tp->forced.n_nodes);
1314 fringe_node_c *fringe_p = tp->fringe.nodes;
1316 n = NRAND(tp->fringe.n_nodes);
1320 fringe_p = fringe_p->next;
1321 } while (fringe_p->off_screen);
1322 add_random_tile(fringe_p, mi);
1326 if (add_forced_tile(mi, p))
1334 reshape_penrose(ModeInfo * mi, int width, int height)
1336 tiling_c *tp = &tilings[MI_SCREEN(mi)];
1338 tp->height = height;
1341 XSCREENSAVER_MODULE ("Penrose", penrose)
1343 #endif /* MODE_penrose */