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author | Franklin Wei <git@fwei.tk> | 2017-04-29 18:21:56 -0400 |
---|---|---|
committer | Franklin Wei <git@fwei.tk> | 2017-04-29 18:24:42 -0400 |
commit | 881746789a489fad85aae8317555f73dbe261556 (patch) | |
tree | cec2946362c4698c8db3c10f3242ef546c2c22dd /apps/plugins/puzzles/src/grid.c | |
parent | 03dd4b92be7dcd5c8ab06da3810887060e06abd5 (diff) | |
download | rockbox-881746789a489fad85aae8317555f73dbe261556.tar.gz rockbox-881746789a489fad85aae8317555f73dbe261556.zip |
puzzles: refactor and resync with upstream
This brings puzzles up-to-date with upstream revision
2d333750272c3967cfd5cd3677572cddeaad5932, though certain changes made
by me, including cursor-only Untangle and some compilation fixes
remain. Upstream code has been moved to its separate subdirectory and
future syncs can be done by simply copying over the new sources.
Change-Id: Ia6506ca5f78c3627165ea6791d38db414ace0804
Diffstat (limited to 'apps/plugins/puzzles/src/grid.c')
-rw-r--r-- | apps/plugins/puzzles/src/grid.c | 3065 |
1 files changed, 3065 insertions, 0 deletions
diff --git a/apps/plugins/puzzles/src/grid.c b/apps/plugins/puzzles/src/grid.c new file mode 100644 index 0000000000..4929b5c7d3 --- /dev/null +++ b/apps/plugins/puzzles/src/grid.c | |||
@@ -0,0 +1,3065 @@ | |||
1 | /* | ||
2 | * (c) Lambros Lambrou 2008 | ||
3 | * | ||
4 | * Code for working with general grids, which can be any planar graph | ||
5 | * with faces, edges and vertices (dots). Includes generators for a few | ||
6 | * types of grid, including square, hexagonal, triangular and others. | ||
7 | */ | ||
8 | |||
9 | #include <stdio.h> | ||
10 | #include <stdlib.h> | ||
11 | #include <string.h> | ||
12 | #include <assert.h> | ||
13 | #include <ctype.h> | ||
14 | #include <math.h> | ||
15 | #include <float.h> | ||
16 | |||
17 | #include "puzzles.h" | ||
18 | #include "tree234.h" | ||
19 | #include "grid.h" | ||
20 | #include "penrose.h" | ||
21 | |||
22 | /* Debugging options */ | ||
23 | |||
24 | /* | ||
25 | #define DEBUG_GRID | ||
26 | */ | ||
27 | |||
28 | /* ---------------------------------------------------------------------- | ||
29 | * Deallocate or dereference a grid | ||
30 | */ | ||
31 | void grid_free(grid *g) | ||
32 | { | ||
33 | assert(g->refcount); | ||
34 | |||
35 | g->refcount--; | ||
36 | if (g->refcount == 0) { | ||
37 | int i; | ||
38 | for (i = 0; i < g->num_faces; i++) { | ||
39 | sfree(g->faces[i].dots); | ||
40 | sfree(g->faces[i].edges); | ||
41 | } | ||
42 | for (i = 0; i < g->num_dots; i++) { | ||
43 | sfree(g->dots[i].faces); | ||
44 | sfree(g->dots[i].edges); | ||
45 | } | ||
46 | sfree(g->faces); | ||
47 | sfree(g->edges); | ||
48 | sfree(g->dots); | ||
49 | sfree(g); | ||
50 | } | ||
51 | } | ||
52 | |||
53 | /* Used by the other grid generators. Create a brand new grid with nothing | ||
54 | * initialised (all lists are NULL) */ | ||
55 | static grid *grid_empty(void) | ||
56 | { | ||
57 | grid *g = snew(grid); | ||
58 | g->faces = NULL; | ||
59 | g->edges = NULL; | ||
60 | g->dots = NULL; | ||
61 | g->num_faces = g->num_edges = g->num_dots = 0; | ||
62 | g->refcount = 1; | ||
63 | g->lowest_x = g->lowest_y = g->highest_x = g->highest_y = 0; | ||
64 | return g; | ||
65 | } | ||
66 | |||
67 | /* Helper function to calculate perpendicular distance from | ||
68 | * a point P to a line AB. A and B mustn't be equal here. | ||
69 | * | ||
70 | * Well-known formula for area A of a triangle: | ||
71 | * / 1 1 1 \ | ||
72 | * 2A = determinant of matrix | px ax bx | | ||
73 | * \ py ay by / | ||
74 | * | ||
75 | * Also well-known: 2A = base * height | ||
76 | * = perpendicular distance * line-length. | ||
77 | * | ||
78 | * Combining gives: distance = determinant / line-length(a,b) | ||
79 | */ | ||
80 | static double point_line_distance(long px, long py, | ||
81 | long ax, long ay, | ||
82 | long bx, long by) | ||
83 | { | ||
84 | long det = ax*by - bx*ay + bx*py - px*by + px*ay - ax*py; | ||
85 | double len; | ||
86 | det = max(det, -det); | ||
87 | len = sqrt(SQ(ax - bx) + SQ(ay - by)); | ||
88 | return det / len; | ||
89 | } | ||
90 | |||
91 | /* Determine nearest edge to where the user clicked. | ||
92 | * (x, y) is the clicked location, converted to grid coordinates. | ||
93 | * Returns the nearest edge, or NULL if no edge is reasonably | ||
94 | * near the position. | ||
95 | * | ||
96 | * Just judging edges by perpendicular distance is not quite right - | ||
97 | * the edge might be "off to one side". So we insist that the triangle | ||
98 | * with (x,y) has acute angles at the edge's dots. | ||
99 | * | ||
100 | * edge1 | ||
101 | * *---------*------ | ||
102 | * | | ||
103 | * | *(x,y) | ||
104 | * edge2 | | ||
105 | * | edge2 is OK, but edge1 is not, even though | ||
106 | * | edge1 is perpendicularly closer to (x,y) | ||
107 | * * | ||
108 | * | ||
109 | */ | ||
110 | grid_edge *grid_nearest_edge(grid *g, int x, int y) | ||
111 | { | ||
112 | grid_edge *best_edge; | ||
113 | double best_distance = 0; | ||
114 | int i; | ||
115 | |||
116 | best_edge = NULL; | ||
117 | |||
118 | for (i = 0; i < g->num_edges; i++) { | ||
119 | grid_edge *e = &g->edges[i]; | ||
120 | long e2; /* squared length of edge */ | ||
121 | long a2, b2; /* squared lengths of other sides */ | ||
122 | double dist; | ||
123 | |||
124 | /* See if edge e is eligible - the triangle must have acute angles | ||
125 | * at the edge's dots. | ||
126 | * Pythagoras formula h^2 = a^2 + b^2 detects right-angles, | ||
127 | * so detect acute angles by testing for h^2 < a^2 + b^2 */ | ||
128 | e2 = SQ((long)e->dot1->x - (long)e->dot2->x) + SQ((long)e->dot1->y - (long)e->dot2->y); | ||
129 | a2 = SQ((long)e->dot1->x - (long)x) + SQ((long)e->dot1->y - (long)y); | ||
130 | b2 = SQ((long)e->dot2->x - (long)x) + SQ((long)e->dot2->y - (long)y); | ||
131 | if (a2 >= e2 + b2) continue; | ||
132 | if (b2 >= e2 + a2) continue; | ||
133 | |||
134 | /* e is eligible so far. Now check the edge is reasonably close | ||
135 | * to where the user clicked. Don't want to toggle an edge if the | ||
136 | * click was way off the grid. | ||
137 | * There is room for experimentation here. We could check the | ||
138 | * perpendicular distance is within a certain fraction of the length | ||
139 | * of the edge. That amounts to testing a rectangular region around | ||
140 | * the edge. | ||
141 | * Alternatively, we could check that the angle at the point is obtuse. | ||
142 | * That would amount to testing a circular region with the edge as | ||
143 | * diameter. */ | ||
144 | dist = point_line_distance((long)x, (long)y, | ||
145 | (long)e->dot1->x, (long)e->dot1->y, | ||
146 | (long)e->dot2->x, (long)e->dot2->y); | ||
147 | /* Is dist more than half edge length ? */ | ||
148 | if (4 * SQ(dist) > e2) | ||
149 | continue; | ||
150 | |||
151 | if (best_edge == NULL || dist < best_distance) { | ||
152 | best_edge = e; | ||
153 | best_distance = dist; | ||
154 | } | ||
155 | } | ||
156 | return best_edge; | ||
157 | } | ||
158 | |||
159 | /* ---------------------------------------------------------------------- | ||
160 | * Grid generation | ||
161 | */ | ||
162 | |||
163 | #ifdef SVG_GRID | ||
164 | |||
165 | #define SVG_DOTS 1 | ||
166 | #define SVG_EDGES 2 | ||
167 | #define SVG_FACES 4 | ||
168 | |||
169 | #define FACE_COLOUR "red" | ||
170 | #define EDGE_COLOUR "blue" | ||
171 | #define DOT_COLOUR "black" | ||
172 | |||
173 | static void grid_output_svg(FILE *fp, grid *g, int which) | ||
174 | { | ||
175 | int i, j; | ||
176 | |||
177 | fprintf(fp,"\ | ||
178 | <?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n\ | ||
179 | <!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 20010904//EN\"\n\ | ||
180 | \"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd\">\n\ | ||
181 | \n\ | ||
182 | <svg xmlns=\"http://www.w3.org/2000/svg\"\n\ | ||
183 | xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n\n"); | ||
184 | |||
185 | if (which & SVG_FACES) { | ||
186 | fprintf(fp, "<g>\n"); | ||
187 | for (i = 0; i < g->num_faces; i++) { | ||
188 | grid_face *f = g->faces + i; | ||
189 | fprintf(fp, "<polygon points=\""); | ||
190 | for (j = 0; j < f->order; j++) { | ||
191 | grid_dot *d = f->dots[j]; | ||
192 | fprintf(fp, "%s%d,%d", (j == 0) ? "" : " ", | ||
193 | d->x, d->y); | ||
194 | } | ||
195 | fprintf(fp, "\" style=\"fill: %s; fill-opacity: 0.2; stroke: %s\" />\n", | ||
196 | FACE_COLOUR, FACE_COLOUR); | ||
197 | } | ||
198 | fprintf(fp, "</g>\n"); | ||
199 | } | ||
200 | if (which & SVG_EDGES) { | ||
201 | fprintf(fp, "<g>\n"); | ||
202 | for (i = 0; i < g->num_edges; i++) { | ||
203 | grid_edge *e = g->edges + i; | ||
204 | grid_dot *d1 = e->dot1, *d2 = e->dot2; | ||
205 | |||
206 | fprintf(fp, "<line x1=\"%d\" y1=\"%d\" x2=\"%d\" y2=\"%d\" " | ||
207 | "style=\"stroke: %s\" />\n", | ||
208 | d1->x, d1->y, d2->x, d2->y, EDGE_COLOUR); | ||
209 | } | ||
210 | fprintf(fp, "</g>\n"); | ||
211 | } | ||
212 | |||
213 | if (which & SVG_DOTS) { | ||
214 | fprintf(fp, "<g>\n"); | ||
215 | for (i = 0; i < g->num_dots; i++) { | ||
216 | grid_dot *d = g->dots + i; | ||
217 | fprintf(fp, "<ellipse cx=\"%d\" cy=\"%d\" rx=\"%d\" ry=\"%d\" fill=\"%s\" />", | ||
218 | d->x, d->y, g->tilesize/20, g->tilesize/20, DOT_COLOUR); | ||
219 | } | ||
220 | fprintf(fp, "</g>\n"); | ||
221 | } | ||
222 | |||
223 | fprintf(fp, "</svg>\n"); | ||
224 | } | ||
225 | #endif | ||
226 | |||
227 | #ifdef SVG_GRID | ||
228 | #include <errno.h> | ||
229 | |||
230 | static void grid_try_svg(grid *g, int which) | ||
231 | { | ||
232 | char *svg = getenv("PUZZLES_SVG_GRID"); | ||
233 | if (svg) { | ||
234 | FILE *svgf = fopen(svg, "w"); | ||
235 | if (svgf) { | ||
236 | grid_output_svg(svgf, g, which); | ||
237 | fclose(svgf); | ||
238 | } else { | ||
239 | fprintf(stderr, "Unable to open file `%s': %s", svg, strerror(errno)); | ||
240 | } | ||
241 | } | ||
242 | } | ||
243 | #endif | ||
244 | |||
245 | /* Show the basic grid information, before doing grid_make_consistent */ | ||
246 | static void grid_debug_basic(grid *g) | ||
247 | { | ||
248 | /* TODO: Maybe we should generate an SVG image of the dots and lines | ||
249 | * of the grid here, before grid_make_consistent. | ||
250 | * Would help with debugging grid generation. */ | ||
251 | #ifdef DEBUG_GRID | ||
252 | int i; | ||
253 | printf("--- Basic Grid Data ---\n"); | ||
254 | for (i = 0; i < g->num_faces; i++) { | ||
255 | grid_face *f = g->faces + i; | ||
256 | printf("Face %d: dots[", i); | ||
257 | int j; | ||
258 | for (j = 0; j < f->order; j++) { | ||
259 | grid_dot *d = f->dots[j]; | ||
260 | printf("%s%d", j ? "," : "", (int)(d - g->dots)); | ||
261 | } | ||
262 | printf("]\n"); | ||
263 | } | ||
264 | #endif | ||
265 | #ifdef SVG_GRID | ||
266 | grid_try_svg(g, SVG_FACES); | ||
267 | #endif | ||
268 | } | ||
269 | |||
270 | /* Show the derived grid information, computed by grid_make_consistent */ | ||
271 | static void grid_debug_derived(grid *g) | ||
272 | { | ||
273 | #ifdef DEBUG_GRID | ||
274 | /* edges */ | ||
275 | int i; | ||
276 | printf("--- Derived Grid Data ---\n"); | ||
277 | for (i = 0; i < g->num_edges; i++) { | ||
278 | grid_edge *e = g->edges + i; | ||
279 | printf("Edge %d: dots[%d,%d] faces[%d,%d]\n", | ||
280 | i, (int)(e->dot1 - g->dots), (int)(e->dot2 - g->dots), | ||
281 | e->face1 ? (int)(e->face1 - g->faces) : -1, | ||
282 | e->face2 ? (int)(e->face2 - g->faces) : -1); | ||
283 | } | ||
284 | /* faces */ | ||
285 | for (i = 0; i < g->num_faces; i++) { | ||
286 | grid_face *f = g->faces + i; | ||
287 | int j; | ||
288 | printf("Face %d: faces[", i); | ||
289 | for (j = 0; j < f->order; j++) { | ||
290 | grid_edge *e = f->edges[j]; | ||
291 | grid_face *f2 = (e->face1 == f) ? e->face2 : e->face1; | ||
292 | printf("%s%d", j ? "," : "", f2 ? (int)(f2 - g->faces) : -1); | ||
293 | } | ||
294 | printf("]\n"); | ||
295 | } | ||
296 | /* dots */ | ||
297 | for (i = 0; i < g->num_dots; i++) { | ||
298 | grid_dot *d = g->dots + i; | ||
299 | int j; | ||
300 | printf("Dot %d: dots[", i); | ||
301 | for (j = 0; j < d->order; j++) { | ||
302 | grid_edge *e = d->edges[j]; | ||
303 | grid_dot *d2 = (e->dot1 == d) ? e->dot2 : e->dot1; | ||
304 | printf("%s%d", j ? "," : "", (int)(d2 - g->dots)); | ||
305 | } | ||
306 | printf("] faces["); | ||
307 | for (j = 0; j < d->order; j++) { | ||
308 | grid_face *f = d->faces[j]; | ||
309 | printf("%s%d", j ? "," : "", f ? (int)(f - g->faces) : -1); | ||
310 | } | ||
311 | printf("]\n"); | ||
312 | } | ||
313 | #endif | ||
314 | #ifdef SVG_GRID | ||
315 | grid_try_svg(g, SVG_DOTS | SVG_EDGES | SVG_FACES); | ||
316 | #endif | ||
317 | } | ||
318 | |||
319 | /* Helper function for building incomplete-edges list in | ||
320 | * grid_make_consistent() */ | ||
321 | static int grid_edge_bydots_cmpfn(void *v1, void *v2) | ||
322 | { | ||
323 | grid_edge *a = v1; | ||
324 | grid_edge *b = v2; | ||
325 | grid_dot *da, *db; | ||
326 | |||
327 | /* Pointer subtraction is valid here, because all dots point into the | ||
328 | * same dot-list (g->dots). | ||
329 | * Edges are not "normalised" - the 2 dots could be stored in any order, | ||
330 | * so we need to take this into account when comparing edges. */ | ||
331 | |||
332 | /* Compare first dots */ | ||
333 | da = (a->dot1 < a->dot2) ? a->dot1 : a->dot2; | ||
334 | db = (b->dot1 < b->dot2) ? b->dot1 : b->dot2; | ||
335 | if (da != db) | ||
336 | return db - da; | ||
337 | /* Compare last dots */ | ||
338 | da = (a->dot1 < a->dot2) ? a->dot2 : a->dot1; | ||
339 | db = (b->dot1 < b->dot2) ? b->dot2 : b->dot1; | ||
340 | if (da != db) | ||
341 | return db - da; | ||
342 | |||
343 | return 0; | ||
344 | } | ||
345 | |||
346 | /* | ||
347 | * 'Vigorously trim' a grid, by which I mean deleting any isolated or | ||
348 | * uninteresting faces. By which, in turn, I mean: ensure that the | ||
349 | * grid is composed solely of faces adjacent to at least one | ||
350 | * 'landlocked' dot (i.e. one not in contact with the infinite | ||
351 | * exterior face), and that all those dots are in a single connected | ||
352 | * component. | ||
353 | * | ||
354 | * This function operates on, and returns, a grid satisfying the | ||
355 | * preconditions to grid_make_consistent() rather than the | ||
356 | * postconditions. (So call it first.) | ||
357 | */ | ||
358 | static void grid_trim_vigorously(grid *g) | ||
359 | { | ||
360 | int *dotpairs, *faces, *dots; | ||
361 | int *dsf; | ||
362 | int i, j, k, size, newfaces, newdots; | ||
363 | |||
364 | /* | ||
365 | * First construct a matrix in which each ordered pair of dots is | ||
366 | * mapped to the index of the face in which those dots occur in | ||
367 | * that order. | ||
368 | */ | ||
369 | dotpairs = snewn(g->num_dots * g->num_dots, int); | ||
370 | for (i = 0; i < g->num_dots; i++) | ||
371 | for (j = 0; j < g->num_dots; j++) | ||
372 | dotpairs[i*g->num_dots+j] = -1; | ||
373 | for (i = 0; i < g->num_faces; i++) { | ||
374 | grid_face *f = g->faces + i; | ||
375 | int dot0 = f->dots[f->order-1] - g->dots; | ||
376 | for (j = 0; j < f->order; j++) { | ||
377 | int dot1 = f->dots[j] - g->dots; | ||
378 | dotpairs[dot0 * g->num_dots + dot1] = i; | ||
379 | dot0 = dot1; | ||
380 | } | ||
381 | } | ||
382 | |||
383 | /* | ||
384 | * Now we can identify landlocked dots: they're the ones all of | ||
385 | * whose edges have a mirror-image counterpart in this matrix. | ||
386 | */ | ||
387 | dots = snewn(g->num_dots, int); | ||
388 | for (i = 0; i < g->num_dots; i++) { | ||
389 | dots[i] = TRUE; | ||
390 | for (j = 0; j < g->num_dots; j++) { | ||
391 | if ((dotpairs[i*g->num_dots+j] >= 0) ^ | ||
392 | (dotpairs[j*g->num_dots+i] >= 0)) | ||
393 | dots[i] = FALSE; /* non-duplicated edge: coastal dot */ | ||
394 | } | ||
395 | } | ||
396 | |||
397 | /* | ||
398 | * Now identify connected pairs of landlocked dots, and form a dsf | ||
399 | * unifying them. | ||
400 | */ | ||
401 | dsf = snew_dsf(g->num_dots); | ||
402 | for (i = 0; i < g->num_dots; i++) | ||
403 | for (j = 0; j < i; j++) | ||
404 | if (dots[i] && dots[j] && | ||
405 | dotpairs[i*g->num_dots+j] >= 0 && | ||
406 | dotpairs[j*g->num_dots+i] >= 0) | ||
407 | dsf_merge(dsf, i, j); | ||
408 | |||
409 | /* | ||
410 | * Now look for the largest component. | ||
411 | */ | ||
412 | size = 0; | ||
413 | j = -1; | ||
414 | for (i = 0; i < g->num_dots; i++) { | ||
415 | int newsize; | ||
416 | if (dots[i] && dsf_canonify(dsf, i) == i && | ||
417 | (newsize = dsf_size(dsf, i)) > size) { | ||
418 | j = i; | ||
419 | size = newsize; | ||
420 | } | ||
421 | } | ||
422 | |||
423 | /* | ||
424 | * Work out which faces we're going to keep (precisely those with | ||
425 | * at least one dot in the same connected component as j) and | ||
426 | * which dots (those required by any face we're keeping). | ||
427 | * | ||
428 | * At this point we reuse the 'dots' array to indicate the dots | ||
429 | * we're keeping, rather than the ones that are landlocked. | ||
430 | */ | ||
431 | faces = snewn(g->num_faces, int); | ||
432 | for (i = 0; i < g->num_faces; i++) | ||
433 | faces[i] = 0; | ||
434 | for (i = 0; i < g->num_dots; i++) | ||
435 | dots[i] = 0; | ||
436 | for (i = 0; i < g->num_faces; i++) { | ||
437 | grid_face *f = g->faces + i; | ||
438 | int keep = FALSE; | ||
439 | for (k = 0; k < f->order; k++) | ||
440 | if (dsf_canonify(dsf, f->dots[k] - g->dots) == j) | ||
441 | keep = TRUE; | ||
442 | if (keep) { | ||
443 | faces[i] = TRUE; | ||
444 | for (k = 0; k < f->order; k++) | ||
445 | dots[f->dots[k]-g->dots] = TRUE; | ||
446 | } | ||
447 | } | ||
448 | |||
449 | /* | ||
450 | * Work out the new indices of those faces and dots, when we | ||
451 | * compact the arrays containing them. | ||
452 | */ | ||
453 | for (i = newfaces = 0; i < g->num_faces; i++) | ||
454 | faces[i] = (faces[i] ? newfaces++ : -1); | ||
455 | for (i = newdots = 0; i < g->num_dots; i++) | ||
456 | dots[i] = (dots[i] ? newdots++ : -1); | ||
457 | |||
458 | /* | ||
459 | * Free the dynamically allocated 'dots' pointer lists in faces | ||
460 | * we're going to discard. | ||
461 | */ | ||
462 | for (i = 0; i < g->num_faces; i++) | ||
463 | if (faces[i] < 0) | ||
464 | sfree(g->faces[i].dots); | ||
465 | |||
466 | /* | ||
467 | * Go through and compact the arrays. | ||
468 | */ | ||
469 | for (i = 0; i < g->num_dots; i++) | ||
470 | if (dots[i] >= 0) { | ||
471 | grid_dot *dnew = g->dots + dots[i], *dold = g->dots + i; | ||
472 | *dnew = *dold; /* structure copy */ | ||
473 | } | ||
474 | for (i = 0; i < g->num_faces; i++) | ||
475 | if (faces[i] >= 0) { | ||
476 | grid_face *fnew = g->faces + faces[i], *fold = g->faces + i; | ||
477 | *fnew = *fold; /* structure copy */ | ||
478 | for (j = 0; j < fnew->order; j++) { | ||
479 | /* | ||
480 | * Reindex the dots in this face. | ||
481 | */ | ||
482 | k = fnew->dots[j] - g->dots; | ||
483 | fnew->dots[j] = g->dots + dots[k]; | ||
484 | } | ||
485 | } | ||
486 | g->num_faces = newfaces; | ||
487 | g->num_dots = newdots; | ||
488 | |||
489 | sfree(dotpairs); | ||
490 | sfree(dsf); | ||
491 | sfree(dots); | ||
492 | sfree(faces); | ||
493 | } | ||
494 | |||
495 | /* Input: grid has its dots and faces initialised: | ||
496 | * - dots have (optionally) x and y coordinates, but no edges or faces | ||
497 | * (pointers are NULL). | ||
498 | * - edges not initialised at all | ||
499 | * - faces initialised and know which dots they have (but no edges yet). The | ||
500 | * dots around each face are assumed to be clockwise. | ||
501 | * | ||
502 | * Output: grid is complete and valid with all relationships defined. | ||
503 | */ | ||
504 | static void grid_make_consistent(grid *g) | ||
505 | { | ||
506 | int i; | ||
507 | tree234 *incomplete_edges; | ||
508 | grid_edge *next_new_edge; /* Where new edge will go into g->edges */ | ||
509 | |||
510 | grid_debug_basic(g); | ||
511 | |||
512 | /* ====== Stage 1 ====== | ||
513 | * Generate edges | ||
514 | */ | ||
515 | |||
516 | /* We know how many dots and faces there are, so we can find the exact | ||
517 | * number of edges from Euler's polyhedral formula: F + V = E + 2 . | ||
518 | * We use "-1", not "-2" here, because Euler's formula includes the | ||
519 | * infinite face, which we don't count. */ | ||
520 | g->num_edges = g->num_faces + g->num_dots - 1; | ||
521 | g->edges = snewn(g->num_edges, grid_edge); | ||
522 | next_new_edge = g->edges; | ||
523 | |||
524 | /* Iterate over faces, and over each face's dots, generating edges as we | ||
525 | * go. As we find each new edge, we can immediately fill in the edge's | ||
526 | * dots, but only one of the edge's faces. Later on in the iteration, we | ||
527 | * will find the same edge again (unless it's on the border), but we will | ||
528 | * know the other face. | ||
529 | * For efficiency, maintain a list of the incomplete edges, sorted by | ||
530 | * their dots. */ | ||
531 | incomplete_edges = newtree234(grid_edge_bydots_cmpfn); | ||
532 | for (i = 0; i < g->num_faces; i++) { | ||
533 | grid_face *f = g->faces + i; | ||
534 | int j; | ||
535 | for (j = 0; j < f->order; j++) { | ||
536 | grid_edge e; /* fake edge for searching */ | ||
537 | grid_edge *edge_found; | ||
538 | int j2 = j + 1; | ||
539 | if (j2 == f->order) | ||
540 | j2 = 0; | ||
541 | e.dot1 = f->dots[j]; | ||
542 | e.dot2 = f->dots[j2]; | ||
543 | /* Use del234 instead of find234, because we always want to | ||
544 | * remove the edge if found */ | ||
545 | edge_found = del234(incomplete_edges, &e); | ||
546 | if (edge_found) { | ||
547 | /* This edge already added, so fill out missing face. | ||
548 | * Edge is already removed from incomplete_edges. */ | ||
549 | edge_found->face2 = f; | ||
550 | } else { | ||
551 | assert(next_new_edge - g->edges < g->num_edges); | ||
552 | next_new_edge->dot1 = e.dot1; | ||
553 | next_new_edge->dot2 = e.dot2; | ||
554 | next_new_edge->face1 = f; | ||
555 | next_new_edge->face2 = NULL; /* potentially infinite face */ | ||
556 | add234(incomplete_edges, next_new_edge); | ||
557 | ++next_new_edge; | ||
558 | } | ||
559 | } | ||
560 | } | ||
561 | freetree234(incomplete_edges); | ||
562 | |||
563 | /* ====== Stage 2 ====== | ||
564 | * For each face, build its edge list. | ||
565 | */ | ||
566 | |||
567 | /* Allocate space for each edge list. Can do this, because each face's | ||
568 | * edge-list is the same size as its dot-list. */ | ||
569 | for (i = 0; i < g->num_faces; i++) { | ||
570 | grid_face *f = g->faces + i; | ||
571 | int j; | ||
572 | f->edges = snewn(f->order, grid_edge*); | ||
573 | /* Preload with NULLs, to help detect potential bugs. */ | ||
574 | for (j = 0; j < f->order; j++) | ||
575 | f->edges[j] = NULL; | ||
576 | } | ||
577 | |||
578 | /* Iterate over each edge, and over both its faces. Add this edge to | ||
579 | * the face's edge-list, after finding where it should go in the | ||
580 | * sequence. */ | ||
581 | for (i = 0; i < g->num_edges; i++) { | ||
582 | grid_edge *e = g->edges + i; | ||
583 | int j; | ||
584 | for (j = 0; j < 2; j++) { | ||
585 | grid_face *f = j ? e->face2 : e->face1; | ||
586 | int k, k2; | ||
587 | if (f == NULL) continue; | ||
588 | /* Find one of the dots around the face */ | ||
589 | for (k = 0; k < f->order; k++) { | ||
590 | if (f->dots[k] == e->dot1) | ||
591 | break; /* found dot1 */ | ||
592 | } | ||
593 | assert(k != f->order); /* Must find the dot around this face */ | ||
594 | |||
595 | /* Labelling scheme: as we walk clockwise around the face, | ||
596 | * starting at dot0 (f->dots[0]), we hit: | ||
597 | * (dot0), edge0, dot1, edge1, dot2,... | ||
598 | * | ||
599 | * 0 | ||
600 | * 0-----1 | ||
601 | * | | ||
602 | * |1 | ||
603 | * | | ||
604 | * 3-----2 | ||
605 | * 2 | ||
606 | * | ||
607 | * Therefore, edgeK joins dotK and dot{K+1} | ||
608 | */ | ||
609 | |||
610 | /* Around this face, either the next dot or the previous dot | ||
611 | * must be e->dot2. Otherwise the edge is wrong. */ | ||
612 | k2 = k + 1; | ||
613 | if (k2 == f->order) | ||
614 | k2 = 0; | ||
615 | if (f->dots[k2] == e->dot2) { | ||
616 | /* dot1(k) and dot2(k2) go clockwise around this face, so add | ||
617 | * this edge at position k (see diagram). */ | ||
618 | assert(f->edges[k] == NULL); | ||
619 | f->edges[k] = e; | ||
620 | continue; | ||
621 | } | ||
622 | /* Try previous dot */ | ||
623 | k2 = k - 1; | ||
624 | if (k2 == -1) | ||
625 | k2 = f->order - 1; | ||
626 | if (f->dots[k2] == e->dot2) { | ||
627 | /* dot1(k) and dot2(k2) go anticlockwise around this face. */ | ||
628 | assert(f->edges[k2] == NULL); | ||
629 | f->edges[k2] = e; | ||
630 | continue; | ||
631 | } | ||
632 | assert(!"Grid broken: bad edge-face relationship"); | ||
633 | } | ||
634 | } | ||
635 | |||
636 | /* ====== Stage 3 ====== | ||
637 | * For each dot, build its edge-list and face-list. | ||
638 | */ | ||
639 | |||
640 | /* We don't know how many edges/faces go around each dot, so we can't | ||
641 | * allocate the right space for these lists. Pre-compute the sizes by | ||
642 | * iterating over each edge and recording a tally against each dot. */ | ||
643 | for (i = 0; i < g->num_dots; i++) { | ||
644 | g->dots[i].order = 0; | ||
645 | } | ||
646 | for (i = 0; i < g->num_edges; i++) { | ||
647 | grid_edge *e = g->edges + i; | ||
648 | ++(e->dot1->order); | ||
649 | ++(e->dot2->order); | ||
650 | } | ||
651 | /* Now we have the sizes, pre-allocate the edge and face lists. */ | ||
652 | for (i = 0; i < g->num_dots; i++) { | ||
653 | grid_dot *d = g->dots + i; | ||
654 | int j; | ||
655 | assert(d->order >= 2); /* sanity check */ | ||
656 | d->edges = snewn(d->order, grid_edge*); | ||
657 | d->faces = snewn(d->order, grid_face*); | ||
658 | for (j = 0; j < d->order; j++) { | ||
659 | d->edges[j] = NULL; | ||
660 | d->faces[j] = NULL; | ||
661 | } | ||
662 | } | ||
663 | /* For each dot, need to find a face that touches it, so we can seed | ||
664 | * the edge-face-edge-face process around each dot. */ | ||
665 | for (i = 0; i < g->num_faces; i++) { | ||
666 | grid_face *f = g->faces + i; | ||
667 | int j; | ||
668 | for (j = 0; j < f->order; j++) { | ||
669 | grid_dot *d = f->dots[j]; | ||
670 | d->faces[0] = f; | ||
671 | } | ||
672 | } | ||
673 | /* Each dot now has a face in its first slot. Generate the remaining | ||
674 | * faces and edges around the dot, by searching both clockwise and | ||
675 | * anticlockwise from the first face. Need to do both directions, | ||
676 | * because of the possibility of hitting the infinite face, which | ||
677 | * blocks progress. But there's only one such face, so we will | ||
678 | * succeed in finding every edge and face this way. */ | ||
679 | for (i = 0; i < g->num_dots; i++) { | ||
680 | grid_dot *d = g->dots + i; | ||
681 | int current_face1 = 0; /* ascends clockwise */ | ||
682 | int current_face2 = 0; /* descends anticlockwise */ | ||
683 | |||
684 | /* Labelling scheme: as we walk clockwise around the dot, starting | ||
685 | * at face0 (d->faces[0]), we hit: | ||
686 | * (face0), edge0, face1, edge1, face2,... | ||
687 | * | ||
688 | * 0 | ||
689 | * | | ||
690 | * 0 | 1 | ||
691 | * | | ||
692 | * -----d-----1 | ||
693 | * | | ||
694 | * | 2 | ||
695 | * | | ||
696 | * 2 | ||
697 | * | ||
698 | * So, for example, face1 should be joined to edge0 and edge1, | ||
699 | * and those edges should appear in an anticlockwise sense around | ||
700 | * that face (see diagram). */ | ||
701 | |||
702 | /* clockwise search */ | ||
703 | while (TRUE) { | ||
704 | grid_face *f = d->faces[current_face1]; | ||
705 | grid_edge *e; | ||
706 | int j; | ||
707 | assert(f != NULL); | ||
708 | /* find dot around this face */ | ||
709 | for (j = 0; j < f->order; j++) { | ||
710 | if (f->dots[j] == d) | ||
711 | break; | ||
712 | } | ||
713 | assert(j != f->order); /* must find dot */ | ||
714 | |||
715 | /* Around f, required edge is anticlockwise from the dot. See | ||
716 | * the other labelling scheme higher up, for why we subtract 1 | ||
717 | * from j. */ | ||
718 | j--; | ||
719 | if (j == -1) | ||
720 | j = f->order - 1; | ||
721 | e = f->edges[j]; | ||
722 | d->edges[current_face1] = e; /* set edge */ | ||
723 | current_face1++; | ||
724 | if (current_face1 == d->order) | ||
725 | break; | ||
726 | else { | ||
727 | /* set face */ | ||
728 | d->faces[current_face1] = | ||
729 | (e->face1 == f) ? e->face2 : e->face1; | ||
730 | if (d->faces[current_face1] == NULL) | ||
731 | break; /* cannot progress beyond infinite face */ | ||
732 | } | ||
733 | } | ||
734 | /* If the clockwise search made it all the way round, don't need to | ||
735 | * bother with the anticlockwise search. */ | ||
736 | if (current_face1 == d->order) | ||
737 | continue; /* this dot is complete, move on to next dot */ | ||
738 | |||
739 | /* anticlockwise search */ | ||
740 | while (TRUE) { | ||
741 | grid_face *f = d->faces[current_face2]; | ||
742 | grid_edge *e; | ||
743 | int j; | ||
744 | assert(f != NULL); | ||
745 | /* find dot around this face */ | ||
746 | for (j = 0; j < f->order; j++) { | ||
747 | if (f->dots[j] == d) | ||
748 | break; | ||
749 | } | ||
750 | assert(j != f->order); /* must find dot */ | ||
751 | |||
752 | /* Around f, required edge is clockwise from the dot. */ | ||
753 | e = f->edges[j]; | ||
754 | |||
755 | current_face2--; | ||
756 | if (current_face2 == -1) | ||
757 | current_face2 = d->order - 1; | ||
758 | d->edges[current_face2] = e; /* set edge */ | ||
759 | |||
760 | /* set face */ | ||
761 | if (current_face2 == current_face1) | ||
762 | break; | ||
763 | d->faces[current_face2] = | ||
764 | (e->face1 == f) ? e->face2 : e->face1; | ||
765 | /* There's only 1 infinite face, so we must get all the way | ||
766 | * to current_face1 before we hit it. */ | ||
767 | assert(d->faces[current_face2]); | ||
768 | } | ||
769 | } | ||
770 | |||
771 | /* ====== Stage 4 ====== | ||
772 | * Compute other grid settings | ||
773 | */ | ||
774 | |||
775 | /* Bounding rectangle */ | ||
776 | for (i = 0; i < g->num_dots; i++) { | ||
777 | grid_dot *d = g->dots + i; | ||
778 | if (i == 0) { | ||
779 | g->lowest_x = g->highest_x = d->x; | ||
780 | g->lowest_y = g->highest_y = d->y; | ||
781 | } else { | ||
782 | g->lowest_x = min(g->lowest_x, d->x); | ||
783 | g->highest_x = max(g->highest_x, d->x); | ||
784 | g->lowest_y = min(g->lowest_y, d->y); | ||
785 | g->highest_y = max(g->highest_y, d->y); | ||
786 | } | ||
787 | } | ||
788 | |||
789 | grid_debug_derived(g); | ||
790 | } | ||
791 | |||
792 | /* Helpers for making grid-generation easier. These functions are only | ||
793 | * intended for use during grid generation. */ | ||
794 | |||
795 | /* Comparison function for the (tree234) sorted dot list */ | ||
796 | static int grid_point_cmp_fn(void *v1, void *v2) | ||
797 | { | ||
798 | grid_dot *p1 = v1; | ||
799 | grid_dot *p2 = v2; | ||
800 | if (p1->y != p2->y) | ||
801 | return p2->y - p1->y; | ||
802 | else | ||
803 | return p2->x - p1->x; | ||
804 | } | ||
805 | /* Add a new face to the grid, with its dot list allocated. | ||
806 | * Assumes there's enough space allocated for the new face in grid->faces */ | ||
807 | static void grid_face_add_new(grid *g, int face_size) | ||
808 | { | ||
809 | int i; | ||
810 | grid_face *new_face = g->faces + g->num_faces; | ||
811 | new_face->order = face_size; | ||
812 | new_face->dots = snewn(face_size, grid_dot*); | ||
813 | for (i = 0; i < face_size; i++) | ||
814 | new_face->dots[i] = NULL; | ||
815 | new_face->edges = NULL; | ||
816 | new_face->has_incentre = FALSE; | ||
817 | g->num_faces++; | ||
818 | } | ||
819 | /* Assumes dot list has enough space */ | ||
820 | static grid_dot *grid_dot_add_new(grid *g, int x, int y) | ||
821 | { | ||
822 | grid_dot *new_dot = g->dots + g->num_dots; | ||
823 | new_dot->order = 0; | ||
824 | new_dot->edges = NULL; | ||
825 | new_dot->faces = NULL; | ||
826 | new_dot->x = x; | ||
827 | new_dot->y = y; | ||
828 | g->num_dots++; | ||
829 | return new_dot; | ||
830 | } | ||
831 | /* Retrieve a dot with these (x,y) coordinates. Either return an existing dot | ||
832 | * in the dot_list, or add a new dot to the grid (and the dot_list) and | ||
833 | * return that. | ||
834 | * Assumes g->dots has enough capacity allocated */ | ||
835 | static grid_dot *grid_get_dot(grid *g, tree234 *dot_list, int x, int y) | ||
836 | { | ||
837 | grid_dot test, *ret; | ||
838 | |||
839 | test.order = 0; | ||
840 | test.edges = NULL; | ||
841 | test.faces = NULL; | ||
842 | test.x = x; | ||
843 | test.y = y; | ||
844 | ret = find234(dot_list, &test, NULL); | ||
845 | if (ret) | ||
846 | return ret; | ||
847 | |||
848 | ret = grid_dot_add_new(g, x, y); | ||
849 | add234(dot_list, ret); | ||
850 | return ret; | ||
851 | } | ||
852 | |||
853 | /* Sets the last face of the grid to include this dot, at this position | ||
854 | * around the face. Assumes num_faces is at least 1 (a new face has | ||
855 | * previously been added, with the required number of dots allocated) */ | ||
856 | static void grid_face_set_dot(grid *g, grid_dot *d, int position) | ||
857 | { | ||
858 | grid_face *last_face = g->faces + g->num_faces - 1; | ||
859 | last_face->dots[position] = d; | ||
860 | } | ||
861 | |||
862 | /* | ||
863 | * Helper routines for grid_find_incentre. | ||
864 | */ | ||
865 | static int solve_2x2_matrix(double mx[4], double vin[2], double vout[2]) | ||
866 | { | ||
867 | double inv[4]; | ||
868 | double det; | ||
869 | det = (mx[0]*mx[3] - mx[1]*mx[2]); | ||
870 | if (det == 0) | ||
871 | return FALSE; | ||
872 | |||
873 | inv[0] = mx[3] / det; | ||
874 | inv[1] = -mx[1] / det; | ||
875 | inv[2] = -mx[2] / det; | ||
876 | inv[3] = mx[0] / det; | ||
877 | |||
878 | vout[0] = inv[0]*vin[0] + inv[1]*vin[1]; | ||
879 | vout[1] = inv[2]*vin[0] + inv[3]*vin[1]; | ||
880 | |||
881 | return TRUE; | ||
882 | } | ||
883 | static int solve_3x3_matrix(double mx[9], double vin[3], double vout[3]) | ||
884 | { | ||
885 | double inv[9]; | ||
886 | double det; | ||
887 | |||
888 | det = (mx[0]*mx[4]*mx[8] + mx[1]*mx[5]*mx[6] + mx[2]*mx[3]*mx[7] - | ||
889 | mx[0]*mx[5]*mx[7] - mx[1]*mx[3]*mx[8] - mx[2]*mx[4]*mx[6]); | ||
890 | if (det == 0) | ||
891 | return FALSE; | ||
892 | |||
893 | inv[0] = (mx[4]*mx[8] - mx[5]*mx[7]) / det; | ||
894 | inv[1] = (mx[2]*mx[7] - mx[1]*mx[8]) / det; | ||
895 | inv[2] = (mx[1]*mx[5] - mx[2]*mx[4]) / det; | ||
896 | inv[3] = (mx[5]*mx[6] - mx[3]*mx[8]) / det; | ||
897 | inv[4] = (mx[0]*mx[8] - mx[2]*mx[6]) / det; | ||
898 | inv[5] = (mx[2]*mx[3] - mx[0]*mx[5]) / det; | ||
899 | inv[6] = (mx[3]*mx[7] - mx[4]*mx[6]) / det; | ||
900 | inv[7] = (mx[1]*mx[6] - mx[0]*mx[7]) / det; | ||
901 | inv[8] = (mx[0]*mx[4] - mx[1]*mx[3]) / det; | ||
902 | |||
903 | vout[0] = inv[0]*vin[0] + inv[1]*vin[1] + inv[2]*vin[2]; | ||
904 | vout[1] = inv[3]*vin[0] + inv[4]*vin[1] + inv[5]*vin[2]; | ||
905 | vout[2] = inv[6]*vin[0] + inv[7]*vin[1] + inv[8]*vin[2]; | ||
906 | |||
907 | return TRUE; | ||
908 | } | ||
909 | |||
910 | void grid_find_incentre(grid_face *f) | ||
911 | { | ||
912 | double xbest, ybest, bestdist; | ||
913 | int i, j, k, m; | ||
914 | grid_dot *edgedot1[3], *edgedot2[3]; | ||
915 | grid_dot *dots[3]; | ||
916 | int nedges, ndots; | ||
917 | |||
918 | if (f->has_incentre) | ||
919 | return; | ||
920 | |||
921 | /* | ||
922 | * Find the point in the polygon with the maximum distance to any | ||
923 | * edge or corner. | ||
924 | * | ||
925 | * Such a point must exist which is in contact with at least three | ||
926 | * edges and/or vertices. (Proof: if it's only in contact with two | ||
927 | * edges and/or vertices, it can't even be at a _local_ maximum - | ||
928 | * any such circle can always be expanded in some direction.) So | ||
929 | * we iterate through all 3-subsets of the combined set of edges | ||
930 | * and vertices; for each subset we generate one or two candidate | ||
931 | * points that might be the incentre, and then we vet each one to | ||
932 | * see if it's inside the polygon and what its maximum radius is. | ||
933 | * | ||
934 | * (There's one case which this algorithm will get noticeably | ||
935 | * wrong, and that's when a continuum of equally good answers | ||
936 | * exists due to parallel edges. Consider a long thin rectangle, | ||
937 | * for instance, or a parallelogram. This algorithm will pick a | ||
938 | * point near one end, and choose the end arbitrarily; obviously a | ||
939 | * nicer point to choose would be in the centre. To fix this I | ||
940 | * would have to introduce a special-case system which detected | ||
941 | * parallel edges in advance, set aside all candidate points | ||
942 | * generated using both edges in a parallel pair, and generated | ||
943 | * some additional candidate points half way between them. Also, | ||
944 | * of course, I'd have to cope with rounding error making such a | ||
945 | * point look worse than one of its endpoints. So I haven't done | ||
946 | * this for the moment, and will cross it if necessary when I come | ||
947 | * to it.) | ||
948 | * | ||
949 | * We don't actually iterate literally over _edges_, in the sense | ||
950 | * of grid_edge structures. Instead, we fill in edgedot1[] and | ||
951 | * edgedot2[] with a pair of dots adjacent in the face's list of | ||
952 | * vertices. This ensures that we get the edges in consistent | ||
953 | * orientation, which we could not do from the grid structure | ||
954 | * alone. (A moment's consideration of an order-3 vertex should | ||
955 | * make it clear that if a notional arrow was written on each | ||
956 | * edge, _at least one_ of the three faces bordering that vertex | ||
957 | * would have to have the two arrows tip-to-tip or tail-to-tail | ||
958 | * rather than tip-to-tail.) | ||
959 | */ | ||
960 | nedges = ndots = 0; | ||
961 | bestdist = 0; | ||
962 | xbest = ybest = 0; | ||
963 | |||
964 | for (i = 0; i+2 < 2*f->order; i++) { | ||
965 | if (i < f->order) { | ||
966 | edgedot1[nedges] = f->dots[i]; | ||
967 | edgedot2[nedges++] = f->dots[(i+1)%f->order]; | ||
968 | } else | ||
969 | dots[ndots++] = f->dots[i - f->order]; | ||
970 | |||
971 | for (j = i+1; j+1 < 2*f->order; j++) { | ||
972 | if (j < f->order) { | ||
973 | edgedot1[nedges] = f->dots[j]; | ||
974 | edgedot2[nedges++] = f->dots[(j+1)%f->order]; | ||
975 | } else | ||
976 | dots[ndots++] = f->dots[j - f->order]; | ||
977 | |||
978 | for (k = j+1; k < 2*f->order; k++) { | ||
979 | double cx[2], cy[2]; /* candidate positions */ | ||
980 | int cn = 0; /* number of candidates */ | ||
981 | |||
982 | if (k < f->order) { | ||
983 | edgedot1[nedges] = f->dots[k]; | ||
984 | edgedot2[nedges++] = f->dots[(k+1)%f->order]; | ||
985 | } else | ||
986 | dots[ndots++] = f->dots[k - f->order]; | ||
987 | |||
988 | /* | ||
989 | * Find a point, or pair of points, equidistant from | ||
990 | * all the specified edges and/or vertices. | ||
991 | */ | ||
992 | if (nedges == 3) { | ||
993 | /* | ||
994 | * Three edges. This is a linear matrix equation: | ||
995 | * each row of the matrix represents the fact that | ||
996 | * the point (x,y) we seek is at distance r from | ||
997 | * that edge, and we solve three of those | ||
998 | * simultaneously to obtain x,y,r. (We ignore r.) | ||
999 | */ | ||
1000 | double matrix[9], vector[3], vector2[3]; | ||
1001 | int m; | ||
1002 | |||
1003 | for (m = 0; m < 3; m++) { | ||
1004 | int x1 = edgedot1[m]->x, x2 = edgedot2[m]->x; | ||
1005 | int y1 = edgedot1[m]->y, y2 = edgedot2[m]->y; | ||
1006 | int dx = x2-x1, dy = y2-y1; | ||
1007 | |||
1008 | /* | ||
1009 | * ((x,y) - (x1,y1)) . (dy,-dx) = r |(dx,dy)| | ||
1010 | * | ||
1011 | * => x dy - y dx - r |(dx,dy)| = (x1 dy - y1 dx) | ||
1012 | */ | ||
1013 | matrix[3*m+0] = dy; | ||
1014 | matrix[3*m+1] = -dx; | ||
1015 | matrix[3*m+2] = -sqrt((double)dx*dx+(double)dy*dy); | ||
1016 | vector[m] = (double)x1*dy - (double)y1*dx; | ||
1017 | } | ||
1018 | |||
1019 | if (solve_3x3_matrix(matrix, vector, vector2)) { | ||
1020 | cx[cn] = vector2[0]; | ||
1021 | cy[cn] = vector2[1]; | ||
1022 | cn++; | ||
1023 | } | ||
1024 | } else if (nedges == 2) { | ||
1025 | /* | ||
1026 | * Two edges and a dot. This will end up in a | ||
1027 | * quadratic equation. | ||
1028 | * | ||
1029 | * First, look at the two edges. Having our point | ||
1030 | * be some distance r from both of them gives rise | ||
1031 | * to a pair of linear equations in x,y,r of the | ||
1032 | * form | ||
1033 | * | ||
1034 | * (x-x1) dy - (y-y1) dx = r sqrt(dx^2+dy^2) | ||
1035 | * | ||
1036 | * We eliminate r between those equations to give | ||
1037 | * us a single linear equation in x,y describing | ||
1038 | * the locus of points equidistant from both lines | ||
1039 | * - i.e. the angle bisector. | ||
1040 | * | ||
1041 | * We then choose one of x,y to be a parameter t, | ||
1042 | * and derive linear formulae for x,y,r in terms | ||
1043 | * of t. This enables us to write down the | ||
1044 | * circular equation (x-xd)^2+(y-yd)^2=r^2 as a | ||
1045 | * quadratic in t; solving that and substituting | ||
1046 | * in for x,y gives us two candidate points. | ||
1047 | */ | ||
1048 | double eqs[2][4]; /* a,b,c,d : ax+by+cr=d */ | ||
1049 | double eq[3]; /* a,b,c: ax+by=c */ | ||
1050 | double xt[2], yt[2], rt[2]; /* a,b: {x,y,r}=at+b */ | ||
1051 | double q[3]; /* a,b,c: at^2+bt+c=0 */ | ||
1052 | double disc; | ||
1053 | |||
1054 | /* Find equations of the two input lines. */ | ||
1055 | for (m = 0; m < 2; m++) { | ||
1056 | int x1 = edgedot1[m]->x, x2 = edgedot2[m]->x; | ||
1057 | int y1 = edgedot1[m]->y, y2 = edgedot2[m]->y; | ||
1058 | int dx = x2-x1, dy = y2-y1; | ||
1059 | |||
1060 | eqs[m][0] = dy; | ||
1061 | eqs[m][1] = -dx; | ||
1062 | eqs[m][2] = -sqrt(dx*dx+dy*dy); | ||
1063 | eqs[m][3] = x1*dy - y1*dx; | ||
1064 | } | ||
1065 | |||
1066 | /* Derive the angle bisector by eliminating r. */ | ||
1067 | eq[0] = eqs[0][0]*eqs[1][2] - eqs[1][0]*eqs[0][2]; | ||
1068 | eq[1] = eqs[0][1]*eqs[1][2] - eqs[1][1]*eqs[0][2]; | ||
1069 | eq[2] = eqs[0][3]*eqs[1][2] - eqs[1][3]*eqs[0][2]; | ||
1070 | |||
1071 | /* Parametrise x and y in terms of some t. */ | ||
1072 | if (fabs(eq[0]) < fabs(eq[1])) { | ||
1073 | /* Parameter is x. */ | ||
1074 | xt[0] = 1; xt[1] = 0; | ||
1075 | yt[0] = -eq[0]/eq[1]; yt[1] = eq[2]/eq[1]; | ||
1076 | } else { | ||
1077 | /* Parameter is y. */ | ||
1078 | yt[0] = 1; yt[1] = 0; | ||
1079 | xt[0] = -eq[1]/eq[0]; xt[1] = eq[2]/eq[0]; | ||
1080 | } | ||
1081 | |||
1082 | /* Find a linear representation of r using eqs[0]. */ | ||
1083 | rt[0] = -(eqs[0][0]*xt[0] + eqs[0][1]*yt[0])/eqs[0][2]; | ||
1084 | rt[1] = (eqs[0][3] - eqs[0][0]*xt[1] - | ||
1085 | eqs[0][1]*yt[1])/eqs[0][2]; | ||
1086 | |||
1087 | /* Construct the quadratic equation. */ | ||
1088 | q[0] = -rt[0]*rt[0]; | ||
1089 | q[1] = -2*rt[0]*rt[1]; | ||
1090 | q[2] = -rt[1]*rt[1]; | ||
1091 | q[0] += xt[0]*xt[0]; | ||
1092 | q[1] += 2*xt[0]*(xt[1]-dots[0]->x); | ||
1093 | q[2] += (xt[1]-dots[0]->x)*(xt[1]-dots[0]->x); | ||
1094 | q[0] += yt[0]*yt[0]; | ||
1095 | q[1] += 2*yt[0]*(yt[1]-dots[0]->y); | ||
1096 | q[2] += (yt[1]-dots[0]->y)*(yt[1]-dots[0]->y); | ||
1097 | |||
1098 | /* And solve it. */ | ||
1099 | disc = q[1]*q[1] - 4*q[0]*q[2]; | ||
1100 | if (disc >= 0) { | ||
1101 | double t; | ||
1102 | |||
1103 | disc = sqrt(disc); | ||
1104 | |||
1105 | t = (-q[1] + disc) / (2*q[0]); | ||
1106 | cx[cn] = xt[0]*t + xt[1]; | ||
1107 | cy[cn] = yt[0]*t + yt[1]; | ||
1108 | cn++; | ||
1109 | |||
1110 | t = (-q[1] - disc) / (2*q[0]); | ||
1111 | cx[cn] = xt[0]*t + xt[1]; | ||
1112 | cy[cn] = yt[0]*t + yt[1]; | ||
1113 | cn++; | ||
1114 | } | ||
1115 | } else if (nedges == 1) { | ||
1116 | /* | ||
1117 | * Two dots and an edge. This one's another | ||
1118 | * quadratic equation. | ||
1119 | * | ||
1120 | * The point we want must lie on the perpendicular | ||
1121 | * bisector of the two dots; that much is obvious. | ||
1122 | * So we can construct a parametrisation of that | ||
1123 | * bisecting line, giving linear formulae for x,y | ||
1124 | * in terms of t. We can also express the distance | ||
1125 | * from the edge as such a linear formula. | ||
1126 | * | ||
1127 | * Then we set that equal to the radius of the | ||
1128 | * circle passing through the two points, which is | ||
1129 | * a Pythagoras exercise; that gives rise to a | ||
1130 | * quadratic in t, which we solve. | ||
1131 | */ | ||
1132 | double xt[2], yt[2], rt[2]; /* a,b: {x,y,r}=at+b */ | ||
1133 | double q[3]; /* a,b,c: at^2+bt+c=0 */ | ||
1134 | double disc; | ||
1135 | double halfsep; | ||
1136 | |||
1137 | /* Find parametric formulae for x,y. */ | ||
1138 | { | ||
1139 | int x1 = dots[0]->x, x2 = dots[1]->x; | ||
1140 | int y1 = dots[0]->y, y2 = dots[1]->y; | ||
1141 | int dx = x2-x1, dy = y2-y1; | ||
1142 | double d = sqrt((double)dx*dx + (double)dy*dy); | ||
1143 | |||
1144 | xt[1] = (x1+x2)/2.0; | ||
1145 | yt[1] = (y1+y2)/2.0; | ||
1146 | /* It's convenient if we have t at standard scale. */ | ||
1147 | xt[0] = -dy/d; | ||
1148 | yt[0] = dx/d; | ||
1149 | |||
1150 | /* Also note down half the separation between | ||
1151 | * the dots, for use in computing the circle radius. */ | ||
1152 | halfsep = 0.5*d; | ||
1153 | } | ||
1154 | |||
1155 | /* Find a parametric formula for r. */ | ||
1156 | { | ||
1157 | int x1 = edgedot1[0]->x, x2 = edgedot2[0]->x; | ||
1158 | int y1 = edgedot1[0]->y, y2 = edgedot2[0]->y; | ||
1159 | int dx = x2-x1, dy = y2-y1; | ||
1160 | double d = sqrt((double)dx*dx + (double)dy*dy); | ||
1161 | rt[0] = (xt[0]*dy - yt[0]*dx) / d; | ||
1162 | rt[1] = ((xt[1]-x1)*dy - (yt[1]-y1)*dx) / d; | ||
1163 | } | ||
1164 | |||
1165 | /* Construct the quadratic equation. */ | ||
1166 | q[0] = rt[0]*rt[0]; | ||
1167 | q[1] = 2*rt[0]*rt[1]; | ||
1168 | q[2] = rt[1]*rt[1]; | ||
1169 | q[0] -= 1; | ||
1170 | q[2] -= halfsep*halfsep; | ||
1171 | |||
1172 | /* And solve it. */ | ||
1173 | disc = q[1]*q[1] - 4*q[0]*q[2]; | ||
1174 | if (disc >= 0) { | ||
1175 | double t; | ||
1176 | |||
1177 | disc = sqrt(disc); | ||
1178 | |||
1179 | t = (-q[1] + disc) / (2*q[0]); | ||
1180 | cx[cn] = xt[0]*t + xt[1]; | ||
1181 | cy[cn] = yt[0]*t + yt[1]; | ||
1182 | cn++; | ||
1183 | |||
1184 | t = (-q[1] - disc) / (2*q[0]); | ||
1185 | cx[cn] = xt[0]*t + xt[1]; | ||
1186 | cy[cn] = yt[0]*t + yt[1]; | ||
1187 | cn++; | ||
1188 | } | ||
1189 | } else if (nedges == 0) { | ||
1190 | /* | ||
1191 | * Three dots. This is another linear matrix | ||
1192 | * equation, this time with each row of the matrix | ||
1193 | * representing the perpendicular bisector between | ||
1194 | * two of the points. Of course we only need two | ||
1195 | * such lines to find their intersection, so we | ||
1196 | * need only solve a 2x2 matrix equation. | ||
1197 | */ | ||
1198 | |||
1199 | double matrix[4], vector[2], vector2[2]; | ||
1200 | int m; | ||
1201 | |||
1202 | for (m = 0; m < 2; m++) { | ||
1203 | int x1 = dots[m]->x, x2 = dots[m+1]->x; | ||
1204 | int y1 = dots[m]->y, y2 = dots[m+1]->y; | ||
1205 | int dx = x2-x1, dy = y2-y1; | ||
1206 | |||
1207 | /* | ||
1208 | * ((x,y) - (x1,y1)) . (dx,dy) = 1/2 |(dx,dy)|^2 | ||
1209 | * | ||
1210 | * => 2x dx + 2y dy = dx^2+dy^2 + (2 x1 dx + 2 y1 dy) | ||
1211 | */ | ||
1212 | matrix[2*m+0] = 2*dx; | ||
1213 | matrix[2*m+1] = 2*dy; | ||
1214 | vector[m] = ((double)dx*dx + (double)dy*dy + | ||
1215 | 2.0*x1*dx + 2.0*y1*dy); | ||
1216 | } | ||
1217 | |||
1218 | if (solve_2x2_matrix(matrix, vector, vector2)) { | ||
1219 | cx[cn] = vector2[0]; | ||
1220 | cy[cn] = vector2[1]; | ||
1221 | cn++; | ||
1222 | } | ||
1223 | } | ||
1224 | |||
1225 | /* | ||
1226 | * Now go through our candidate points and see if any | ||
1227 | * of them are better than what we've got so far. | ||
1228 | */ | ||
1229 | for (m = 0; m < cn; m++) { | ||
1230 | double x = cx[m], y = cy[m]; | ||
1231 | |||
1232 | /* | ||
1233 | * First, disqualify the point if it's not inside | ||
1234 | * the polygon, which we work out by counting the | ||
1235 | * edges to the right of the point. (For | ||
1236 | * tiebreaking purposes when edges start or end on | ||
1237 | * our y-coordinate or go right through it, we | ||
1238 | * consider our point to be offset by a small | ||
1239 | * _positive_ epsilon in both the x- and | ||
1240 | * y-direction.) | ||
1241 | */ | ||
1242 | int e, in = 0; | ||
1243 | for (e = 0; e < f->order; e++) { | ||
1244 | int xs = f->edges[e]->dot1->x; | ||
1245 | int xe = f->edges[e]->dot2->x; | ||
1246 | int ys = f->edges[e]->dot1->y; | ||
1247 | int ye = f->edges[e]->dot2->y; | ||
1248 | if ((y >= ys && y < ye) || (y >= ye && y < ys)) { | ||
1249 | /* | ||
1250 | * The line goes past our y-position. Now we need | ||
1251 | * to know if its x-coordinate when it does so is | ||
1252 | * to our right. | ||
1253 | * | ||
1254 | * The x-coordinate in question is mathematically | ||
1255 | * (y - ys) * (xe - xs) / (ye - ys), and we want | ||
1256 | * to know whether (x - xs) >= that. Of course we | ||
1257 | * avoid the division, so we can work in integers; | ||
1258 | * to do this we must multiply both sides of the | ||
1259 | * inequality by ye - ys, which means we must | ||
1260 | * first check that's not negative. | ||
1261 | */ | ||
1262 | int num = xe - xs, denom = ye - ys; | ||
1263 | if (denom < 0) { | ||
1264 | num = -num; | ||
1265 | denom = -denom; | ||
1266 | } | ||
1267 | if ((x - xs) * denom >= (y - ys) * num) | ||
1268 | in ^= 1; | ||
1269 | } | ||
1270 | } | ||
1271 | |||
1272 | if (in) { | ||
1273 | #ifdef HUGE_VAL | ||
1274 | double mindist = HUGE_VAL; | ||
1275 | #else | ||
1276 | #ifdef DBL_MAX | ||
1277 | double mindist = DBL_MAX; | ||
1278 | #else | ||
1279 | #error No way to get maximum floating-point number. | ||
1280 | #endif | ||
1281 | #endif | ||
1282 | int e, d; | ||
1283 | |||
1284 | /* | ||
1285 | * This point is inside the polygon, so now we check | ||
1286 | * its minimum distance to every edge and corner. | ||
1287 | * First the corners ... | ||
1288 | */ | ||
1289 | for (d = 0; d < f->order; d++) { | ||
1290 | int xp = f->dots[d]->x; | ||
1291 | int yp = f->dots[d]->y; | ||
1292 | double dx = x - xp, dy = y - yp; | ||
1293 | double dist = dx*dx + dy*dy; | ||
1294 | if (mindist > dist) | ||
1295 | mindist = dist; | ||
1296 | } | ||
1297 | |||
1298 | /* | ||
1299 | * ... and now also check the perpendicular distance | ||
1300 | * to every edge, if the perpendicular lies between | ||
1301 | * the edge's endpoints. | ||
1302 | */ | ||
1303 | for (e = 0; e < f->order; e++) { | ||
1304 | int xs = f->edges[e]->dot1->x; | ||
1305 | int xe = f->edges[e]->dot2->x; | ||
1306 | int ys = f->edges[e]->dot1->y; | ||
1307 | int ye = f->edges[e]->dot2->y; | ||
1308 | |||
1309 | /* | ||
1310 | * If s and e are our endpoints, and p our | ||
1311 | * candidate circle centre, the foot of a | ||
1312 | * perpendicular from p to the line se lies | ||
1313 | * between s and e if and only if (p-s).(e-s) lies | ||
1314 | * strictly between 0 and (e-s).(e-s). | ||
1315 | */ | ||
1316 | int edx = xe - xs, edy = ye - ys; | ||
1317 | double pdx = x - xs, pdy = y - ys; | ||
1318 | double pde = pdx * edx + pdy * edy; | ||
1319 | long ede = (long)edx * edx + (long)edy * edy; | ||
1320 | if (0 < pde && pde < ede) { | ||
1321 | /* | ||
1322 | * Yes, the nearest point on this edge is | ||
1323 | * closer than either endpoint, so we must | ||
1324 | * take it into account by measuring the | ||
1325 | * perpendicular distance to the edge and | ||
1326 | * checking its square against mindist. | ||
1327 | */ | ||
1328 | |||
1329 | double pdre = pdx * edy - pdy * edx; | ||
1330 | double sqlen = pdre * pdre / ede; | ||
1331 | |||
1332 | if (mindist > sqlen) | ||
1333 | mindist = sqlen; | ||
1334 | } | ||
1335 | } | ||
1336 | |||
1337 | /* | ||
1338 | * Right. Now we know the biggest circle around this | ||
1339 | * point, so we can check it against bestdist. | ||
1340 | */ | ||
1341 | if (bestdist < mindist) { | ||
1342 | bestdist = mindist; | ||
1343 | xbest = x; | ||
1344 | ybest = y; | ||
1345 | } | ||
1346 | } | ||
1347 | } | ||
1348 | |||
1349 | if (k < f->order) | ||
1350 | nedges--; | ||
1351 | else | ||
1352 | ndots--; | ||
1353 | } | ||
1354 | if (j < f->order) | ||
1355 | nedges--; | ||
1356 | else | ||
1357 | ndots--; | ||
1358 | } | ||
1359 | if (i < f->order) | ||
1360 | nedges--; | ||
1361 | else | ||
1362 | ndots--; | ||
1363 | } | ||
1364 | |||
1365 | assert(bestdist > 0); | ||
1366 | |||
1367 | f->has_incentre = TRUE; | ||
1368 | f->ix = xbest + 0.5; /* round to nearest */ | ||
1369 | f->iy = ybest + 0.5; | ||
1370 | } | ||
1371 | |||
1372 | /* ------ Generate various types of grid ------ */ | ||
1373 | |||
1374 | /* General method is to generate faces, by calculating their dot coordinates. | ||
1375 | * As new faces are added, we keep track of all the dots so we can tell when | ||
1376 | * a new face reuses an existing dot. For example, two squares touching at an | ||
1377 | * edge would generate six unique dots: four dots from the first face, then | ||
1378 | * two additional dots for the second face, because we detect the other two | ||
1379 | * dots have already been taken up. This list is stored in a tree234 | ||
1380 | * called "points". No extra memory-allocation needed here - we store the | ||
1381 | * actual grid_dot* pointers, which all point into the g->dots list. | ||
1382 | * For this reason, we have to calculate coordinates in such a way as to | ||
1383 | * eliminate any rounding errors, so we can detect when a dot on one | ||
1384 | * face precisely lands on a dot of a different face. No floating-point | ||
1385 | * arithmetic here! | ||
1386 | */ | ||
1387 | |||
1388 | #define SQUARE_TILESIZE 20 | ||
1389 | |||
1390 | static void grid_size_square(int width, int height, | ||
1391 | int *tilesize, int *xextent, int *yextent) | ||
1392 | { | ||
1393 | int a = SQUARE_TILESIZE; | ||
1394 | |||
1395 | *tilesize = a; | ||
1396 | *xextent = width * a; | ||
1397 | *yextent = height * a; | ||
1398 | } | ||
1399 | |||
1400 | static grid *grid_new_square(int width, int height, const char *desc) | ||
1401 | { | ||
1402 | int x, y; | ||
1403 | /* Side length */ | ||
1404 | int a = SQUARE_TILESIZE; | ||
1405 | |||
1406 | /* Upper bounds - don't have to be exact */ | ||
1407 | int max_faces = width * height; | ||
1408 | int max_dots = (width + 1) * (height + 1); | ||
1409 | |||
1410 | tree234 *points; | ||
1411 | |||
1412 | grid *g = grid_empty(); | ||
1413 | g->tilesize = a; | ||
1414 | g->faces = snewn(max_faces, grid_face); | ||
1415 | g->dots = snewn(max_dots, grid_dot); | ||
1416 | |||
1417 | points = newtree234(grid_point_cmp_fn); | ||
1418 | |||
1419 | /* generate square faces */ | ||
1420 | for (y = 0; y < height; y++) { | ||
1421 | for (x = 0; x < width; x++) { | ||
1422 | grid_dot *d; | ||
1423 | /* face position */ | ||
1424 | int px = a * x; | ||
1425 | int py = a * y; | ||
1426 | |||
1427 | grid_face_add_new(g, 4); | ||
1428 | d = grid_get_dot(g, points, px, py); | ||
1429 | grid_face_set_dot(g, d, 0); | ||
1430 | d = grid_get_dot(g, points, px + a, py); | ||
1431 | grid_face_set_dot(g, d, 1); | ||
1432 | d = grid_get_dot(g, points, px + a, py + a); | ||
1433 | grid_face_set_dot(g, d, 2); | ||
1434 | d = grid_get_dot(g, points, px, py + a); | ||
1435 | grid_face_set_dot(g, d, 3); | ||
1436 | } | ||
1437 | } | ||
1438 | |||
1439 | freetree234(points); | ||
1440 | assert(g->num_faces <= max_faces); | ||
1441 | assert(g->num_dots <= max_dots); | ||
1442 | |||
1443 | grid_make_consistent(g); | ||
1444 | return g; | ||
1445 | } | ||
1446 | |||
1447 | #define HONEY_TILESIZE 45 | ||
1448 | /* Vector for side of hexagon - ratio is close to sqrt(3) */ | ||
1449 | #define HONEY_A 15 | ||
1450 | #define HONEY_B 26 | ||
1451 | |||
1452 | static void grid_size_honeycomb(int width, int height, | ||
1453 | int *tilesize, int *xextent, int *yextent) | ||
1454 | { | ||
1455 | int a = HONEY_A; | ||
1456 | int b = HONEY_B; | ||
1457 | |||
1458 | *tilesize = HONEY_TILESIZE; | ||
1459 | *xextent = (3 * a * (width-1)) + 4*a; | ||
1460 | *yextent = (2 * b * (height-1)) + 3*b; | ||
1461 | } | ||
1462 | |||
1463 | static grid *grid_new_honeycomb(int width, int height, const char *desc) | ||
1464 | { | ||
1465 | int x, y; | ||
1466 | int a = HONEY_A; | ||
1467 | int b = HONEY_B; | ||
1468 | |||
1469 | /* Upper bounds - don't have to be exact */ | ||
1470 | int max_faces = width * height; | ||
1471 | int max_dots = 2 * (width + 1) * (height + 1); | ||
1472 | |||
1473 | tree234 *points; | ||
1474 | |||
1475 | grid *g = grid_empty(); | ||
1476 | g->tilesize = HONEY_TILESIZE; | ||
1477 | g->faces = snewn(max_faces, grid_face); | ||
1478 | g->dots = snewn(max_dots, grid_dot); | ||
1479 | |||
1480 | points = newtree234(grid_point_cmp_fn); | ||
1481 | |||
1482 | /* generate hexagonal faces */ | ||
1483 | for (y = 0; y < height; y++) { | ||
1484 | for (x = 0; x < width; x++) { | ||
1485 | grid_dot *d; | ||
1486 | /* face centre */ | ||
1487 | int cx = 3 * a * x; | ||
1488 | int cy = 2 * b * y; | ||
1489 | if (x % 2) | ||
1490 | cy += b; | ||
1491 | grid_face_add_new(g, 6); | ||
1492 | |||
1493 | d = grid_get_dot(g, points, cx - a, cy - b); | ||
1494 | grid_face_set_dot(g, d, 0); | ||
1495 | d = grid_get_dot(g, points, cx + a, cy - b); | ||
1496 | grid_face_set_dot(g, d, 1); | ||
1497 | d = grid_get_dot(g, points, cx + 2*a, cy); | ||
1498 | grid_face_set_dot(g, d, 2); | ||
1499 | d = grid_get_dot(g, points, cx + a, cy + b); | ||
1500 | grid_face_set_dot(g, d, 3); | ||
1501 | d = grid_get_dot(g, points, cx - a, cy + b); | ||
1502 | grid_face_set_dot(g, d, 4); | ||
1503 | d = grid_get_dot(g, points, cx - 2*a, cy); | ||
1504 | grid_face_set_dot(g, d, 5); | ||
1505 | } | ||
1506 | } | ||
1507 | |||
1508 | freetree234(points); | ||
1509 | assert(g->num_faces <= max_faces); | ||
1510 | assert(g->num_dots <= max_dots); | ||
1511 | |||
1512 | grid_make_consistent(g); | ||
1513 | return g; | ||
1514 | } | ||
1515 | |||
1516 | #define TRIANGLE_TILESIZE 18 | ||
1517 | /* Vector for side of triangle - ratio is close to sqrt(3) */ | ||
1518 | #define TRIANGLE_VEC_X 15 | ||
1519 | #define TRIANGLE_VEC_Y 26 | ||
1520 | |||
1521 | static void grid_size_triangular(int width, int height, | ||
1522 | int *tilesize, int *xextent, int *yextent) | ||
1523 | { | ||
1524 | int vec_x = TRIANGLE_VEC_X; | ||
1525 | int vec_y = TRIANGLE_VEC_Y; | ||
1526 | |||
1527 | *tilesize = TRIANGLE_TILESIZE; | ||
1528 | *xextent = (width+1) * 2 * vec_x; | ||
1529 | *yextent = height * vec_y; | ||
1530 | } | ||
1531 | |||
1532 | static char *grid_validate_desc_triangular(grid_type type, int width, | ||
1533 | int height, const char *desc) | ||
1534 | { | ||
1535 | /* | ||
1536 | * Triangular grids: an absent description is valid (indicating | ||
1537 | * the old-style approach which had 'ears', i.e. triangles | ||
1538 | * connected to only one other face, at some grid corners), and so | ||
1539 | * is a description reading just "0" (indicating the new-style | ||
1540 | * approach in which those ears are trimmed off). Anything else is | ||
1541 | * illegal. | ||
1542 | */ | ||
1543 | |||
1544 | if (!desc || !strcmp(desc, "0")) | ||
1545 | return NULL; | ||
1546 | |||
1547 | return "Unrecognised grid description."; | ||
1548 | } | ||
1549 | |||
1550 | /* Doesn't use the previous method of generation, it pre-dates it! | ||
1551 | * A triangular grid is just about simple enough to do by "brute force" */ | ||
1552 | static grid *grid_new_triangular(int width, int height, const char *desc) | ||
1553 | { | ||
1554 | int x,y; | ||
1555 | int version = (desc == NULL ? -1 : atoi(desc)); | ||
1556 | |||
1557 | /* Vector for side of triangle - ratio is close to sqrt(3) */ | ||
1558 | int vec_x = TRIANGLE_VEC_X; | ||
1559 | int vec_y = TRIANGLE_VEC_Y; | ||
1560 | |||
1561 | int index; | ||
1562 | |||
1563 | /* convenient alias */ | ||
1564 | int w = width + 1; | ||
1565 | |||
1566 | grid *g = grid_empty(); | ||
1567 | g->tilesize = TRIANGLE_TILESIZE; | ||
1568 | |||
1569 | if (version == -1) { | ||
1570 | /* | ||
1571 | * Old-style triangular grid generation, preserved as-is for | ||
1572 | * backwards compatibility with old game ids, in which it's | ||
1573 | * just a little asymmetric and there are 'ears' (faces linked | ||
1574 | * to only one other face) at two grid corners. | ||
1575 | * | ||
1576 | * Example old-style game ids, which should still work, and in | ||
1577 | * which you should see the ears in the TL/BR corners on the | ||
1578 | * first one and in the TL/BL corners on the second: | ||
1579 | * | ||
1580 | * 5x5t1:2c2a1a2a201a1a1a1112a1a2b1211f0b21a2a2a0a | ||
1581 | * 5x6t1:a022a212h1a1d1a12c2b11a012b1a20d1a0a12e | ||
1582 | */ | ||
1583 | |||
1584 | g->num_faces = width * height * 2; | ||
1585 | g->num_dots = (width + 1) * (height + 1); | ||
1586 | g->faces = snewn(g->num_faces, grid_face); | ||
1587 | g->dots = snewn(g->num_dots, grid_dot); | ||
1588 | |||
1589 | /* generate dots */ | ||
1590 | index = 0; | ||
1591 | for (y = 0; y <= height; y++) { | ||
1592 | for (x = 0; x <= width; x++) { | ||
1593 | grid_dot *d = g->dots + index; | ||
1594 | /* odd rows are offset to the right */ | ||
1595 | d->order = 0; | ||
1596 | d->edges = NULL; | ||
1597 | d->faces = NULL; | ||
1598 | d->x = x * 2 * vec_x + ((y % 2) ? vec_x : 0); | ||
1599 | d->y = y * vec_y; | ||
1600 | index++; | ||
1601 | } | ||
1602 | } | ||
1603 | |||
1604 | /* generate faces */ | ||
1605 | index = 0; | ||
1606 | for (y = 0; y < height; y++) { | ||
1607 | for (x = 0; x < width; x++) { | ||
1608 | /* initialise two faces for this (x,y) */ | ||
1609 | grid_face *f1 = g->faces + index; | ||
1610 | grid_face *f2 = f1 + 1; | ||
1611 | f1->edges = NULL; | ||
1612 | f1->order = 3; | ||
1613 | f1->dots = snewn(f1->order, grid_dot*); | ||
1614 | f1->has_incentre = FALSE; | ||
1615 | f2->edges = NULL; | ||
1616 | f2->order = 3; | ||
1617 | f2->dots = snewn(f2->order, grid_dot*); | ||
1618 | f2->has_incentre = FALSE; | ||
1619 | |||
1620 | /* face descriptions depend on whether the row-number is | ||
1621 | * odd or even */ | ||
1622 | if (y % 2) { | ||
1623 | f1->dots[0] = g->dots + y * w + x; | ||
1624 | f1->dots[1] = g->dots + (y + 1) * w + x + 1; | ||
1625 | f1->dots[2] = g->dots + (y + 1) * w + x; | ||
1626 | f2->dots[0] = g->dots + y * w + x; | ||
1627 | f2->dots[1] = g->dots + y * w + x + 1; | ||
1628 | f2->dots[2] = g->dots + (y + 1) * w + x + 1; | ||
1629 | } else { | ||
1630 | f1->dots[0] = g->dots + y * w + x; | ||
1631 | f1->dots[1] = g->dots + y * w + x + 1; | ||
1632 | f1->dots[2] = g->dots + (y + 1) * w + x; | ||
1633 | f2->dots[0] = g->dots + y * w + x + 1; | ||
1634 | f2->dots[1] = g->dots + (y + 1) * w + x + 1; | ||
1635 | f2->dots[2] = g->dots + (y + 1) * w + x; | ||
1636 | } | ||
1637 | index += 2; | ||
1638 | } | ||
1639 | } | ||
1640 | } else { | ||
1641 | /* | ||
1642 | * New-style approach, in which there are never any 'ears', | ||
1643 | * and if height is even then the grid is nicely 4-way | ||
1644 | * symmetric. | ||
1645 | * | ||
1646 | * Example new-style grids: | ||
1647 | * | ||
1648 | * 5x5t1:0_21120b11a1a01a1a00c1a0b211021c1h1a2a1a0a | ||
1649 | * 5x6t1:0_a1212c22c2a02a2f22a0c12a110d0e1c0c0a101121a1 | ||
1650 | */ | ||
1651 | tree234 *points = newtree234(grid_point_cmp_fn); | ||
1652 | /* Upper bounds - don't have to be exact */ | ||
1653 | int max_faces = height * (2*width+1); | ||
1654 | int max_dots = (height+1) * (width+1) * 4; | ||
1655 | |||
1656 | g->faces = snewn(max_faces, grid_face); | ||
1657 | g->dots = snewn(max_dots, grid_dot); | ||
1658 | |||
1659 | for (y = 0; y < height; y++) { | ||
1660 | /* | ||
1661 | * Each row contains (width+1) triangles one way up, and | ||
1662 | * (width) triangles the other way up. Which way up is | ||
1663 | * which varies with parity of y. Also, the dots around | ||
1664 | * each face will flip direction with parity of y, so we | ||
1665 | * set up n1 and n2 to cope with that easily. | ||
1666 | */ | ||
1667 | int y0, y1, n1, n2; | ||
1668 | y0 = y1 = y * vec_y; | ||
1669 | if (y % 2) { | ||
1670 | y1 += vec_y; | ||
1671 | n1 = 2; n2 = 1; | ||
1672 | } else { | ||
1673 | y0 += vec_y; | ||
1674 | n1 = 1; n2 = 2; | ||
1675 | } | ||
1676 | |||
1677 | for (x = 0; x <= width; x++) { | ||
1678 | int x0 = 2*x * vec_x, x1 = x0 + vec_x, x2 = x1 + vec_x; | ||
1679 | |||
1680 | /* | ||
1681 | * If the grid has odd height, then we skip the first | ||
1682 | * and last triangles on this row, otherwise they'll | ||
1683 | * end up as ears. | ||
1684 | */ | ||
1685 | if (height % 2 == 1 && y == height-1 && (x == 0 || x == width)) | ||
1686 | continue; | ||
1687 | |||
1688 | grid_face_add_new(g, 3); | ||
1689 | grid_face_set_dot(g, grid_get_dot(g, points, x0, y0), 0); | ||
1690 | grid_face_set_dot(g, grid_get_dot(g, points, x1, y1), n1); | ||
1691 | grid_face_set_dot(g, grid_get_dot(g, points, x2, y0), n2); | ||
1692 | } | ||
1693 | |||
1694 | for (x = 0; x < width; x++) { | ||
1695 | int x0 = (2*x+1) * vec_x, x1 = x0 + vec_x, x2 = x1 + vec_x; | ||
1696 | |||
1697 | grid_face_add_new(g, 3); | ||
1698 | grid_face_set_dot(g, grid_get_dot(g, points, x0, y1), 0); | ||
1699 | grid_face_set_dot(g, grid_get_dot(g, points, x1, y0), n2); | ||
1700 | grid_face_set_dot(g, grid_get_dot(g, points, x2, y1), n1); | ||
1701 | } | ||
1702 | } | ||
1703 | |||
1704 | freetree234(points); | ||
1705 | assert(g->num_faces <= max_faces); | ||
1706 | assert(g->num_dots <= max_dots); | ||
1707 | } | ||
1708 | |||
1709 | grid_make_consistent(g); | ||
1710 | return g; | ||
1711 | } | ||
1712 | |||
1713 | #define SNUBSQUARE_TILESIZE 18 | ||
1714 | /* Vector for side of triangle - ratio is close to sqrt(3) */ | ||
1715 | #define SNUBSQUARE_A 15 | ||
1716 | #define SNUBSQUARE_B 26 | ||
1717 | |||
1718 | static void grid_size_snubsquare(int width, int height, | ||
1719 | int *tilesize, int *xextent, int *yextent) | ||
1720 | { | ||
1721 | int a = SNUBSQUARE_A; | ||
1722 | int b = SNUBSQUARE_B; | ||
1723 | |||
1724 | *tilesize = SNUBSQUARE_TILESIZE; | ||
1725 | *xextent = (a+b) * (width-1) + a + b; | ||
1726 | *yextent = (a+b) * (height-1) + a + b; | ||
1727 | } | ||
1728 | |||
1729 | static grid *grid_new_snubsquare(int width, int height, const char *desc) | ||
1730 | { | ||
1731 | int x, y; | ||
1732 | int a = SNUBSQUARE_A; | ||
1733 | int b = SNUBSQUARE_B; | ||
1734 | |||
1735 | /* Upper bounds - don't have to be exact */ | ||
1736 | int max_faces = 3 * width * height; | ||
1737 | int max_dots = 2 * (width + 1) * (height + 1); | ||
1738 | |||
1739 | tree234 *points; | ||
1740 | |||
1741 | grid *g = grid_empty(); | ||
1742 | g->tilesize = SNUBSQUARE_TILESIZE; | ||
1743 | g->faces = snewn(max_faces, grid_face); | ||
1744 | g->dots = snewn(max_dots, grid_dot); | ||
1745 | |||
1746 | points = newtree234(grid_point_cmp_fn); | ||
1747 | |||
1748 | for (y = 0; y < height; y++) { | ||
1749 | for (x = 0; x < width; x++) { | ||
1750 | grid_dot *d; | ||
1751 | /* face position */ | ||
1752 | int px = (a + b) * x; | ||
1753 | int py = (a + b) * y; | ||
1754 | |||
1755 | /* generate square faces */ | ||
1756 | grid_face_add_new(g, 4); | ||
1757 | if ((x + y) % 2) { | ||
1758 | d = grid_get_dot(g, points, px + a, py); | ||
1759 | grid_face_set_dot(g, d, 0); | ||
1760 | d = grid_get_dot(g, points, px + a + b, py + a); | ||
1761 | grid_face_set_dot(g, d, 1); | ||
1762 | d = grid_get_dot(g, points, px + b, py + a + b); | ||
1763 | grid_face_set_dot(g, d, 2); | ||
1764 | d = grid_get_dot(g, points, px, py + b); | ||
1765 | grid_face_set_dot(g, d, 3); | ||
1766 | } else { | ||
1767 | d = grid_get_dot(g, points, px + b, py); | ||
1768 | grid_face_set_dot(g, d, 0); | ||
1769 | d = grid_get_dot(g, points, px + a + b, py + b); | ||
1770 | grid_face_set_dot(g, d, 1); | ||
1771 | d = grid_get_dot(g, points, px + a, py + a + b); | ||
1772 | grid_face_set_dot(g, d, 2); | ||
1773 | d = grid_get_dot(g, points, px, py + a); | ||
1774 | grid_face_set_dot(g, d, 3); | ||
1775 | } | ||
1776 | |||
1777 | /* generate up/down triangles */ | ||
1778 | if (x > 0) { | ||
1779 | grid_face_add_new(g, 3); | ||
1780 | if ((x + y) % 2) { | ||
1781 | d = grid_get_dot(g, points, px + a, py); | ||
1782 | grid_face_set_dot(g, d, 0); | ||
1783 | d = grid_get_dot(g, points, px, py + b); | ||
1784 | grid_face_set_dot(g, d, 1); | ||
1785 | d = grid_get_dot(g, points, px - a, py); | ||
1786 | grid_face_set_dot(g, d, 2); | ||
1787 | } else { | ||
1788 | d = grid_get_dot(g, points, px, py + a); | ||
1789 | grid_face_set_dot(g, d, 0); | ||
1790 | d = grid_get_dot(g, points, px + a, py + a + b); | ||
1791 | grid_face_set_dot(g, d, 1); | ||
1792 | d = grid_get_dot(g, points, px - a, py + a + b); | ||
1793 | grid_face_set_dot(g, d, 2); | ||
1794 | } | ||
1795 | } | ||
1796 | |||
1797 | /* generate left/right triangles */ | ||
1798 | if (y > 0) { | ||
1799 | grid_face_add_new(g, 3); | ||
1800 | if ((x + y) % 2) { | ||
1801 | d = grid_get_dot(g, points, px + a, py); | ||
1802 | grid_face_set_dot(g, d, 0); | ||
1803 | d = grid_get_dot(g, points, px + a + b, py - a); | ||
1804 | grid_face_set_dot(g, d, 1); | ||
1805 | d = grid_get_dot(g, points, px + a + b, py + a); | ||
1806 | grid_face_set_dot(g, d, 2); | ||
1807 | } else { | ||
1808 | d = grid_get_dot(g, points, px, py - a); | ||
1809 | grid_face_set_dot(g, d, 0); | ||
1810 | d = grid_get_dot(g, points, px + b, py); | ||
1811 | grid_face_set_dot(g, d, 1); | ||
1812 | d = grid_get_dot(g, points, px, py + a); | ||
1813 | grid_face_set_dot(g, d, 2); | ||
1814 | } | ||
1815 | } | ||
1816 | } | ||
1817 | } | ||
1818 | |||
1819 | freetree234(points); | ||
1820 | assert(g->num_faces <= max_faces); | ||
1821 | assert(g->num_dots <= max_dots); | ||
1822 | |||
1823 | grid_make_consistent(g); | ||
1824 | return g; | ||
1825 | } | ||
1826 | |||
1827 | #define CAIRO_TILESIZE 40 | ||
1828 | /* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */ | ||
1829 | #define CAIRO_A 14 | ||
1830 | #define CAIRO_B 31 | ||
1831 | |||
1832 | static void grid_size_cairo(int width, int height, | ||
1833 | int *tilesize, int *xextent, int *yextent) | ||
1834 | { | ||
1835 | int b = CAIRO_B; /* a unused in determining grid size. */ | ||
1836 | |||
1837 | *tilesize = CAIRO_TILESIZE; | ||
1838 | *xextent = 2*b*(width-1) + 2*b; | ||
1839 | *yextent = 2*b*(height-1) + 2*b; | ||
1840 | } | ||
1841 | |||
1842 | static grid *grid_new_cairo(int width, int height, const char *desc) | ||
1843 | { | ||
1844 | int x, y; | ||
1845 | int a = CAIRO_A; | ||
1846 | int b = CAIRO_B; | ||
1847 | |||
1848 | /* Upper bounds - don't have to be exact */ | ||
1849 | int max_faces = 2 * width * height; | ||
1850 | int max_dots = 3 * (width + 1) * (height + 1); | ||
1851 | |||
1852 | tree234 *points; | ||
1853 | |||
1854 | grid *g = grid_empty(); | ||
1855 | g->tilesize = CAIRO_TILESIZE; | ||
1856 | g->faces = snewn(max_faces, grid_face); | ||
1857 | g->dots = snewn(max_dots, grid_dot); | ||
1858 | |||
1859 | points = newtree234(grid_point_cmp_fn); | ||
1860 | |||
1861 | for (y = 0; y < height; y++) { | ||
1862 | for (x = 0; x < width; x++) { | ||
1863 | grid_dot *d; | ||
1864 | /* cell position */ | ||
1865 | int px = 2 * b * x; | ||
1866 | int py = 2 * b * y; | ||
1867 | |||
1868 | /* horizontal pentagons */ | ||
1869 | if (y > 0) { | ||
1870 | grid_face_add_new(g, 5); | ||
1871 | if ((x + y) % 2) { | ||
1872 | d = grid_get_dot(g, points, px + a, py - b); | ||
1873 | grid_face_set_dot(g, d, 0); | ||
1874 | d = grid_get_dot(g, points, px + 2*b - a, py - b); | ||
1875 | grid_face_set_dot(g, d, 1); | ||
1876 | d = grid_get_dot(g, points, px + 2*b, py); | ||
1877 | grid_face_set_dot(g, d, 2); | ||
1878 | d = grid_get_dot(g, points, px + b, py + a); | ||
1879 | grid_face_set_dot(g, d, 3); | ||
1880 | d = grid_get_dot(g, points, px, py); | ||
1881 | grid_face_set_dot(g, d, 4); | ||
1882 | } else { | ||
1883 | d = grid_get_dot(g, points, px, py); | ||
1884 | grid_face_set_dot(g, d, 0); | ||
1885 | d = grid_get_dot(g, points, px + b, py - a); | ||
1886 | grid_face_set_dot(g, d, 1); | ||
1887 | d = grid_get_dot(g, points, px + 2*b, py); | ||
1888 | grid_face_set_dot(g, d, 2); | ||
1889 | d = grid_get_dot(g, points, px + 2*b - a, py + b); | ||
1890 | grid_face_set_dot(g, d, 3); | ||
1891 | d = grid_get_dot(g, points, px + a, py + b); | ||
1892 | grid_face_set_dot(g, d, 4); | ||
1893 | } | ||
1894 | } | ||
1895 | /* vertical pentagons */ | ||
1896 | if (x > 0) { | ||
1897 | grid_face_add_new(g, 5); | ||
1898 | if ((x + y) % 2) { | ||
1899 | d = grid_get_dot(g, points, px, py); | ||
1900 | grid_face_set_dot(g, d, 0); | ||
1901 | d = grid_get_dot(g, points, px + b, py + a); | ||
1902 | grid_face_set_dot(g, d, 1); | ||
1903 | d = grid_get_dot(g, points, px + b, py + 2*b - a); | ||
1904 | grid_face_set_dot(g, d, 2); | ||
1905 | d = grid_get_dot(g, points, px, py + 2*b); | ||
1906 | grid_face_set_dot(g, d, 3); | ||
1907 | d = grid_get_dot(g, points, px - a, py + b); | ||
1908 | grid_face_set_dot(g, d, 4); | ||
1909 | } else { | ||
1910 | d = grid_get_dot(g, points, px, py); | ||
1911 | grid_face_set_dot(g, d, 0); | ||
1912 | d = grid_get_dot(g, points, px + a, py + b); | ||
1913 | grid_face_set_dot(g, d, 1); | ||
1914 | d = grid_get_dot(g, points, px, py + 2*b); | ||
1915 | grid_face_set_dot(g, d, 2); | ||
1916 | d = grid_get_dot(g, points, px - b, py + 2*b - a); | ||
1917 | grid_face_set_dot(g, d, 3); | ||
1918 | d = grid_get_dot(g, points, px - b, py + a); | ||
1919 | grid_face_set_dot(g, d, 4); | ||
1920 | } | ||
1921 | } | ||
1922 | } | ||
1923 | } | ||
1924 | |||
1925 | freetree234(points); | ||
1926 | assert(g->num_faces <= max_faces); | ||
1927 | assert(g->num_dots <= max_dots); | ||
1928 | |||
1929 | grid_make_consistent(g); | ||
1930 | return g; | ||
1931 | } | ||
1932 | |||
1933 | #define GREATHEX_TILESIZE 18 | ||
1934 | /* Vector for side of triangle - ratio is close to sqrt(3) */ | ||
1935 | #define GREATHEX_A 15 | ||
1936 | #define GREATHEX_B 26 | ||
1937 | |||
1938 | static void grid_size_greathexagonal(int width, int height, | ||
1939 | int *tilesize, int *xextent, int *yextent) | ||
1940 | { | ||
1941 | int a = GREATHEX_A; | ||
1942 | int b = GREATHEX_B; | ||
1943 | |||
1944 | *tilesize = GREATHEX_TILESIZE; | ||
1945 | *xextent = (3*a + b) * (width-1) + 4*a; | ||
1946 | *yextent = (2*a + 2*b) * (height-1) + 3*b + a; | ||
1947 | } | ||
1948 | |||
1949 | static grid *grid_new_greathexagonal(int width, int height, const char *desc) | ||
1950 | { | ||
1951 | int x, y; | ||
1952 | int a = GREATHEX_A; | ||
1953 | int b = GREATHEX_B; | ||
1954 | |||
1955 | /* Upper bounds - don't have to be exact */ | ||
1956 | int max_faces = 6 * (width + 1) * (height + 1); | ||
1957 | int max_dots = 6 * width * height; | ||
1958 | |||
1959 | tree234 *points; | ||
1960 | |||
1961 | grid *g = grid_empty(); | ||
1962 | g->tilesize = GREATHEX_TILESIZE; | ||
1963 | g->faces = snewn(max_faces, grid_face); | ||
1964 | g->dots = snewn(max_dots, grid_dot); | ||
1965 | |||
1966 | points = newtree234(grid_point_cmp_fn); | ||
1967 | |||
1968 | for (y = 0; y < height; y++) { | ||
1969 | for (x = 0; x < width; x++) { | ||
1970 | grid_dot *d; | ||
1971 | /* centre of hexagon */ | ||
1972 | int px = (3*a + b) * x; | ||
1973 | int py = (2*a + 2*b) * y; | ||
1974 | if (x % 2) | ||
1975 | py += a + b; | ||
1976 | |||
1977 | /* hexagon */ | ||
1978 | grid_face_add_new(g, 6); | ||
1979 | d = grid_get_dot(g, points, px - a, py - b); | ||
1980 | grid_face_set_dot(g, d, 0); | ||
1981 | d = grid_get_dot(g, points, px + a, py - b); | ||
1982 | grid_face_set_dot(g, d, 1); | ||
1983 | d = grid_get_dot(g, points, px + 2*a, py); | ||
1984 | grid_face_set_dot(g, d, 2); | ||
1985 | d = grid_get_dot(g, points, px + a, py + b); | ||
1986 | grid_face_set_dot(g, d, 3); | ||
1987 | d = grid_get_dot(g, points, px - a, py + b); | ||
1988 | grid_face_set_dot(g, d, 4); | ||
1989 | d = grid_get_dot(g, points, px - 2*a, py); | ||
1990 | grid_face_set_dot(g, d, 5); | ||
1991 | |||
1992 | /* square below hexagon */ | ||
1993 | if (y < height - 1) { | ||
1994 | grid_face_add_new(g, 4); | ||
1995 | d = grid_get_dot(g, points, px - a, py + b); | ||
1996 | grid_face_set_dot(g, d, 0); | ||
1997 | d = grid_get_dot(g, points, px + a, py + b); | ||
1998 | grid_face_set_dot(g, d, 1); | ||
1999 | d = grid_get_dot(g, points, px + a, py + 2*a + b); | ||
2000 | grid_face_set_dot(g, d, 2); | ||
2001 | d = grid_get_dot(g, points, px - a, py + 2*a + b); | ||
2002 | grid_face_set_dot(g, d, 3); | ||
2003 | } | ||
2004 | |||
2005 | /* square below right */ | ||
2006 | if ((x < width - 1) && (((x % 2) == 0) || (y < height - 1))) { | ||
2007 | grid_face_add_new(g, 4); | ||
2008 | d = grid_get_dot(g, points, px + 2*a, py); | ||
2009 | grid_face_set_dot(g, d, 0); | ||
2010 | d = grid_get_dot(g, points, px + 2*a + b, py + a); | ||
2011 | grid_face_set_dot(g, d, 1); | ||
2012 | d = grid_get_dot(g, points, px + a + b, py + a + b); | ||
2013 | grid_face_set_dot(g, d, 2); | ||
2014 | d = grid_get_dot(g, points, px + a, py + b); | ||
2015 | grid_face_set_dot(g, d, 3); | ||
2016 | } | ||
2017 | |||
2018 | /* square below left */ | ||
2019 | if ((x > 0) && (((x % 2) == 0) || (y < height - 1))) { | ||
2020 | grid_face_add_new(g, 4); | ||
2021 | d = grid_get_dot(g, points, px - 2*a, py); | ||
2022 | grid_face_set_dot(g, d, 0); | ||
2023 | d = grid_get_dot(g, points, px - a, py + b); | ||
2024 | grid_face_set_dot(g, d, 1); | ||
2025 | d = grid_get_dot(g, points, px - a - b, py + a + b); | ||
2026 | grid_face_set_dot(g, d, 2); | ||
2027 | d = grid_get_dot(g, points, px - 2*a - b, py + a); | ||
2028 | grid_face_set_dot(g, d, 3); | ||
2029 | } | ||
2030 | |||
2031 | /* Triangle below right */ | ||
2032 | if ((x < width - 1) && (y < height - 1)) { | ||
2033 | grid_face_add_new(g, 3); | ||
2034 | d = grid_get_dot(g, points, px + a, py + b); | ||
2035 | grid_face_set_dot(g, d, 0); | ||
2036 | d = grid_get_dot(g, points, px + a + b, py + a + b); | ||
2037 | grid_face_set_dot(g, d, 1); | ||
2038 | d = grid_get_dot(g, points, px + a, py + 2*a + b); | ||
2039 | grid_face_set_dot(g, d, 2); | ||
2040 | } | ||
2041 | |||
2042 | /* Triangle below left */ | ||
2043 | if ((x > 0) && (y < height - 1)) { | ||
2044 | grid_face_add_new(g, 3); | ||
2045 | d = grid_get_dot(g, points, px - a, py + b); | ||
2046 | grid_face_set_dot(g, d, 0); | ||
2047 | d = grid_get_dot(g, points, px - a, py + 2*a + b); | ||
2048 | grid_face_set_dot(g, d, 1); | ||
2049 | d = grid_get_dot(g, points, px - a - b, py + a + b); | ||
2050 | grid_face_set_dot(g, d, 2); | ||
2051 | } | ||
2052 | } | ||
2053 | } | ||
2054 | |||
2055 | freetree234(points); | ||
2056 | assert(g->num_faces <= max_faces); | ||
2057 | assert(g->num_dots <= max_dots); | ||
2058 | |||
2059 | grid_make_consistent(g); | ||
2060 | return g; | ||
2061 | } | ||
2062 | |||
2063 | #define OCTAGONAL_TILESIZE 40 | ||
2064 | /* b/a approx sqrt(2) */ | ||
2065 | #define OCTAGONAL_A 29 | ||
2066 | #define OCTAGONAL_B 41 | ||
2067 | |||
2068 | static void grid_size_octagonal(int width, int height, | ||
2069 | int *tilesize, int *xextent, int *yextent) | ||
2070 | { | ||
2071 | int a = OCTAGONAL_A; | ||
2072 | int b = OCTAGONAL_B; | ||
2073 | |||
2074 | *tilesize = OCTAGONAL_TILESIZE; | ||
2075 | *xextent = (2*a + b) * width; | ||
2076 | *yextent = (2*a + b) * height; | ||
2077 | } | ||
2078 | |||
2079 | static grid *grid_new_octagonal(int width, int height, const char *desc) | ||
2080 | { | ||
2081 | int x, y; | ||
2082 | int a = OCTAGONAL_A; | ||
2083 | int b = OCTAGONAL_B; | ||
2084 | |||
2085 | /* Upper bounds - don't have to be exact */ | ||
2086 | int max_faces = 2 * width * height; | ||
2087 | int max_dots = 4 * (width + 1) * (height + 1); | ||
2088 | |||
2089 | tree234 *points; | ||
2090 | |||
2091 | grid *g = grid_empty(); | ||
2092 | g->tilesize = OCTAGONAL_TILESIZE; | ||
2093 | g->faces = snewn(max_faces, grid_face); | ||
2094 | g->dots = snewn(max_dots, grid_dot); | ||
2095 | |||
2096 | points = newtree234(grid_point_cmp_fn); | ||
2097 | |||
2098 | for (y = 0; y < height; y++) { | ||
2099 | for (x = 0; x < width; x++) { | ||
2100 | grid_dot *d; | ||
2101 | /* cell position */ | ||
2102 | int px = (2*a + b) * x; | ||
2103 | int py = (2*a + b) * y; | ||
2104 | /* octagon */ | ||
2105 | grid_face_add_new(g, 8); | ||
2106 | d = grid_get_dot(g, points, px + a, py); | ||
2107 | grid_face_set_dot(g, d, 0); | ||
2108 | d = grid_get_dot(g, points, px + a + b, py); | ||
2109 | grid_face_set_dot(g, d, 1); | ||
2110 | d = grid_get_dot(g, points, px + 2*a + b, py + a); | ||
2111 | grid_face_set_dot(g, d, 2); | ||
2112 | d = grid_get_dot(g, points, px + 2*a + b, py + a + b); | ||
2113 | grid_face_set_dot(g, d, 3); | ||
2114 | d = grid_get_dot(g, points, px + a + b, py + 2*a + b); | ||
2115 | grid_face_set_dot(g, d, 4); | ||
2116 | d = grid_get_dot(g, points, px + a, py + 2*a + b); | ||
2117 | grid_face_set_dot(g, d, 5); | ||
2118 | d = grid_get_dot(g, points, px, py + a + b); | ||
2119 | grid_face_set_dot(g, d, 6); | ||
2120 | d = grid_get_dot(g, points, px, py + a); | ||
2121 | grid_face_set_dot(g, d, 7); | ||
2122 | |||
2123 | /* diamond */ | ||
2124 | if ((x > 0) && (y > 0)) { | ||
2125 | grid_face_add_new(g, 4); | ||
2126 | d = grid_get_dot(g, points, px, py - a); | ||
2127 | grid_face_set_dot(g, d, 0); | ||
2128 | d = grid_get_dot(g, points, px + a, py); | ||
2129 | grid_face_set_dot(g, d, 1); | ||
2130 | d = grid_get_dot(g, points, px, py + a); | ||
2131 | grid_face_set_dot(g, d, 2); | ||
2132 | d = grid_get_dot(g, points, px - a, py); | ||
2133 | grid_face_set_dot(g, d, 3); | ||
2134 | } | ||
2135 | } | ||
2136 | } | ||
2137 | |||
2138 | freetree234(points); | ||
2139 | assert(g->num_faces <= max_faces); | ||
2140 | assert(g->num_dots <= max_dots); | ||
2141 | |||
2142 | grid_make_consistent(g); | ||
2143 | return g; | ||
2144 | } | ||
2145 | |||
2146 | #define KITE_TILESIZE 40 | ||
2147 | /* b/a approx sqrt(3) */ | ||
2148 | #define KITE_A 15 | ||
2149 | #define KITE_B 26 | ||
2150 | |||
2151 | static void grid_size_kites(int width, int height, | ||
2152 | int *tilesize, int *xextent, int *yextent) | ||
2153 | { | ||
2154 | int a = KITE_A; | ||
2155 | int b = KITE_B; | ||
2156 | |||
2157 | *tilesize = KITE_TILESIZE; | ||
2158 | *xextent = 4*b * width + 2*b; | ||
2159 | *yextent = 6*a * (height-1) + 8*a; | ||
2160 | } | ||
2161 | |||
2162 | static grid *grid_new_kites(int width, int height, const char *desc) | ||
2163 | { | ||
2164 | int x, y; | ||
2165 | int a = KITE_A; | ||
2166 | int b = KITE_B; | ||
2167 | |||
2168 | /* Upper bounds - don't have to be exact */ | ||
2169 | int max_faces = 6 * width * height; | ||
2170 | int max_dots = 6 * (width + 1) * (height + 1); | ||
2171 | |||
2172 | tree234 *points; | ||
2173 | |||
2174 | grid *g = grid_empty(); | ||
2175 | g->tilesize = KITE_TILESIZE; | ||
2176 | g->faces = snewn(max_faces, grid_face); | ||
2177 | g->dots = snewn(max_dots, grid_dot); | ||
2178 | |||
2179 | points = newtree234(grid_point_cmp_fn); | ||
2180 | |||
2181 | for (y = 0; y < height; y++) { | ||
2182 | for (x = 0; x < width; x++) { | ||
2183 | grid_dot *d; | ||
2184 | /* position of order-6 dot */ | ||
2185 | int px = 4*b * x; | ||
2186 | int py = 6*a * y; | ||
2187 | if (y % 2) | ||
2188 | px += 2*b; | ||
2189 | |||
2190 | /* kite pointing up-left */ | ||
2191 | grid_face_add_new(g, 4); | ||
2192 | d = grid_get_dot(g, points, px, py); | ||
2193 | grid_face_set_dot(g, d, 0); | ||
2194 | d = grid_get_dot(g, points, px + 2*b, py); | ||
2195 | grid_face_set_dot(g, d, 1); | ||
2196 | d = grid_get_dot(g, points, px + 2*b, py + 2*a); | ||
2197 | grid_face_set_dot(g, d, 2); | ||
2198 | d = grid_get_dot(g, points, px + b, py + 3*a); | ||
2199 | grid_face_set_dot(g, d, 3); | ||
2200 | |||
2201 | /* kite pointing up */ | ||
2202 | grid_face_add_new(g, 4); | ||
2203 | d = grid_get_dot(g, points, px, py); | ||
2204 | grid_face_set_dot(g, d, 0); | ||
2205 | d = grid_get_dot(g, points, px + b, py + 3*a); | ||
2206 | grid_face_set_dot(g, d, 1); | ||
2207 | d = grid_get_dot(g, points, px, py + 4*a); | ||
2208 | grid_face_set_dot(g, d, 2); | ||
2209 | d = grid_get_dot(g, points, px - b, py + 3*a); | ||
2210 | grid_face_set_dot(g, d, 3); | ||
2211 | |||
2212 | /* kite pointing up-right */ | ||
2213 | grid_face_add_new(g, 4); | ||
2214 | d = grid_get_dot(g, points, px, py); | ||
2215 | grid_face_set_dot(g, d, 0); | ||
2216 | d = grid_get_dot(g, points, px - b, py + 3*a); | ||
2217 | grid_face_set_dot(g, d, 1); | ||
2218 | d = grid_get_dot(g, points, px - 2*b, py + 2*a); | ||
2219 | grid_face_set_dot(g, d, 2); | ||
2220 | d = grid_get_dot(g, points, px - 2*b, py); | ||
2221 | grid_face_set_dot(g, d, 3); | ||
2222 | |||
2223 | /* kite pointing down-right */ | ||
2224 | grid_face_add_new(g, 4); | ||
2225 | d = grid_get_dot(g, points, px, py); | ||
2226 | grid_face_set_dot(g, d, 0); | ||
2227 | d = grid_get_dot(g, points, px - 2*b, py); | ||
2228 | grid_face_set_dot(g, d, 1); | ||
2229 | d = grid_get_dot(g, points, px - 2*b, py - 2*a); | ||
2230 | grid_face_set_dot(g, d, 2); | ||
2231 | d = grid_get_dot(g, points, px - b, py - 3*a); | ||
2232 | grid_face_set_dot(g, d, 3); | ||
2233 | |||
2234 | /* kite pointing down */ | ||
2235 | grid_face_add_new(g, 4); | ||
2236 | d = grid_get_dot(g, points, px, py); | ||
2237 | grid_face_set_dot(g, d, 0); | ||
2238 | d = grid_get_dot(g, points, px - b, py - 3*a); | ||
2239 | grid_face_set_dot(g, d, 1); | ||
2240 | d = grid_get_dot(g, points, px, py - 4*a); | ||
2241 | grid_face_set_dot(g, d, 2); | ||
2242 | d = grid_get_dot(g, points, px + b, py - 3*a); | ||
2243 | grid_face_set_dot(g, d, 3); | ||
2244 | |||
2245 | /* kite pointing down-left */ | ||
2246 | grid_face_add_new(g, 4); | ||
2247 | d = grid_get_dot(g, points, px, py); | ||
2248 | grid_face_set_dot(g, d, 0); | ||
2249 | d = grid_get_dot(g, points, px + b, py - 3*a); | ||
2250 | grid_face_set_dot(g, d, 1); | ||
2251 | d = grid_get_dot(g, points, px + 2*b, py - 2*a); | ||
2252 | grid_face_set_dot(g, d, 2); | ||
2253 | d = grid_get_dot(g, points, px + 2*b, py); | ||
2254 | grid_face_set_dot(g, d, 3); | ||
2255 | } | ||
2256 | } | ||
2257 | |||
2258 | freetree234(points); | ||
2259 | assert(g->num_faces <= max_faces); | ||
2260 | assert(g->num_dots <= max_dots); | ||
2261 | |||
2262 | grid_make_consistent(g); | ||
2263 | return g; | ||
2264 | } | ||
2265 | |||
2266 | #define FLORET_TILESIZE 150 | ||
2267 | /* -py/px is close to tan(30 - atan(sqrt(3)/9)) | ||
2268 | * using py=26 makes everything lean to the left, rather than right | ||
2269 | */ | ||
2270 | #define FLORET_PX 75 | ||
2271 | #define FLORET_PY -26 | ||
2272 | |||
2273 | static void grid_size_floret(int width, int height, | ||
2274 | int *tilesize, int *xextent, int *yextent) | ||
2275 | { | ||
2276 | int px = FLORET_PX, py = FLORET_PY; /* |( 75, -26)| = 79.43 */ | ||
2277 | int qx = 4*px/5, qy = -py*2; /* |( 60, 52)| = 79.40 */ | ||
2278 | int ry = qy-py; | ||
2279 | /* rx unused in determining grid size. */ | ||
2280 | |||
2281 | *tilesize = FLORET_TILESIZE; | ||
2282 | *xextent = (6*px+3*qx)/2 * (width-1) + 4*qx + 2*px; | ||
2283 | *yextent = (5*qy-4*py) * (height-1) + 4*qy + 2*ry; | ||
2284 | } | ||
2285 | |||
2286 | static grid *grid_new_floret(int width, int height, const char *desc) | ||
2287 | { | ||
2288 | int x, y; | ||
2289 | /* Vectors for sides; weird numbers needed to keep puzzle aligned with window | ||
2290 | * -py/px is close to tan(30 - atan(sqrt(3)/9)) | ||
2291 | * using py=26 makes everything lean to the left, rather than right | ||
2292 | */ | ||
2293 | int px = FLORET_PX, py = FLORET_PY; /* |( 75, -26)| = 79.43 */ | ||
2294 | int qx = 4*px/5, qy = -py*2; /* |( 60, 52)| = 79.40 */ | ||
2295 | int rx = qx-px, ry = qy-py; /* |(-15, 78)| = 79.38 */ | ||
2296 | |||
2297 | /* Upper bounds - don't have to be exact */ | ||
2298 | int max_faces = 6 * width * height; | ||
2299 | int max_dots = 9 * (width + 1) * (height + 1); | ||
2300 | |||
2301 | tree234 *points; | ||
2302 | |||
2303 | grid *g = grid_empty(); | ||
2304 | g->tilesize = FLORET_TILESIZE; | ||
2305 | g->faces = snewn(max_faces, grid_face); | ||
2306 | g->dots = snewn(max_dots, grid_dot); | ||
2307 | |||
2308 | points = newtree234(grid_point_cmp_fn); | ||
2309 | |||
2310 | /* generate pentagonal faces */ | ||
2311 | for (y = 0; y < height; y++) { | ||
2312 | for (x = 0; x < width; x++) { | ||
2313 | grid_dot *d; | ||
2314 | /* face centre */ | ||
2315 | int cx = (6*px+3*qx)/2 * x; | ||
2316 | int cy = (4*py-5*qy) * y; | ||
2317 | if (x % 2) | ||
2318 | cy -= (4*py-5*qy)/2; | ||
2319 | else if (y && y == height-1) | ||
2320 | continue; /* make better looking grids? try 3x3 for instance */ | ||
2321 | |||
2322 | grid_face_add_new(g, 5); | ||
2323 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); | ||
2324 | d = grid_get_dot(g, points, cx+2*rx , cy+2*ry ); grid_face_set_dot(g, d, 1); | ||
2325 | d = grid_get_dot(g, points, cx+2*rx+qx, cy+2*ry+qy); grid_face_set_dot(g, d, 2); | ||
2326 | d = grid_get_dot(g, points, cx+2*qx+rx, cy+2*qy+ry); grid_face_set_dot(g, d, 3); | ||
2327 | d = grid_get_dot(g, points, cx+2*qx , cy+2*qy ); grid_face_set_dot(g, d, 4); | ||
2328 | |||
2329 | grid_face_add_new(g, 5); | ||
2330 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); | ||
2331 | d = grid_get_dot(g, points, cx+2*qx , cy+2*qy ); grid_face_set_dot(g, d, 1); | ||
2332 | d = grid_get_dot(g, points, cx+2*qx+px, cy+2*qy+py); grid_face_set_dot(g, d, 2); | ||
2333 | d = grid_get_dot(g, points, cx+2*px+qx, cy+2*py+qy); grid_face_set_dot(g, d, 3); | ||
2334 | d = grid_get_dot(g, points, cx+2*px , cy+2*py ); grid_face_set_dot(g, d, 4); | ||
2335 | |||
2336 | grid_face_add_new(g, 5); | ||
2337 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); | ||
2338 | d = grid_get_dot(g, points, cx+2*px , cy+2*py ); grid_face_set_dot(g, d, 1); | ||
2339 | d = grid_get_dot(g, points, cx+2*px-rx, cy+2*py-ry); grid_face_set_dot(g, d, 2); | ||
2340 | d = grid_get_dot(g, points, cx-2*rx+px, cy-2*ry+py); grid_face_set_dot(g, d, 3); | ||
2341 | d = grid_get_dot(g, points, cx-2*rx , cy-2*ry ); grid_face_set_dot(g, d, 4); | ||
2342 | |||
2343 | grid_face_add_new(g, 5); | ||
2344 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); | ||
2345 | d = grid_get_dot(g, points, cx-2*rx , cy-2*ry ); grid_face_set_dot(g, d, 1); | ||
2346 | d = grid_get_dot(g, points, cx-2*rx-qx, cy-2*ry-qy); grid_face_set_dot(g, d, 2); | ||
2347 | d = grid_get_dot(g, points, cx-2*qx-rx, cy-2*qy-ry); grid_face_set_dot(g, d, 3); | ||
2348 | d = grid_get_dot(g, points, cx-2*qx , cy-2*qy ); grid_face_set_dot(g, d, 4); | ||
2349 | |||
2350 | grid_face_add_new(g, 5); | ||
2351 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); | ||
2352 | d = grid_get_dot(g, points, cx-2*qx , cy-2*qy ); grid_face_set_dot(g, d, 1); | ||
2353 | d = grid_get_dot(g, points, cx-2*qx-px, cy-2*qy-py); grid_face_set_dot(g, d, 2); | ||
2354 | d = grid_get_dot(g, points, cx-2*px-qx, cy-2*py-qy); grid_face_set_dot(g, d, 3); | ||
2355 | d = grid_get_dot(g, points, cx-2*px , cy-2*py ); grid_face_set_dot(g, d, 4); | ||
2356 | |||
2357 | grid_face_add_new(g, 5); | ||
2358 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); | ||
2359 | d = grid_get_dot(g, points, cx-2*px , cy-2*py ); grid_face_set_dot(g, d, 1); | ||
2360 | d = grid_get_dot(g, points, cx-2*px+rx, cy-2*py+ry); grid_face_set_dot(g, d, 2); | ||
2361 | d = grid_get_dot(g, points, cx+2*rx-px, cy+2*ry-py); grid_face_set_dot(g, d, 3); | ||
2362 | d = grid_get_dot(g, points, cx+2*rx , cy+2*ry ); grid_face_set_dot(g, d, 4); | ||
2363 | } | ||
2364 | } | ||
2365 | |||
2366 | freetree234(points); | ||
2367 | assert(g->num_faces <= max_faces); | ||
2368 | assert(g->num_dots <= max_dots); | ||
2369 | |||
2370 | grid_make_consistent(g); | ||
2371 | return g; | ||
2372 | } | ||
2373 | |||
2374 | /* DODEC_* are used for dodecagonal and great-dodecagonal grids. */ | ||
2375 | #define DODEC_TILESIZE 26 | ||
2376 | /* Vector for side of triangle - ratio is close to sqrt(3) */ | ||
2377 | #define DODEC_A 15 | ||
2378 | #define DODEC_B 26 | ||
2379 | |||
2380 | static void grid_size_dodecagonal(int width, int height, | ||
2381 | int *tilesize, int *xextent, int *yextent) | ||
2382 | { | ||
2383 | int a = DODEC_A; | ||
2384 | int b = DODEC_B; | ||
2385 | |||
2386 | *tilesize = DODEC_TILESIZE; | ||
2387 | *xextent = (4*a + 2*b) * (width-1) + 3*(2*a + b); | ||
2388 | *yextent = (3*a + 2*b) * (height-1) + 2*(2*a + b); | ||
2389 | } | ||
2390 | |||
2391 | static grid *grid_new_dodecagonal(int width, int height, const char *desc) | ||
2392 | { | ||
2393 | int x, y; | ||
2394 | int a = DODEC_A; | ||
2395 | int b = DODEC_B; | ||
2396 | |||
2397 | /* Upper bounds - don't have to be exact */ | ||
2398 | int max_faces = 3 * width * height; | ||
2399 | int max_dots = 14 * width * height; | ||
2400 | |||
2401 | tree234 *points; | ||
2402 | |||
2403 | grid *g = grid_empty(); | ||
2404 | g->tilesize = DODEC_TILESIZE; | ||
2405 | g->faces = snewn(max_faces, grid_face); | ||
2406 | g->dots = snewn(max_dots, grid_dot); | ||
2407 | |||
2408 | points = newtree234(grid_point_cmp_fn); | ||
2409 | |||
2410 | for (y = 0; y < height; y++) { | ||
2411 | for (x = 0; x < width; x++) { | ||
2412 | grid_dot *d; | ||
2413 | /* centre of dodecagon */ | ||
2414 | int px = (4*a + 2*b) * x; | ||
2415 | int py = (3*a + 2*b) * y; | ||
2416 | if (y % 2) | ||
2417 | px += 2*a + b; | ||
2418 | |||
2419 | /* dodecagon */ | ||
2420 | grid_face_add_new(g, 12); | ||
2421 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); | ||
2422 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 1); | ||
2423 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a )); grid_face_set_dot(g, d, 2); | ||
2424 | d = grid_get_dot(g, points, px + (2*a + b), py + ( a )); grid_face_set_dot(g, d, 3); | ||
2425 | d = grid_get_dot(g, points, px + ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 4); | ||
2426 | d = grid_get_dot(g, points, px + ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 5); | ||
2427 | d = grid_get_dot(g, points, px - ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 6); | ||
2428 | d = grid_get_dot(g, points, px - ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 7); | ||
2429 | d = grid_get_dot(g, points, px - (2*a + b), py + ( a )); grid_face_set_dot(g, d, 8); | ||
2430 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a )); grid_face_set_dot(g, d, 9); | ||
2431 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 10); | ||
2432 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 11); | ||
2433 | |||
2434 | /* triangle below dodecagon */ | ||
2435 | if ((y < height - 1 && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2)))) { | ||
2436 | grid_face_add_new(g, 3); | ||
2437 | d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0); | ||
2438 | d = grid_get_dot(g, points, px , py + (2*a + 2*b)); grid_face_set_dot(g, d, 1); | ||
2439 | d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 2); | ||
2440 | } | ||
2441 | |||
2442 | /* triangle above dodecagon */ | ||
2443 | if ((y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2)))) { | ||
2444 | grid_face_add_new(g, 3); | ||
2445 | d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 0); | ||
2446 | d = grid_get_dot(g, points, px , py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); | ||
2447 | d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 2); | ||
2448 | } | ||
2449 | } | ||
2450 | } | ||
2451 | |||
2452 | freetree234(points); | ||
2453 | assert(g->num_faces <= max_faces); | ||
2454 | assert(g->num_dots <= max_dots); | ||
2455 | |||
2456 | grid_make_consistent(g); | ||
2457 | return g; | ||
2458 | } | ||
2459 | |||
2460 | static void grid_size_greatdodecagonal(int width, int height, | ||
2461 | int *tilesize, int *xextent, int *yextent) | ||
2462 | { | ||
2463 | int a = DODEC_A; | ||
2464 | int b = DODEC_B; | ||
2465 | |||
2466 | *tilesize = DODEC_TILESIZE; | ||
2467 | *xextent = (6*a + 2*b) * (width-1) + 2*(2*a + b) + 3*a + b; | ||
2468 | *yextent = (3*a + 3*b) * (height-1) + 2*(2*a + b); | ||
2469 | } | ||
2470 | |||
2471 | static grid *grid_new_greatdodecagonal(int width, int height, const char *desc) | ||
2472 | { | ||
2473 | int x, y; | ||
2474 | /* Vector for side of triangle - ratio is close to sqrt(3) */ | ||
2475 | int a = DODEC_A; | ||
2476 | int b = DODEC_B; | ||
2477 | |||
2478 | /* Upper bounds - don't have to be exact */ | ||
2479 | int max_faces = 30 * width * height; | ||
2480 | int max_dots = 200 * width * height; | ||
2481 | |||
2482 | tree234 *points; | ||
2483 | |||
2484 | grid *g = grid_empty(); | ||
2485 | g->tilesize = DODEC_TILESIZE; | ||
2486 | g->faces = snewn(max_faces, grid_face); | ||
2487 | g->dots = snewn(max_dots, grid_dot); | ||
2488 | |||
2489 | points = newtree234(grid_point_cmp_fn); | ||
2490 | |||
2491 | for (y = 0; y < height; y++) { | ||
2492 | for (x = 0; x < width; x++) { | ||
2493 | grid_dot *d; | ||
2494 | /* centre of dodecagon */ | ||
2495 | int px = (6*a + 2*b) * x; | ||
2496 | int py = (3*a + 3*b) * y; | ||
2497 | if (y % 2) | ||
2498 | px += 3*a + b; | ||
2499 | |||
2500 | /* dodecagon */ | ||
2501 | grid_face_add_new(g, 12); | ||
2502 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); | ||
2503 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 1); | ||
2504 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a )); grid_face_set_dot(g, d, 2); | ||
2505 | d = grid_get_dot(g, points, px + (2*a + b), py + ( a )); grid_face_set_dot(g, d, 3); | ||
2506 | d = grid_get_dot(g, points, px + ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 4); | ||
2507 | d = grid_get_dot(g, points, px + ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 5); | ||
2508 | d = grid_get_dot(g, points, px - ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 6); | ||
2509 | d = grid_get_dot(g, points, px - ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 7); | ||
2510 | d = grid_get_dot(g, points, px - (2*a + b), py + ( a )); grid_face_set_dot(g, d, 8); | ||
2511 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a )); grid_face_set_dot(g, d, 9); | ||
2512 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 10); | ||
2513 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 11); | ||
2514 | |||
2515 | /* hexagon below dodecagon */ | ||
2516 | if (y < height - 1 && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) { | ||
2517 | grid_face_add_new(g, 6); | ||
2518 | d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0); | ||
2519 | d = grid_get_dot(g, points, px + 2*a, py + (2*a + 2*b)); grid_face_set_dot(g, d, 1); | ||
2520 | d = grid_get_dot(g, points, px + a, py + (2*a + 3*b)); grid_face_set_dot(g, d, 2); | ||
2521 | d = grid_get_dot(g, points, px - a, py + (2*a + 3*b)); grid_face_set_dot(g, d, 3); | ||
2522 | d = grid_get_dot(g, points, px - 2*a, py + (2*a + 2*b)); grid_face_set_dot(g, d, 4); | ||
2523 | d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 5); | ||
2524 | } | ||
2525 | |||
2526 | /* hexagon above dodecagon */ | ||
2527 | if (y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) { | ||
2528 | grid_face_add_new(g, 6); | ||
2529 | d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 0); | ||
2530 | d = grid_get_dot(g, points, px - 2*a, py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); | ||
2531 | d = grid_get_dot(g, points, px - a, py - (2*a + 3*b)); grid_face_set_dot(g, d, 2); | ||
2532 | d = grid_get_dot(g, points, px + a, py - (2*a + 3*b)); grid_face_set_dot(g, d, 3); | ||
2533 | d = grid_get_dot(g, points, px + 2*a, py - (2*a + 2*b)); grid_face_set_dot(g, d, 4); | ||
2534 | d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 5); | ||
2535 | } | ||
2536 | |||
2537 | /* square on right of dodecagon */ | ||
2538 | if (x < width - 1) { | ||
2539 | grid_face_add_new(g, 4); | ||
2540 | d = grid_get_dot(g, points, px + 2*a + b, py - a); grid_face_set_dot(g, d, 0); | ||
2541 | d = grid_get_dot(g, points, px + 4*a + b, py - a); grid_face_set_dot(g, d, 1); | ||
2542 | d = grid_get_dot(g, points, px + 4*a + b, py + a); grid_face_set_dot(g, d, 2); | ||
2543 | d = grid_get_dot(g, points, px + 2*a + b, py + a); grid_face_set_dot(g, d, 3); | ||
2544 | } | ||
2545 | |||
2546 | /* square on top right of dodecagon */ | ||
2547 | if (y && (x < width - 1 || !(y % 2))) { | ||
2548 | grid_face_add_new(g, 4); | ||
2549 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); | ||
2550 | d = grid_get_dot(g, points, px + (2*a ), py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); | ||
2551 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a + 2*b)); grid_face_set_dot(g, d, 2); | ||
2552 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 3); | ||
2553 | } | ||
2554 | |||
2555 | /* square on top left of dodecagon */ | ||
2556 | if (y && (x || (y % 2))) { | ||
2557 | grid_face_add_new(g, 4); | ||
2558 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 0); | ||
2559 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a + 2*b)); grid_face_set_dot(g, d, 1); | ||
2560 | d = grid_get_dot(g, points, px - (2*a ), py - (2*a + 2*b)); grid_face_set_dot(g, d, 2); | ||
2561 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 3); | ||
2562 | } | ||
2563 | } | ||
2564 | } | ||
2565 | |||
2566 | freetree234(points); | ||
2567 | assert(g->num_faces <= max_faces); | ||
2568 | assert(g->num_dots <= max_dots); | ||
2569 | |||
2570 | grid_make_consistent(g); | ||
2571 | return g; | ||
2572 | } | ||
2573 | |||
2574 | static void grid_size_greatgreatdodecagonal(int width, int height, | ||
2575 | int *tilesize, int *xextent, int *yextent) | ||
2576 | { | ||
2577 | int a = DODEC_A; | ||
2578 | int b = DODEC_B; | ||
2579 | |||
2580 | *tilesize = DODEC_TILESIZE; | ||
2581 | *xextent = (4*a + 4*b) * (width-1) + 2*(2*a + b) + 2*a + 2*b; | ||
2582 | *yextent = (6*a + 2*b) * (height-1) + 2*(2*a + b); | ||
2583 | } | ||
2584 | |||
2585 | static grid *grid_new_greatgreatdodecagonal(int width, int height, const char *desc) | ||
2586 | { | ||
2587 | int x, y; | ||
2588 | /* Vector for side of triangle - ratio is close to sqrt(3) */ | ||
2589 | int a = DODEC_A; | ||
2590 | int b = DODEC_B; | ||
2591 | |||
2592 | /* Upper bounds - don't have to be exact */ | ||
2593 | int max_faces = 50 * width * height; | ||
2594 | int max_dots = 300 * width * height; | ||
2595 | |||
2596 | tree234 *points; | ||
2597 | |||
2598 | grid *g = grid_empty(); | ||
2599 | g->tilesize = DODEC_TILESIZE; | ||
2600 | g->faces = snewn(max_faces, grid_face); | ||
2601 | g->dots = snewn(max_dots, grid_dot); | ||
2602 | |||
2603 | points = newtree234(grid_point_cmp_fn); | ||
2604 | |||
2605 | for (y = 0; y < height; y++) { | ||
2606 | for (x = 0; x < width; x++) { | ||
2607 | grid_dot *d; | ||
2608 | /* centre of dodecagon */ | ||
2609 | int px = (4*a + 4*b) * x; | ||
2610 | int py = (6*a + 2*b) * y; | ||
2611 | if (y % 2) | ||
2612 | px += 2*a + 2*b; | ||
2613 | |||
2614 | /* dodecagon */ | ||
2615 | grid_face_add_new(g, 12); | ||
2616 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); | ||
2617 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 1); | ||
2618 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a )); grid_face_set_dot(g, d, 2); | ||
2619 | d = grid_get_dot(g, points, px + (2*a + b), py + ( a )); grid_face_set_dot(g, d, 3); | ||
2620 | d = grid_get_dot(g, points, px + ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 4); | ||
2621 | d = grid_get_dot(g, points, px + ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 5); | ||
2622 | d = grid_get_dot(g, points, px - ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 6); | ||
2623 | d = grid_get_dot(g, points, px - ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 7); | ||
2624 | d = grid_get_dot(g, points, px - (2*a + b), py + ( a )); grid_face_set_dot(g, d, 8); | ||
2625 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a )); grid_face_set_dot(g, d, 9); | ||
2626 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 10); | ||
2627 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 11); | ||
2628 | |||
2629 | /* hexagon on top right of dodecagon */ | ||
2630 | if (y && (x < width - 1 || !(y % 2))) { | ||
2631 | grid_face_add_new(g, 6); | ||
2632 | d = grid_get_dot(g, points, px + (a + 2*b), py - (4*a + b)); grid_face_set_dot(g, d, 0); | ||
2633 | d = grid_get_dot(g, points, px + (a + 2*b), py - (2*a + b)); grid_face_set_dot(g, d, 1); | ||
2634 | d = grid_get_dot(g, points, px + (a + b), py - ( a + b)); grid_face_set_dot(g, d, 2); | ||
2635 | d = grid_get_dot(g, points, px + (a ), py - (2*a + b)); grid_face_set_dot(g, d, 3); | ||
2636 | d = grid_get_dot(g, points, px + (a ), py - (4*a + b)); grid_face_set_dot(g, d, 4); | ||
2637 | d = grid_get_dot(g, points, px + (a + b), py - (5*a + b)); grid_face_set_dot(g, d, 5); | ||
2638 | } | ||
2639 | |||
2640 | /* hexagon on right of dodecagon*/ | ||
2641 | if (x < width - 1) { | ||
2642 | grid_face_add_new(g, 6); | ||
2643 | d = grid_get_dot(g, points, px + (2*a + 3*b), py - a); grid_face_set_dot(g, d, 0); | ||
2644 | d = grid_get_dot(g, points, px + (2*a + 3*b), py + a); grid_face_set_dot(g, d, 1); | ||
2645 | d = grid_get_dot(g, points, px + (2*a + 2*b), py + 2*a); grid_face_set_dot(g, d, 2); | ||
2646 | d = grid_get_dot(g, points, px + (2*a + b), py + a); grid_face_set_dot(g, d, 3); | ||
2647 | d = grid_get_dot(g, points, px + (2*a + b), py - a); grid_face_set_dot(g, d, 4); | ||
2648 | d = grid_get_dot(g, points, px + (2*a + 2*b), py - 2*a); grid_face_set_dot(g, d, 5); | ||
2649 | } | ||
2650 | |||
2651 | /* hexagon on bottom right of dodecagon */ | ||
2652 | if ((y < height - 1) && (x < width - 1 || !(y % 2))) { | ||
2653 | grid_face_add_new(g, 6); | ||
2654 | d = grid_get_dot(g, points, px + (a + 2*b), py + (2*a + b)); grid_face_set_dot(g, d, 0); | ||
2655 | d = grid_get_dot(g, points, px + (a + 2*b), py + (4*a + b)); grid_face_set_dot(g, d, 1); | ||
2656 | d = grid_get_dot(g, points, px + (a + b), py + (5*a + b)); grid_face_set_dot(g, d, 2); | ||
2657 | d = grid_get_dot(g, points, px + (a ), py + (4*a + b)); grid_face_set_dot(g, d, 3); | ||
2658 | d = grid_get_dot(g, points, px + (a ), py + (2*a + b)); grid_face_set_dot(g, d, 4); | ||
2659 | d = grid_get_dot(g, points, px + (a + b), py + ( a + b)); grid_face_set_dot(g, d, 5); | ||
2660 | } | ||
2661 | |||
2662 | /* square on top right of dodecagon */ | ||
2663 | if (y && (x < width - 1 )) { | ||
2664 | grid_face_add_new(g, 4); | ||
2665 | d = grid_get_dot(g, points, px + ( a + 2*b), py - (2*a + b)); grid_face_set_dot(g, d, 0); | ||
2666 | d = grid_get_dot(g, points, px + (2*a + 2*b), py - (2*a )); grid_face_set_dot(g, d, 1); | ||
2667 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a )); grid_face_set_dot(g, d, 2); | ||
2668 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 3); | ||
2669 | } | ||
2670 | |||
2671 | /* square on bottom right of dodecagon */ | ||
2672 | if ((y < height - 1) && (x < width - 1 )) { | ||
2673 | grid_face_add_new(g, 4); | ||
2674 | d = grid_get_dot(g, points, px + (2*a + 2*b), py + (2*a )); grid_face_set_dot(g, d, 0); | ||
2675 | d = grid_get_dot(g, points, px + ( a + 2*b), py + (2*a + b)); grid_face_set_dot(g, d, 1); | ||
2676 | d = grid_get_dot(g, points, px + ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 2); | ||
2677 | d = grid_get_dot(g, points, px + (2*a + b), py + ( a )); grid_face_set_dot(g, d, 3); | ||
2678 | } | ||
2679 | |||
2680 | /* square below dodecagon */ | ||
2681 | if ((y < height - 1) && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) { | ||
2682 | grid_face_add_new(g, 4); | ||
2683 | d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0); | ||
2684 | d = grid_get_dot(g, points, px + a, py + (4*a + b)); grid_face_set_dot(g, d, 1); | ||
2685 | d = grid_get_dot(g, points, px - a, py + (4*a + b)); grid_face_set_dot(g, d, 2); | ||
2686 | d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 3); | ||
2687 | } | ||
2688 | |||
2689 | /* square on bottom left of dodecagon */ | ||
2690 | if (x && (y < height - 1)) { | ||
2691 | grid_face_add_new(g, 4); | ||
2692 | d = grid_get_dot(g, points, px - (2*a + b), py + ( a )); grid_face_set_dot(g, d, 0); | ||
2693 | d = grid_get_dot(g, points, px - ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 1); | ||
2694 | d = grid_get_dot(g, points, px - ( a + 2*b), py + (2*a + b)); grid_face_set_dot(g, d, 2); | ||
2695 | d = grid_get_dot(g, points, px - (2*a + 2*b), py + (2*a )); grid_face_set_dot(g, d, 3); | ||
2696 | } | ||
2697 | |||
2698 | /* square on top left of dodecagon */ | ||
2699 | if (x && y) { | ||
2700 | grid_face_add_new(g, 4); | ||
2701 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 0); | ||
2702 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a )); grid_face_set_dot(g, d, 1); | ||
2703 | d = grid_get_dot(g, points, px - (2*a + 2*b), py - (2*a )); grid_face_set_dot(g, d, 2); | ||
2704 | d = grid_get_dot(g, points, px - ( a + 2*b), py - (2*a + b)); grid_face_set_dot(g, d, 3); | ||
2705 | |||
2706 | } | ||
2707 | |||
2708 | /* square above dodecagon */ | ||
2709 | if (y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) { | ||
2710 | grid_face_add_new(g, 4); | ||
2711 | d = grid_get_dot(g, points, px + a, py - (4*a + b)); grid_face_set_dot(g, d, 0); | ||
2712 | d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 1); | ||
2713 | d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 2); | ||
2714 | d = grid_get_dot(g, points, px - a, py - (4*a + b)); grid_face_set_dot(g, d, 3); | ||
2715 | } | ||
2716 | |||
2717 | /* upper triangle (v) */ | ||
2718 | if (y && (x < width - 1)) { | ||
2719 | grid_face_add_new(g, 3); | ||
2720 | d = grid_get_dot(g, points, px + (3*a + 2*b), py - (2*a + b)); grid_face_set_dot(g, d, 0); | ||
2721 | d = grid_get_dot(g, points, px + (2*a + 2*b), py - (2*a )); grid_face_set_dot(g, d, 1); | ||
2722 | d = grid_get_dot(g, points, px + ( a + 2*b), py - (2*a + b)); grid_face_set_dot(g, d, 2); | ||
2723 | } | ||
2724 | |||
2725 | /* lower triangle (^) */ | ||
2726 | if ((y < height - 1) && (x < width - 1)) { | ||
2727 | grid_face_add_new(g, 3); | ||
2728 | d = grid_get_dot(g, points, px + (3*a + 2*b), py + (2*a + b)); grid_face_set_dot(g, d, 0); | ||
2729 | d = grid_get_dot(g, points, px + ( a + 2*b), py + (2*a + b)); grid_face_set_dot(g, d, 1); | ||
2730 | d = grid_get_dot(g, points, px + (2*a + 2*b), py + (2*a )); grid_face_set_dot(g, d, 2); | ||
2731 | } | ||
2732 | } | ||
2733 | } | ||
2734 | |||
2735 | freetree234(points); | ||
2736 | assert(g->num_faces <= max_faces); | ||
2737 | assert(g->num_dots <= max_dots); | ||
2738 | |||
2739 | grid_make_consistent(g); | ||
2740 | return g; | ||
2741 | } | ||
2742 | |||
2743 | typedef struct setface_ctx | ||
2744 | { | ||
2745 | int xmin, xmax, ymin, ymax; | ||
2746 | |||
2747 | grid *g; | ||
2748 | tree234 *points; | ||
2749 | } setface_ctx; | ||
2750 | |||
2751 | static double round_int_nearest_away(double r) | ||
2752 | { | ||
2753 | return (r > 0.0) ? floor(r + 0.5) : ceil(r - 0.5); | ||
2754 | } | ||
2755 | |||
2756 | static int set_faces(penrose_state *state, vector *vs, int n, int depth) | ||
2757 | { | ||
2758 | setface_ctx *sf_ctx = (setface_ctx *)state->ctx; | ||
2759 | int i; | ||
2760 | int xs[4], ys[4]; | ||
2761 | |||
2762 | if (depth < state->max_depth) return 0; | ||
2763 | #ifdef DEBUG_PENROSE | ||
2764 | if (n != 4) return 0; /* triangles are sent as debugging. */ | ||
2765 | #endif | ||
2766 | |||
2767 | for (i = 0; i < n; i++) { | ||
2768 | double tx = v_x(vs, i), ty = v_y(vs, i); | ||
2769 | |||
2770 | xs[i] = (int)round_int_nearest_away(tx); | ||
2771 | ys[i] = (int)round_int_nearest_away(ty); | ||
2772 | |||
2773 | if (xs[i] < sf_ctx->xmin || xs[i] > sf_ctx->xmax) return 0; | ||
2774 | if (ys[i] < sf_ctx->ymin || ys[i] > sf_ctx->ymax) return 0; | ||
2775 | } | ||
2776 | |||
2777 | grid_face_add_new(sf_ctx->g, n); | ||
2778 | debug(("penrose: new face l=%f gen=%d...", | ||
2779 | penrose_side_length(state->start_size, depth), depth)); | ||
2780 | for (i = 0; i < n; i++) { | ||
2781 | grid_dot *d = grid_get_dot(sf_ctx->g, sf_ctx->points, | ||
2782 | xs[i], ys[i]); | ||
2783 | grid_face_set_dot(sf_ctx->g, d, i); | ||
2784 | debug((" ... dot 0x%x (%d,%d) (was %2.2f,%2.2f)", | ||
2785 | d, d->x, d->y, v_x(vs, i), v_y(vs, i))); | ||
2786 | } | ||
2787 | |||
2788 | return 0; | ||
2789 | } | ||
2790 | |||
2791 | #define PENROSE_TILESIZE 100 | ||
2792 | |||
2793 | static void grid_size_penrose(int width, int height, | ||
2794 | int *tilesize, int *xextent, int *yextent) | ||
2795 | { | ||
2796 | int l = PENROSE_TILESIZE; | ||
2797 | |||
2798 | *tilesize = l; | ||
2799 | *xextent = l * width; | ||
2800 | *yextent = l * height; | ||
2801 | } | ||
2802 | |||
2803 | static grid *grid_new_penrose(int width, int height, int which, const char *desc); /* forward reference */ | ||
2804 | |||
2805 | static char *grid_new_desc_penrose(grid_type type, int width, int height, random_state *rs) | ||
2806 | { | ||
2807 | int tilesize = PENROSE_TILESIZE, startsz, depth, xoff, yoff, aoff; | ||
2808 | double outer_radius; | ||
2809 | int inner_radius; | ||
2810 | char gd[255]; | ||
2811 | int which = (type == GRID_PENROSE_P2 ? PENROSE_P2 : PENROSE_P3); | ||
2812 | grid *g; | ||
2813 | |||
2814 | while (1) { | ||
2815 | /* We want to produce a random bit of penrose tiling, so we | ||
2816 | * calculate a random offset (within the patch that penrose.c | ||
2817 | * calculates for us) and an angle (multiple of 36) to rotate | ||
2818 | * the patch. */ | ||
2819 | |||
2820 | penrose_calculate_size(which, tilesize, width, height, | ||
2821 | &outer_radius, &startsz, &depth); | ||
2822 | |||
2823 | /* Calculate radius of (circumcircle of) patch, subtract from | ||
2824 | * radius calculated. */ | ||
2825 | inner_radius = (int)(outer_radius - sqrt(width*width + height*height)); | ||
2826 | |||
2827 | /* Pick a random offset (the easy way: choose within outer | ||
2828 | * square, discarding while it's outside the circle) */ | ||
2829 | do { | ||
2830 | xoff = random_upto(rs, 2*inner_radius) - inner_radius; | ||
2831 | yoff = random_upto(rs, 2*inner_radius) - inner_radius; | ||
2832 | } while (sqrt(xoff*xoff+yoff*yoff) > inner_radius); | ||
2833 | |||
2834 | aoff = random_upto(rs, 360/36) * 36; | ||
2835 | |||
2836 | debug(("grid_desc: ts %d, %dx%d patch, orad %2.2f irad %d", | ||
2837 | tilesize, width, height, outer_radius, inner_radius)); | ||
2838 | debug((" -> xoff %d yoff %d aoff %d", xoff, yoff, aoff)); | ||
2839 | |||
2840 | sprintf(gd, "G%d,%d,%d", xoff, yoff, aoff); | ||
2841 | |||
2842 | /* | ||
2843 | * Now test-generate our grid, to make sure it actually | ||
2844 | * produces something. | ||
2845 | */ | ||
2846 | g = grid_new_penrose(width, height, which, gd); | ||
2847 | if (g) { | ||
2848 | grid_free(g); | ||
2849 | break; | ||
2850 | } | ||
2851 | /* If not, go back to the top of this while loop and try again | ||
2852 | * with a different random offset. */ | ||
2853 | } | ||
2854 | |||
2855 | return dupstr(gd); | ||
2856 | } | ||
2857 | |||
2858 | static char *grid_validate_desc_penrose(grid_type type, int width, int height, | ||
2859 | const char *desc) | ||
2860 | { | ||
2861 | int tilesize = PENROSE_TILESIZE, startsz, depth, xoff, yoff, aoff, inner_radius; | ||
2862 | double outer_radius; | ||
2863 | int which = (type == GRID_PENROSE_P2 ? PENROSE_P2 : PENROSE_P3); | ||
2864 | grid *g; | ||
2865 | |||
2866 | if (!desc) | ||
2867 | return "Missing grid description string."; | ||
2868 | |||
2869 | penrose_calculate_size(which, tilesize, width, height, | ||
2870 | &outer_radius, &startsz, &depth); | ||
2871 | inner_radius = (int)(outer_radius - sqrt(width*width + height*height)); | ||
2872 | |||
2873 | if (sscanf(desc, "G%d,%d,%d", &xoff, &yoff, &aoff) != 3) | ||
2874 | return "Invalid format grid description string."; | ||
2875 | |||
2876 | if (sqrt(xoff*xoff + yoff*yoff) > inner_radius) | ||
2877 | return "Patch offset out of bounds."; | ||
2878 | if ((aoff % 36) != 0 || aoff < 0 || aoff >= 360) | ||
2879 | return "Angle offset out of bounds."; | ||
2880 | |||
2881 | /* | ||
2882 | * Test-generate to ensure these parameters don't end us up with | ||
2883 | * no grid at all. | ||
2884 | */ | ||
2885 | g = grid_new_penrose(width, height, which, desc); | ||
2886 | if (!g) | ||
2887 | return "Patch coordinates do not identify a usable grid fragment"; | ||
2888 | grid_free(g); | ||
2889 | |||
2890 | return NULL; | ||
2891 | } | ||
2892 | |||
2893 | /* | ||
2894 | * We're asked for a grid of a particular size, and we generate enough | ||
2895 | * of the tiling so we can be sure to have enough random grid from which | ||
2896 | * to pick. | ||
2897 | */ | ||
2898 | |||
2899 | static grid *grid_new_penrose(int width, int height, int which, const char *desc) | ||
2900 | { | ||
2901 | int max_faces, max_dots, tilesize = PENROSE_TILESIZE; | ||
2902 | int xsz, ysz, xoff, yoff, aoff; | ||
2903 | double rradius; | ||
2904 | |||
2905 | tree234 *points; | ||
2906 | grid *g; | ||
2907 | |||
2908 | penrose_state ps; | ||
2909 | setface_ctx sf_ctx; | ||
2910 | |||
2911 | penrose_calculate_size(which, tilesize, width, height, | ||
2912 | &rradius, &ps.start_size, &ps.max_depth); | ||
2913 | |||
2914 | debug(("penrose: w%d h%d, tile size %d, start size %d, depth %d", | ||
2915 | width, height, tilesize, ps.start_size, ps.max_depth)); | ||
2916 | |||
2917 | ps.new_tile = set_faces; | ||
2918 | ps.ctx = &sf_ctx; | ||
2919 | |||
2920 | max_faces = (width*3) * (height*3); /* somewhat paranoid... */ | ||
2921 | max_dots = max_faces * 4; /* ditto... */ | ||
2922 | |||
2923 | g = grid_empty(); | ||
2924 | g->tilesize = tilesize; | ||
2925 | g->faces = snewn(max_faces, grid_face); | ||
2926 | g->dots = snewn(max_dots, grid_dot); | ||
2927 | |||
2928 | points = newtree234(grid_point_cmp_fn); | ||
2929 | |||
2930 | memset(&sf_ctx, 0, sizeof(sf_ctx)); | ||
2931 | sf_ctx.g = g; | ||
2932 | sf_ctx.points = points; | ||
2933 | |||
2934 | if (desc != NULL) { | ||
2935 | if (sscanf(desc, "G%d,%d,%d", &xoff, &yoff, &aoff) != 3) | ||
2936 | assert(!"Invalid grid description."); | ||
2937 | } else { | ||
2938 | xoff = yoff = aoff = 0; | ||
2939 | } | ||
2940 | |||
2941 | xsz = width * tilesize; | ||
2942 | ysz = height * tilesize; | ||
2943 | |||
2944 | sf_ctx.xmin = xoff - xsz/2; | ||
2945 | sf_ctx.xmax = xoff + xsz/2; | ||
2946 | sf_ctx.ymin = yoff - ysz/2; | ||
2947 | sf_ctx.ymax = yoff + ysz/2; | ||
2948 | |||
2949 | debug(("penrose: centre (%f, %f) xsz %f ysz %f", | ||
2950 | 0.0, 0.0, xsz, ysz)); | ||
2951 | debug(("penrose: x range (%f --> %f), y range (%f --> %f)", | ||
2952 | sf_ctx.xmin, sf_ctx.xmax, sf_ctx.ymin, sf_ctx.ymax)); | ||
2953 | |||
2954 | penrose(&ps, which, aoff); | ||
2955 | |||
2956 | freetree234(points); | ||
2957 | assert(g->num_faces <= max_faces); | ||
2958 | assert(g->num_dots <= max_dots); | ||
2959 | |||
2960 | debug(("penrose: %d faces total (equivalent to %d wide by %d high)", | ||
2961 | g->num_faces, g->num_faces/height, g->num_faces/width)); | ||
2962 | |||
2963 | /* | ||
2964 | * Return NULL if we ended up with an empty grid, either because | ||
2965 | * the initial generation was over too small a rectangle to | ||
2966 | * encompass any face or because grid_trim_vigorously ended up | ||
2967 | * removing absolutely everything. | ||
2968 | */ | ||
2969 | if (g->num_faces == 0 || g->num_dots == 0) { | ||
2970 | grid_free(g); | ||
2971 | return NULL; | ||
2972 | } | ||
2973 | grid_trim_vigorously(g); | ||
2974 | if (g->num_faces == 0 || g->num_dots == 0) { | ||
2975 | grid_free(g); | ||
2976 | return NULL; | ||
2977 | } | ||
2978 | |||
2979 | grid_make_consistent(g); | ||
2980 | |||
2981 | /* | ||
2982 | * Centre the grid in its originally promised rectangle. | ||
2983 | */ | ||
2984 | g->lowest_x -= ((sf_ctx.xmax - sf_ctx.xmin) - | ||
2985 | (g->highest_x - g->lowest_x)) / 2; | ||
2986 | g->highest_x = g->lowest_x + (sf_ctx.xmax - sf_ctx.xmin); | ||
2987 | g->lowest_y -= ((sf_ctx.ymax - sf_ctx.ymin) - | ||
2988 | (g->highest_y - g->lowest_y)) / 2; | ||
2989 | g->highest_y = g->lowest_y + (sf_ctx.ymax - sf_ctx.ymin); | ||
2990 | |||
2991 | return g; | ||
2992 | } | ||
2993 | |||
2994 | static void grid_size_penrose_p2_kite(int width, int height, | ||
2995 | int *tilesize, int *xextent, int *yextent) | ||
2996 | { | ||
2997 | grid_size_penrose(width, height, tilesize, xextent, yextent); | ||
2998 | } | ||
2999 | |||
3000 | static void grid_size_penrose_p3_thick(int width, int height, | ||
3001 | int *tilesize, int *xextent, int *yextent) | ||
3002 | { | ||
3003 | grid_size_penrose(width, height, tilesize, xextent, yextent); | ||
3004 | } | ||
3005 | |||
3006 | static grid *grid_new_penrose_p2_kite(int width, int height, const char *desc) | ||
3007 | { | ||
3008 | return grid_new_penrose(width, height, PENROSE_P2, desc); | ||
3009 | } | ||
3010 | |||
3011 | static grid *grid_new_penrose_p3_thick(int width, int height, const char *desc) | ||
3012 | { | ||
3013 | return grid_new_penrose(width, height, PENROSE_P3, desc); | ||
3014 | } | ||
3015 | |||
3016 | /* ----------- End of grid generators ------------- */ | ||
3017 | |||
3018 | #define FNNEW(upper,lower) &grid_new_ ## lower, | ||
3019 | #define FNSZ(upper,lower) &grid_size_ ## lower, | ||
3020 | |||
3021 | static grid *(*(grid_news[]))(int, int, const char*) = { GRIDGEN_LIST(FNNEW) }; | ||
3022 | static void(*(grid_sizes[]))(int, int, int*, int*, int*) = { GRIDGEN_LIST(FNSZ) }; | ||
3023 | |||
3024 | char *grid_new_desc(grid_type type, int width, int height, random_state *rs) | ||
3025 | { | ||
3026 | if (type == GRID_PENROSE_P2 || type == GRID_PENROSE_P3) { | ||
3027 | return grid_new_desc_penrose(type, width, height, rs); | ||
3028 | } else if (type == GRID_TRIANGULAR) { | ||
3029 | return dupstr("0"); /* up-to-date version of triangular grid */ | ||
3030 | } else { | ||
3031 | return NULL; | ||
3032 | } | ||
3033 | } | ||
3034 | |||
3035 | char *grid_validate_desc(grid_type type, int width, int height, | ||
3036 | const char *desc) | ||
3037 | { | ||
3038 | if (type == GRID_PENROSE_P2 || type == GRID_PENROSE_P3) { | ||
3039 | return grid_validate_desc_penrose(type, width, height, desc); | ||
3040 | } else if (type == GRID_TRIANGULAR) { | ||
3041 | return grid_validate_desc_triangular(type, width, height, desc); | ||
3042 | } else { | ||
3043 | if (desc != NULL) | ||
3044 | return "Grid description strings not used with this grid type"; | ||
3045 | return NULL; | ||
3046 | } | ||
3047 | } | ||
3048 | |||
3049 | grid *grid_new(grid_type type, int width, int height, const char *desc) | ||
3050 | { | ||
3051 | char *err = grid_validate_desc(type, width, height, desc); | ||
3052 | if (err) assert(!"Invalid grid description."); | ||
3053 | |||
3054 | return grid_news[type](width, height, desc); | ||
3055 | } | ||
3056 | |||
3057 | void grid_compute_size(grid_type type, int width, int height, | ||
3058 | int *tilesize, int *xextent, int *yextent) | ||
3059 | { | ||
3060 | grid_sizes[type](width, height, tilesize, xextent, yextent); | ||
3061 | } | ||
3062 | |||
3063 | /* ----------- End of grid helpers ------------- */ | ||
3064 | |||
3065 | /* vim: set shiftwidth=4 tabstop=8: */ | ||