7c95608a |
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> |
fd66a01d |
15 | #include <float.h> |
7c95608a |
16 | |
17 | #include "puzzles.h" |
18 | #include "tree234.h" |
19 | #include "grid.h" |
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20 | #include "penrose.h" |
7c95608a |
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) */ |
fd66a01d |
55 | static grid *grid_empty(void) |
7c95608a |
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; |
7c95608a |
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 | */ |
b1535c90 |
80 | static double point_line_distance(long px, long py, |
81 | long ax, long ay, |
82 | long bx, long by) |
7c95608a |
83 | { |
b1535c90 |
84 | long det = ax*by - bx*ay + bx*py - px*by + px*ay - ax*py; |
1515b973 |
85 | double len; |
7c95608a |
86 | det = max(det, -det); |
1515b973 |
87 | len = sqrt(SQ(ax - bx) + SQ(ay - by)); |
7c95608a |
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 | * |
f839ef77 |
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. |
7c95608a |
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 | { |
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112 | grid_edge *best_edge; |
113 | double best_distance = 0; |
114 | int i; |
115 | |
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116 | best_edge = NULL; |
117 | |
f839ef77 |
118 | for (i = 0; i < g->num_edges; i++) { |
119 | grid_edge *e = &g->edges[i]; |
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120 | long e2; /* squared length of edge */ |
121 | long a2, b2; /* squared lengths of other sides */ |
7c95608a |
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 */ |
b1535c90 |
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); |
7c95608a |
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. */ |
b1535c90 |
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); |
7c95608a |
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 | |
cebf0b0d |
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 |
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228 | #include <errno.h> |
229 | |
cebf0b0d |
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 | |
7c95608a |
245 | /* Show the basic grid information, before doing grid_make_consistent */ |
cebf0b0d |
246 | static void grid_debug_basic(grid *g) |
7c95608a |
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. */ |
cebf0b0d |
251 | #ifdef DEBUG_GRID |
7c95608a |
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 | } |
cebf0b0d |
264 | #endif |
265 | #ifdef SVG_GRID |
266 | grid_try_svg(g, SVG_FACES); |
267 | #endif |
7c95608a |
268 | } |
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269 | |
7c95608a |
270 | /* Show the derived grid information, computed by grid_make_consistent */ |
cebf0b0d |
271 | static void grid_debug_derived(grid *g) |
7c95608a |
272 | { |
cebf0b0d |
273 | #ifdef DEBUG_GRID |
7c95608a |
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 | } |
cebf0b0d |
313 | #endif |
314 | #ifdef SVG_GRID |
315 | grid_try_svg(g, SVG_DOTS | SVG_EDGES | SVG_FACES); |
316 | #endif |
7c95608a |
317 | } |
7c95608a |
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 | |
cebf0b0d |
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 | /* |
a6bd4b9c |
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 | /* |
cebf0b0d |
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 | |
7c95608a |
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 | |
cebf0b0d |
510 | grid_debug_basic(g); |
7c95608a |
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; |
ac5deb9c |
521 | debug(("allocating room for %d edges\n", g->num_edges)); |
7c95608a |
522 | g->edges = snewn(g->num_edges, grid_edge); |
523 | next_new_edge = g->edges; |
524 | |
525 | /* Iterate over faces, and over each face's dots, generating edges as we |
526 | * go. As we find each new edge, we can immediately fill in the edge's |
527 | * dots, but only one of the edge's faces. Later on in the iteration, we |
528 | * will find the same edge again (unless it's on the border), but we will |
529 | * know the other face. |
530 | * For efficiency, maintain a list of the incomplete edges, sorted by |
531 | * their dots. */ |
532 | incomplete_edges = newtree234(grid_edge_bydots_cmpfn); |
533 | for (i = 0; i < g->num_faces; i++) { |
534 | grid_face *f = g->faces + i; |
535 | int j; |
ac5deb9c |
536 | assert(f->order > 2); |
7c95608a |
537 | for (j = 0; j < f->order; j++) { |
538 | grid_edge e; /* fake edge for searching */ |
539 | grid_edge *edge_found; |
540 | int j2 = j + 1; |
541 | if (j2 == f->order) |
542 | j2 = 0; |
543 | e.dot1 = f->dots[j]; |
544 | e.dot2 = f->dots[j2]; |
545 | /* Use del234 instead of find234, because we always want to |
546 | * remove the edge if found */ |
547 | edge_found = del234(incomplete_edges, &e); |
548 | if (edge_found) { |
549 | /* This edge already added, so fill out missing face. |
550 | * Edge is already removed from incomplete_edges. */ |
551 | edge_found->face2 = f; |
552 | } else { |
553 | assert(next_new_edge - g->edges < g->num_edges); |
554 | next_new_edge->dot1 = e.dot1; |
555 | next_new_edge->dot2 = e.dot2; |
556 | next_new_edge->face1 = f; |
557 | next_new_edge->face2 = NULL; /* potentially infinite face */ |
558 | add234(incomplete_edges, next_new_edge); |
559 | ++next_new_edge; |
560 | } |
561 | } |
562 | } |
563 | freetree234(incomplete_edges); |
564 | |
565 | /* ====== Stage 2 ====== |
566 | * For each face, build its edge list. |
567 | */ |
568 | |
569 | /* Allocate space for each edge list. Can do this, because each face's |
570 | * edge-list is the same size as its dot-list. */ |
571 | for (i = 0; i < g->num_faces; i++) { |
572 | grid_face *f = g->faces + i; |
573 | int j; |
574 | f->edges = snewn(f->order, grid_edge*); |
575 | /* Preload with NULLs, to help detect potential bugs. */ |
576 | for (j = 0; j < f->order; j++) |
577 | f->edges[j] = NULL; |
578 | } |
579 | |
580 | /* Iterate over each edge, and over both its faces. Add this edge to |
581 | * the face's edge-list, after finding where it should go in the |
582 | * sequence. */ |
583 | for (i = 0; i < g->num_edges; i++) { |
584 | grid_edge *e = g->edges + i; |
585 | int j; |
586 | for (j = 0; j < 2; j++) { |
587 | grid_face *f = j ? e->face2 : e->face1; |
588 | int k, k2; |
589 | if (f == NULL) continue; |
590 | /* Find one of the dots around the face */ |
591 | for (k = 0; k < f->order; k++) { |
592 | if (f->dots[k] == e->dot1) |
593 | break; /* found dot1 */ |
594 | } |
595 | assert(k != f->order); /* Must find the dot around this face */ |
596 | |
597 | /* Labelling scheme: as we walk clockwise around the face, |
598 | * starting at dot0 (f->dots[0]), we hit: |
599 | * (dot0), edge0, dot1, edge1, dot2,... |
600 | * |
601 | * 0 |
602 | * 0-----1 |
603 | * | |
604 | * |1 |
605 | * | |
606 | * 3-----2 |
607 | * 2 |
608 | * |
609 | * Therefore, edgeK joins dotK and dot{K+1} |
610 | */ |
611 | |
612 | /* Around this face, either the next dot or the previous dot |
613 | * must be e->dot2. Otherwise the edge is wrong. */ |
614 | k2 = k + 1; |
615 | if (k2 == f->order) |
616 | k2 = 0; |
617 | if (f->dots[k2] == e->dot2) { |
618 | /* dot1(k) and dot2(k2) go clockwise around this face, so add |
619 | * this edge at position k (see diagram). */ |
620 | assert(f->edges[k] == NULL); |
621 | f->edges[k] = e; |
622 | continue; |
623 | } |
624 | /* Try previous dot */ |
625 | k2 = k - 1; |
626 | if (k2 == -1) |
627 | k2 = f->order - 1; |
628 | if (f->dots[k2] == e->dot2) { |
629 | /* dot1(k) and dot2(k2) go anticlockwise around this face. */ |
630 | assert(f->edges[k2] == NULL); |
631 | f->edges[k2] = e; |
632 | continue; |
633 | } |
634 | assert(!"Grid broken: bad edge-face relationship"); |
635 | } |
636 | } |
637 | |
638 | /* ====== Stage 3 ====== |
639 | * For each dot, build its edge-list and face-list. |
640 | */ |
641 | |
642 | /* We don't know how many edges/faces go around each dot, so we can't |
643 | * allocate the right space for these lists. Pre-compute the sizes by |
644 | * iterating over each edge and recording a tally against each dot. */ |
645 | for (i = 0; i < g->num_dots; i++) { |
646 | g->dots[i].order = 0; |
647 | } |
648 | for (i = 0; i < g->num_edges; i++) { |
649 | grid_edge *e = g->edges + i; |
650 | ++(e->dot1->order); |
651 | ++(e->dot2->order); |
652 | } |
653 | /* Now we have the sizes, pre-allocate the edge and face lists. */ |
654 | for (i = 0; i < g->num_dots; i++) { |
655 | grid_dot *d = g->dots + i; |
656 | int j; |
657 | assert(d->order >= 2); /* sanity check */ |
658 | d->edges = snewn(d->order, grid_edge*); |
659 | d->faces = snewn(d->order, grid_face*); |
660 | for (j = 0; j < d->order; j++) { |
661 | d->edges[j] = NULL; |
662 | d->faces[j] = NULL; |
663 | } |
664 | } |
665 | /* For each dot, need to find a face that touches it, so we can seed |
666 | * the edge-face-edge-face process around each dot. */ |
667 | for (i = 0; i < g->num_faces; i++) { |
668 | grid_face *f = g->faces + i; |
669 | int j; |
670 | for (j = 0; j < f->order; j++) { |
671 | grid_dot *d = f->dots[j]; |
672 | d->faces[0] = f; |
673 | } |
674 | } |
675 | /* Each dot now has a face in its first slot. Generate the remaining |
676 | * faces and edges around the dot, by searching both clockwise and |
677 | * anticlockwise from the first face. Need to do both directions, |
678 | * because of the possibility of hitting the infinite face, which |
679 | * blocks progress. But there's only one such face, so we will |
680 | * succeed in finding every edge and face this way. */ |
681 | for (i = 0; i < g->num_dots; i++) { |
682 | grid_dot *d = g->dots + i; |
683 | int current_face1 = 0; /* ascends clockwise */ |
684 | int current_face2 = 0; /* descends anticlockwise */ |
685 | |
686 | /* Labelling scheme: as we walk clockwise around the dot, starting |
687 | * at face0 (d->faces[0]), we hit: |
688 | * (face0), edge0, face1, edge1, face2,... |
689 | * |
690 | * 0 |
691 | * | |
692 | * 0 | 1 |
693 | * | |
694 | * -----d-----1 |
695 | * | |
696 | * | 2 |
697 | * | |
698 | * 2 |
699 | * |
700 | * So, for example, face1 should be joined to edge0 and edge1, |
701 | * and those edges should appear in an anticlockwise sense around |
702 | * that face (see diagram). */ |
703 | |
704 | /* clockwise search */ |
705 | while (TRUE) { |
706 | grid_face *f = d->faces[current_face1]; |
707 | grid_edge *e; |
708 | int j; |
709 | assert(f != NULL); |
710 | /* find dot around this face */ |
711 | for (j = 0; j < f->order; j++) { |
712 | if (f->dots[j] == d) |
713 | break; |
714 | } |
715 | assert(j != f->order); /* must find dot */ |
716 | |
717 | /* Around f, required edge is anticlockwise from the dot. See |
718 | * the other labelling scheme higher up, for why we subtract 1 |
719 | * from j. */ |
720 | j--; |
721 | if (j == -1) |
722 | j = f->order - 1; |
723 | e = f->edges[j]; |
724 | d->edges[current_face1] = e; /* set edge */ |
725 | current_face1++; |
726 | if (current_face1 == d->order) |
727 | break; |
728 | else { |
729 | /* set face */ |
730 | d->faces[current_face1] = |
731 | (e->face1 == f) ? e->face2 : e->face1; |
732 | if (d->faces[current_face1] == NULL) |
733 | break; /* cannot progress beyond infinite face */ |
734 | } |
735 | } |
736 | /* If the clockwise search made it all the way round, don't need to |
737 | * bother with the anticlockwise search. */ |
738 | if (current_face1 == d->order) |
739 | continue; /* this dot is complete, move on to next dot */ |
740 | |
741 | /* anticlockwise search */ |
742 | while (TRUE) { |
743 | grid_face *f = d->faces[current_face2]; |
744 | grid_edge *e; |
745 | int j; |
746 | assert(f != NULL); |
747 | /* find dot around this face */ |
748 | for (j = 0; j < f->order; j++) { |
749 | if (f->dots[j] == d) |
750 | break; |
751 | } |
752 | assert(j != f->order); /* must find dot */ |
753 | |
754 | /* Around f, required edge is clockwise from the dot. */ |
755 | e = f->edges[j]; |
756 | |
757 | current_face2--; |
758 | if (current_face2 == -1) |
759 | current_face2 = d->order - 1; |
760 | d->edges[current_face2] = e; /* set edge */ |
761 | |
762 | /* set face */ |
763 | if (current_face2 == current_face1) |
764 | break; |
765 | d->faces[current_face2] = |
766 | (e->face1 == f) ? e->face2 : e->face1; |
767 | /* There's only 1 infinite face, so we must get all the way |
768 | * to current_face1 before we hit it. */ |
769 | assert(d->faces[current_face2]); |
770 | } |
771 | } |
772 | |
773 | /* ====== Stage 4 ====== |
774 | * Compute other grid settings |
775 | */ |
776 | |
777 | /* Bounding rectangle */ |
778 | for (i = 0; i < g->num_dots; i++) { |
779 | grid_dot *d = g->dots + i; |
780 | if (i == 0) { |
781 | g->lowest_x = g->highest_x = d->x; |
782 | g->lowest_y = g->highest_y = d->y; |
783 | } else { |
784 | g->lowest_x = min(g->lowest_x, d->x); |
785 | g->highest_x = max(g->highest_x, d->x); |
786 | g->lowest_y = min(g->lowest_y, d->y); |
787 | g->highest_y = max(g->highest_y, d->y); |
788 | } |
789 | } |
cebf0b0d |
790 | |
791 | grid_debug_derived(g); |
7c95608a |
792 | } |
793 | |
794 | /* Helpers for making grid-generation easier. These functions are only |
795 | * intended for use during grid generation. */ |
796 | |
797 | /* Comparison function for the (tree234) sorted dot list */ |
798 | static int grid_point_cmp_fn(void *v1, void *v2) |
799 | { |
800 | grid_dot *p1 = v1; |
801 | grid_dot *p2 = v2; |
802 | if (p1->y != p2->y) |
803 | return p2->y - p1->y; |
804 | else |
805 | return p2->x - p1->x; |
806 | } |
807 | /* Add a new face to the grid, with its dot list allocated. |
808 | * Assumes there's enough space allocated for the new face in grid->faces */ |
809 | static void grid_face_add_new(grid *g, int face_size) |
810 | { |
811 | int i; |
812 | grid_face *new_face = g->faces + g->num_faces; |
813 | new_face->order = face_size; |
814 | new_face->dots = snewn(face_size, grid_dot*); |
815 | for (i = 0; i < face_size; i++) |
816 | new_face->dots[i] = NULL; |
817 | new_face->edges = NULL; |
a10bec21 |
818 | new_face->has_incentre = FALSE; |
7c95608a |
819 | g->num_faces++; |
820 | } |
821 | /* Assumes dot list has enough space */ |
822 | static grid_dot *grid_dot_add_new(grid *g, int x, int y) |
823 | { |
824 | grid_dot *new_dot = g->dots + g->num_dots; |
825 | new_dot->order = 0; |
826 | new_dot->edges = NULL; |
827 | new_dot->faces = NULL; |
828 | new_dot->x = x; |
829 | new_dot->y = y; |
830 | g->num_dots++; |
831 | return new_dot; |
832 | } |
833 | /* Retrieve a dot with these (x,y) coordinates. Either return an existing dot |
834 | * in the dot_list, or add a new dot to the grid (and the dot_list) and |
835 | * return that. |
836 | * Assumes g->dots has enough capacity allocated */ |
837 | static grid_dot *grid_get_dot(grid *g, tree234 *dot_list, int x, int y) |
838 | { |
3466f373 |
839 | grid_dot test, *ret; |
840 | |
841 | test.order = 0; |
842 | test.edges = NULL; |
843 | test.faces = NULL; |
844 | test.x = x; |
845 | test.y = y; |
846 | ret = find234(dot_list, &test, NULL); |
7c95608a |
847 | if (ret) |
848 | return ret; |
849 | |
850 | ret = grid_dot_add_new(g, x, y); |
851 | add234(dot_list, ret); |
852 | return ret; |
853 | } |
854 | |
855 | /* Sets the last face of the grid to include this dot, at this position |
856 | * around the face. Assumes num_faces is at least 1 (a new face has |
857 | * previously been added, with the required number of dots allocated) */ |
858 | static void grid_face_set_dot(grid *g, grid_dot *d, int position) |
859 | { |
860 | grid_face *last_face = g->faces + g->num_faces - 1; |
861 | last_face->dots[position] = d; |
862 | } |
863 | |
e64991db |
864 | /* |
865 | * Helper routines for grid_find_incentre. |
866 | */ |
867 | static int solve_2x2_matrix(double mx[4], double vin[2], double vout[2]) |
868 | { |
869 | double inv[4]; |
870 | double det; |
871 | det = (mx[0]*mx[3] - mx[1]*mx[2]); |
872 | if (det == 0) |
873 | return FALSE; |
874 | |
875 | inv[0] = mx[3] / det; |
876 | inv[1] = -mx[1] / det; |
877 | inv[2] = -mx[2] / det; |
878 | inv[3] = mx[0] / det; |
879 | |
880 | vout[0] = inv[0]*vin[0] + inv[1]*vin[1]; |
881 | vout[1] = inv[2]*vin[0] + inv[3]*vin[1]; |
882 | |
883 | return TRUE; |
884 | } |
885 | static int solve_3x3_matrix(double mx[9], double vin[3], double vout[3]) |
886 | { |
887 | double inv[9]; |
888 | double det; |
889 | |
890 | det = (mx[0]*mx[4]*mx[8] + mx[1]*mx[5]*mx[6] + mx[2]*mx[3]*mx[7] - |
891 | mx[0]*mx[5]*mx[7] - mx[1]*mx[3]*mx[8] - mx[2]*mx[4]*mx[6]); |
892 | if (det == 0) |
893 | return FALSE; |
894 | |
895 | inv[0] = (mx[4]*mx[8] - mx[5]*mx[7]) / det; |
896 | inv[1] = (mx[2]*mx[7] - mx[1]*mx[8]) / det; |
897 | inv[2] = (mx[1]*mx[5] - mx[2]*mx[4]) / det; |
898 | inv[3] = (mx[5]*mx[6] - mx[3]*mx[8]) / det; |
899 | inv[4] = (mx[0]*mx[8] - mx[2]*mx[6]) / det; |
900 | inv[5] = (mx[2]*mx[3] - mx[0]*mx[5]) / det; |
901 | inv[6] = (mx[3]*mx[7] - mx[4]*mx[6]) / det; |
902 | inv[7] = (mx[1]*mx[6] - mx[0]*mx[7]) / det; |
903 | inv[8] = (mx[0]*mx[4] - mx[1]*mx[3]) / det; |
904 | |
905 | vout[0] = inv[0]*vin[0] + inv[1]*vin[1] + inv[2]*vin[2]; |
906 | vout[1] = inv[3]*vin[0] + inv[4]*vin[1] + inv[5]*vin[2]; |
907 | vout[2] = inv[6]*vin[0] + inv[7]*vin[1] + inv[8]*vin[2]; |
908 | |
909 | return TRUE; |
910 | } |
911 | |
912 | void grid_find_incentre(grid_face *f) |
913 | { |
914 | double xbest, ybest, bestdist; |
915 | int i, j, k, m; |
916 | grid_dot *edgedot1[3], *edgedot2[3]; |
917 | grid_dot *dots[3]; |
918 | int nedges, ndots; |
919 | |
920 | if (f->has_incentre) |
921 | return; |
922 | |
923 | /* |
924 | * Find the point in the polygon with the maximum distance to any |
925 | * edge or corner. |
926 | * |
927 | * Such a point must exist which is in contact with at least three |
928 | * edges and/or vertices. (Proof: if it's only in contact with two |
929 | * edges and/or vertices, it can't even be at a _local_ maximum - |
930 | * any such circle can always be expanded in some direction.) So |
931 | * we iterate through all 3-subsets of the combined set of edges |
932 | * and vertices; for each subset we generate one or two candidate |
933 | * points that might be the incentre, and then we vet each one to |
934 | * see if it's inside the polygon and what its maximum radius is. |
935 | * |
936 | * (There's one case which this algorithm will get noticeably |
937 | * wrong, and that's when a continuum of equally good answers |
938 | * exists due to parallel edges. Consider a long thin rectangle, |
939 | * for instance, or a parallelogram. This algorithm will pick a |
940 | * point near one end, and choose the end arbitrarily; obviously a |
941 | * nicer point to choose would be in the centre. To fix this I |
942 | * would have to introduce a special-case system which detected |
943 | * parallel edges in advance, set aside all candidate points |
944 | * generated using both edges in a parallel pair, and generated |
945 | * some additional candidate points half way between them. Also, |
946 | * of course, I'd have to cope with rounding error making such a |
947 | * point look worse than one of its endpoints. So I haven't done |
948 | * this for the moment, and will cross it if necessary when I come |
949 | * to it.) |
950 | * |
951 | * We don't actually iterate literally over _edges_, in the sense |
952 | * of grid_edge structures. Instead, we fill in edgedot1[] and |
953 | * edgedot2[] with a pair of dots adjacent in the face's list of |
954 | * vertices. This ensures that we get the edges in consistent |
955 | * orientation, which we could not do from the grid structure |
956 | * alone. (A moment's consideration of an order-3 vertex should |
957 | * make it clear that if a notional arrow was written on each |
958 | * edge, _at least one_ of the three faces bordering that vertex |
959 | * would have to have the two arrows tip-to-tip or tail-to-tail |
960 | * rather than tip-to-tail.) |
961 | */ |
962 | nedges = ndots = 0; |
963 | bestdist = 0; |
964 | xbest = ybest = 0; |
965 | |
966 | for (i = 0; i+2 < 2*f->order; i++) { |
967 | if (i < f->order) { |
968 | edgedot1[nedges] = f->dots[i]; |
969 | edgedot2[nedges++] = f->dots[(i+1)%f->order]; |
970 | } else |
971 | dots[ndots++] = f->dots[i - f->order]; |
972 | |
973 | for (j = i+1; j+1 < 2*f->order; j++) { |
974 | if (j < f->order) { |
975 | edgedot1[nedges] = f->dots[j]; |
976 | edgedot2[nedges++] = f->dots[(j+1)%f->order]; |
977 | } else |
978 | dots[ndots++] = f->dots[j - f->order]; |
979 | |
980 | for (k = j+1; k < 2*f->order; k++) { |
981 | double cx[2], cy[2]; /* candidate positions */ |
982 | int cn = 0; /* number of candidates */ |
983 | |
984 | if (k < f->order) { |
985 | edgedot1[nedges] = f->dots[k]; |
986 | edgedot2[nedges++] = f->dots[(k+1)%f->order]; |
987 | } else |
988 | dots[ndots++] = f->dots[k - f->order]; |
989 | |
990 | /* |
991 | * Find a point, or pair of points, equidistant from |
992 | * all the specified edges and/or vertices. |
993 | */ |
994 | if (nedges == 3) { |
995 | /* |
996 | * Three edges. This is a linear matrix equation: |
997 | * each row of the matrix represents the fact that |
998 | * the point (x,y) we seek is at distance r from |
999 | * that edge, and we solve three of those |
1000 | * simultaneously to obtain x,y,r. (We ignore r.) |
1001 | */ |
1002 | double matrix[9], vector[3], vector2[3]; |
1003 | int m; |
1004 | |
1005 | for (m = 0; m < 3; m++) { |
1006 | int x1 = edgedot1[m]->x, x2 = edgedot2[m]->x; |
1007 | int y1 = edgedot1[m]->y, y2 = edgedot2[m]->y; |
1008 | int dx = x2-x1, dy = y2-y1; |
1009 | |
1010 | /* |
1011 | * ((x,y) - (x1,y1)) . (dy,-dx) = r |(dx,dy)| |
1012 | * |
1013 | * => x dy - y dx - r |(dx,dy)| = (x1 dy - y1 dx) |
1014 | */ |
1015 | matrix[3*m+0] = dy; |
1016 | matrix[3*m+1] = -dx; |
1017 | matrix[3*m+2] = -sqrt((double)dx*dx+(double)dy*dy); |
1018 | vector[m] = (double)x1*dy - (double)y1*dx; |
1019 | } |
1020 | |
1021 | if (solve_3x3_matrix(matrix, vector, vector2)) { |
1022 | cx[cn] = vector2[0]; |
1023 | cy[cn] = vector2[1]; |
1024 | cn++; |
1025 | } |
1026 | } else if (nedges == 2) { |
1027 | /* |
1028 | * Two edges and a dot. This will end up in a |
1029 | * quadratic equation. |
1030 | * |
1031 | * First, look at the two edges. Having our point |
1032 | * be some distance r from both of them gives rise |
1033 | * to a pair of linear equations in x,y,r of the |
1034 | * form |
1035 | * |
1036 | * (x-x1) dy - (y-y1) dx = r sqrt(dx^2+dy^2) |
1037 | * |
1038 | * We eliminate r between those equations to give |
1039 | * us a single linear equation in x,y describing |
1040 | * the locus of points equidistant from both lines |
1041 | * - i.e. the angle bisector. |
1042 | * |
1043 | * We then choose one of x,y to be a parameter t, |
1044 | * and derive linear formulae for x,y,r in terms |
1045 | * of t. This enables us to write down the |
1046 | * circular equation (x-xd)^2+(y-yd)^2=r^2 as a |
1047 | * quadratic in t; solving that and substituting |
1048 | * in for x,y gives us two candidate points. |
1049 | */ |
1050 | double eqs[2][4]; /* a,b,c,d : ax+by+cr=d */ |
1051 | double eq[3]; /* a,b,c: ax+by=c */ |
1052 | double xt[2], yt[2], rt[2]; /* a,b: {x,y,r}=at+b */ |
1053 | double q[3]; /* a,b,c: at^2+bt+c=0 */ |
1054 | double disc; |
1055 | |
1056 | /* Find equations of the two input lines. */ |
1057 | for (m = 0; m < 2; m++) { |
1058 | int x1 = edgedot1[m]->x, x2 = edgedot2[m]->x; |
1059 | int y1 = edgedot1[m]->y, y2 = edgedot2[m]->y; |
1060 | int dx = x2-x1, dy = y2-y1; |
1061 | |
1062 | eqs[m][0] = dy; |
1063 | eqs[m][1] = -dx; |
1064 | eqs[m][2] = -sqrt(dx*dx+dy*dy); |
1065 | eqs[m][3] = x1*dy - y1*dx; |
1066 | } |
1067 | |
1068 | /* Derive the angle bisector by eliminating r. */ |
1069 | eq[0] = eqs[0][0]*eqs[1][2] - eqs[1][0]*eqs[0][2]; |
1070 | eq[1] = eqs[0][1]*eqs[1][2] - eqs[1][1]*eqs[0][2]; |
1071 | eq[2] = eqs[0][3]*eqs[1][2] - eqs[1][3]*eqs[0][2]; |
1072 | |
1073 | /* Parametrise x and y in terms of some t. */ |
1074 | if (abs(eq[0]) < abs(eq[1])) { |
1075 | /* Parameter is x. */ |
1076 | xt[0] = 1; xt[1] = 0; |
1077 | yt[0] = -eq[0]/eq[1]; yt[1] = eq[2]/eq[1]; |
1078 | } else { |
1079 | /* Parameter is y. */ |
1080 | yt[0] = 1; yt[1] = 0; |
1081 | xt[0] = -eq[1]/eq[0]; xt[1] = eq[2]/eq[0]; |
1082 | } |
1083 | |
1084 | /* Find a linear representation of r using eqs[0]. */ |
1085 | rt[0] = -(eqs[0][0]*xt[0] + eqs[0][1]*yt[0])/eqs[0][2]; |
1086 | rt[1] = (eqs[0][3] - eqs[0][0]*xt[1] - |
1087 | eqs[0][1]*yt[1])/eqs[0][2]; |
1088 | |
1089 | /* Construct the quadratic equation. */ |
1090 | q[0] = -rt[0]*rt[0]; |
1091 | q[1] = -2*rt[0]*rt[1]; |
1092 | q[2] = -rt[1]*rt[1]; |
1093 | q[0] += xt[0]*xt[0]; |
1094 | q[1] += 2*xt[0]*(xt[1]-dots[0]->x); |
1095 | q[2] += (xt[1]-dots[0]->x)*(xt[1]-dots[0]->x); |
1096 | q[0] += yt[0]*yt[0]; |
1097 | q[1] += 2*yt[0]*(yt[1]-dots[0]->y); |
1098 | q[2] += (yt[1]-dots[0]->y)*(yt[1]-dots[0]->y); |
1099 | |
1100 | /* And solve it. */ |
1101 | disc = q[1]*q[1] - 4*q[0]*q[2]; |
1102 | if (disc >= 0) { |
1103 | double t; |
1104 | |
1105 | disc = sqrt(disc); |
1106 | |
1107 | t = (-q[1] + disc) / (2*q[0]); |
1108 | cx[cn] = xt[0]*t + xt[1]; |
1109 | cy[cn] = yt[0]*t + yt[1]; |
1110 | cn++; |
1111 | |
1112 | t = (-q[1] - disc) / (2*q[0]); |
1113 | cx[cn] = xt[0]*t + xt[1]; |
1114 | cy[cn] = yt[0]*t + yt[1]; |
1115 | cn++; |
1116 | } |
1117 | } else if (nedges == 1) { |
1118 | /* |
1119 | * Two dots and an edge. This one's another |
1120 | * quadratic equation. |
1121 | * |
1122 | * The point we want must lie on the perpendicular |
1123 | * bisector of the two dots; that much is obvious. |
1124 | * So we can construct a parametrisation of that |
1125 | * bisecting line, giving linear formulae for x,y |
1126 | * in terms of t. We can also express the distance |
1127 | * from the edge as such a linear formula. |
1128 | * |
1129 | * Then we set that equal to the radius of the |
1130 | * circle passing through the two points, which is |
1131 | * a Pythagoras exercise; that gives rise to a |
1132 | * quadratic in t, which we solve. |
1133 | */ |
1134 | double xt[2], yt[2], rt[2]; /* a,b: {x,y,r}=at+b */ |
1135 | double q[3]; /* a,b,c: at^2+bt+c=0 */ |
1136 | double disc; |
1137 | double halfsep; |
1138 | |
1139 | /* Find parametric formulae for x,y. */ |
1140 | { |
1141 | int x1 = dots[0]->x, x2 = dots[1]->x; |
1142 | int y1 = dots[0]->y, y2 = dots[1]->y; |
1143 | int dx = x2-x1, dy = y2-y1; |
1144 | double d = sqrt((double)dx*dx + (double)dy*dy); |
1145 | |
1146 | xt[1] = (x1+x2)/2.0; |
1147 | yt[1] = (y1+y2)/2.0; |
1148 | /* It's convenient if we have t at standard scale. */ |
1149 | xt[0] = -dy/d; |
1150 | yt[0] = dx/d; |
1151 | |
1152 | /* Also note down half the separation between |
1153 | * the dots, for use in computing the circle radius. */ |
1154 | halfsep = 0.5*d; |
1155 | } |
1156 | |
1157 | /* Find a parametric formula for r. */ |
1158 | { |
1159 | int x1 = edgedot1[0]->x, x2 = edgedot2[0]->x; |
1160 | int y1 = edgedot1[0]->y, y2 = edgedot2[0]->y; |
1161 | int dx = x2-x1, dy = y2-y1; |
1162 | double d = sqrt((double)dx*dx + (double)dy*dy); |
1163 | rt[0] = (xt[0]*dy - yt[0]*dx) / d; |
1164 | rt[1] = ((xt[1]-x1)*dy - (yt[1]-y1)*dx) / d; |
1165 | } |
1166 | |
1167 | /* Construct the quadratic equation. */ |
1168 | q[0] = rt[0]*rt[0]; |
1169 | q[1] = 2*rt[0]*rt[1]; |
1170 | q[2] = rt[1]*rt[1]; |
1171 | q[0] -= 1; |
1172 | q[2] -= halfsep*halfsep; |
1173 | |
1174 | /* And solve it. */ |
1175 | disc = q[1]*q[1] - 4*q[0]*q[2]; |
1176 | if (disc >= 0) { |
1177 | double t; |
1178 | |
1179 | disc = sqrt(disc); |
1180 | |
1181 | t = (-q[1] + disc) / (2*q[0]); |
1182 | cx[cn] = xt[0]*t + xt[1]; |
1183 | cy[cn] = yt[0]*t + yt[1]; |
1184 | cn++; |
1185 | |
1186 | t = (-q[1] - disc) / (2*q[0]); |
1187 | cx[cn] = xt[0]*t + xt[1]; |
1188 | cy[cn] = yt[0]*t + yt[1]; |
1189 | cn++; |
1190 | } |
1191 | } else if (nedges == 0) { |
1192 | /* |
1193 | * Three dots. This is another linear matrix |
1194 | * equation, this time with each row of the matrix |
1195 | * representing the perpendicular bisector between |
1196 | * two of the points. Of course we only need two |
1197 | * such lines to find their intersection, so we |
1198 | * need only solve a 2x2 matrix equation. |
1199 | */ |
1200 | |
1201 | double matrix[4], vector[2], vector2[2]; |
1202 | int m; |
1203 | |
1204 | for (m = 0; m < 2; m++) { |
1205 | int x1 = dots[m]->x, x2 = dots[m+1]->x; |
1206 | int y1 = dots[m]->y, y2 = dots[m+1]->y; |
1207 | int dx = x2-x1, dy = y2-y1; |
1208 | |
1209 | /* |
1210 | * ((x,y) - (x1,y1)) . (dx,dy) = 1/2 |(dx,dy)|^2 |
1211 | * |
1212 | * => 2x dx + 2y dy = dx^2+dy^2 + (2 x1 dx + 2 y1 dy) |
1213 | */ |
1214 | matrix[2*m+0] = 2*dx; |
1215 | matrix[2*m+1] = 2*dy; |
1216 | vector[m] = ((double)dx*dx + (double)dy*dy + |
1217 | 2.0*x1*dx + 2.0*y1*dy); |
1218 | } |
1219 | |
1220 | if (solve_2x2_matrix(matrix, vector, vector2)) { |
1221 | cx[cn] = vector2[0]; |
1222 | cy[cn] = vector2[1]; |
1223 | cn++; |
1224 | } |
1225 | } |
1226 | |
1227 | /* |
1228 | * Now go through our candidate points and see if any |
1229 | * of them are better than what we've got so far. |
1230 | */ |
1231 | for (m = 0; m < cn; m++) { |
1232 | double x = cx[m], y = cy[m]; |
1233 | |
1234 | /* |
1235 | * First, disqualify the point if it's not inside |
1236 | * the polygon, which we work out by counting the |
1237 | * edges to the right of the point. (For |
1238 | * tiebreaking purposes when edges start or end on |
1239 | * our y-coordinate or go right through it, we |
1240 | * consider our point to be offset by a small |
1241 | * _positive_ epsilon in both the x- and |
1242 | * y-direction.) |
1243 | */ |
1244 | int e, in = 0; |
1245 | for (e = 0; e < f->order; e++) { |
1246 | int xs = f->edges[e]->dot1->x; |
1247 | int xe = f->edges[e]->dot2->x; |
1248 | int ys = f->edges[e]->dot1->y; |
1249 | int ye = f->edges[e]->dot2->y; |
1250 | if ((y >= ys && y < ye) || (y >= ye && y < ys)) { |
1251 | /* |
1252 | * The line goes past our y-position. Now we need |
1253 | * to know if its x-coordinate when it does so is |
1254 | * to our right. |
1255 | * |
1256 | * The x-coordinate in question is mathematically |
1257 | * (y - ys) * (xe - xs) / (ye - ys), and we want |
1258 | * to know whether (x - xs) >= that. Of course we |
1259 | * avoid the division, so we can work in integers; |
1260 | * to do this we must multiply both sides of the |
1261 | * inequality by ye - ys, which means we must |
1262 | * first check that's not negative. |
1263 | */ |
1264 | int num = xe - xs, denom = ye - ys; |
1265 | if (denom < 0) { |
1266 | num = -num; |
1267 | denom = -denom; |
1268 | } |
1269 | if ((x - xs) * denom >= (y - ys) * num) |
1270 | in ^= 1; |
1271 | } |
1272 | } |
1273 | |
1274 | if (in) { |
fd66a01d |
1275 | #ifdef HUGE_VAL |
e64991db |
1276 | double mindist = HUGE_VAL; |
fd66a01d |
1277 | #else |
1278 | #ifdef DBL_MAX |
1279 | double mindist = DBL_MAX; |
1280 | #else |
1281 | #error No way to get maximum floating-point number. |
1282 | #endif |
1283 | #endif |
e64991db |
1284 | int e, d; |
1285 | |
1286 | /* |
1287 | * This point is inside the polygon, so now we check |
1288 | * its minimum distance to every edge and corner. |
1289 | * First the corners ... |
1290 | */ |
1291 | for (d = 0; d < f->order; d++) { |
1292 | int xp = f->dots[d]->x; |
1293 | int yp = f->dots[d]->y; |
1294 | double dx = x - xp, dy = y - yp; |
1295 | double dist = dx*dx + dy*dy; |
1296 | if (mindist > dist) |
1297 | mindist = dist; |
1298 | } |
1299 | |
1300 | /* |
1301 | * ... and now also check the perpendicular distance |
1302 | * to every edge, if the perpendicular lies between |
1303 | * the edge's endpoints. |
1304 | */ |
1305 | for (e = 0; e < f->order; e++) { |
1306 | int xs = f->edges[e]->dot1->x; |
1307 | int xe = f->edges[e]->dot2->x; |
1308 | int ys = f->edges[e]->dot1->y; |
1309 | int ye = f->edges[e]->dot2->y; |
1310 | |
1311 | /* |
1312 | * If s and e are our endpoints, and p our |
1313 | * candidate circle centre, the foot of a |
1314 | * perpendicular from p to the line se lies |
1315 | * between s and e if and only if (p-s).(e-s) lies |
1316 | * strictly between 0 and (e-s).(e-s). |
1317 | */ |
1318 | int edx = xe - xs, edy = ye - ys; |
1319 | double pdx = x - xs, pdy = y - ys; |
1320 | double pde = pdx * edx + pdy * edy; |
1321 | long ede = (long)edx * edx + (long)edy * edy; |
1322 | if (0 < pde && pde < ede) { |
1323 | /* |
1324 | * Yes, the nearest point on this edge is |
1325 | * closer than either endpoint, so we must |
1326 | * take it into account by measuring the |
1327 | * perpendicular distance to the edge and |
1328 | * checking its square against mindist. |
1329 | */ |
1330 | |
1331 | double pdre = pdx * edy - pdy * edx; |
1332 | double sqlen = pdre * pdre / ede; |
1333 | |
1334 | if (mindist > sqlen) |
1335 | mindist = sqlen; |
1336 | } |
1337 | } |
1338 | |
1339 | /* |
1340 | * Right. Now we know the biggest circle around this |
1341 | * point, so we can check it against bestdist. |
1342 | */ |
1343 | if (bestdist < mindist) { |
1344 | bestdist = mindist; |
1345 | xbest = x; |
1346 | ybest = y; |
1347 | } |
1348 | } |
1349 | } |
1350 | |
1351 | if (k < f->order) |
1352 | nedges--; |
1353 | else |
1354 | ndots--; |
1355 | } |
1356 | if (j < f->order) |
1357 | nedges--; |
1358 | else |
1359 | ndots--; |
1360 | } |
1361 | if (i < f->order) |
1362 | nedges--; |
1363 | else |
1364 | ndots--; |
1365 | } |
1366 | |
1367 | assert(bestdist > 0); |
1368 | |
1369 | f->has_incentre = TRUE; |
1370 | f->ix = xbest + 0.5; /* round to nearest */ |
1371 | f->iy = ybest + 0.5; |
1372 | } |
1373 | |
43a45950 |
1374 | /* Generate the dual to a grid |
1375 | * Returns a new dynamically-allocated grid whose dots are the |
1376 | * faces of the input, and whose faces are the dots of the input. |
1377 | * A few modifications are made: dots on input that have only two |
1378 | * edges are deleted, and the infinite exterior face is also removed |
1379 | * before conversion. |
1380 | */ |
1381 | static grid *grid_dual(grid *g) |
1382 | { |
1383 | grid *new_g; |
ac5deb9c |
1384 | int i, j, k; |
43a45950 |
1385 | tree234* points; |
1386 | |
1387 | new_g = grid_empty(); |
1388 | new_g->tilesize = g->tilesize; |
1389 | new_g->faces = snewn(g->num_dots, grid_face); |
1390 | new_g->dots = snewn(g->num_faces, grid_dot); |
1391 | debug(("taking the dual of a grid with %d faces and %d dots\n", |
1392 | g->num_faces,g->num_dots)); |
1393 | |
1394 | points = newtree234(grid_point_cmp_fn); |
1395 | |
1396 | for (i=0;i<g->num_faces;i++) |
1397 | { |
1398 | grid_find_incentre(&(g->faces[i])); |
1399 | } |
1400 | for (i=0;i<g->num_dots;i++) |
1401 | { |
1402 | int order; |
1403 | grid_dot *d; |
1404 | |
1405 | d = &(g->dots[i]); |
1406 | |
1407 | order = d->order; |
1408 | for (j=0;j<d->order;j++) |
1409 | { |
1410 | if (!d->faces[j]) order--; |
1411 | } |
1412 | if (order>2) |
1413 | { |
1414 | grid_face_add_new(new_g, order); |
ac5deb9c |
1415 | for (j=0,k=0;j<d->order;j++) |
43a45950 |
1416 | { |
1417 | grid_dot *new_d; |
1418 | if (d->faces[j]) |
1419 | { |
1420 | new_d = grid_get_dot(new_g, points, |
1421 | d->faces[j]->ix, d->faces[j]->iy); |
ac5deb9c |
1422 | grid_face_set_dot(new_g, new_d, k++); |
43a45950 |
1423 | } |
1424 | } |
ac5deb9c |
1425 | assert(k==order); |
43a45950 |
1426 | } |
1427 | } |
1428 | |
1429 | freetree234(points); |
1430 | assert(new_g->num_faces <= g->num_dots); |
1431 | assert(new_g->num_dots <= g->num_faces); |
1432 | |
1433 | debug(("dual has %d faces and %d dots\n", |
1434 | new_g->num_faces,new_g->num_dots)); |
1435 | grid_make_consistent(new_g); |
1436 | return new_g; |
1437 | } |
7c95608a |
1438 | /* ------ Generate various types of grid ------ */ |
1439 | |
1440 | /* General method is to generate faces, by calculating their dot coordinates. |
1441 | * As new faces are added, we keep track of all the dots so we can tell when |
1442 | * a new face reuses an existing dot. For example, two squares touching at an |
1443 | * edge would generate six unique dots: four dots from the first face, then |
1444 | * two additional dots for the second face, because we detect the other two |
1445 | * dots have already been taken up. This list is stored in a tree234 |
1446 | * called "points". No extra memory-allocation needed here - we store the |
1447 | * actual grid_dot* pointers, which all point into the g->dots list. |
1448 | * For this reason, we have to calculate coordinates in such a way as to |
1449 | * eliminate any rounding errors, so we can detect when a dot on one |
1450 | * face precisely lands on a dot of a different face. No floating-point |
1451 | * arithmetic here! |
1452 | */ |
1453 | |
cebf0b0d |
1454 | #define SQUARE_TILESIZE 20 |
1455 | |
fd66a01d |
1456 | static void grid_size_square(int width, int height, |
cebf0b0d |
1457 | int *tilesize, int *xextent, int *yextent) |
1458 | { |
1459 | int a = SQUARE_TILESIZE; |
1460 | |
1461 | *tilesize = a; |
1462 | *xextent = width * a; |
1463 | *yextent = height * a; |
1464 | } |
1465 | |
fd66a01d |
1466 | static grid *grid_new_square(int width, int height, char *desc) |
7c95608a |
1467 | { |
1468 | int x, y; |
1469 | /* Side length */ |
cebf0b0d |
1470 | int a = SQUARE_TILESIZE; |
7c95608a |
1471 | |
1472 | /* Upper bounds - don't have to be exact */ |
1473 | int max_faces = width * height; |
1474 | int max_dots = (width + 1) * (height + 1); |
1475 | |
1476 | tree234 *points; |
1477 | |
cebf0b0d |
1478 | grid *g = grid_empty(); |
7c95608a |
1479 | g->tilesize = a; |
1480 | g->faces = snewn(max_faces, grid_face); |
1481 | g->dots = snewn(max_dots, grid_dot); |
1482 | |
1483 | points = newtree234(grid_point_cmp_fn); |
1484 | |
1485 | /* generate square faces */ |
1486 | for (y = 0; y < height; y++) { |
1487 | for (x = 0; x < width; x++) { |
1488 | grid_dot *d; |
1489 | /* face position */ |
1490 | int px = a * x; |
1491 | int py = a * y; |
1492 | |
1493 | grid_face_add_new(g, 4); |
1494 | d = grid_get_dot(g, points, px, py); |
1495 | grid_face_set_dot(g, d, 0); |
1496 | d = grid_get_dot(g, points, px + a, py); |
1497 | grid_face_set_dot(g, d, 1); |
1498 | d = grid_get_dot(g, points, px + a, py + a); |
1499 | grid_face_set_dot(g, d, 2); |
1500 | d = grid_get_dot(g, points, px, py + a); |
1501 | grid_face_set_dot(g, d, 3); |
1502 | } |
1503 | } |
1504 | |
1505 | freetree234(points); |
1506 | assert(g->num_faces <= max_faces); |
1507 | assert(g->num_dots <= max_dots); |
7c95608a |
1508 | |
1509 | grid_make_consistent(g); |
1510 | return g; |
1511 | } |
1512 | |
cebf0b0d |
1513 | #define HONEY_TILESIZE 45 |
1514 | /* Vector for side of hexagon - ratio is close to sqrt(3) */ |
1515 | #define HONEY_A 15 |
1516 | #define HONEY_B 26 |
1517 | |
fd66a01d |
1518 | static void grid_size_honeycomb(int width, int height, |
cebf0b0d |
1519 | int *tilesize, int *xextent, int *yextent) |
1520 | { |
1521 | int a = HONEY_A; |
1522 | int b = HONEY_B; |
1523 | |
1524 | *tilesize = HONEY_TILESIZE; |
1525 | *xextent = (3 * a * (width-1)) + 4*a; |
1526 | *yextent = (2 * b * (height-1)) + 3*b; |
1527 | } |
1528 | |
fd66a01d |
1529 | static grid *grid_new_honeycomb(int width, int height, char *desc) |
7c95608a |
1530 | { |
1531 | int x, y; |
cebf0b0d |
1532 | int a = HONEY_A; |
1533 | int b = HONEY_B; |
7c95608a |
1534 | |
1535 | /* Upper bounds - don't have to be exact */ |
1536 | int max_faces = width * height; |
1537 | int max_dots = 2 * (width + 1) * (height + 1); |
cebf0b0d |
1538 | |
7c95608a |
1539 | tree234 *points; |
1540 | |
cebf0b0d |
1541 | grid *g = grid_empty(); |
1542 | g->tilesize = HONEY_TILESIZE; |
7c95608a |
1543 | g->faces = snewn(max_faces, grid_face); |
1544 | g->dots = snewn(max_dots, grid_dot); |
1545 | |
1546 | points = newtree234(grid_point_cmp_fn); |
1547 | |
1548 | /* generate hexagonal faces */ |
1549 | for (y = 0; y < height; y++) { |
1550 | for (x = 0; x < width; x++) { |
1551 | grid_dot *d; |
1552 | /* face centre */ |
1553 | int cx = 3 * a * x; |
1554 | int cy = 2 * b * y; |
1555 | if (x % 2) |
1556 | cy += b; |
1557 | grid_face_add_new(g, 6); |
1558 | |
1559 | d = grid_get_dot(g, points, cx - a, cy - b); |
1560 | grid_face_set_dot(g, d, 0); |
1561 | d = grid_get_dot(g, points, cx + a, cy - b); |
1562 | grid_face_set_dot(g, d, 1); |
1563 | d = grid_get_dot(g, points, cx + 2*a, cy); |
1564 | grid_face_set_dot(g, d, 2); |
1565 | d = grid_get_dot(g, points, cx + a, cy + b); |
1566 | grid_face_set_dot(g, d, 3); |
1567 | d = grid_get_dot(g, points, cx - a, cy + b); |
1568 | grid_face_set_dot(g, d, 4); |
1569 | d = grid_get_dot(g, points, cx - 2*a, cy); |
1570 | grid_face_set_dot(g, d, 5); |
1571 | } |
1572 | } |
1573 | |
1574 | freetree234(points); |
1575 | assert(g->num_faces <= max_faces); |
1576 | assert(g->num_dots <= max_dots); |
7c95608a |
1577 | |
1578 | grid_make_consistent(g); |
1579 | return g; |
1580 | } |
1581 | |
cebf0b0d |
1582 | #define TRIANGLE_TILESIZE 18 |
1583 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
1584 | #define TRIANGLE_VEC_X 15 |
1585 | #define TRIANGLE_VEC_Y 26 |
1586 | |
fd66a01d |
1587 | static void grid_size_triangular(int width, int height, |
cebf0b0d |
1588 | int *tilesize, int *xextent, int *yextent) |
1589 | { |
1590 | int vec_x = TRIANGLE_VEC_X; |
1591 | int vec_y = TRIANGLE_VEC_Y; |
1592 | |
1593 | *tilesize = TRIANGLE_TILESIZE; |
1594 | *xextent = width * 2 * vec_x + vec_x; |
1595 | *yextent = height * vec_y; |
1596 | } |
1597 | |
7c95608a |
1598 | /* Doesn't use the previous method of generation, it pre-dates it! |
1599 | * A triangular grid is just about simple enough to do by "brute force" */ |
fd66a01d |
1600 | static grid *grid_new_triangular(int width, int height, char *desc) |
7c95608a |
1601 | { |
1602 | int x,y; |
1603 | |
1604 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
cebf0b0d |
1605 | int vec_x = TRIANGLE_VEC_X; |
1606 | int vec_y = TRIANGLE_VEC_Y; |
7c95608a |
1607 | |
1608 | int index; |
1609 | |
1610 | /* convenient alias */ |
1611 | int w = width + 1; |
1612 | |
cebf0b0d |
1613 | grid *g = grid_empty(); |
1614 | g->tilesize = TRIANGLE_TILESIZE; |
7c95608a |
1615 | |
1616 | g->num_faces = width * height * 2; |
1617 | g->num_dots = (width + 1) * (height + 1); |
1618 | g->faces = snewn(g->num_faces, grid_face); |
1619 | g->dots = snewn(g->num_dots, grid_dot); |
1620 | |
1621 | /* generate dots */ |
1622 | index = 0; |
1623 | for (y = 0; y <= height; y++) { |
1624 | for (x = 0; x <= width; x++) { |
1625 | grid_dot *d = g->dots + index; |
1626 | /* odd rows are offset to the right */ |
1627 | d->order = 0; |
1628 | d->edges = NULL; |
1629 | d->faces = NULL; |
1630 | d->x = x * 2 * vec_x + ((y % 2) ? vec_x : 0); |
1631 | d->y = y * vec_y; |
1632 | index++; |
1633 | } |
1634 | } |
1635 | |
1636 | /* generate faces */ |
1637 | index = 0; |
1638 | for (y = 0; y < height; y++) { |
1639 | for (x = 0; x < width; x++) { |
1640 | /* initialise two faces for this (x,y) */ |
1641 | grid_face *f1 = g->faces + index; |
1642 | grid_face *f2 = f1 + 1; |
1643 | f1->edges = NULL; |
1644 | f1->order = 3; |
1645 | f1->dots = snewn(f1->order, grid_dot*); |
18eb897f |
1646 | f1->has_incentre = FALSE; |
7c95608a |
1647 | f2->edges = NULL; |
1648 | f2->order = 3; |
1649 | f2->dots = snewn(f2->order, grid_dot*); |
18eb897f |
1650 | f2->has_incentre = FALSE; |
7c95608a |
1651 | |
1652 | /* face descriptions depend on whether the row-number is |
1653 | * odd or even */ |
1654 | if (y % 2) { |
1655 | f1->dots[0] = g->dots + y * w + x; |
1656 | f1->dots[1] = g->dots + (y + 1) * w + x + 1; |
1657 | f1->dots[2] = g->dots + (y + 1) * w + x; |
1658 | f2->dots[0] = g->dots + y * w + x; |
1659 | f2->dots[1] = g->dots + y * w + x + 1; |
1660 | f2->dots[2] = g->dots + (y + 1) * w + x + 1; |
1661 | } else { |
1662 | f1->dots[0] = g->dots + y * w + x; |
1663 | f1->dots[1] = g->dots + y * w + x + 1; |
1664 | f1->dots[2] = g->dots + (y + 1) * w + x; |
1665 | f2->dots[0] = g->dots + y * w + x + 1; |
1666 | f2->dots[1] = g->dots + (y + 1) * w + x + 1; |
1667 | f2->dots[2] = g->dots + (y + 1) * w + x; |
1668 | } |
1669 | index += 2; |
1670 | } |
1671 | } |
1672 | |
7c95608a |
1673 | grid_make_consistent(g); |
1674 | return g; |
1675 | } |
1676 | |
cebf0b0d |
1677 | #define SNUBSQUARE_TILESIZE 18 |
1678 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
1679 | #define SNUBSQUARE_A 15 |
1680 | #define SNUBSQUARE_B 26 |
1681 | |
fd66a01d |
1682 | static void grid_size_snubsquare(int width, int height, |
cebf0b0d |
1683 | int *tilesize, int *xextent, int *yextent) |
1684 | { |
1685 | int a = SNUBSQUARE_A; |
1686 | int b = SNUBSQUARE_B; |
1687 | |
1688 | *tilesize = SNUBSQUARE_TILESIZE; |
1689 | *xextent = (a+b) * (width-1) + a + b; |
1690 | *yextent = (a+b) * (height-1) + a + b; |
1691 | } |
1692 | |
fd66a01d |
1693 | static grid *grid_new_snubsquare(int width, int height, char *desc) |
7c95608a |
1694 | { |
1695 | int x, y; |
cebf0b0d |
1696 | int a = SNUBSQUARE_A; |
1697 | int b = SNUBSQUARE_B; |
7c95608a |
1698 | |
1699 | /* Upper bounds - don't have to be exact */ |
1700 | int max_faces = 3 * width * height; |
1701 | int max_dots = 2 * (width + 1) * (height + 1); |
cebf0b0d |
1702 | |
7c95608a |
1703 | tree234 *points; |
1704 | |
cebf0b0d |
1705 | grid *g = grid_empty(); |
1706 | g->tilesize = SNUBSQUARE_TILESIZE; |
7c95608a |
1707 | g->faces = snewn(max_faces, grid_face); |
1708 | g->dots = snewn(max_dots, grid_dot); |
1709 | |
1710 | points = newtree234(grid_point_cmp_fn); |
1711 | |
1712 | for (y = 0; y < height; y++) { |
1713 | for (x = 0; x < width; x++) { |
1714 | grid_dot *d; |
1715 | /* face position */ |
1716 | int px = (a + b) * x; |
1717 | int py = (a + b) * y; |
1718 | |
1719 | /* generate square faces */ |
1720 | grid_face_add_new(g, 4); |
1721 | if ((x + y) % 2) { |
1722 | d = grid_get_dot(g, points, px + a, py); |
1723 | grid_face_set_dot(g, d, 0); |
1724 | d = grid_get_dot(g, points, px + a + b, py + a); |
1725 | grid_face_set_dot(g, d, 1); |
1726 | d = grid_get_dot(g, points, px + b, py + a + b); |
1727 | grid_face_set_dot(g, d, 2); |
1728 | d = grid_get_dot(g, points, px, py + b); |
1729 | grid_face_set_dot(g, d, 3); |
1730 | } else { |
1731 | d = grid_get_dot(g, points, px + b, py); |
1732 | grid_face_set_dot(g, d, 0); |
1733 | d = grid_get_dot(g, points, px + a + b, py + b); |
1734 | grid_face_set_dot(g, d, 1); |
1735 | d = grid_get_dot(g, points, px + a, py + a + b); |
1736 | grid_face_set_dot(g, d, 2); |
1737 | d = grid_get_dot(g, points, px, py + a); |
1738 | grid_face_set_dot(g, d, 3); |
1739 | } |
1740 | |
1741 | /* generate up/down triangles */ |
1742 | if (x > 0) { |
1743 | grid_face_add_new(g, 3); |
1744 | if ((x + y) % 2) { |
1745 | d = grid_get_dot(g, points, px + a, py); |
1746 | grid_face_set_dot(g, d, 0); |
1747 | d = grid_get_dot(g, points, px, py + b); |
1748 | grid_face_set_dot(g, d, 1); |
1749 | d = grid_get_dot(g, points, px - a, py); |
1750 | grid_face_set_dot(g, d, 2); |
1751 | } else { |
1752 | d = grid_get_dot(g, points, px, py + a); |
1753 | grid_face_set_dot(g, d, 0); |
1754 | d = grid_get_dot(g, points, px + a, py + a + b); |
1755 | grid_face_set_dot(g, d, 1); |
1756 | d = grid_get_dot(g, points, px - a, py + a + b); |
1757 | grid_face_set_dot(g, d, 2); |
1758 | } |
1759 | } |
1760 | |
1761 | /* generate left/right triangles */ |
1762 | if (y > 0) { |
1763 | grid_face_add_new(g, 3); |
1764 | if ((x + y) % 2) { |
1765 | d = grid_get_dot(g, points, px + a, py); |
1766 | grid_face_set_dot(g, d, 0); |
1767 | d = grid_get_dot(g, points, px + a + b, py - a); |
1768 | grid_face_set_dot(g, d, 1); |
1769 | d = grid_get_dot(g, points, px + a + b, py + a); |
1770 | grid_face_set_dot(g, d, 2); |
1771 | } else { |
1772 | d = grid_get_dot(g, points, px, py - a); |
1773 | grid_face_set_dot(g, d, 0); |
1774 | d = grid_get_dot(g, points, px + b, py); |
1775 | grid_face_set_dot(g, d, 1); |
1776 | d = grid_get_dot(g, points, px, py + a); |
1777 | grid_face_set_dot(g, d, 2); |
1778 | } |
1779 | } |
1780 | } |
1781 | } |
1782 | |
1783 | freetree234(points); |
1784 | assert(g->num_faces <= max_faces); |
1785 | assert(g->num_dots <= max_dots); |
7c95608a |
1786 | |
1787 | grid_make_consistent(g); |
1788 | return g; |
1789 | } |
1790 | |
cebf0b0d |
1791 | #define CAIRO_TILESIZE 40 |
1792 | /* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */ |
1793 | #define CAIRO_A 14 |
1794 | #define CAIRO_B 31 |
1795 | |
fd66a01d |
1796 | static void grid_size_cairo(int width, int height, |
cebf0b0d |
1797 | int *tilesize, int *xextent, int *yextent) |
1798 | { |
1799 | int b = CAIRO_B; /* a unused in determining grid size. */ |
1800 | |
1801 | *tilesize = CAIRO_TILESIZE; |
1802 | *xextent = 2*b*(width-1) + 2*b; |
1803 | *yextent = 2*b*(height-1) + 2*b; |
1804 | } |
1805 | |
fd66a01d |
1806 | static grid *grid_new_cairo(int width, int height, char *desc) |
7c95608a |
1807 | { |
1808 | int x, y; |
cebf0b0d |
1809 | int a = CAIRO_A; |
1810 | int b = CAIRO_B; |
7c95608a |
1811 | |
1812 | /* Upper bounds - don't have to be exact */ |
1813 | int max_faces = 2 * width * height; |
1814 | int max_dots = 3 * (width + 1) * (height + 1); |
cebf0b0d |
1815 | |
7c95608a |
1816 | tree234 *points; |
1817 | |
cebf0b0d |
1818 | grid *g = grid_empty(); |
1819 | g->tilesize = CAIRO_TILESIZE; |
7c95608a |
1820 | g->faces = snewn(max_faces, grid_face); |
1821 | g->dots = snewn(max_dots, grid_dot); |
1822 | |
1823 | points = newtree234(grid_point_cmp_fn); |
1824 | |
1825 | for (y = 0; y < height; y++) { |
1826 | for (x = 0; x < width; x++) { |
1827 | grid_dot *d; |
1828 | /* cell position */ |
1829 | int px = 2 * b * x; |
1830 | int py = 2 * b * y; |
1831 | |
1832 | /* horizontal pentagons */ |
1833 | if (y > 0) { |
1834 | grid_face_add_new(g, 5); |
1835 | if ((x + y) % 2) { |
1836 | d = grid_get_dot(g, points, px + a, py - b); |
1837 | grid_face_set_dot(g, d, 0); |
1838 | d = grid_get_dot(g, points, px + 2*b - a, py - b); |
1839 | grid_face_set_dot(g, d, 1); |
1840 | d = grid_get_dot(g, points, px + 2*b, py); |
1841 | grid_face_set_dot(g, d, 2); |
1842 | d = grid_get_dot(g, points, px + b, py + a); |
1843 | grid_face_set_dot(g, d, 3); |
1844 | d = grid_get_dot(g, points, px, py); |
1845 | grid_face_set_dot(g, d, 4); |
1846 | } else { |
1847 | d = grid_get_dot(g, points, px, py); |
1848 | grid_face_set_dot(g, d, 0); |
1849 | d = grid_get_dot(g, points, px + b, py - a); |
1850 | grid_face_set_dot(g, d, 1); |
1851 | d = grid_get_dot(g, points, px + 2*b, py); |
1852 | grid_face_set_dot(g, d, 2); |
1853 | d = grid_get_dot(g, points, px + 2*b - a, py + b); |
1854 | grid_face_set_dot(g, d, 3); |
1855 | d = grid_get_dot(g, points, px + a, py + b); |
1856 | grid_face_set_dot(g, d, 4); |
1857 | } |
1858 | } |
1859 | /* vertical pentagons */ |
1860 | if (x > 0) { |
1861 | grid_face_add_new(g, 5); |
1862 | if ((x + y) % 2) { |
1863 | d = grid_get_dot(g, points, px, py); |
1864 | grid_face_set_dot(g, d, 0); |
1865 | d = grid_get_dot(g, points, px + b, py + a); |
1866 | grid_face_set_dot(g, d, 1); |
1867 | d = grid_get_dot(g, points, px + b, py + 2*b - a); |
1868 | grid_face_set_dot(g, d, 2); |
1869 | d = grid_get_dot(g, points, px, py + 2*b); |
1870 | grid_face_set_dot(g, d, 3); |
1871 | d = grid_get_dot(g, points, px - a, py + b); |
1872 | grid_face_set_dot(g, d, 4); |
1873 | } else { |
1874 | d = grid_get_dot(g, points, px, py); |
1875 | grid_face_set_dot(g, d, 0); |
1876 | d = grid_get_dot(g, points, px + a, py + b); |
1877 | grid_face_set_dot(g, d, 1); |
1878 | d = grid_get_dot(g, points, px, py + 2*b); |
1879 | grid_face_set_dot(g, d, 2); |
1880 | d = grid_get_dot(g, points, px - b, py + 2*b - a); |
1881 | grid_face_set_dot(g, d, 3); |
1882 | d = grid_get_dot(g, points, px - b, py + a); |
1883 | grid_face_set_dot(g, d, 4); |
1884 | } |
1885 | } |
1886 | } |
1887 | } |
1888 | |
1889 | freetree234(points); |
1890 | assert(g->num_faces <= max_faces); |
1891 | assert(g->num_dots <= max_dots); |
7c95608a |
1892 | |
1893 | grid_make_consistent(g); |
1894 | return g; |
1895 | } |
1896 | |
cebf0b0d |
1897 | #define GREATHEX_TILESIZE 18 |
1898 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
1899 | #define GREATHEX_A 15 |
1900 | #define GREATHEX_B 26 |
1901 | |
fd66a01d |
1902 | static void grid_size_greathexagonal(int width, int height, |
cebf0b0d |
1903 | int *tilesize, int *xextent, int *yextent) |
1904 | { |
1905 | int a = GREATHEX_A; |
1906 | int b = GREATHEX_B; |
1907 | |
1908 | *tilesize = GREATHEX_TILESIZE; |
1909 | *xextent = (3*a + b) * (width-1) + 4*a; |
1910 | *yextent = (2*a + 2*b) * (height-1) + 3*b + a; |
1911 | } |
1912 | |
fd66a01d |
1913 | static grid *grid_new_greathexagonal(int width, int height, char *desc) |
7c95608a |
1914 | { |
1915 | int x, y; |
cebf0b0d |
1916 | int a = GREATHEX_A; |
1917 | int b = GREATHEX_B; |
7c95608a |
1918 | |
1919 | /* Upper bounds - don't have to be exact */ |
1920 | int max_faces = 6 * (width + 1) * (height + 1); |
1921 | int max_dots = 6 * width * height; |
1922 | |
1923 | tree234 *points; |
1924 | |
cebf0b0d |
1925 | grid *g = grid_empty(); |
1926 | g->tilesize = GREATHEX_TILESIZE; |
7c95608a |
1927 | g->faces = snewn(max_faces, grid_face); |
1928 | g->dots = snewn(max_dots, grid_dot); |
1929 | |
1930 | points = newtree234(grid_point_cmp_fn); |
1931 | |
1932 | for (y = 0; y < height; y++) { |
1933 | for (x = 0; x < width; x++) { |
1934 | grid_dot *d; |
1935 | /* centre of hexagon */ |
1936 | int px = (3*a + b) * x; |
1937 | int py = (2*a + 2*b) * y; |
1938 | if (x % 2) |
1939 | py += a + b; |
1940 | |
1941 | /* hexagon */ |
1942 | grid_face_add_new(g, 6); |
1943 | d = grid_get_dot(g, points, px - a, py - b); |
1944 | grid_face_set_dot(g, d, 0); |
1945 | d = grid_get_dot(g, points, px + a, py - b); |
1946 | grid_face_set_dot(g, d, 1); |
1947 | d = grid_get_dot(g, points, px + 2*a, py); |
1948 | grid_face_set_dot(g, d, 2); |
1949 | d = grid_get_dot(g, points, px + a, py + b); |
1950 | grid_face_set_dot(g, d, 3); |
1951 | d = grid_get_dot(g, points, px - a, py + b); |
1952 | grid_face_set_dot(g, d, 4); |
1953 | d = grid_get_dot(g, points, px - 2*a, py); |
1954 | grid_face_set_dot(g, d, 5); |
1955 | |
1956 | /* square below hexagon */ |
1957 | if (y < height - 1) { |
1958 | grid_face_add_new(g, 4); |
1959 | d = grid_get_dot(g, points, px - a, py + b); |
1960 | grid_face_set_dot(g, d, 0); |
1961 | d = grid_get_dot(g, points, px + a, py + b); |
1962 | grid_face_set_dot(g, d, 1); |
1963 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
1964 | grid_face_set_dot(g, d, 2); |
1965 | d = grid_get_dot(g, points, px - a, py + 2*a + b); |
1966 | grid_face_set_dot(g, d, 3); |
1967 | } |
1968 | |
1969 | /* square below right */ |
1970 | if ((x < width - 1) && (((x % 2) == 0) || (y < height - 1))) { |
1971 | grid_face_add_new(g, 4); |
1972 | d = grid_get_dot(g, points, px + 2*a, py); |
1973 | grid_face_set_dot(g, d, 0); |
1974 | d = grid_get_dot(g, points, px + 2*a + b, py + a); |
1975 | grid_face_set_dot(g, d, 1); |
1976 | d = grid_get_dot(g, points, px + a + b, py + a + b); |
1977 | grid_face_set_dot(g, d, 2); |
1978 | d = grid_get_dot(g, points, px + a, py + b); |
1979 | grid_face_set_dot(g, d, 3); |
1980 | } |
1981 | |
1982 | /* square below left */ |
1983 | if ((x > 0) && (((x % 2) == 0) || (y < height - 1))) { |
1984 | grid_face_add_new(g, 4); |
1985 | d = grid_get_dot(g, points, px - 2*a, py); |
1986 | grid_face_set_dot(g, d, 0); |
1987 | d = grid_get_dot(g, points, px - a, py + b); |
1988 | grid_face_set_dot(g, d, 1); |
1989 | d = grid_get_dot(g, points, px - a - b, py + a + b); |
1990 | grid_face_set_dot(g, d, 2); |
1991 | d = grid_get_dot(g, points, px - 2*a - b, py + a); |
1992 | grid_face_set_dot(g, d, 3); |
1993 | } |
1994 | |
1995 | /* Triangle below right */ |
1996 | if ((x < width - 1) && (y < height - 1)) { |
1997 | grid_face_add_new(g, 3); |
1998 | d = grid_get_dot(g, points, px + a, py + b); |
1999 | grid_face_set_dot(g, d, 0); |
2000 | d = grid_get_dot(g, points, px + a + b, py + a + b); |
2001 | grid_face_set_dot(g, d, 1); |
2002 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
2003 | grid_face_set_dot(g, d, 2); |
2004 | } |
2005 | |
2006 | /* Triangle below left */ |
2007 | if ((x > 0) && (y < height - 1)) { |
2008 | grid_face_add_new(g, 3); |
2009 | d = grid_get_dot(g, points, px - a, py + b); |
2010 | grid_face_set_dot(g, d, 0); |
2011 | d = grid_get_dot(g, points, px - a, py + 2*a + b); |
2012 | grid_face_set_dot(g, d, 1); |
2013 | d = grid_get_dot(g, points, px - a - b, py + a + b); |
2014 | grid_face_set_dot(g, d, 2); |
2015 | } |
2016 | } |
2017 | } |
2018 | |
2019 | freetree234(points); |
2020 | assert(g->num_faces <= max_faces); |
2021 | assert(g->num_dots <= max_dots); |
7c95608a |
2022 | |
2023 | grid_make_consistent(g); |
2024 | return g; |
2025 | } |
cebf0b0d |
2026 | #define OCTAGONAL_TILESIZE 40 |
2027 | /* b/a approx sqrt(2) */ |
2028 | #define OCTAGONAL_A 29 |
2029 | #define OCTAGONAL_B 41 |
2030 | |
fd66a01d |
2031 | static void grid_size_octagonal(int width, int height, |
cebf0b0d |
2032 | int *tilesize, int *xextent, int *yextent) |
2033 | { |
2034 | int a = OCTAGONAL_A; |
2035 | int b = OCTAGONAL_B; |
2036 | |
2037 | *tilesize = OCTAGONAL_TILESIZE; |
2038 | *xextent = (2*a + b) * width; |
2039 | *yextent = (2*a + b) * height; |
2040 | } |
2041 | |
fd66a01d |
2042 | static grid *grid_new_octagonal(int width, int height, char *desc) |
7c95608a |
2043 | { |
2044 | int x, y; |
cebf0b0d |
2045 | int a = OCTAGONAL_A; |
2046 | int b = OCTAGONAL_B; |
7c95608a |
2047 | |
2048 | /* Upper bounds - don't have to be exact */ |
2049 | int max_faces = 2 * width * height; |
2050 | int max_dots = 4 * (width + 1) * (height + 1); |
2051 | |
2052 | tree234 *points; |
2053 | |
cebf0b0d |
2054 | grid *g = grid_empty(); |
2055 | g->tilesize = OCTAGONAL_TILESIZE; |
7c95608a |
2056 | g->faces = snewn(max_faces, grid_face); |
2057 | g->dots = snewn(max_dots, grid_dot); |
2058 | |
2059 | points = newtree234(grid_point_cmp_fn); |
2060 | |
2061 | for (y = 0; y < height; y++) { |
2062 | for (x = 0; x < width; x++) { |
2063 | grid_dot *d; |
2064 | /* cell position */ |
2065 | int px = (2*a + b) * x; |
2066 | int py = (2*a + b) * y; |
2067 | /* octagon */ |
2068 | grid_face_add_new(g, 8); |
2069 | d = grid_get_dot(g, points, px + a, py); |
2070 | grid_face_set_dot(g, d, 0); |
2071 | d = grid_get_dot(g, points, px + a + b, py); |
2072 | grid_face_set_dot(g, d, 1); |
2073 | d = grid_get_dot(g, points, px + 2*a + b, py + a); |
2074 | grid_face_set_dot(g, d, 2); |
2075 | d = grid_get_dot(g, points, px + 2*a + b, py + a + b); |
2076 | grid_face_set_dot(g, d, 3); |
2077 | d = grid_get_dot(g, points, px + a + b, py + 2*a + b); |
2078 | grid_face_set_dot(g, d, 4); |
2079 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
2080 | grid_face_set_dot(g, d, 5); |
2081 | d = grid_get_dot(g, points, px, py + a + b); |
2082 | grid_face_set_dot(g, d, 6); |
2083 | d = grid_get_dot(g, points, px, py + a); |
2084 | grid_face_set_dot(g, d, 7); |
2085 | |
2086 | /* diamond */ |
2087 | if ((x > 0) && (y > 0)) { |
2088 | grid_face_add_new(g, 4); |
2089 | d = grid_get_dot(g, points, px, py - a); |
2090 | grid_face_set_dot(g, d, 0); |
2091 | d = grid_get_dot(g, points, px + a, py); |
2092 | grid_face_set_dot(g, d, 1); |
2093 | d = grid_get_dot(g, points, px, py + a); |
2094 | grid_face_set_dot(g, d, 2); |
2095 | d = grid_get_dot(g, points, px - a, py); |
2096 | grid_face_set_dot(g, d, 3); |
2097 | } |
2098 | } |
2099 | } |
2100 | |
2101 | freetree234(points); |
2102 | assert(g->num_faces <= max_faces); |
2103 | assert(g->num_dots <= max_dots); |
7c95608a |
2104 | |
2105 | grid_make_consistent(g); |
2106 | return g; |
2107 | } |
2108 | |
cebf0b0d |
2109 | #define KITE_TILESIZE 40 |
2110 | /* b/a approx sqrt(3) */ |
2111 | #define KITE_A 15 |
2112 | #define KITE_B 26 |
2113 | |
fd66a01d |
2114 | static void grid_size_kites(int width, int height, |
cebf0b0d |
2115 | int *tilesize, int *xextent, int *yextent) |
2116 | { |
2117 | int a = KITE_A; |
2118 | int b = KITE_B; |
2119 | |
2120 | *tilesize = KITE_TILESIZE; |
2121 | *xextent = 4*b * width + 2*b; |
2122 | *yextent = 6*a * (height-1) + 8*a; |
2123 | } |
2124 | |
fd66a01d |
2125 | static grid *grid_new_kites(int width, int height, char *desc) |
7c95608a |
2126 | { |
2127 | int x, y; |
cebf0b0d |
2128 | int a = KITE_A; |
2129 | int b = KITE_B; |
7c95608a |
2130 | |
2131 | /* Upper bounds - don't have to be exact */ |
2132 | int max_faces = 6 * width * height; |
2133 | int max_dots = 6 * (width + 1) * (height + 1); |
2134 | |
2135 | tree234 *points; |
2136 | |
cebf0b0d |
2137 | grid *g = grid_empty(); |
2138 | g->tilesize = KITE_TILESIZE; |
7c95608a |
2139 | g->faces = snewn(max_faces, grid_face); |
2140 | g->dots = snewn(max_dots, grid_dot); |
2141 | |
2142 | points = newtree234(grid_point_cmp_fn); |
2143 | |
2144 | for (y = 0; y < height; y++) { |
2145 | for (x = 0; x < width; x++) { |
2146 | grid_dot *d; |
2147 | /* position of order-6 dot */ |
2148 | int px = 4*b * x; |
2149 | int py = 6*a * y; |
2150 | if (y % 2) |
2151 | px += 2*b; |
2152 | |
2153 | /* kite pointing up-left */ |
2154 | grid_face_add_new(g, 4); |
2155 | d = grid_get_dot(g, points, px, py); |
2156 | grid_face_set_dot(g, d, 0); |
2157 | d = grid_get_dot(g, points, px + 2*b, py); |
2158 | grid_face_set_dot(g, d, 1); |
2159 | d = grid_get_dot(g, points, px + 2*b, py + 2*a); |
2160 | grid_face_set_dot(g, d, 2); |
2161 | d = grid_get_dot(g, points, px + b, py + 3*a); |
2162 | grid_face_set_dot(g, d, 3); |
2163 | |
2164 | /* kite pointing up */ |
2165 | grid_face_add_new(g, 4); |
2166 | d = grid_get_dot(g, points, px, py); |
2167 | grid_face_set_dot(g, d, 0); |
2168 | d = grid_get_dot(g, points, px + b, py + 3*a); |
2169 | grid_face_set_dot(g, d, 1); |
2170 | d = grid_get_dot(g, points, px, py + 4*a); |
2171 | grid_face_set_dot(g, d, 2); |
2172 | d = grid_get_dot(g, points, px - b, py + 3*a); |
2173 | grid_face_set_dot(g, d, 3); |
2174 | |
2175 | /* kite pointing up-right */ |
2176 | grid_face_add_new(g, 4); |
2177 | d = grid_get_dot(g, points, px, py); |
2178 | grid_face_set_dot(g, d, 0); |
2179 | d = grid_get_dot(g, points, px - b, py + 3*a); |
2180 | grid_face_set_dot(g, d, 1); |
2181 | d = grid_get_dot(g, points, px - 2*b, py + 2*a); |
2182 | grid_face_set_dot(g, d, 2); |
2183 | d = grid_get_dot(g, points, px - 2*b, py); |
2184 | grid_face_set_dot(g, d, 3); |
2185 | |
2186 | /* kite pointing down-right */ |
2187 | grid_face_add_new(g, 4); |
2188 | d = grid_get_dot(g, points, px, py); |
2189 | grid_face_set_dot(g, d, 0); |
2190 | d = grid_get_dot(g, points, px - 2*b, py); |
2191 | grid_face_set_dot(g, d, 1); |
2192 | d = grid_get_dot(g, points, px - 2*b, py - 2*a); |
2193 | grid_face_set_dot(g, d, 2); |
2194 | d = grid_get_dot(g, points, px - b, py - 3*a); |
2195 | grid_face_set_dot(g, d, 3); |
2196 | |
2197 | /* kite pointing down */ |
2198 | grid_face_add_new(g, 4); |
2199 | d = grid_get_dot(g, points, px, py); |
2200 | grid_face_set_dot(g, d, 0); |
2201 | d = grid_get_dot(g, points, px - b, py - 3*a); |
2202 | grid_face_set_dot(g, d, 1); |
2203 | d = grid_get_dot(g, points, px, py - 4*a); |
2204 | grid_face_set_dot(g, d, 2); |
2205 | d = grid_get_dot(g, points, px + b, py - 3*a); |
2206 | grid_face_set_dot(g, d, 3); |
2207 | |
2208 | /* kite pointing down-left */ |
2209 | grid_face_add_new(g, 4); |
2210 | d = grid_get_dot(g, points, px, py); |
2211 | grid_face_set_dot(g, d, 0); |
2212 | d = grid_get_dot(g, points, px + b, py - 3*a); |
2213 | grid_face_set_dot(g, d, 1); |
2214 | d = grid_get_dot(g, points, px + 2*b, py - 2*a); |
2215 | grid_face_set_dot(g, d, 2); |
2216 | d = grid_get_dot(g, points, px + 2*b, py); |
2217 | grid_face_set_dot(g, d, 3); |
2218 | } |
2219 | } |
2220 | |
2221 | freetree234(points); |
2222 | assert(g->num_faces <= max_faces); |
2223 | assert(g->num_dots <= max_dots); |
7c95608a |
2224 | |
2225 | grid_make_consistent(g); |
2226 | return g; |
2227 | } |
2228 | |
cebf0b0d |
2229 | #define FLORET_TILESIZE 150 |
2230 | /* -py/px is close to tan(30 - atan(sqrt(3)/9)) |
2231 | * using py=26 makes everything lean to the left, rather than right |
2232 | */ |
2233 | #define FLORET_PX 75 |
2234 | #define FLORET_PY -26 |
2235 | |
fd66a01d |
2236 | static void grid_size_floret(int width, int height, |
cebf0b0d |
2237 | int *tilesize, int *xextent, int *yextent) |
2238 | { |
2239 | int px = FLORET_PX, py = FLORET_PY; /* |( 75, -26)| = 79.43 */ |
2240 | int qx = 4*px/5, qy = -py*2; /* |( 60, 52)| = 79.40 */ |
2241 | int ry = qy-py; |
2242 | /* rx unused in determining grid size. */ |
2243 | |
2244 | *tilesize = FLORET_TILESIZE; |
2245 | *xextent = (6*px+3*qx)/2 * (width-1) + 4*qx + 2*px; |
2246 | *yextent = (5*qy-4*py) * (height-1) + 4*qy + 2*ry; |
2247 | } |
2248 | |
fd66a01d |
2249 | static grid *grid_new_floret(int width, int height, char *desc) |
e30d39f6 |
2250 | { |
2251 | int x, y; |
2252 | /* Vectors for sides; weird numbers needed to keep puzzle aligned with window |
2253 | * -py/px is close to tan(30 - atan(sqrt(3)/9)) |
2254 | * using py=26 makes everything lean to the left, rather than right |
2255 | */ |
cebf0b0d |
2256 | int px = FLORET_PX, py = FLORET_PY; /* |( 75, -26)| = 79.43 */ |
2257 | int qx = 4*px/5, qy = -py*2; /* |( 60, 52)| = 79.40 */ |
2258 | int rx = qx-px, ry = qy-py; /* |(-15, 78)| = 79.38 */ |
e30d39f6 |
2259 | |
2260 | /* Upper bounds - don't have to be exact */ |
2261 | int max_faces = 6 * width * height; |
2262 | int max_dots = 9 * (width + 1) * (height + 1); |
cebf0b0d |
2263 | |
e30d39f6 |
2264 | tree234 *points; |
2265 | |
cebf0b0d |
2266 | grid *g = grid_empty(); |
2267 | g->tilesize = FLORET_TILESIZE; |
e30d39f6 |
2268 | g->faces = snewn(max_faces, grid_face); |
2269 | g->dots = snewn(max_dots, grid_dot); |
2270 | |
2271 | points = newtree234(grid_point_cmp_fn); |
2272 | |
2273 | /* generate pentagonal faces */ |
2274 | for (y = 0; y < height; y++) { |
2275 | for (x = 0; x < width; x++) { |
2276 | grid_dot *d; |
2277 | /* face centre */ |
2278 | int cx = (6*px+3*qx)/2 * x; |
2279 | int cy = (4*py-5*qy) * y; |
2280 | if (x % 2) |
2281 | cy -= (4*py-5*qy)/2; |
2282 | else if (y && y == height-1) |
2283 | continue; /* make better looking grids? try 3x3 for instance */ |
2284 | |
2285 | grid_face_add_new(g, 5); |
2286 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
2287 | d = grid_get_dot(g, points, cx+2*rx , cy+2*ry ); grid_face_set_dot(g, d, 1); |
2288 | d = grid_get_dot(g, points, cx+2*rx+qx, cy+2*ry+qy); grid_face_set_dot(g, d, 2); |
2289 | d = grid_get_dot(g, points, cx+2*qx+rx, cy+2*qy+ry); grid_face_set_dot(g, d, 3); |
2290 | d = grid_get_dot(g, points, cx+2*qx , cy+2*qy ); grid_face_set_dot(g, d, 4); |
2291 | |
2292 | grid_face_add_new(g, 5); |
2293 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
2294 | d = grid_get_dot(g, points, cx+2*qx , cy+2*qy ); grid_face_set_dot(g, d, 1); |
2295 | d = grid_get_dot(g, points, cx+2*qx+px, cy+2*qy+py); grid_face_set_dot(g, d, 2); |
2296 | d = grid_get_dot(g, points, cx+2*px+qx, cy+2*py+qy); grid_face_set_dot(g, d, 3); |
2297 | d = grid_get_dot(g, points, cx+2*px , cy+2*py ); grid_face_set_dot(g, d, 4); |
2298 | |
2299 | grid_face_add_new(g, 5); |
2300 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
2301 | d = grid_get_dot(g, points, cx+2*px , cy+2*py ); grid_face_set_dot(g, d, 1); |
2302 | d = grid_get_dot(g, points, cx+2*px-rx, cy+2*py-ry); grid_face_set_dot(g, d, 2); |
2303 | d = grid_get_dot(g, points, cx-2*rx+px, cy-2*ry+py); grid_face_set_dot(g, d, 3); |
2304 | d = grid_get_dot(g, points, cx-2*rx , cy-2*ry ); grid_face_set_dot(g, d, 4); |
2305 | |
2306 | grid_face_add_new(g, 5); |
2307 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
2308 | d = grid_get_dot(g, points, cx-2*rx , cy-2*ry ); grid_face_set_dot(g, d, 1); |
2309 | d = grid_get_dot(g, points, cx-2*rx-qx, cy-2*ry-qy); grid_face_set_dot(g, d, 2); |
2310 | d = grid_get_dot(g, points, cx-2*qx-rx, cy-2*qy-ry); grid_face_set_dot(g, d, 3); |
2311 | d = grid_get_dot(g, points, cx-2*qx , cy-2*qy ); grid_face_set_dot(g, d, 4); |
2312 | |
2313 | grid_face_add_new(g, 5); |
2314 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
2315 | d = grid_get_dot(g, points, cx-2*qx , cy-2*qy ); grid_face_set_dot(g, d, 1); |
2316 | d = grid_get_dot(g, points, cx-2*qx-px, cy-2*qy-py); grid_face_set_dot(g, d, 2); |
2317 | d = grid_get_dot(g, points, cx-2*px-qx, cy-2*py-qy); grid_face_set_dot(g, d, 3); |
2318 | d = grid_get_dot(g, points, cx-2*px , cy-2*py ); grid_face_set_dot(g, d, 4); |
2319 | |
2320 | grid_face_add_new(g, 5); |
2321 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
2322 | d = grid_get_dot(g, points, cx-2*px , cy-2*py ); grid_face_set_dot(g, d, 1); |
2323 | d = grid_get_dot(g, points, cx-2*px+rx, cy-2*py+ry); grid_face_set_dot(g, d, 2); |
2324 | d = grid_get_dot(g, points, cx+2*rx-px, cy+2*ry-py); grid_face_set_dot(g, d, 3); |
2325 | d = grid_get_dot(g, points, cx+2*rx , cy+2*ry ); grid_face_set_dot(g, d, 4); |
2326 | } |
2327 | } |
2328 | |
2329 | freetree234(points); |
2330 | assert(g->num_faces <= max_faces); |
2331 | assert(g->num_dots <= max_dots); |
e30d39f6 |
2332 | |
2333 | grid_make_consistent(g); |
2334 | return g; |
2335 | } |
2336 | |
cebf0b0d |
2337 | /* DODEC_* are used for dodecagonal and great-dodecagonal grids. */ |
2338 | #define DODEC_TILESIZE 26 |
2339 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
2340 | #define DODEC_A 15 |
2341 | #define DODEC_B 26 |
2342 | |
fd66a01d |
2343 | static void grid_size_dodecagonal(int width, int height, |
cebf0b0d |
2344 | int *tilesize, int *xextent, int *yextent) |
2345 | { |
2346 | int a = DODEC_A; |
2347 | int b = DODEC_B; |
2348 | |
2349 | *tilesize = DODEC_TILESIZE; |
2350 | *xextent = (4*a + 2*b) * (width-1) + 3*(2*a + b); |
2351 | *yextent = (3*a + 2*b) * (height-1) + 2*(2*a + b); |
2352 | } |
2353 | |
fd66a01d |
2354 | static grid *grid_new_dodecagonal(int width, int height, char *desc) |
918a098a |
2355 | { |
2356 | int x, y; |
cebf0b0d |
2357 | int a = DODEC_A; |
2358 | int b = DODEC_B; |
918a098a |
2359 | |
2360 | /* Upper bounds - don't have to be exact */ |
2361 | int max_faces = 3 * width * height; |
2362 | int max_dots = 14 * width * height; |
2363 | |
2364 | tree234 *points; |
2365 | |
cebf0b0d |
2366 | grid *g = grid_empty(); |
2367 | g->tilesize = DODEC_TILESIZE; |
918a098a |
2368 | g->faces = snewn(max_faces, grid_face); |
2369 | g->dots = snewn(max_dots, grid_dot); |
2370 | |
2371 | points = newtree234(grid_point_cmp_fn); |
2372 | |
2373 | for (y = 0; y < height; y++) { |
2374 | for (x = 0; x < width; x++) { |
2375 | grid_dot *d; |
2376 | /* centre of dodecagon */ |
2377 | int px = (4*a + 2*b) * x; |
2378 | int py = (3*a + 2*b) * y; |
2379 | if (y % 2) |
2380 | px += 2*a + b; |
2381 | |
2382 | /* dodecagon */ |
2383 | grid_face_add_new(g, 12); |
2384 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); |
2385 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 1); |
2386 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a )); grid_face_set_dot(g, d, 2); |
2387 | d = grid_get_dot(g, points, px + (2*a + b), py + ( a )); grid_face_set_dot(g, d, 3); |
2388 | d = grid_get_dot(g, points, px + ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 4); |
2389 | d = grid_get_dot(g, points, px + ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 5); |
2390 | d = grid_get_dot(g, points, px - ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 6); |
2391 | d = grid_get_dot(g, points, px - ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 7); |
2392 | d = grid_get_dot(g, points, px - (2*a + b), py + ( a )); grid_face_set_dot(g, d, 8); |
2393 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a )); grid_face_set_dot(g, d, 9); |
2394 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 10); |
2395 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 11); |
2396 | |
2397 | /* triangle below dodecagon */ |
2398 | if ((y < height - 1 && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2)))) { |
2399 | grid_face_add_new(g, 3); |
2400 | d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0); |
2401 | d = grid_get_dot(g, points, px , py + (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
2402 | d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 2); |
2403 | } |
2404 | |
2405 | /* triangle above dodecagon */ |
2406 | if ((y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2)))) { |
2407 | grid_face_add_new(g, 3); |
2408 | d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 0); |
2409 | d = grid_get_dot(g, points, px , py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
2410 | d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 2); |
2411 | } |
2412 | } |
2413 | } |
2414 | |
2415 | freetree234(points); |
2416 | assert(g->num_faces <= max_faces); |
2417 | assert(g->num_dots <= max_dots); |
2418 | |
2419 | grid_make_consistent(g); |
2420 | return g; |
2421 | } |
2422 | |
fd66a01d |
2423 | static void grid_size_greatdodecagonal(int width, int height, |
cebf0b0d |
2424 | int *tilesize, int *xextent, int *yextent) |
2425 | { |
2426 | int a = DODEC_A; |
2427 | int b = DODEC_B; |
2428 | |
2429 | *tilesize = DODEC_TILESIZE; |
2430 | *xextent = (6*a + 2*b) * (width-1) + 2*(2*a + b) + 3*a + b; |
2431 | *yextent = (3*a + 3*b) * (height-1) + 2*(2*a + b); |
2432 | } |
2433 | |
fd66a01d |
2434 | static grid *grid_new_greatdodecagonal(int width, int height, char *desc) |
918a098a |
2435 | { |
2436 | int x, y; |
2437 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
cebf0b0d |
2438 | int a = DODEC_A; |
2439 | int b = DODEC_B; |
918a098a |
2440 | |
2441 | /* Upper bounds - don't have to be exact */ |
2442 | int max_faces = 30 * width * height; |
2443 | int max_dots = 200 * width * height; |
2444 | |
2445 | tree234 *points; |
2446 | |
cebf0b0d |
2447 | grid *g = grid_empty(); |
2448 | g->tilesize = DODEC_TILESIZE; |
918a098a |
2449 | g->faces = snewn(max_faces, grid_face); |
2450 | g->dots = snewn(max_dots, grid_dot); |
2451 | |
2452 | points = newtree234(grid_point_cmp_fn); |
2453 | |
2454 | for (y = 0; y < height; y++) { |
2455 | for (x = 0; x < width; x++) { |
2456 | grid_dot *d; |
2457 | /* centre of dodecagon */ |
2458 | int px = (6*a + 2*b) * x; |
2459 | int py = (3*a + 3*b) * y; |
2460 | if (y % 2) |
2461 | px += 3*a + b; |
2462 | |
2463 | /* dodecagon */ |
2464 | grid_face_add_new(g, 12); |
2465 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); |
2466 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 1); |
2467 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a )); grid_face_set_dot(g, d, 2); |
2468 | d = grid_get_dot(g, points, px + (2*a + b), py + ( a )); grid_face_set_dot(g, d, 3); |
2469 | d = grid_get_dot(g, points, px + ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 4); |
2470 | d = grid_get_dot(g, points, px + ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 5); |
2471 | d = grid_get_dot(g, points, px - ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 6); |
2472 | d = grid_get_dot(g, points, px - ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 7); |
2473 | d = grid_get_dot(g, points, px - (2*a + b), py + ( a )); grid_face_set_dot(g, d, 8); |
2474 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a )); grid_face_set_dot(g, d, 9); |
2475 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 10); |
2476 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 11); |
2477 | |
2478 | /* hexagon below dodecagon */ |
2479 | if (y < height - 1 && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) { |
2480 | grid_face_add_new(g, 6); |
2481 | d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0); |
2482 | d = grid_get_dot(g, points, px + 2*a, py + (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
2483 | d = grid_get_dot(g, points, px + a, py + (2*a + 3*b)); grid_face_set_dot(g, d, 2); |
2484 | d = grid_get_dot(g, points, px - a, py + (2*a + 3*b)); grid_face_set_dot(g, d, 3); |
2485 | d = grid_get_dot(g, points, px - 2*a, py + (2*a + 2*b)); grid_face_set_dot(g, d, 4); |
2486 | d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 5); |
2487 | } |
2488 | |
2489 | /* hexagon above dodecagon */ |
2490 | if (y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) { |
2491 | grid_face_add_new(g, 6); |
2492 | d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 0); |
2493 | d = grid_get_dot(g, points, px - 2*a, py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
2494 | d = grid_get_dot(g, points, px - a, py - (2*a + 3*b)); grid_face_set_dot(g, d, 2); |
2495 | d = grid_get_dot(g, points, px + a, py - (2*a + 3*b)); grid_face_set_dot(g, d, 3); |
2496 | d = grid_get_dot(g, points, px + 2*a, py - (2*a + 2*b)); grid_face_set_dot(g, d, 4); |
2497 | d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 5); |
2498 | } |
2499 | |
2500 | /* square on right of dodecagon */ |
2501 | if (x < width - 1) { |
2502 | grid_face_add_new(g, 4); |
2503 | d = grid_get_dot(g, points, px + 2*a + b, py - a); grid_face_set_dot(g, d, 0); |
2504 | d = grid_get_dot(g, points, px + 4*a + b, py - a); grid_face_set_dot(g, d, 1); |
2505 | d = grid_get_dot(g, points, px + 4*a + b, py + a); grid_face_set_dot(g, d, 2); |
2506 | d = grid_get_dot(g, points, px + 2*a + b, py + a); grid_face_set_dot(g, d, 3); |
2507 | } |
2508 | |
2509 | /* square on top right of dodecagon */ |
2510 | if (y && (x < width - 1 || !(y % 2))) { |
2511 | grid_face_add_new(g, 4); |
2512 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); |
2513 | d = grid_get_dot(g, points, px + (2*a ), py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
2514 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a + 2*b)); grid_face_set_dot(g, d, 2); |
2515 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 3); |
2516 | } |
2517 | |
2518 | /* square on top left of dodecagon */ |
2519 | if (y && (x || (y % 2))) { |
2520 | grid_face_add_new(g, 4); |
2521 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 0); |
2522 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a + 2*b)); grid_face_set_dot(g, d, 1); |
2523 | d = grid_get_dot(g, points, px - (2*a ), py - (2*a + 2*b)); grid_face_set_dot(g, d, 2); |
2524 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 3); |
2525 | } |
2526 | } |
2527 | } |
2528 | |
2529 | freetree234(points); |
2530 | assert(g->num_faces <= max_faces); |
2531 | assert(g->num_dots <= max_dots); |
2532 | |
2533 | grid_make_consistent(g); |
2534 | return g; |
2535 | } |
2536 | |
cebf0b0d |
2537 | typedef struct setface_ctx |
2538 | { |
2539 | int xmin, xmax, ymin, ymax; |
cebf0b0d |
2540 | |
2541 | grid *g; |
2542 | tree234 *points; |
2543 | } setface_ctx; |
2544 | |
fd66a01d |
2545 | static double round_int_nearest_away(double r) |
cebf0b0d |
2546 | { |
2547 | return (r > 0.0) ? floor(r + 0.5) : ceil(r - 0.5); |
2548 | } |
2549 | |
fd66a01d |
2550 | static int set_faces(penrose_state *state, vector *vs, int n, int depth) |
cebf0b0d |
2551 | { |
2552 | setface_ctx *sf_ctx = (setface_ctx *)state->ctx; |
2553 | int i; |
2554 | int xs[4], ys[4]; |
cebf0b0d |
2555 | |
2556 | if (depth < state->max_depth) return 0; |
2557 | #ifdef DEBUG_PENROSE |
2558 | if (n != 4) return 0; /* triangles are sent as debugging. */ |
2559 | #endif |
2560 | |
2561 | for (i = 0; i < n; i++) { |
2562 | double tx = v_x(vs, i), ty = v_y(vs, i); |
2563 | |
a15e5ee3 |
2564 | xs[i] = (int)round_int_nearest_away(tx); |
2565 | ys[i] = (int)round_int_nearest_away(ty); |
cebf0b0d |
2566 | |
2567 | if (xs[i] < sf_ctx->xmin || xs[i] > sf_ctx->xmax) return 0; |
2568 | if (ys[i] < sf_ctx->ymin || ys[i] > sf_ctx->ymax) return 0; |
2569 | } |
2570 | |
2571 | grid_face_add_new(sf_ctx->g, n); |
2572 | debug(("penrose: new face l=%f gen=%d...", |
2573 | penrose_side_length(state->start_size, depth), depth)); |
2574 | for (i = 0; i < n; i++) { |
2575 | grid_dot *d = grid_get_dot(sf_ctx->g, sf_ctx->points, |
2576 | xs[i], ys[i]); |
2577 | grid_face_set_dot(sf_ctx->g, d, i); |
2578 | debug((" ... dot 0x%x (%d,%d) (was %2.2f,%2.2f)", |
2579 | d, d->x, d->y, v_x(vs, i), v_y(vs, i))); |
2580 | } |
2581 | |
2582 | return 0; |
2583 | } |
2584 | |
2585 | #define PENROSE_TILESIZE 100 |
2586 | |
fd66a01d |
2587 | static void grid_size_penrose(int width, int height, |
cebf0b0d |
2588 | int *tilesize, int *xextent, int *yextent) |
2589 | { |
2590 | int l = PENROSE_TILESIZE; |
2591 | |
2592 | *tilesize = l; |
2593 | *xextent = l * width; |
2594 | *yextent = l * height; |
2595 | } |
2596 | |
2597 | static char *grid_new_desc_penrose(grid_type type, int width, int height, random_state *rs) |
2598 | { |
2599 | int tilesize = PENROSE_TILESIZE, startsz, depth, xoff, yoff, aoff; |
2600 | double outer_radius; |
2601 | int inner_radius; |
2602 | char gd[255]; |
2603 | int which = (type == GRID_PENROSE_P2 ? PENROSE_P2 : PENROSE_P3); |
2604 | |
2605 | /* We want to produce a random bit of penrose tiling, so we calculate |
2606 | * a random offset (within the patch that penrose.c calculates for us) |
2607 | * and an angle (multiple of 36) to rotate the patch. */ |
2608 | |
2609 | penrose_calculate_size(which, tilesize, width, height, |
2610 | &outer_radius, &startsz, &depth); |
2611 | |
2612 | /* Calculate radius of (circumcircle of) patch, subtract from |
2613 | * radius calculated. */ |
2614 | inner_radius = (int)(outer_radius - sqrt(width*width + height*height)); |
2615 | |
2616 | /* Pick a random offset (the easy way: choose within outer square, |
2617 | * discarding while it's outside the circle) */ |
2618 | do { |
2619 | xoff = random_upto(rs, 2*inner_radius) - inner_radius; |
2620 | yoff = random_upto(rs, 2*inner_radius) - inner_radius; |
2621 | } while (sqrt(xoff*xoff+yoff*yoff) > inner_radius); |
2622 | |
2623 | aoff = random_upto(rs, 360/36) * 36; |
2624 | |
2625 | debug(("grid_desc: ts %d, %dx%d patch, orad %2.2f irad %d", |
2626 | tilesize, width, height, outer_radius, inner_radius)); |
2627 | debug((" -> xoff %d yoff %d aoff %d", xoff, yoff, aoff)); |
2628 | |
2629 | sprintf(gd, "G%d,%d,%d", xoff, yoff, aoff); |
2630 | |
2631 | return dupstr(gd); |
2632 | } |
2633 | |
2634 | static char *grid_validate_desc_penrose(grid_type type, int width, int height, char *desc) |
2635 | { |
2636 | int tilesize = PENROSE_TILESIZE, startsz, depth, xoff, yoff, aoff, inner_radius; |
2637 | double outer_radius; |
2638 | int which = (type == GRID_PENROSE_P2 ? PENROSE_P2 : PENROSE_P3); |
2639 | |
2640 | if (!desc) |
2641 | return "Missing grid description string."; |
2642 | |
2643 | penrose_calculate_size(which, tilesize, width, height, |
2644 | &outer_radius, &startsz, &depth); |
2645 | inner_radius = (int)(outer_radius - sqrt(width*width + height*height)); |
2646 | |
2647 | if (sscanf(desc, "G%d,%d,%d", &xoff, &yoff, &aoff) != 3) |
2648 | return "Invalid format grid description string."; |
2649 | |
2650 | if (sqrt(xoff*xoff + yoff*yoff) > inner_radius) |
2651 | return "Patch offset out of bounds."; |
2652 | if ((aoff % 36) != 0 || aoff < 0 || aoff >= 360) |
2653 | return "Angle offset out of bounds."; |
2654 | |
2655 | return NULL; |
2656 | } |
2657 | |
2658 | /* |
2659 | * We're asked for a grid of a particular size, and we generate enough |
2660 | * of the tiling so we can be sure to have enough random grid from which |
2661 | * to pick. |
2662 | */ |
2663 | |
2664 | static grid *grid_new_penrose(int width, int height, int which, char *desc) |
2665 | { |
2666 | int max_faces, max_dots, tilesize = PENROSE_TILESIZE; |
a15e5ee3 |
2667 | int xsz, ysz, xoff, yoff, aoff; |
cebf0b0d |
2668 | double rradius; |
2669 | |
2670 | tree234 *points; |
2671 | grid *g; |
2672 | |
2673 | penrose_state ps; |
2674 | setface_ctx sf_ctx; |
2675 | |
2676 | penrose_calculate_size(which, tilesize, width, height, |
2677 | &rradius, &ps.start_size, &ps.max_depth); |
2678 | |
2679 | debug(("penrose: w%d h%d, tile size %d, start size %d, depth %d", |
2680 | width, height, tilesize, ps.start_size, ps.max_depth)); |
2681 | |
2682 | ps.new_tile = set_faces; |
2683 | ps.ctx = &sf_ctx; |
2684 | |
2685 | max_faces = (width*3) * (height*3); /* somewhat paranoid... */ |
2686 | max_dots = max_faces * 4; /* ditto... */ |
2687 | |
2688 | g = grid_empty(); |
2689 | g->tilesize = tilesize; |
2690 | g->faces = snewn(max_faces, grid_face); |
2691 | g->dots = snewn(max_dots, grid_dot); |
2692 | |
2693 | points = newtree234(grid_point_cmp_fn); |
2694 | |
2695 | memset(&sf_ctx, 0, sizeof(sf_ctx)); |
2696 | sf_ctx.g = g; |
2697 | sf_ctx.points = points; |
2698 | |
2699 | if (desc != NULL) { |
a15e5ee3 |
2700 | if (sscanf(desc, "G%d,%d,%d", &xoff, &yoff, &aoff) != 3) |
cebf0b0d |
2701 | assert(!"Invalid grid description."); |
2702 | } else { |
2703 | xoff = yoff = 0; |
2704 | } |
2705 | |
2706 | xsz = width * tilesize; |
2707 | ysz = height * tilesize; |
2708 | |
2709 | sf_ctx.xmin = xoff - xsz/2; |
2710 | sf_ctx.xmax = xoff + xsz/2; |
2711 | sf_ctx.ymin = yoff - ysz/2; |
2712 | sf_ctx.ymax = yoff + ysz/2; |
2713 | |
2714 | debug(("penrose: centre (%f, %f) xsz %f ysz %f", |
2715 | 0.0, 0.0, xsz, ysz)); |
2716 | debug(("penrose: x range (%f --> %f), y range (%f --> %f)", |
2717 | sf_ctx.xmin, sf_ctx.xmax, sf_ctx.ymin, sf_ctx.ymax)); |
2718 | |
a15e5ee3 |
2719 | penrose(&ps, which, aoff); |
cebf0b0d |
2720 | |
2721 | freetree234(points); |
2722 | assert(g->num_faces <= max_faces); |
2723 | assert(g->num_dots <= max_dots); |
2724 | |
2725 | debug(("penrose: %d faces total (equivalent to %d wide by %d high)", |
2726 | g->num_faces, g->num_faces/height, g->num_faces/width)); |
2727 | |
2728 | grid_trim_vigorously(g); |
2729 | grid_make_consistent(g); |
2730 | |
2731 | /* |
2732 | * Centre the grid in its originally promised rectangle. |
2733 | */ |
2734 | g->lowest_x -= ((sf_ctx.xmax - sf_ctx.xmin) - |
2735 | (g->highest_x - g->lowest_x)) / 2; |
2736 | g->highest_x = g->lowest_x + (sf_ctx.xmax - sf_ctx.xmin); |
2737 | g->lowest_y -= ((sf_ctx.ymax - sf_ctx.ymin) - |
2738 | (g->highest_y - g->lowest_y)) / 2; |
2739 | g->highest_y = g->lowest_y + (sf_ctx.ymax - sf_ctx.ymin); |
2740 | |
2741 | return g; |
2742 | } |
2743 | |
fd66a01d |
2744 | static void grid_size_penrose_p2_kite(int width, int height, |
cebf0b0d |
2745 | int *tilesize, int *xextent, int *yextent) |
2746 | { |
2747 | grid_size_penrose(width, height, tilesize, xextent, yextent); |
2748 | } |
2749 | |
fd66a01d |
2750 | static void grid_size_penrose_p3_thick(int width, int height, |
cebf0b0d |
2751 | int *tilesize, int *xextent, int *yextent) |
2752 | { |
2753 | grid_size_penrose(width, height, tilesize, xextent, yextent); |
2754 | } |
2755 | |
fd66a01d |
2756 | static grid *grid_new_penrose_p2_kite(int width, int height, char *desc) |
cebf0b0d |
2757 | { |
2758 | return grid_new_penrose(width, height, PENROSE_P2, desc); |
2759 | } |
2760 | |
fd66a01d |
2761 | static grid *grid_new_penrose_p3_thick(int width, int height, char *desc) |
cebf0b0d |
2762 | { |
2763 | return grid_new_penrose(width, height, PENROSE_P3, desc); |
2764 | } |
2765 | |
7c95608a |
2766 | /* ----------- End of grid generators ------------- */ |
cebf0b0d |
2767 | |
2768 | #define FNNEW(upper,lower) &grid_new_ ## lower, |
2769 | #define FNSZ(upper,lower) &grid_size_ ## lower, |
2770 | |
2771 | static grid *(*(grid_news[]))(int, int, char*) = { GRIDGEN_LIST(FNNEW) }; |
2772 | static void(*(grid_sizes[]))(int, int, int*, int*, int*) = { GRIDGEN_LIST(FNSZ) }; |
2773 | |
ac5deb9c |
2774 | char *grid_new_desc(grid_type type, int width, int height, int dual, random_state *rs) |
cebf0b0d |
2775 | { |
2776 | if (type != GRID_PENROSE_P2 && type != GRID_PENROSE_P3) |
2777 | return NULL; |
2778 | |
2779 | return grid_new_desc_penrose(type, width, height, rs); |
2780 | } |
2781 | |
ac5deb9c |
2782 | char *grid_validate_desc(grid_type type, int width, int height, int dual, char *desc) |
cebf0b0d |
2783 | { |
2784 | if (type != GRID_PENROSE_P2 && type != GRID_PENROSE_P3) { |
2785 | if (desc != NULL) |
2786 | return "Grid description strings not used with this grid type"; |
2787 | return NULL; |
2788 | } |
2789 | |
2790 | return grid_validate_desc_penrose(type, width, height, desc); |
2791 | } |
2792 | |
ac5deb9c |
2793 | grid *grid_new(grid_type type, int width, int height, int dual, char *desc) |
cebf0b0d |
2794 | { |
ac5deb9c |
2795 | char *err = grid_validate_desc(type, width, height, dual, desc); |
cebf0b0d |
2796 | if (err) assert(!"Invalid grid description."); |
2797 | |
ac5deb9c |
2798 | if (!dual) |
2799 | { |
2800 | return grid_news[type](width, height, desc); |
2801 | } |
2802 | else |
2803 | { |
2804 | grid *temp; |
2805 | grid *g; |
2806 | |
2807 | temp = grid_news[type](width, height, desc); |
2808 | g = grid_dual(temp); |
2809 | grid_free(temp); |
2810 | return g; |
2811 | } |
cebf0b0d |
2812 | } |
2813 | |
2814 | void grid_compute_size(grid_type type, int width, int height, |
2815 | int *tilesize, int *xextent, int *yextent) |
2816 | { |
2817 | grid_sizes[type](width, height, tilesize, xextent, yextent); |
2818 | } |
2819 | |
2820 | /* ----------- End of grid helpers ------------- */ |
2821 | |
2822 | /* vim: set shiftwidth=4 tabstop=8: */ |