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