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> |
15 | |
16 | #include "puzzles.h" |
17 | #include "tree234.h" |
18 | #include "grid.h" |
19 | |
20 | /* Debugging options */ |
21 | |
22 | /* |
23 | #define DEBUG_GRID |
24 | */ |
25 | |
26 | /* ---------------------------------------------------------------------- |
27 | * Deallocate or dereference a grid |
28 | */ |
29 | void grid_free(grid *g) |
30 | { |
31 | assert(g->refcount); |
32 | |
33 | g->refcount--; |
34 | if (g->refcount == 0) { |
35 | int i; |
36 | for (i = 0; i < g->num_faces; i++) { |
37 | sfree(g->faces[i].dots); |
38 | sfree(g->faces[i].edges); |
39 | } |
40 | for (i = 0; i < g->num_dots; i++) { |
41 | sfree(g->dots[i].faces); |
42 | sfree(g->dots[i].edges); |
43 | } |
44 | sfree(g->faces); |
45 | sfree(g->edges); |
46 | sfree(g->dots); |
47 | sfree(g); |
48 | } |
49 | } |
50 | |
51 | /* Used by the other grid generators. Create a brand new grid with nothing |
52 | * initialised (all lists are NULL) */ |
b1535c90 |
53 | static grid *grid_new(void) |
7c95608a |
54 | { |
55 | grid *g = snew(grid); |
56 | g->faces = NULL; |
57 | g->edges = NULL; |
58 | g->dots = NULL; |
59 | g->num_faces = g->num_edges = g->num_dots = 0; |
60 | g->middle_face = NULL; |
61 | g->refcount = 1; |
62 | g->lowest_x = g->lowest_y = g->highest_x = g->highest_y = 0; |
63 | return g; |
64 | } |
65 | |
66 | /* Helper function to calculate perpendicular distance from |
67 | * a point P to a line AB. A and B mustn't be equal here. |
68 | * |
69 | * Well-known formula for area A of a triangle: |
70 | * / 1 1 1 \ |
71 | * 2A = determinant of matrix | px ax bx | |
72 | * \ py ay by / |
73 | * |
74 | * Also well-known: 2A = base * height |
75 | * = perpendicular distance * line-length. |
76 | * |
77 | * Combining gives: distance = determinant / line-length(a,b) |
78 | */ |
b1535c90 |
79 | static double point_line_distance(long px, long py, |
80 | long ax, long ay, |
81 | long bx, long by) |
7c95608a |
82 | { |
b1535c90 |
83 | long det = ax*by - bx*ay + bx*py - px*by + px*ay - ax*py; |
1515b973 |
84 | double len; |
7c95608a |
85 | det = max(det, -det); |
1515b973 |
86 | len = sqrt(SQ(ax - bx) + SQ(ay - by)); |
7c95608a |
87 | return det / len; |
88 | } |
89 | |
90 | /* Determine nearest edge to where the user clicked. |
91 | * (x, y) is the clicked location, converted to grid coordinates. |
92 | * Returns the nearest edge, or NULL if no edge is reasonably |
93 | * near the position. |
94 | * |
95 | * This algorithm is nice and generic, and doesn't depend on any particular |
96 | * geometric layout of the grid: |
97 | * Start at any dot (pick one next to middle_face). |
98 | * Walk along a path by choosing, from all nearby dots, the one that is |
99 | * nearest the target (x,y). Hopefully end up at the dot which is closest |
100 | * to (x,y). Should work, as long as faces aren't too badly shaped. |
101 | * Then examine each edge around this dot, and pick whichever one is |
102 | * closest (perpendicular distance) to (x,y). |
103 | * Using perpendicular distance is not quite right - the edge might be |
104 | * "off to one side". So we insist that the triangle with (x,y) has |
105 | * acute angles at the edge's dots. |
106 | * |
107 | * edge1 |
108 | * *---------*------ |
109 | * | |
110 | * | *(x,y) |
111 | * edge2 | |
112 | * | edge2 is OK, but edge1 is not, even though |
113 | * | edge1 is perpendicularly closer to (x,y) |
114 | * * |
115 | * |
116 | */ |
117 | grid_edge *grid_nearest_edge(grid *g, int x, int y) |
118 | { |
119 | grid_dot *cur; |
120 | grid_edge *best_edge; |
121 | double best_distance = 0; |
122 | int i; |
123 | |
124 | cur = g->middle_face->dots[0]; |
125 | |
126 | for (;;) { |
127 | /* Target to beat */ |
b1535c90 |
128 | long dist = SQ((long)cur->x - (long)x) + SQ((long)cur->y - (long)y); |
7c95608a |
129 | /* Look for nearer dot - if found, store in 'new'. */ |
130 | grid_dot *new = cur; |
131 | int i; |
132 | /* Search all dots in all faces touching this dot. Some shapes |
133 | * (such as in Cairo) don't quite work properly if we only search |
134 | * the dot's immediate neighbours. */ |
135 | for (i = 0; i < cur->order; i++) { |
136 | grid_face *f = cur->faces[i]; |
137 | int j; |
138 | if (!f) continue; |
139 | for (j = 0; j < f->order; j++) { |
b1535c90 |
140 | long new_dist; |
7c95608a |
141 | grid_dot *d = f->dots[j]; |
142 | if (d == cur) continue; |
b1535c90 |
143 | new_dist = SQ((long)d->x - (long)x) + SQ((long)d->y - (long)y); |
d84df751 |
144 | if (new_dist < dist) { /* found closer dot */ |
7c95608a |
145 | new = d; |
d84df751 |
146 | dist = new_dist; |
7c95608a |
147 | } |
148 | } |
7c95608a |
149 | } |
150 | |
151 | if (new == cur) { |
152 | /* Didn't find a closer dot among the neighbours of 'cur' */ |
153 | break; |
154 | } else { |
155 | cur = new; |
156 | } |
157 | } |
7c95608a |
158 | /* 'cur' is nearest dot, so find which of the dot's edges is closest. */ |
159 | best_edge = NULL; |
160 | |
161 | for (i = 0; i < cur->order; i++) { |
162 | grid_edge *e = cur->edges[i]; |
b1535c90 |
163 | long e2; /* squared length of edge */ |
164 | long a2, b2; /* squared lengths of other sides */ |
7c95608a |
165 | double dist; |
166 | |
167 | /* See if edge e is eligible - the triangle must have acute angles |
168 | * at the edge's dots. |
169 | * Pythagoras formula h^2 = a^2 + b^2 detects right-angles, |
170 | * so detect acute angles by testing for h^2 < a^2 + b^2 */ |
b1535c90 |
171 | e2 = SQ((long)e->dot1->x - (long)e->dot2->x) + SQ((long)e->dot1->y - (long)e->dot2->y); |
172 | a2 = SQ((long)e->dot1->x - (long)x) + SQ((long)e->dot1->y - (long)y); |
173 | b2 = SQ((long)e->dot2->x - (long)x) + SQ((long)e->dot2->y - (long)y); |
7c95608a |
174 | if (a2 >= e2 + b2) continue; |
175 | if (b2 >= e2 + a2) continue; |
176 | |
177 | /* e is eligible so far. Now check the edge is reasonably close |
178 | * to where the user clicked. Don't want to toggle an edge if the |
179 | * click was way off the grid. |
180 | * There is room for experimentation here. We could check the |
181 | * perpendicular distance is within a certain fraction of the length |
182 | * of the edge. That amounts to testing a rectangular region around |
183 | * the edge. |
184 | * Alternatively, we could check that the angle at the point is obtuse. |
185 | * That would amount to testing a circular region with the edge as |
186 | * diameter. */ |
b1535c90 |
187 | dist = point_line_distance((long)x, (long)y, |
188 | (long)e->dot1->x, (long)e->dot1->y, |
189 | (long)e->dot2->x, (long)e->dot2->y); |
7c95608a |
190 | /* Is dist more than half edge length ? */ |
191 | if (4 * SQ(dist) > e2) |
192 | continue; |
193 | |
194 | if (best_edge == NULL || dist < best_distance) { |
195 | best_edge = e; |
196 | best_distance = dist; |
197 | } |
198 | } |
199 | return best_edge; |
200 | } |
201 | |
202 | /* ---------------------------------------------------------------------- |
203 | * Grid generation |
204 | */ |
205 | |
206 | #ifdef DEBUG_GRID |
207 | /* Show the basic grid information, before doing grid_make_consistent */ |
208 | static void grid_print_basic(grid *g) |
209 | { |
210 | /* TODO: Maybe we should generate an SVG image of the dots and lines |
211 | * of the grid here, before grid_make_consistent. |
212 | * Would help with debugging grid generation. */ |
213 | int i; |
214 | printf("--- Basic Grid Data ---\n"); |
215 | for (i = 0; i < g->num_faces; i++) { |
216 | grid_face *f = g->faces + i; |
217 | printf("Face %d: dots[", i); |
218 | int j; |
219 | for (j = 0; j < f->order; j++) { |
220 | grid_dot *d = f->dots[j]; |
221 | printf("%s%d", j ? "," : "", (int)(d - g->dots)); |
222 | } |
223 | printf("]\n"); |
224 | } |
225 | printf("Middle face: %d\n", (int)(g->middle_face - g->faces)); |
226 | } |
227 | /* Show the derived grid information, computed by grid_make_consistent */ |
228 | static void grid_print_derived(grid *g) |
229 | { |
230 | /* edges */ |
231 | int i; |
232 | printf("--- Derived Grid Data ---\n"); |
233 | for (i = 0; i < g->num_edges; i++) { |
234 | grid_edge *e = g->edges + i; |
235 | printf("Edge %d: dots[%d,%d] faces[%d,%d]\n", |
236 | i, (int)(e->dot1 - g->dots), (int)(e->dot2 - g->dots), |
237 | e->face1 ? (int)(e->face1 - g->faces) : -1, |
238 | e->face2 ? (int)(e->face2 - g->faces) : -1); |
239 | } |
240 | /* faces */ |
241 | for (i = 0; i < g->num_faces; i++) { |
242 | grid_face *f = g->faces + i; |
243 | int j; |
244 | printf("Face %d: faces[", i); |
245 | for (j = 0; j < f->order; j++) { |
246 | grid_edge *e = f->edges[j]; |
247 | grid_face *f2 = (e->face1 == f) ? e->face2 : e->face1; |
248 | printf("%s%d", j ? "," : "", f2 ? (int)(f2 - g->faces) : -1); |
249 | } |
250 | printf("]\n"); |
251 | } |
252 | /* dots */ |
253 | for (i = 0; i < g->num_dots; i++) { |
254 | grid_dot *d = g->dots + i; |
255 | int j; |
256 | printf("Dot %d: dots[", i); |
257 | for (j = 0; j < d->order; j++) { |
258 | grid_edge *e = d->edges[j]; |
259 | grid_dot *d2 = (e->dot1 == d) ? e->dot2 : e->dot1; |
260 | printf("%s%d", j ? "," : "", (int)(d2 - g->dots)); |
261 | } |
262 | printf("] faces["); |
263 | for (j = 0; j < d->order; j++) { |
264 | grid_face *f = d->faces[j]; |
265 | printf("%s%d", j ? "," : "", f ? (int)(f - g->faces) : -1); |
266 | } |
267 | printf("]\n"); |
268 | } |
269 | } |
270 | #endif /* DEBUG_GRID */ |
271 | |
272 | /* Helper function for building incomplete-edges list in |
273 | * grid_make_consistent() */ |
274 | static int grid_edge_bydots_cmpfn(void *v1, void *v2) |
275 | { |
276 | grid_edge *a = v1; |
277 | grid_edge *b = v2; |
278 | grid_dot *da, *db; |
279 | |
280 | /* Pointer subtraction is valid here, because all dots point into the |
281 | * same dot-list (g->dots). |
282 | * Edges are not "normalised" - the 2 dots could be stored in any order, |
283 | * so we need to take this into account when comparing edges. */ |
284 | |
285 | /* Compare first dots */ |
286 | da = (a->dot1 < a->dot2) ? a->dot1 : a->dot2; |
287 | db = (b->dot1 < b->dot2) ? b->dot1 : b->dot2; |
288 | if (da != db) |
289 | return db - da; |
290 | /* Compare last dots */ |
291 | da = (a->dot1 < a->dot2) ? a->dot2 : a->dot1; |
292 | db = (b->dot1 < b->dot2) ? b->dot2 : b->dot1; |
293 | if (da != db) |
294 | return db - da; |
295 | |
296 | return 0; |
297 | } |
298 | |
299 | /* Input: grid has its dots and faces initialised: |
300 | * - dots have (optionally) x and y coordinates, but no edges or faces |
301 | * (pointers are NULL). |
302 | * - edges not initialised at all |
303 | * - faces initialised and know which dots they have (but no edges yet). The |
304 | * dots around each face are assumed to be clockwise. |
305 | * |
306 | * Output: grid is complete and valid with all relationships defined. |
307 | */ |
308 | static void grid_make_consistent(grid *g) |
309 | { |
310 | int i; |
311 | tree234 *incomplete_edges; |
312 | grid_edge *next_new_edge; /* Where new edge will go into g->edges */ |
313 | |
314 | #ifdef DEBUG_GRID |
315 | grid_print_basic(g); |
316 | #endif |
317 | |
318 | /* ====== Stage 1 ====== |
319 | * Generate edges |
320 | */ |
321 | |
322 | /* We know how many dots and faces there are, so we can find the exact |
323 | * number of edges from Euler's polyhedral formula: F + V = E + 2 . |
324 | * We use "-1", not "-2" here, because Euler's formula includes the |
325 | * infinite face, which we don't count. */ |
326 | g->num_edges = g->num_faces + g->num_dots - 1; |
327 | g->edges = snewn(g->num_edges, grid_edge); |
328 | next_new_edge = g->edges; |
329 | |
330 | /* Iterate over faces, and over each face's dots, generating edges as we |
331 | * go. As we find each new edge, we can immediately fill in the edge's |
332 | * dots, but only one of the edge's faces. Later on in the iteration, we |
333 | * will find the same edge again (unless it's on the border), but we will |
334 | * know the other face. |
335 | * For efficiency, maintain a list of the incomplete edges, sorted by |
336 | * their dots. */ |
337 | incomplete_edges = newtree234(grid_edge_bydots_cmpfn); |
338 | for (i = 0; i < g->num_faces; i++) { |
339 | grid_face *f = g->faces + i; |
340 | int j; |
341 | for (j = 0; j < f->order; j++) { |
342 | grid_edge e; /* fake edge for searching */ |
343 | grid_edge *edge_found; |
344 | int j2 = j + 1; |
345 | if (j2 == f->order) |
346 | j2 = 0; |
347 | e.dot1 = f->dots[j]; |
348 | e.dot2 = f->dots[j2]; |
349 | /* Use del234 instead of find234, because we always want to |
350 | * remove the edge if found */ |
351 | edge_found = del234(incomplete_edges, &e); |
352 | if (edge_found) { |
353 | /* This edge already added, so fill out missing face. |
354 | * Edge is already removed from incomplete_edges. */ |
355 | edge_found->face2 = f; |
356 | } else { |
357 | assert(next_new_edge - g->edges < g->num_edges); |
358 | next_new_edge->dot1 = e.dot1; |
359 | next_new_edge->dot2 = e.dot2; |
360 | next_new_edge->face1 = f; |
361 | next_new_edge->face2 = NULL; /* potentially infinite face */ |
362 | add234(incomplete_edges, next_new_edge); |
363 | ++next_new_edge; |
364 | } |
365 | } |
366 | } |
367 | freetree234(incomplete_edges); |
368 | |
369 | /* ====== Stage 2 ====== |
370 | * For each face, build its edge list. |
371 | */ |
372 | |
373 | /* Allocate space for each edge list. Can do this, because each face's |
374 | * edge-list is the same size as its dot-list. */ |
375 | for (i = 0; i < g->num_faces; i++) { |
376 | grid_face *f = g->faces + i; |
377 | int j; |
378 | f->edges = snewn(f->order, grid_edge*); |
379 | /* Preload with NULLs, to help detect potential bugs. */ |
380 | for (j = 0; j < f->order; j++) |
381 | f->edges[j] = NULL; |
382 | } |
383 | |
384 | /* Iterate over each edge, and over both its faces. Add this edge to |
385 | * the face's edge-list, after finding where it should go in the |
386 | * sequence. */ |
387 | for (i = 0; i < g->num_edges; i++) { |
388 | grid_edge *e = g->edges + i; |
389 | int j; |
390 | for (j = 0; j < 2; j++) { |
391 | grid_face *f = j ? e->face2 : e->face1; |
392 | int k, k2; |
393 | if (f == NULL) continue; |
394 | /* Find one of the dots around the face */ |
395 | for (k = 0; k < f->order; k++) { |
396 | if (f->dots[k] == e->dot1) |
397 | break; /* found dot1 */ |
398 | } |
399 | assert(k != f->order); /* Must find the dot around this face */ |
400 | |
401 | /* Labelling scheme: as we walk clockwise around the face, |
402 | * starting at dot0 (f->dots[0]), we hit: |
403 | * (dot0), edge0, dot1, edge1, dot2,... |
404 | * |
405 | * 0 |
406 | * 0-----1 |
407 | * | |
408 | * |1 |
409 | * | |
410 | * 3-----2 |
411 | * 2 |
412 | * |
413 | * Therefore, edgeK joins dotK and dot{K+1} |
414 | */ |
415 | |
416 | /* Around this face, either the next dot or the previous dot |
417 | * must be e->dot2. Otherwise the edge is wrong. */ |
418 | k2 = k + 1; |
419 | if (k2 == f->order) |
420 | k2 = 0; |
421 | if (f->dots[k2] == e->dot2) { |
422 | /* dot1(k) and dot2(k2) go clockwise around this face, so add |
423 | * this edge at position k (see diagram). */ |
424 | assert(f->edges[k] == NULL); |
425 | f->edges[k] = e; |
426 | continue; |
427 | } |
428 | /* Try previous dot */ |
429 | k2 = k - 1; |
430 | if (k2 == -1) |
431 | k2 = f->order - 1; |
432 | if (f->dots[k2] == e->dot2) { |
433 | /* dot1(k) and dot2(k2) go anticlockwise around this face. */ |
434 | assert(f->edges[k2] == NULL); |
435 | f->edges[k2] = e; |
436 | continue; |
437 | } |
438 | assert(!"Grid broken: bad edge-face relationship"); |
439 | } |
440 | } |
441 | |
442 | /* ====== Stage 3 ====== |
443 | * For each dot, build its edge-list and face-list. |
444 | */ |
445 | |
446 | /* We don't know how many edges/faces go around each dot, so we can't |
447 | * allocate the right space for these lists. Pre-compute the sizes by |
448 | * iterating over each edge and recording a tally against each dot. */ |
449 | for (i = 0; i < g->num_dots; i++) { |
450 | g->dots[i].order = 0; |
451 | } |
452 | for (i = 0; i < g->num_edges; i++) { |
453 | grid_edge *e = g->edges + i; |
454 | ++(e->dot1->order); |
455 | ++(e->dot2->order); |
456 | } |
457 | /* Now we have the sizes, pre-allocate the edge and face lists. */ |
458 | for (i = 0; i < g->num_dots; i++) { |
459 | grid_dot *d = g->dots + i; |
460 | int j; |
461 | assert(d->order >= 2); /* sanity check */ |
462 | d->edges = snewn(d->order, grid_edge*); |
463 | d->faces = snewn(d->order, grid_face*); |
464 | for (j = 0; j < d->order; j++) { |
465 | d->edges[j] = NULL; |
466 | d->faces[j] = NULL; |
467 | } |
468 | } |
469 | /* For each dot, need to find a face that touches it, so we can seed |
470 | * the edge-face-edge-face process around each dot. */ |
471 | for (i = 0; i < g->num_faces; i++) { |
472 | grid_face *f = g->faces + i; |
473 | int j; |
474 | for (j = 0; j < f->order; j++) { |
475 | grid_dot *d = f->dots[j]; |
476 | d->faces[0] = f; |
477 | } |
478 | } |
479 | /* Each dot now has a face in its first slot. Generate the remaining |
480 | * faces and edges around the dot, by searching both clockwise and |
481 | * anticlockwise from the first face. Need to do both directions, |
482 | * because of the possibility of hitting the infinite face, which |
483 | * blocks progress. But there's only one such face, so we will |
484 | * succeed in finding every edge and face this way. */ |
485 | for (i = 0; i < g->num_dots; i++) { |
486 | grid_dot *d = g->dots + i; |
487 | int current_face1 = 0; /* ascends clockwise */ |
488 | int current_face2 = 0; /* descends anticlockwise */ |
489 | |
490 | /* Labelling scheme: as we walk clockwise around the dot, starting |
491 | * at face0 (d->faces[0]), we hit: |
492 | * (face0), edge0, face1, edge1, face2,... |
493 | * |
494 | * 0 |
495 | * | |
496 | * 0 | 1 |
497 | * | |
498 | * -----d-----1 |
499 | * | |
500 | * | 2 |
501 | * | |
502 | * 2 |
503 | * |
504 | * So, for example, face1 should be joined to edge0 and edge1, |
505 | * and those edges should appear in an anticlockwise sense around |
506 | * that face (see diagram). */ |
507 | |
508 | /* clockwise search */ |
509 | while (TRUE) { |
510 | grid_face *f = d->faces[current_face1]; |
511 | grid_edge *e; |
512 | int j; |
513 | assert(f != NULL); |
514 | /* find dot around this face */ |
515 | for (j = 0; j < f->order; j++) { |
516 | if (f->dots[j] == d) |
517 | break; |
518 | } |
519 | assert(j != f->order); /* must find dot */ |
520 | |
521 | /* Around f, required edge is anticlockwise from the dot. See |
522 | * the other labelling scheme higher up, for why we subtract 1 |
523 | * from j. */ |
524 | j--; |
525 | if (j == -1) |
526 | j = f->order - 1; |
527 | e = f->edges[j]; |
528 | d->edges[current_face1] = e; /* set edge */ |
529 | current_face1++; |
530 | if (current_face1 == d->order) |
531 | break; |
532 | else { |
533 | /* set face */ |
534 | d->faces[current_face1] = |
535 | (e->face1 == f) ? e->face2 : e->face1; |
536 | if (d->faces[current_face1] == NULL) |
537 | break; /* cannot progress beyond infinite face */ |
538 | } |
539 | } |
540 | /* If the clockwise search made it all the way round, don't need to |
541 | * bother with the anticlockwise search. */ |
542 | if (current_face1 == d->order) |
543 | continue; /* this dot is complete, move on to next dot */ |
544 | |
545 | /* anticlockwise search */ |
546 | while (TRUE) { |
547 | grid_face *f = d->faces[current_face2]; |
548 | grid_edge *e; |
549 | int j; |
550 | assert(f != NULL); |
551 | /* find dot around this face */ |
552 | for (j = 0; j < f->order; j++) { |
553 | if (f->dots[j] == d) |
554 | break; |
555 | } |
556 | assert(j != f->order); /* must find dot */ |
557 | |
558 | /* Around f, required edge is clockwise from the dot. */ |
559 | e = f->edges[j]; |
560 | |
561 | current_face2--; |
562 | if (current_face2 == -1) |
563 | current_face2 = d->order - 1; |
564 | d->edges[current_face2] = e; /* set edge */ |
565 | |
566 | /* set face */ |
567 | if (current_face2 == current_face1) |
568 | break; |
569 | d->faces[current_face2] = |
570 | (e->face1 == f) ? e->face2 : e->face1; |
571 | /* There's only 1 infinite face, so we must get all the way |
572 | * to current_face1 before we hit it. */ |
573 | assert(d->faces[current_face2]); |
574 | } |
575 | } |
576 | |
577 | /* ====== Stage 4 ====== |
578 | * Compute other grid settings |
579 | */ |
580 | |
581 | /* Bounding rectangle */ |
582 | for (i = 0; i < g->num_dots; i++) { |
583 | grid_dot *d = g->dots + i; |
584 | if (i == 0) { |
585 | g->lowest_x = g->highest_x = d->x; |
586 | g->lowest_y = g->highest_y = d->y; |
587 | } else { |
588 | g->lowest_x = min(g->lowest_x, d->x); |
589 | g->highest_x = max(g->highest_x, d->x); |
590 | g->lowest_y = min(g->lowest_y, d->y); |
591 | g->highest_y = max(g->highest_y, d->y); |
592 | } |
593 | } |
594 | |
595 | #ifdef DEBUG_GRID |
596 | grid_print_derived(g); |
597 | #endif |
598 | } |
599 | |
600 | /* Helpers for making grid-generation easier. These functions are only |
601 | * intended for use during grid generation. */ |
602 | |
603 | /* Comparison function for the (tree234) sorted dot list */ |
604 | static int grid_point_cmp_fn(void *v1, void *v2) |
605 | { |
606 | grid_dot *p1 = v1; |
607 | grid_dot *p2 = v2; |
608 | if (p1->y != p2->y) |
609 | return p2->y - p1->y; |
610 | else |
611 | return p2->x - p1->x; |
612 | } |
613 | /* Add a new face to the grid, with its dot list allocated. |
614 | * Assumes there's enough space allocated for the new face in grid->faces */ |
615 | static void grid_face_add_new(grid *g, int face_size) |
616 | { |
617 | int i; |
618 | grid_face *new_face = g->faces + g->num_faces; |
619 | new_face->order = face_size; |
620 | new_face->dots = snewn(face_size, grid_dot*); |
621 | for (i = 0; i < face_size; i++) |
622 | new_face->dots[i] = NULL; |
623 | new_face->edges = NULL; |
624 | g->num_faces++; |
625 | } |
626 | /* Assumes dot list has enough space */ |
627 | static grid_dot *grid_dot_add_new(grid *g, int x, int y) |
628 | { |
629 | grid_dot *new_dot = g->dots + g->num_dots; |
630 | new_dot->order = 0; |
631 | new_dot->edges = NULL; |
632 | new_dot->faces = NULL; |
633 | new_dot->x = x; |
634 | new_dot->y = y; |
635 | g->num_dots++; |
636 | return new_dot; |
637 | } |
638 | /* Retrieve a dot with these (x,y) coordinates. Either return an existing dot |
639 | * in the dot_list, or add a new dot to the grid (and the dot_list) and |
640 | * return that. |
641 | * Assumes g->dots has enough capacity allocated */ |
642 | static grid_dot *grid_get_dot(grid *g, tree234 *dot_list, int x, int y) |
643 | { |
3466f373 |
644 | grid_dot test, *ret; |
645 | |
646 | test.order = 0; |
647 | test.edges = NULL; |
648 | test.faces = NULL; |
649 | test.x = x; |
650 | test.y = y; |
651 | ret = find234(dot_list, &test, NULL); |
7c95608a |
652 | if (ret) |
653 | return ret; |
654 | |
655 | ret = grid_dot_add_new(g, x, y); |
656 | add234(dot_list, ret); |
657 | return ret; |
658 | } |
659 | |
660 | /* Sets the last face of the grid to include this dot, at this position |
661 | * around the face. Assumes num_faces is at least 1 (a new face has |
662 | * previously been added, with the required number of dots allocated) */ |
663 | static void grid_face_set_dot(grid *g, grid_dot *d, int position) |
664 | { |
665 | grid_face *last_face = g->faces + g->num_faces - 1; |
666 | last_face->dots[position] = d; |
667 | } |
668 | |
669 | /* ------ Generate various types of grid ------ */ |
670 | |
671 | /* General method is to generate faces, by calculating their dot coordinates. |
672 | * As new faces are added, we keep track of all the dots so we can tell when |
673 | * a new face reuses an existing dot. For example, two squares touching at an |
674 | * edge would generate six unique dots: four dots from the first face, then |
675 | * two additional dots for the second face, because we detect the other two |
676 | * dots have already been taken up. This list is stored in a tree234 |
677 | * called "points". No extra memory-allocation needed here - we store the |
678 | * actual grid_dot* pointers, which all point into the g->dots list. |
679 | * For this reason, we have to calculate coordinates in such a way as to |
680 | * eliminate any rounding errors, so we can detect when a dot on one |
681 | * face precisely lands on a dot of a different face. No floating-point |
682 | * arithmetic here! |
683 | */ |
684 | |
685 | grid *grid_new_square(int width, int height) |
686 | { |
687 | int x, y; |
688 | /* Side length */ |
689 | int a = 20; |
690 | |
691 | /* Upper bounds - don't have to be exact */ |
692 | int max_faces = width * height; |
693 | int max_dots = (width + 1) * (height + 1); |
694 | |
695 | tree234 *points; |
696 | |
697 | grid *g = grid_new(); |
698 | g->tilesize = a; |
699 | g->faces = snewn(max_faces, grid_face); |
700 | g->dots = snewn(max_dots, grid_dot); |
701 | |
702 | points = newtree234(grid_point_cmp_fn); |
703 | |
704 | /* generate square faces */ |
705 | for (y = 0; y < height; y++) { |
706 | for (x = 0; x < width; x++) { |
707 | grid_dot *d; |
708 | /* face position */ |
709 | int px = a * x; |
710 | int py = a * y; |
711 | |
712 | grid_face_add_new(g, 4); |
713 | d = grid_get_dot(g, points, px, py); |
714 | grid_face_set_dot(g, d, 0); |
715 | d = grid_get_dot(g, points, px + a, py); |
716 | grid_face_set_dot(g, d, 1); |
717 | d = grid_get_dot(g, points, px + a, py + a); |
718 | grid_face_set_dot(g, d, 2); |
719 | d = grid_get_dot(g, points, px, py + a); |
720 | grid_face_set_dot(g, d, 3); |
721 | } |
722 | } |
723 | |
724 | freetree234(points); |
725 | assert(g->num_faces <= max_faces); |
726 | assert(g->num_dots <= max_dots); |
727 | g->middle_face = g->faces + (height/2) * width + (width/2); |
728 | |
729 | grid_make_consistent(g); |
730 | return g; |
731 | } |
732 | |
733 | grid *grid_new_honeycomb(int width, int height) |
734 | { |
735 | int x, y; |
736 | /* Vector for side of hexagon - ratio is close to sqrt(3) */ |
737 | int a = 15; |
738 | int b = 26; |
739 | |
740 | /* Upper bounds - don't have to be exact */ |
741 | int max_faces = width * height; |
742 | int max_dots = 2 * (width + 1) * (height + 1); |
743 | |
744 | tree234 *points; |
745 | |
746 | grid *g = grid_new(); |
747 | g->tilesize = 3 * a; |
748 | g->faces = snewn(max_faces, grid_face); |
749 | g->dots = snewn(max_dots, grid_dot); |
750 | |
751 | points = newtree234(grid_point_cmp_fn); |
752 | |
753 | /* generate hexagonal faces */ |
754 | for (y = 0; y < height; y++) { |
755 | for (x = 0; x < width; x++) { |
756 | grid_dot *d; |
757 | /* face centre */ |
758 | int cx = 3 * a * x; |
759 | int cy = 2 * b * y; |
760 | if (x % 2) |
761 | cy += b; |
762 | grid_face_add_new(g, 6); |
763 | |
764 | d = grid_get_dot(g, points, cx - a, cy - b); |
765 | grid_face_set_dot(g, d, 0); |
766 | d = grid_get_dot(g, points, cx + a, cy - b); |
767 | grid_face_set_dot(g, d, 1); |
768 | d = grid_get_dot(g, points, cx + 2*a, cy); |
769 | grid_face_set_dot(g, d, 2); |
770 | d = grid_get_dot(g, points, cx + a, cy + b); |
771 | grid_face_set_dot(g, d, 3); |
772 | d = grid_get_dot(g, points, cx - a, cy + b); |
773 | grid_face_set_dot(g, d, 4); |
774 | d = grid_get_dot(g, points, cx - 2*a, cy); |
775 | grid_face_set_dot(g, d, 5); |
776 | } |
777 | } |
778 | |
779 | freetree234(points); |
780 | assert(g->num_faces <= max_faces); |
781 | assert(g->num_dots <= max_dots); |
782 | g->middle_face = g->faces + (height/2) * width + (width/2); |
783 | |
784 | grid_make_consistent(g); |
785 | return g; |
786 | } |
787 | |
788 | /* Doesn't use the previous method of generation, it pre-dates it! |
789 | * A triangular grid is just about simple enough to do by "brute force" */ |
790 | grid *grid_new_triangular(int width, int height) |
791 | { |
792 | int x,y; |
793 | |
794 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
795 | int vec_x = 15; |
796 | int vec_y = 26; |
797 | |
798 | int index; |
799 | |
800 | /* convenient alias */ |
801 | int w = width + 1; |
802 | |
803 | grid *g = grid_new(); |
804 | g->tilesize = 18; /* adjust to your taste */ |
805 | |
806 | g->num_faces = width * height * 2; |
807 | g->num_dots = (width + 1) * (height + 1); |
808 | g->faces = snewn(g->num_faces, grid_face); |
809 | g->dots = snewn(g->num_dots, grid_dot); |
810 | |
811 | /* generate dots */ |
812 | index = 0; |
813 | for (y = 0; y <= height; y++) { |
814 | for (x = 0; x <= width; x++) { |
815 | grid_dot *d = g->dots + index; |
816 | /* odd rows are offset to the right */ |
817 | d->order = 0; |
818 | d->edges = NULL; |
819 | d->faces = NULL; |
820 | d->x = x * 2 * vec_x + ((y % 2) ? vec_x : 0); |
821 | d->y = y * vec_y; |
822 | index++; |
823 | } |
824 | } |
825 | |
826 | /* generate faces */ |
827 | index = 0; |
828 | for (y = 0; y < height; y++) { |
829 | for (x = 0; x < width; x++) { |
830 | /* initialise two faces for this (x,y) */ |
831 | grid_face *f1 = g->faces + index; |
832 | grid_face *f2 = f1 + 1; |
833 | f1->edges = NULL; |
834 | f1->order = 3; |
835 | f1->dots = snewn(f1->order, grid_dot*); |
836 | f2->edges = NULL; |
837 | f2->order = 3; |
838 | f2->dots = snewn(f2->order, grid_dot*); |
839 | |
840 | /* face descriptions depend on whether the row-number is |
841 | * odd or even */ |
842 | if (y % 2) { |
843 | f1->dots[0] = g->dots + y * w + x; |
844 | f1->dots[1] = g->dots + (y + 1) * w + x + 1; |
845 | f1->dots[2] = g->dots + (y + 1) * w + x; |
846 | f2->dots[0] = g->dots + y * w + x; |
847 | f2->dots[1] = g->dots + y * w + x + 1; |
848 | f2->dots[2] = g->dots + (y + 1) * w + x + 1; |
849 | } else { |
850 | f1->dots[0] = g->dots + y * w + x; |
851 | f1->dots[1] = g->dots + y * w + x + 1; |
852 | f1->dots[2] = g->dots + (y + 1) * w + x; |
853 | f2->dots[0] = g->dots + y * w + x + 1; |
854 | f2->dots[1] = g->dots + (y + 1) * w + x + 1; |
855 | f2->dots[2] = g->dots + (y + 1) * w + x; |
856 | } |
857 | index += 2; |
858 | } |
859 | } |
860 | |
861 | /* "+ width" takes us to the middle of the row, because each row has |
862 | * (2*width) faces. */ |
863 | g->middle_face = g->faces + (height / 2) * 2 * width + width; |
864 | |
865 | grid_make_consistent(g); |
866 | return g; |
867 | } |
868 | |
869 | grid *grid_new_snubsquare(int width, int height) |
870 | { |
871 | int x, y; |
872 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
873 | int a = 15; |
874 | int b = 26; |
875 | |
876 | /* Upper bounds - don't have to be exact */ |
877 | int max_faces = 3 * width * height; |
878 | int max_dots = 2 * (width + 1) * (height + 1); |
879 | |
880 | tree234 *points; |
881 | |
882 | grid *g = grid_new(); |
883 | g->tilesize = 18; |
884 | g->faces = snewn(max_faces, grid_face); |
885 | g->dots = snewn(max_dots, grid_dot); |
886 | |
887 | points = newtree234(grid_point_cmp_fn); |
888 | |
889 | for (y = 0; y < height; y++) { |
890 | for (x = 0; x < width; x++) { |
891 | grid_dot *d; |
892 | /* face position */ |
893 | int px = (a + b) * x; |
894 | int py = (a + b) * y; |
895 | |
896 | /* generate square faces */ |
897 | grid_face_add_new(g, 4); |
898 | if ((x + y) % 2) { |
899 | d = grid_get_dot(g, points, px + a, py); |
900 | grid_face_set_dot(g, d, 0); |
901 | d = grid_get_dot(g, points, px + a + b, py + a); |
902 | grid_face_set_dot(g, d, 1); |
903 | d = grid_get_dot(g, points, px + b, py + a + b); |
904 | grid_face_set_dot(g, d, 2); |
905 | d = grid_get_dot(g, points, px, py + b); |
906 | grid_face_set_dot(g, d, 3); |
907 | } else { |
908 | d = grid_get_dot(g, points, px + b, py); |
909 | grid_face_set_dot(g, d, 0); |
910 | d = grid_get_dot(g, points, px + a + b, py + b); |
911 | grid_face_set_dot(g, d, 1); |
912 | d = grid_get_dot(g, points, px + a, py + a + b); |
913 | grid_face_set_dot(g, d, 2); |
914 | d = grid_get_dot(g, points, px, py + a); |
915 | grid_face_set_dot(g, d, 3); |
916 | } |
917 | |
918 | /* generate up/down triangles */ |
919 | if (x > 0) { |
920 | grid_face_add_new(g, 3); |
921 | if ((x + y) % 2) { |
922 | d = grid_get_dot(g, points, px + a, py); |
923 | grid_face_set_dot(g, d, 0); |
924 | d = grid_get_dot(g, points, px, py + b); |
925 | grid_face_set_dot(g, d, 1); |
926 | d = grid_get_dot(g, points, px - a, py); |
927 | grid_face_set_dot(g, d, 2); |
928 | } else { |
929 | d = grid_get_dot(g, points, px, py + a); |
930 | grid_face_set_dot(g, d, 0); |
931 | d = grid_get_dot(g, points, px + a, py + a + b); |
932 | grid_face_set_dot(g, d, 1); |
933 | d = grid_get_dot(g, points, px - a, py + a + b); |
934 | grid_face_set_dot(g, d, 2); |
935 | } |
936 | } |
937 | |
938 | /* generate left/right triangles */ |
939 | if (y > 0) { |
940 | grid_face_add_new(g, 3); |
941 | if ((x + y) % 2) { |
942 | d = grid_get_dot(g, points, px + a, py); |
943 | grid_face_set_dot(g, d, 0); |
944 | d = grid_get_dot(g, points, px + a + b, py - a); |
945 | grid_face_set_dot(g, d, 1); |
946 | d = grid_get_dot(g, points, px + a + b, py + a); |
947 | grid_face_set_dot(g, d, 2); |
948 | } else { |
949 | d = grid_get_dot(g, points, px, py - a); |
950 | grid_face_set_dot(g, d, 0); |
951 | d = grid_get_dot(g, points, px + b, py); |
952 | grid_face_set_dot(g, d, 1); |
953 | d = grid_get_dot(g, points, px, py + a); |
954 | grid_face_set_dot(g, d, 2); |
955 | } |
956 | } |
957 | } |
958 | } |
959 | |
960 | freetree234(points); |
961 | assert(g->num_faces <= max_faces); |
962 | assert(g->num_dots <= max_dots); |
963 | g->middle_face = g->faces + (height/2) * width + (width/2); |
964 | |
965 | grid_make_consistent(g); |
966 | return g; |
967 | } |
968 | |
969 | grid *grid_new_cairo(int width, int height) |
970 | { |
971 | int x, y; |
972 | /* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */ |
973 | int a = 14; |
974 | int b = 31; |
975 | |
976 | /* Upper bounds - don't have to be exact */ |
977 | int max_faces = 2 * width * height; |
978 | int max_dots = 3 * (width + 1) * (height + 1); |
979 | |
980 | tree234 *points; |
981 | |
982 | grid *g = grid_new(); |
983 | g->tilesize = 40; |
984 | g->faces = snewn(max_faces, grid_face); |
985 | g->dots = snewn(max_dots, grid_dot); |
986 | |
987 | points = newtree234(grid_point_cmp_fn); |
988 | |
989 | for (y = 0; y < height; y++) { |
990 | for (x = 0; x < width; x++) { |
991 | grid_dot *d; |
992 | /* cell position */ |
993 | int px = 2 * b * x; |
994 | int py = 2 * b * y; |
995 | |
996 | /* horizontal pentagons */ |
997 | if (y > 0) { |
998 | grid_face_add_new(g, 5); |
999 | if ((x + y) % 2) { |
1000 | d = grid_get_dot(g, points, px + a, py - b); |
1001 | grid_face_set_dot(g, d, 0); |
1002 | d = grid_get_dot(g, points, px + 2*b - a, py - b); |
1003 | grid_face_set_dot(g, d, 1); |
1004 | d = grid_get_dot(g, points, px + 2*b, py); |
1005 | grid_face_set_dot(g, d, 2); |
1006 | d = grid_get_dot(g, points, px + b, py + a); |
1007 | grid_face_set_dot(g, d, 3); |
1008 | d = grid_get_dot(g, points, px, py); |
1009 | grid_face_set_dot(g, d, 4); |
1010 | } else { |
1011 | d = grid_get_dot(g, points, px, py); |
1012 | grid_face_set_dot(g, d, 0); |
1013 | d = grid_get_dot(g, points, px + b, py - a); |
1014 | grid_face_set_dot(g, d, 1); |
1015 | d = grid_get_dot(g, points, px + 2*b, py); |
1016 | grid_face_set_dot(g, d, 2); |
1017 | d = grid_get_dot(g, points, px + 2*b - a, py + b); |
1018 | grid_face_set_dot(g, d, 3); |
1019 | d = grid_get_dot(g, points, px + a, py + b); |
1020 | grid_face_set_dot(g, d, 4); |
1021 | } |
1022 | } |
1023 | /* vertical pentagons */ |
1024 | if (x > 0) { |
1025 | grid_face_add_new(g, 5); |
1026 | if ((x + y) % 2) { |
1027 | d = grid_get_dot(g, points, px, py); |
1028 | grid_face_set_dot(g, d, 0); |
1029 | d = grid_get_dot(g, points, px + b, py + a); |
1030 | grid_face_set_dot(g, d, 1); |
1031 | d = grid_get_dot(g, points, px + b, py + 2*b - a); |
1032 | grid_face_set_dot(g, d, 2); |
1033 | d = grid_get_dot(g, points, px, py + 2*b); |
1034 | grid_face_set_dot(g, d, 3); |
1035 | d = grid_get_dot(g, points, px - a, py + b); |
1036 | grid_face_set_dot(g, d, 4); |
1037 | } else { |
1038 | d = grid_get_dot(g, points, px, py); |
1039 | grid_face_set_dot(g, d, 0); |
1040 | d = grid_get_dot(g, points, px + a, py + b); |
1041 | grid_face_set_dot(g, d, 1); |
1042 | d = grid_get_dot(g, points, px, py + 2*b); |
1043 | grid_face_set_dot(g, d, 2); |
1044 | d = grid_get_dot(g, points, px - b, py + 2*b - a); |
1045 | grid_face_set_dot(g, d, 3); |
1046 | d = grid_get_dot(g, points, px - b, py + a); |
1047 | grid_face_set_dot(g, d, 4); |
1048 | } |
1049 | } |
1050 | } |
1051 | } |
1052 | |
1053 | freetree234(points); |
1054 | assert(g->num_faces <= max_faces); |
1055 | assert(g->num_dots <= max_dots); |
1056 | g->middle_face = g->faces + (height/2) * width + (width/2); |
1057 | |
1058 | grid_make_consistent(g); |
1059 | return g; |
1060 | } |
1061 | |
1062 | grid *grid_new_greathexagonal(int width, int height) |
1063 | { |
1064 | int x, y; |
1065 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
1066 | int a = 15; |
1067 | int b = 26; |
1068 | |
1069 | /* Upper bounds - don't have to be exact */ |
1070 | int max_faces = 6 * (width + 1) * (height + 1); |
1071 | int max_dots = 6 * width * height; |
1072 | |
1073 | tree234 *points; |
1074 | |
1075 | grid *g = grid_new(); |
1076 | g->tilesize = 18; |
1077 | g->faces = snewn(max_faces, grid_face); |
1078 | g->dots = snewn(max_dots, grid_dot); |
1079 | |
1080 | points = newtree234(grid_point_cmp_fn); |
1081 | |
1082 | for (y = 0; y < height; y++) { |
1083 | for (x = 0; x < width; x++) { |
1084 | grid_dot *d; |
1085 | /* centre of hexagon */ |
1086 | int px = (3*a + b) * x; |
1087 | int py = (2*a + 2*b) * y; |
1088 | if (x % 2) |
1089 | py += a + b; |
1090 | |
1091 | /* hexagon */ |
1092 | grid_face_add_new(g, 6); |
1093 | d = grid_get_dot(g, points, px - a, py - b); |
1094 | grid_face_set_dot(g, d, 0); |
1095 | d = grid_get_dot(g, points, px + a, py - b); |
1096 | grid_face_set_dot(g, d, 1); |
1097 | d = grid_get_dot(g, points, px + 2*a, py); |
1098 | grid_face_set_dot(g, d, 2); |
1099 | d = grid_get_dot(g, points, px + a, py + b); |
1100 | grid_face_set_dot(g, d, 3); |
1101 | d = grid_get_dot(g, points, px - a, py + b); |
1102 | grid_face_set_dot(g, d, 4); |
1103 | d = grid_get_dot(g, points, px - 2*a, py); |
1104 | grid_face_set_dot(g, d, 5); |
1105 | |
1106 | /* square below hexagon */ |
1107 | if (y < height - 1) { |
1108 | grid_face_add_new(g, 4); |
1109 | d = grid_get_dot(g, points, px - a, py + b); |
1110 | grid_face_set_dot(g, d, 0); |
1111 | d = grid_get_dot(g, points, px + a, py + b); |
1112 | grid_face_set_dot(g, d, 1); |
1113 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
1114 | grid_face_set_dot(g, d, 2); |
1115 | d = grid_get_dot(g, points, px - a, py + 2*a + b); |
1116 | grid_face_set_dot(g, d, 3); |
1117 | } |
1118 | |
1119 | /* square below right */ |
1120 | if ((x < width - 1) && (((x % 2) == 0) || (y < height - 1))) { |
1121 | grid_face_add_new(g, 4); |
1122 | d = grid_get_dot(g, points, px + 2*a, py); |
1123 | grid_face_set_dot(g, d, 0); |
1124 | d = grid_get_dot(g, points, px + 2*a + b, py + a); |
1125 | grid_face_set_dot(g, d, 1); |
1126 | d = grid_get_dot(g, points, px + a + b, py + a + b); |
1127 | grid_face_set_dot(g, d, 2); |
1128 | d = grid_get_dot(g, points, px + a, py + b); |
1129 | grid_face_set_dot(g, d, 3); |
1130 | } |
1131 | |
1132 | /* square below left */ |
1133 | if ((x > 0) && (((x % 2) == 0) || (y < height - 1))) { |
1134 | grid_face_add_new(g, 4); |
1135 | d = grid_get_dot(g, points, px - 2*a, py); |
1136 | grid_face_set_dot(g, d, 0); |
1137 | d = grid_get_dot(g, points, px - a, py + b); |
1138 | grid_face_set_dot(g, d, 1); |
1139 | d = grid_get_dot(g, points, px - a - b, py + a + b); |
1140 | grid_face_set_dot(g, d, 2); |
1141 | d = grid_get_dot(g, points, px - 2*a - b, py + a); |
1142 | grid_face_set_dot(g, d, 3); |
1143 | } |
1144 | |
1145 | /* Triangle below right */ |
1146 | if ((x < width - 1) && (y < height - 1)) { |
1147 | grid_face_add_new(g, 3); |
1148 | d = grid_get_dot(g, points, px + a, py + b); |
1149 | grid_face_set_dot(g, d, 0); |
1150 | d = grid_get_dot(g, points, px + a + b, py + a + b); |
1151 | grid_face_set_dot(g, d, 1); |
1152 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
1153 | grid_face_set_dot(g, d, 2); |
1154 | } |
1155 | |
1156 | /* Triangle below left */ |
1157 | if ((x > 0) && (y < height - 1)) { |
1158 | grid_face_add_new(g, 3); |
1159 | d = grid_get_dot(g, points, px - a, py + b); |
1160 | grid_face_set_dot(g, d, 0); |
1161 | d = grid_get_dot(g, points, px - a, py + 2*a + b); |
1162 | grid_face_set_dot(g, d, 1); |
1163 | d = grid_get_dot(g, points, px - a - b, py + a + b); |
1164 | grid_face_set_dot(g, d, 2); |
1165 | } |
1166 | } |
1167 | } |
1168 | |
1169 | freetree234(points); |
1170 | assert(g->num_faces <= max_faces); |
1171 | assert(g->num_dots <= max_dots); |
1172 | g->middle_face = g->faces + (height/2) * width + (width/2); |
1173 | |
1174 | grid_make_consistent(g); |
1175 | return g; |
1176 | } |
1177 | |
1178 | grid *grid_new_octagonal(int width, int height) |
1179 | { |
1180 | int x, y; |
1181 | /* b/a approx sqrt(2) */ |
1182 | int a = 29; |
1183 | int b = 41; |
1184 | |
1185 | /* Upper bounds - don't have to be exact */ |
1186 | int max_faces = 2 * width * height; |
1187 | int max_dots = 4 * (width + 1) * (height + 1); |
1188 | |
1189 | tree234 *points; |
1190 | |
1191 | grid *g = grid_new(); |
1192 | g->tilesize = 40; |
1193 | g->faces = snewn(max_faces, grid_face); |
1194 | g->dots = snewn(max_dots, grid_dot); |
1195 | |
1196 | points = newtree234(grid_point_cmp_fn); |
1197 | |
1198 | for (y = 0; y < height; y++) { |
1199 | for (x = 0; x < width; x++) { |
1200 | grid_dot *d; |
1201 | /* cell position */ |
1202 | int px = (2*a + b) * x; |
1203 | int py = (2*a + b) * y; |
1204 | /* octagon */ |
1205 | grid_face_add_new(g, 8); |
1206 | d = grid_get_dot(g, points, px + a, py); |
1207 | grid_face_set_dot(g, d, 0); |
1208 | d = grid_get_dot(g, points, px + a + b, py); |
1209 | grid_face_set_dot(g, d, 1); |
1210 | d = grid_get_dot(g, points, px + 2*a + b, py + a); |
1211 | grid_face_set_dot(g, d, 2); |
1212 | d = grid_get_dot(g, points, px + 2*a + b, py + a + b); |
1213 | grid_face_set_dot(g, d, 3); |
1214 | d = grid_get_dot(g, points, px + a + b, py + 2*a + b); |
1215 | grid_face_set_dot(g, d, 4); |
1216 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
1217 | grid_face_set_dot(g, d, 5); |
1218 | d = grid_get_dot(g, points, px, py + a + b); |
1219 | grid_face_set_dot(g, d, 6); |
1220 | d = grid_get_dot(g, points, px, py + a); |
1221 | grid_face_set_dot(g, d, 7); |
1222 | |
1223 | /* diamond */ |
1224 | if ((x > 0) && (y > 0)) { |
1225 | grid_face_add_new(g, 4); |
1226 | d = grid_get_dot(g, points, px, py - a); |
1227 | grid_face_set_dot(g, d, 0); |
1228 | d = grid_get_dot(g, points, px + a, py); |
1229 | grid_face_set_dot(g, d, 1); |
1230 | d = grid_get_dot(g, points, px, py + a); |
1231 | grid_face_set_dot(g, d, 2); |
1232 | d = grid_get_dot(g, points, px - a, py); |
1233 | grid_face_set_dot(g, d, 3); |
1234 | } |
1235 | } |
1236 | } |
1237 | |
1238 | freetree234(points); |
1239 | assert(g->num_faces <= max_faces); |
1240 | assert(g->num_dots <= max_dots); |
1241 | g->middle_face = g->faces + (height/2) * width + (width/2); |
1242 | |
1243 | grid_make_consistent(g); |
1244 | return g; |
1245 | } |
1246 | |
1247 | grid *grid_new_kites(int width, int height) |
1248 | { |
1249 | int x, y; |
1250 | /* b/a approx sqrt(3) */ |
1251 | int a = 15; |
1252 | int b = 26; |
1253 | |
1254 | /* Upper bounds - don't have to be exact */ |
1255 | int max_faces = 6 * width * height; |
1256 | int max_dots = 6 * (width + 1) * (height + 1); |
1257 | |
1258 | tree234 *points; |
1259 | |
1260 | grid *g = grid_new(); |
1261 | g->tilesize = 40; |
1262 | g->faces = snewn(max_faces, grid_face); |
1263 | g->dots = snewn(max_dots, grid_dot); |
1264 | |
1265 | points = newtree234(grid_point_cmp_fn); |
1266 | |
1267 | for (y = 0; y < height; y++) { |
1268 | for (x = 0; x < width; x++) { |
1269 | grid_dot *d; |
1270 | /* position of order-6 dot */ |
1271 | int px = 4*b * x; |
1272 | int py = 6*a * y; |
1273 | if (y % 2) |
1274 | px += 2*b; |
1275 | |
1276 | /* kite pointing up-left */ |
1277 | grid_face_add_new(g, 4); |
1278 | d = grid_get_dot(g, points, px, py); |
1279 | grid_face_set_dot(g, d, 0); |
1280 | d = grid_get_dot(g, points, px + 2*b, py); |
1281 | grid_face_set_dot(g, d, 1); |
1282 | d = grid_get_dot(g, points, px + 2*b, py + 2*a); |
1283 | grid_face_set_dot(g, d, 2); |
1284 | d = grid_get_dot(g, points, px + b, py + 3*a); |
1285 | grid_face_set_dot(g, d, 3); |
1286 | |
1287 | /* kite pointing up */ |
1288 | grid_face_add_new(g, 4); |
1289 | d = grid_get_dot(g, points, px, py); |
1290 | grid_face_set_dot(g, d, 0); |
1291 | d = grid_get_dot(g, points, px + b, py + 3*a); |
1292 | grid_face_set_dot(g, d, 1); |
1293 | d = grid_get_dot(g, points, px, py + 4*a); |
1294 | grid_face_set_dot(g, d, 2); |
1295 | d = grid_get_dot(g, points, px - b, py + 3*a); |
1296 | grid_face_set_dot(g, d, 3); |
1297 | |
1298 | /* kite pointing up-right */ |
1299 | grid_face_add_new(g, 4); |
1300 | d = grid_get_dot(g, points, px, py); |
1301 | grid_face_set_dot(g, d, 0); |
1302 | d = grid_get_dot(g, points, px - b, py + 3*a); |
1303 | grid_face_set_dot(g, d, 1); |
1304 | d = grid_get_dot(g, points, px - 2*b, py + 2*a); |
1305 | grid_face_set_dot(g, d, 2); |
1306 | d = grid_get_dot(g, points, px - 2*b, py); |
1307 | grid_face_set_dot(g, d, 3); |
1308 | |
1309 | /* kite pointing down-right */ |
1310 | grid_face_add_new(g, 4); |
1311 | d = grid_get_dot(g, points, px, py); |
1312 | grid_face_set_dot(g, d, 0); |
1313 | d = grid_get_dot(g, points, px - 2*b, py); |
1314 | grid_face_set_dot(g, d, 1); |
1315 | d = grid_get_dot(g, points, px - 2*b, py - 2*a); |
1316 | grid_face_set_dot(g, d, 2); |
1317 | d = grid_get_dot(g, points, px - b, py - 3*a); |
1318 | grid_face_set_dot(g, d, 3); |
1319 | |
1320 | /* kite pointing down */ |
1321 | grid_face_add_new(g, 4); |
1322 | d = grid_get_dot(g, points, px, py); |
1323 | grid_face_set_dot(g, d, 0); |
1324 | d = grid_get_dot(g, points, px - b, py - 3*a); |
1325 | grid_face_set_dot(g, d, 1); |
1326 | d = grid_get_dot(g, points, px, py - 4*a); |
1327 | grid_face_set_dot(g, d, 2); |
1328 | d = grid_get_dot(g, points, px + b, py - 3*a); |
1329 | grid_face_set_dot(g, d, 3); |
1330 | |
1331 | /* kite pointing down-left */ |
1332 | grid_face_add_new(g, 4); |
1333 | d = grid_get_dot(g, points, px, py); |
1334 | grid_face_set_dot(g, d, 0); |
1335 | d = grid_get_dot(g, points, px + b, py - 3*a); |
1336 | grid_face_set_dot(g, d, 1); |
1337 | d = grid_get_dot(g, points, px + 2*b, py - 2*a); |
1338 | grid_face_set_dot(g, d, 2); |
1339 | d = grid_get_dot(g, points, px + 2*b, py); |
1340 | grid_face_set_dot(g, d, 3); |
1341 | } |
1342 | } |
1343 | |
1344 | freetree234(points); |
1345 | assert(g->num_faces <= max_faces); |
1346 | assert(g->num_dots <= max_dots); |
1347 | g->middle_face = g->faces + 6 * ((height/2) * width + (width/2)); |
1348 | |
1349 | grid_make_consistent(g); |
1350 | return g; |
1351 | } |
1352 | |
1353 | /* ----------- End of grid generators ------------- */ |