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); |
7c95608a |
144 | if (new_dist < dist) { |
145 | new = d; |
146 | break; /* found closer dot */ |
147 | } |
148 | } |
149 | if (new != cur) |
150 | break; /* found closer dot */ |
151 | } |
152 | |
153 | if (new == cur) { |
154 | /* Didn't find a closer dot among the neighbours of 'cur' */ |
155 | break; |
156 | } else { |
157 | cur = new; |
158 | } |
159 | } |
7c95608a |
160 | /* 'cur' is nearest dot, so find which of the dot's edges is closest. */ |
161 | best_edge = NULL; |
162 | |
163 | for (i = 0; i < cur->order; i++) { |
164 | grid_edge *e = cur->edges[i]; |
b1535c90 |
165 | long e2; /* squared length of edge */ |
166 | long a2, b2; /* squared lengths of other sides */ |
7c95608a |
167 | double dist; |
168 | |
169 | /* See if edge e is eligible - the triangle must have acute angles |
170 | * at the edge's dots. |
171 | * Pythagoras formula h^2 = a^2 + b^2 detects right-angles, |
172 | * so detect acute angles by testing for h^2 < a^2 + b^2 */ |
b1535c90 |
173 | e2 = SQ((long)e->dot1->x - (long)e->dot2->x) + SQ((long)e->dot1->y - (long)e->dot2->y); |
174 | a2 = SQ((long)e->dot1->x - (long)x) + SQ((long)e->dot1->y - (long)y); |
175 | b2 = SQ((long)e->dot2->x - (long)x) + SQ((long)e->dot2->y - (long)y); |
7c95608a |
176 | if (a2 >= e2 + b2) continue; |
177 | if (b2 >= e2 + a2) continue; |
178 | |
179 | /* e is eligible so far. Now check the edge is reasonably close |
180 | * to where the user clicked. Don't want to toggle an edge if the |
181 | * click was way off the grid. |
182 | * There is room for experimentation here. We could check the |
183 | * perpendicular distance is within a certain fraction of the length |
184 | * of the edge. That amounts to testing a rectangular region around |
185 | * the edge. |
186 | * Alternatively, we could check that the angle at the point is obtuse. |
187 | * That would amount to testing a circular region with the edge as |
188 | * diameter. */ |
b1535c90 |
189 | dist = point_line_distance((long)x, (long)y, |
190 | (long)e->dot1->x, (long)e->dot1->y, |
191 | (long)e->dot2->x, (long)e->dot2->y); |
7c95608a |
192 | /* Is dist more than half edge length ? */ |
193 | if (4 * SQ(dist) > e2) |
194 | continue; |
195 | |
196 | if (best_edge == NULL || dist < best_distance) { |
197 | best_edge = e; |
198 | best_distance = dist; |
199 | } |
200 | } |
201 | return best_edge; |
202 | } |
203 | |
204 | /* ---------------------------------------------------------------------- |
205 | * Grid generation |
206 | */ |
207 | |
208 | #ifdef DEBUG_GRID |
209 | /* Show the basic grid information, before doing grid_make_consistent */ |
210 | static void grid_print_basic(grid *g) |
211 | { |
212 | /* TODO: Maybe we should generate an SVG image of the dots and lines |
213 | * of the grid here, before grid_make_consistent. |
214 | * Would help with debugging grid generation. */ |
215 | int i; |
216 | printf("--- Basic Grid Data ---\n"); |
217 | for (i = 0; i < g->num_faces; i++) { |
218 | grid_face *f = g->faces + i; |
219 | printf("Face %d: dots[", i); |
220 | int j; |
221 | for (j = 0; j < f->order; j++) { |
222 | grid_dot *d = f->dots[j]; |
223 | printf("%s%d", j ? "," : "", (int)(d - g->dots)); |
224 | } |
225 | printf("]\n"); |
226 | } |
227 | printf("Middle face: %d\n", (int)(g->middle_face - g->faces)); |
228 | } |
229 | /* Show the derived grid information, computed by grid_make_consistent */ |
230 | static void grid_print_derived(grid *g) |
231 | { |
232 | /* edges */ |
233 | int i; |
234 | printf("--- Derived Grid Data ---\n"); |
235 | for (i = 0; i < g->num_edges; i++) { |
236 | grid_edge *e = g->edges + i; |
237 | printf("Edge %d: dots[%d,%d] faces[%d,%d]\n", |
238 | i, (int)(e->dot1 - g->dots), (int)(e->dot2 - g->dots), |
239 | e->face1 ? (int)(e->face1 - g->faces) : -1, |
240 | e->face2 ? (int)(e->face2 - g->faces) : -1); |
241 | } |
242 | /* faces */ |
243 | for (i = 0; i < g->num_faces; i++) { |
244 | grid_face *f = g->faces + i; |
245 | int j; |
246 | printf("Face %d: faces[", i); |
247 | for (j = 0; j < f->order; j++) { |
248 | grid_edge *e = f->edges[j]; |
249 | grid_face *f2 = (e->face1 == f) ? e->face2 : e->face1; |
250 | printf("%s%d", j ? "," : "", f2 ? (int)(f2 - g->faces) : -1); |
251 | } |
252 | printf("]\n"); |
253 | } |
254 | /* dots */ |
255 | for (i = 0; i < g->num_dots; i++) { |
256 | grid_dot *d = g->dots + i; |
257 | int j; |
258 | printf("Dot %d: dots[", i); |
259 | for (j = 0; j < d->order; j++) { |
260 | grid_edge *e = d->edges[j]; |
261 | grid_dot *d2 = (e->dot1 == d) ? e->dot2 : e->dot1; |
262 | printf("%s%d", j ? "," : "", (int)(d2 - g->dots)); |
263 | } |
264 | printf("] faces["); |
265 | for (j = 0; j < d->order; j++) { |
266 | grid_face *f = d->faces[j]; |
267 | printf("%s%d", j ? "," : "", f ? (int)(f - g->faces) : -1); |
268 | } |
269 | printf("]\n"); |
270 | } |
271 | } |
272 | #endif /* DEBUG_GRID */ |
273 | |
274 | /* Helper function for building incomplete-edges list in |
275 | * grid_make_consistent() */ |
276 | static int grid_edge_bydots_cmpfn(void *v1, void *v2) |
277 | { |
278 | grid_edge *a = v1; |
279 | grid_edge *b = v2; |
280 | grid_dot *da, *db; |
281 | |
282 | /* Pointer subtraction is valid here, because all dots point into the |
283 | * same dot-list (g->dots). |
284 | * Edges are not "normalised" - the 2 dots could be stored in any order, |
285 | * so we need to take this into account when comparing edges. */ |
286 | |
287 | /* Compare first dots */ |
288 | da = (a->dot1 < a->dot2) ? a->dot1 : a->dot2; |
289 | db = (b->dot1 < b->dot2) ? b->dot1 : b->dot2; |
290 | if (da != db) |
291 | return db - da; |
292 | /* Compare last dots */ |
293 | da = (a->dot1 < a->dot2) ? a->dot2 : a->dot1; |
294 | db = (b->dot1 < b->dot2) ? b->dot2 : b->dot1; |
295 | if (da != db) |
296 | return db - da; |
297 | |
298 | return 0; |
299 | } |
300 | |
301 | /* Input: grid has its dots and faces initialised: |
302 | * - dots have (optionally) x and y coordinates, but no edges or faces |
303 | * (pointers are NULL). |
304 | * - edges not initialised at all |
305 | * - faces initialised and know which dots they have (but no edges yet). The |
306 | * dots around each face are assumed to be clockwise. |
307 | * |
308 | * Output: grid is complete and valid with all relationships defined. |
309 | */ |
310 | static void grid_make_consistent(grid *g) |
311 | { |
312 | int i; |
313 | tree234 *incomplete_edges; |
314 | grid_edge *next_new_edge; /* Where new edge will go into g->edges */ |
315 | |
316 | #ifdef DEBUG_GRID |
317 | grid_print_basic(g); |
318 | #endif |
319 | |
320 | /* ====== Stage 1 ====== |
321 | * Generate edges |
322 | */ |
323 | |
324 | /* We know how many dots and faces there are, so we can find the exact |
325 | * number of edges from Euler's polyhedral formula: F + V = E + 2 . |
326 | * We use "-1", not "-2" here, because Euler's formula includes the |
327 | * infinite face, which we don't count. */ |
328 | g->num_edges = g->num_faces + g->num_dots - 1; |
329 | g->edges = snewn(g->num_edges, grid_edge); |
330 | next_new_edge = g->edges; |
331 | |
332 | /* Iterate over faces, and over each face's dots, generating edges as we |
333 | * go. As we find each new edge, we can immediately fill in the edge's |
334 | * dots, but only one of the edge's faces. Later on in the iteration, we |
335 | * will find the same edge again (unless it's on the border), but we will |
336 | * know the other face. |
337 | * For efficiency, maintain a list of the incomplete edges, sorted by |
338 | * their dots. */ |
339 | incomplete_edges = newtree234(grid_edge_bydots_cmpfn); |
340 | for (i = 0; i < g->num_faces; i++) { |
341 | grid_face *f = g->faces + i; |
342 | int j; |
343 | for (j = 0; j < f->order; j++) { |
344 | grid_edge e; /* fake edge for searching */ |
345 | grid_edge *edge_found; |
346 | int j2 = j + 1; |
347 | if (j2 == f->order) |
348 | j2 = 0; |
349 | e.dot1 = f->dots[j]; |
350 | e.dot2 = f->dots[j2]; |
351 | /* Use del234 instead of find234, because we always want to |
352 | * remove the edge if found */ |
353 | edge_found = del234(incomplete_edges, &e); |
354 | if (edge_found) { |
355 | /* This edge already added, so fill out missing face. |
356 | * Edge is already removed from incomplete_edges. */ |
357 | edge_found->face2 = f; |
358 | } else { |
359 | assert(next_new_edge - g->edges < g->num_edges); |
360 | next_new_edge->dot1 = e.dot1; |
361 | next_new_edge->dot2 = e.dot2; |
362 | next_new_edge->face1 = f; |
363 | next_new_edge->face2 = NULL; /* potentially infinite face */ |
364 | add234(incomplete_edges, next_new_edge); |
365 | ++next_new_edge; |
366 | } |
367 | } |
368 | } |
369 | freetree234(incomplete_edges); |
370 | |
371 | /* ====== Stage 2 ====== |
372 | * For each face, build its edge list. |
373 | */ |
374 | |
375 | /* Allocate space for each edge list. Can do this, because each face's |
376 | * edge-list is the same size as its dot-list. */ |
377 | for (i = 0; i < g->num_faces; i++) { |
378 | grid_face *f = g->faces + i; |
379 | int j; |
380 | f->edges = snewn(f->order, grid_edge*); |
381 | /* Preload with NULLs, to help detect potential bugs. */ |
382 | for (j = 0; j < f->order; j++) |
383 | f->edges[j] = NULL; |
384 | } |
385 | |
386 | /* Iterate over each edge, and over both its faces. Add this edge to |
387 | * the face's edge-list, after finding where it should go in the |
388 | * sequence. */ |
389 | for (i = 0; i < g->num_edges; i++) { |
390 | grid_edge *e = g->edges + i; |
391 | int j; |
392 | for (j = 0; j < 2; j++) { |
393 | grid_face *f = j ? e->face2 : e->face1; |
394 | int k, k2; |
395 | if (f == NULL) continue; |
396 | /* Find one of the dots around the face */ |
397 | for (k = 0; k < f->order; k++) { |
398 | if (f->dots[k] == e->dot1) |
399 | break; /* found dot1 */ |
400 | } |
401 | assert(k != f->order); /* Must find the dot around this face */ |
402 | |
403 | /* Labelling scheme: as we walk clockwise around the face, |
404 | * starting at dot0 (f->dots[0]), we hit: |
405 | * (dot0), edge0, dot1, edge1, dot2,... |
406 | * |
407 | * 0 |
408 | * 0-----1 |
409 | * | |
410 | * |1 |
411 | * | |
412 | * 3-----2 |
413 | * 2 |
414 | * |
415 | * Therefore, edgeK joins dotK and dot{K+1} |
416 | */ |
417 | |
418 | /* Around this face, either the next dot or the previous dot |
419 | * must be e->dot2. Otherwise the edge is wrong. */ |
420 | k2 = k + 1; |
421 | if (k2 == f->order) |
422 | k2 = 0; |
423 | if (f->dots[k2] == e->dot2) { |
424 | /* dot1(k) and dot2(k2) go clockwise around this face, so add |
425 | * this edge at position k (see diagram). */ |
426 | assert(f->edges[k] == NULL); |
427 | f->edges[k] = e; |
428 | continue; |
429 | } |
430 | /* Try previous dot */ |
431 | k2 = k - 1; |
432 | if (k2 == -1) |
433 | k2 = f->order - 1; |
434 | if (f->dots[k2] == e->dot2) { |
435 | /* dot1(k) and dot2(k2) go anticlockwise around this face. */ |
436 | assert(f->edges[k2] == NULL); |
437 | f->edges[k2] = e; |
438 | continue; |
439 | } |
440 | assert(!"Grid broken: bad edge-face relationship"); |
441 | } |
442 | } |
443 | |
444 | /* ====== Stage 3 ====== |
445 | * For each dot, build its edge-list and face-list. |
446 | */ |
447 | |
448 | /* We don't know how many edges/faces go around each dot, so we can't |
449 | * allocate the right space for these lists. Pre-compute the sizes by |
450 | * iterating over each edge and recording a tally against each dot. */ |
451 | for (i = 0; i < g->num_dots; i++) { |
452 | g->dots[i].order = 0; |
453 | } |
454 | for (i = 0; i < g->num_edges; i++) { |
455 | grid_edge *e = g->edges + i; |
456 | ++(e->dot1->order); |
457 | ++(e->dot2->order); |
458 | } |
459 | /* Now we have the sizes, pre-allocate the edge and face lists. */ |
460 | for (i = 0; i < g->num_dots; i++) { |
461 | grid_dot *d = g->dots + i; |
462 | int j; |
463 | assert(d->order >= 2); /* sanity check */ |
464 | d->edges = snewn(d->order, grid_edge*); |
465 | d->faces = snewn(d->order, grid_face*); |
466 | for (j = 0; j < d->order; j++) { |
467 | d->edges[j] = NULL; |
468 | d->faces[j] = NULL; |
469 | } |
470 | } |
471 | /* For each dot, need to find a face that touches it, so we can seed |
472 | * the edge-face-edge-face process around each dot. */ |
473 | for (i = 0; i < g->num_faces; i++) { |
474 | grid_face *f = g->faces + i; |
475 | int j; |
476 | for (j = 0; j < f->order; j++) { |
477 | grid_dot *d = f->dots[j]; |
478 | d->faces[0] = f; |
479 | } |
480 | } |
481 | /* Each dot now has a face in its first slot. Generate the remaining |
482 | * faces and edges around the dot, by searching both clockwise and |
483 | * anticlockwise from the first face. Need to do both directions, |
484 | * because of the possibility of hitting the infinite face, which |
485 | * blocks progress. But there's only one such face, so we will |
486 | * succeed in finding every edge and face this way. */ |
487 | for (i = 0; i < g->num_dots; i++) { |
488 | grid_dot *d = g->dots + i; |
489 | int current_face1 = 0; /* ascends clockwise */ |
490 | int current_face2 = 0; /* descends anticlockwise */ |
491 | |
492 | /* Labelling scheme: as we walk clockwise around the dot, starting |
493 | * at face0 (d->faces[0]), we hit: |
494 | * (face0), edge0, face1, edge1, face2,... |
495 | * |
496 | * 0 |
497 | * | |
498 | * 0 | 1 |
499 | * | |
500 | * -----d-----1 |
501 | * | |
502 | * | 2 |
503 | * | |
504 | * 2 |
505 | * |
506 | * So, for example, face1 should be joined to edge0 and edge1, |
507 | * and those edges should appear in an anticlockwise sense around |
508 | * that face (see diagram). */ |
509 | |
510 | /* clockwise search */ |
511 | while (TRUE) { |
512 | grid_face *f = d->faces[current_face1]; |
513 | grid_edge *e; |
514 | int j; |
515 | assert(f != NULL); |
516 | /* find dot around this face */ |
517 | for (j = 0; j < f->order; j++) { |
518 | if (f->dots[j] == d) |
519 | break; |
520 | } |
521 | assert(j != f->order); /* must find dot */ |
522 | |
523 | /* Around f, required edge is anticlockwise from the dot. See |
524 | * the other labelling scheme higher up, for why we subtract 1 |
525 | * from j. */ |
526 | j--; |
527 | if (j == -1) |
528 | j = f->order - 1; |
529 | e = f->edges[j]; |
530 | d->edges[current_face1] = e; /* set edge */ |
531 | current_face1++; |
532 | if (current_face1 == d->order) |
533 | break; |
534 | else { |
535 | /* set face */ |
536 | d->faces[current_face1] = |
537 | (e->face1 == f) ? e->face2 : e->face1; |
538 | if (d->faces[current_face1] == NULL) |
539 | break; /* cannot progress beyond infinite face */ |
540 | } |
541 | } |
542 | /* If the clockwise search made it all the way round, don't need to |
543 | * bother with the anticlockwise search. */ |
544 | if (current_face1 == d->order) |
545 | continue; /* this dot is complete, move on to next dot */ |
546 | |
547 | /* anticlockwise search */ |
548 | while (TRUE) { |
549 | grid_face *f = d->faces[current_face2]; |
550 | grid_edge *e; |
551 | int j; |
552 | assert(f != NULL); |
553 | /* find dot around this face */ |
554 | for (j = 0; j < f->order; j++) { |
555 | if (f->dots[j] == d) |
556 | break; |
557 | } |
558 | assert(j != f->order); /* must find dot */ |
559 | |
560 | /* Around f, required edge is clockwise from the dot. */ |
561 | e = f->edges[j]; |
562 | |
563 | current_face2--; |
564 | if (current_face2 == -1) |
565 | current_face2 = d->order - 1; |
566 | d->edges[current_face2] = e; /* set edge */ |
567 | |
568 | /* set face */ |
569 | if (current_face2 == current_face1) |
570 | break; |
571 | d->faces[current_face2] = |
572 | (e->face1 == f) ? e->face2 : e->face1; |
573 | /* There's only 1 infinite face, so we must get all the way |
574 | * to current_face1 before we hit it. */ |
575 | assert(d->faces[current_face2]); |
576 | } |
577 | } |
578 | |
579 | /* ====== Stage 4 ====== |
580 | * Compute other grid settings |
581 | */ |
582 | |
583 | /* Bounding rectangle */ |
584 | for (i = 0; i < g->num_dots; i++) { |
585 | grid_dot *d = g->dots + i; |
586 | if (i == 0) { |
587 | g->lowest_x = g->highest_x = d->x; |
588 | g->lowest_y = g->highest_y = d->y; |
589 | } else { |
590 | g->lowest_x = min(g->lowest_x, d->x); |
591 | g->highest_x = max(g->highest_x, d->x); |
592 | g->lowest_y = min(g->lowest_y, d->y); |
593 | g->highest_y = max(g->highest_y, d->y); |
594 | } |
595 | } |
596 | |
597 | #ifdef DEBUG_GRID |
598 | grid_print_derived(g); |
599 | #endif |
600 | } |
601 | |
602 | /* Helpers for making grid-generation easier. These functions are only |
603 | * intended for use during grid generation. */ |
604 | |
605 | /* Comparison function for the (tree234) sorted dot list */ |
606 | static int grid_point_cmp_fn(void *v1, void *v2) |
607 | { |
608 | grid_dot *p1 = v1; |
609 | grid_dot *p2 = v2; |
610 | if (p1->y != p2->y) |
611 | return p2->y - p1->y; |
612 | else |
613 | return p2->x - p1->x; |
614 | } |
615 | /* Add a new face to the grid, with its dot list allocated. |
616 | * Assumes there's enough space allocated for the new face in grid->faces */ |
617 | static void grid_face_add_new(grid *g, int face_size) |
618 | { |
619 | int i; |
620 | grid_face *new_face = g->faces + g->num_faces; |
621 | new_face->order = face_size; |
622 | new_face->dots = snewn(face_size, grid_dot*); |
623 | for (i = 0; i < face_size; i++) |
624 | new_face->dots[i] = NULL; |
625 | new_face->edges = NULL; |
626 | g->num_faces++; |
627 | } |
628 | /* Assumes dot list has enough space */ |
629 | static grid_dot *grid_dot_add_new(grid *g, int x, int y) |
630 | { |
631 | grid_dot *new_dot = g->dots + g->num_dots; |
632 | new_dot->order = 0; |
633 | new_dot->edges = NULL; |
634 | new_dot->faces = NULL; |
635 | new_dot->x = x; |
636 | new_dot->y = y; |
637 | g->num_dots++; |
638 | return new_dot; |
639 | } |
640 | /* Retrieve a dot with these (x,y) coordinates. Either return an existing dot |
641 | * in the dot_list, or add a new dot to the grid (and the dot_list) and |
642 | * return that. |
643 | * Assumes g->dots has enough capacity allocated */ |
644 | static grid_dot *grid_get_dot(grid *g, tree234 *dot_list, int x, int y) |
645 | { |
3466f373 |
646 | grid_dot test, *ret; |
647 | |
648 | test.order = 0; |
649 | test.edges = NULL; |
650 | test.faces = NULL; |
651 | test.x = x; |
652 | test.y = y; |
653 | ret = find234(dot_list, &test, NULL); |
7c95608a |
654 | if (ret) |
655 | return ret; |
656 | |
657 | ret = grid_dot_add_new(g, x, y); |
658 | add234(dot_list, ret); |
659 | return ret; |
660 | } |
661 | |
662 | /* Sets the last face of the grid to include this dot, at this position |
663 | * around the face. Assumes num_faces is at least 1 (a new face has |
664 | * previously been added, with the required number of dots allocated) */ |
665 | static void grid_face_set_dot(grid *g, grid_dot *d, int position) |
666 | { |
667 | grid_face *last_face = g->faces + g->num_faces - 1; |
668 | last_face->dots[position] = d; |
669 | } |
670 | |
671 | /* ------ Generate various types of grid ------ */ |
672 | |
673 | /* General method is to generate faces, by calculating their dot coordinates. |
674 | * As new faces are added, we keep track of all the dots so we can tell when |
675 | * a new face reuses an existing dot. For example, two squares touching at an |
676 | * edge would generate six unique dots: four dots from the first face, then |
677 | * two additional dots for the second face, because we detect the other two |
678 | * dots have already been taken up. This list is stored in a tree234 |
679 | * called "points". No extra memory-allocation needed here - we store the |
680 | * actual grid_dot* pointers, which all point into the g->dots list. |
681 | * For this reason, we have to calculate coordinates in such a way as to |
682 | * eliminate any rounding errors, so we can detect when a dot on one |
683 | * face precisely lands on a dot of a different face. No floating-point |
684 | * arithmetic here! |
685 | */ |
686 | |
687 | grid *grid_new_square(int width, int height) |
688 | { |
689 | int x, y; |
690 | /* Side length */ |
691 | int a = 20; |
692 | |
693 | /* Upper bounds - don't have to be exact */ |
694 | int max_faces = width * height; |
695 | int max_dots = (width + 1) * (height + 1); |
696 | |
697 | tree234 *points; |
698 | |
699 | grid *g = grid_new(); |
700 | g->tilesize = a; |
701 | g->faces = snewn(max_faces, grid_face); |
702 | g->dots = snewn(max_dots, grid_dot); |
703 | |
704 | points = newtree234(grid_point_cmp_fn); |
705 | |
706 | /* generate square faces */ |
707 | for (y = 0; y < height; y++) { |
708 | for (x = 0; x < width; x++) { |
709 | grid_dot *d; |
710 | /* face position */ |
711 | int px = a * x; |
712 | int py = a * y; |
713 | |
714 | grid_face_add_new(g, 4); |
715 | d = grid_get_dot(g, points, px, py); |
716 | grid_face_set_dot(g, d, 0); |
717 | d = grid_get_dot(g, points, px + a, py); |
718 | grid_face_set_dot(g, d, 1); |
719 | d = grid_get_dot(g, points, px + a, py + a); |
720 | grid_face_set_dot(g, d, 2); |
721 | d = grid_get_dot(g, points, px, py + a); |
722 | grid_face_set_dot(g, d, 3); |
723 | } |
724 | } |
725 | |
726 | freetree234(points); |
727 | assert(g->num_faces <= max_faces); |
728 | assert(g->num_dots <= max_dots); |
729 | g->middle_face = g->faces + (height/2) * width + (width/2); |
730 | |
731 | grid_make_consistent(g); |
732 | return g; |
733 | } |
734 | |
735 | grid *grid_new_honeycomb(int width, int height) |
736 | { |
737 | int x, y; |
738 | /* Vector for side of hexagon - ratio is close to sqrt(3) */ |
739 | int a = 15; |
740 | int b = 26; |
741 | |
742 | /* Upper bounds - don't have to be exact */ |
743 | int max_faces = width * height; |
744 | int max_dots = 2 * (width + 1) * (height + 1); |
745 | |
746 | tree234 *points; |
747 | |
748 | grid *g = grid_new(); |
749 | g->tilesize = 3 * a; |
750 | g->faces = snewn(max_faces, grid_face); |
751 | g->dots = snewn(max_dots, grid_dot); |
752 | |
753 | points = newtree234(grid_point_cmp_fn); |
754 | |
755 | /* generate hexagonal faces */ |
756 | for (y = 0; y < height; y++) { |
757 | for (x = 0; x < width; x++) { |
758 | grid_dot *d; |
759 | /* face centre */ |
760 | int cx = 3 * a * x; |
761 | int cy = 2 * b * y; |
762 | if (x % 2) |
763 | cy += b; |
764 | grid_face_add_new(g, 6); |
765 | |
766 | d = grid_get_dot(g, points, cx - a, cy - b); |
767 | grid_face_set_dot(g, d, 0); |
768 | d = grid_get_dot(g, points, cx + a, cy - b); |
769 | grid_face_set_dot(g, d, 1); |
770 | d = grid_get_dot(g, points, cx + 2*a, cy); |
771 | grid_face_set_dot(g, d, 2); |
772 | d = grid_get_dot(g, points, cx + a, cy + b); |
773 | grid_face_set_dot(g, d, 3); |
774 | d = grid_get_dot(g, points, cx - a, cy + b); |
775 | grid_face_set_dot(g, d, 4); |
776 | d = grid_get_dot(g, points, cx - 2*a, cy); |
777 | grid_face_set_dot(g, d, 5); |
778 | } |
779 | } |
780 | |
781 | freetree234(points); |
782 | assert(g->num_faces <= max_faces); |
783 | assert(g->num_dots <= max_dots); |
784 | g->middle_face = g->faces + (height/2) * width + (width/2); |
785 | |
786 | grid_make_consistent(g); |
787 | return g; |
788 | } |
789 | |
790 | /* Doesn't use the previous method of generation, it pre-dates it! |
791 | * A triangular grid is just about simple enough to do by "brute force" */ |
792 | grid *grid_new_triangular(int width, int height) |
793 | { |
794 | int x,y; |
795 | |
796 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
797 | int vec_x = 15; |
798 | int vec_y = 26; |
799 | |
800 | int index; |
801 | |
802 | /* convenient alias */ |
803 | int w = width + 1; |
804 | |
805 | grid *g = grid_new(); |
806 | g->tilesize = 18; /* adjust to your taste */ |
807 | |
808 | g->num_faces = width * height * 2; |
809 | g->num_dots = (width + 1) * (height + 1); |
810 | g->faces = snewn(g->num_faces, grid_face); |
811 | g->dots = snewn(g->num_dots, grid_dot); |
812 | |
813 | /* generate dots */ |
814 | index = 0; |
815 | for (y = 0; y <= height; y++) { |
816 | for (x = 0; x <= width; x++) { |
817 | grid_dot *d = g->dots + index; |
818 | /* odd rows are offset to the right */ |
819 | d->order = 0; |
820 | d->edges = NULL; |
821 | d->faces = NULL; |
822 | d->x = x * 2 * vec_x + ((y % 2) ? vec_x : 0); |
823 | d->y = y * vec_y; |
824 | index++; |
825 | } |
826 | } |
827 | |
828 | /* generate faces */ |
829 | index = 0; |
830 | for (y = 0; y < height; y++) { |
831 | for (x = 0; x < width; x++) { |
832 | /* initialise two faces for this (x,y) */ |
833 | grid_face *f1 = g->faces + index; |
834 | grid_face *f2 = f1 + 1; |
835 | f1->edges = NULL; |
836 | f1->order = 3; |
837 | f1->dots = snewn(f1->order, grid_dot*); |
838 | f2->edges = NULL; |
839 | f2->order = 3; |
840 | f2->dots = snewn(f2->order, grid_dot*); |
841 | |
842 | /* face descriptions depend on whether the row-number is |
843 | * odd or even */ |
844 | if (y % 2) { |
845 | f1->dots[0] = g->dots + y * w + x; |
846 | f1->dots[1] = g->dots + (y + 1) * w + x + 1; |
847 | f1->dots[2] = g->dots + (y + 1) * w + x; |
848 | f2->dots[0] = g->dots + y * w + x; |
849 | f2->dots[1] = g->dots + y * w + x + 1; |
850 | f2->dots[2] = g->dots + (y + 1) * w + x + 1; |
851 | } else { |
852 | f1->dots[0] = g->dots + y * w + x; |
853 | f1->dots[1] = g->dots + y * w + x + 1; |
854 | f1->dots[2] = g->dots + (y + 1) * w + x; |
855 | f2->dots[0] = g->dots + y * w + x + 1; |
856 | f2->dots[1] = g->dots + (y + 1) * w + x + 1; |
857 | f2->dots[2] = g->dots + (y + 1) * w + x; |
858 | } |
859 | index += 2; |
860 | } |
861 | } |
862 | |
863 | /* "+ width" takes us to the middle of the row, because each row has |
864 | * (2*width) faces. */ |
865 | g->middle_face = g->faces + (height / 2) * 2 * width + width; |
866 | |
867 | grid_make_consistent(g); |
868 | return g; |
869 | } |
870 | |
871 | grid *grid_new_snubsquare(int width, int height) |
872 | { |
873 | int x, y; |
874 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
875 | int a = 15; |
876 | int b = 26; |
877 | |
878 | /* Upper bounds - don't have to be exact */ |
879 | int max_faces = 3 * width * height; |
880 | int max_dots = 2 * (width + 1) * (height + 1); |
881 | |
882 | tree234 *points; |
883 | |
884 | grid *g = grid_new(); |
885 | g->tilesize = 18; |
886 | g->faces = snewn(max_faces, grid_face); |
887 | g->dots = snewn(max_dots, grid_dot); |
888 | |
889 | points = newtree234(grid_point_cmp_fn); |
890 | |
891 | for (y = 0; y < height; y++) { |
892 | for (x = 0; x < width; x++) { |
893 | grid_dot *d; |
894 | /* face position */ |
895 | int px = (a + b) * x; |
896 | int py = (a + b) * y; |
897 | |
898 | /* generate square faces */ |
899 | grid_face_add_new(g, 4); |
900 | if ((x + y) % 2) { |
901 | d = grid_get_dot(g, points, px + a, py); |
902 | grid_face_set_dot(g, d, 0); |
903 | d = grid_get_dot(g, points, px + a + b, py + a); |
904 | grid_face_set_dot(g, d, 1); |
905 | d = grid_get_dot(g, points, px + b, py + a + b); |
906 | grid_face_set_dot(g, d, 2); |
907 | d = grid_get_dot(g, points, px, py + b); |
908 | grid_face_set_dot(g, d, 3); |
909 | } else { |
910 | d = grid_get_dot(g, points, px + b, py); |
911 | grid_face_set_dot(g, d, 0); |
912 | d = grid_get_dot(g, points, px + a + b, py + b); |
913 | grid_face_set_dot(g, d, 1); |
914 | d = grid_get_dot(g, points, px + a, py + a + b); |
915 | grid_face_set_dot(g, d, 2); |
916 | d = grid_get_dot(g, points, px, py + a); |
917 | grid_face_set_dot(g, d, 3); |
918 | } |
919 | |
920 | /* generate up/down triangles */ |
921 | if (x > 0) { |
922 | grid_face_add_new(g, 3); |
923 | if ((x + y) % 2) { |
924 | d = grid_get_dot(g, points, px + a, py); |
925 | grid_face_set_dot(g, d, 0); |
926 | d = grid_get_dot(g, points, px, py + b); |
927 | grid_face_set_dot(g, d, 1); |
928 | d = grid_get_dot(g, points, px - a, py); |
929 | grid_face_set_dot(g, d, 2); |
930 | } else { |
931 | d = grid_get_dot(g, points, px, py + a); |
932 | grid_face_set_dot(g, d, 0); |
933 | d = grid_get_dot(g, points, px + a, py + a + b); |
934 | grid_face_set_dot(g, d, 1); |
935 | d = grid_get_dot(g, points, px - a, py + a + b); |
936 | grid_face_set_dot(g, d, 2); |
937 | } |
938 | } |
939 | |
940 | /* generate left/right triangles */ |
941 | if (y > 0) { |
942 | grid_face_add_new(g, 3); |
943 | if ((x + y) % 2) { |
944 | d = grid_get_dot(g, points, px + a, py); |
945 | grid_face_set_dot(g, d, 0); |
946 | d = grid_get_dot(g, points, px + a + b, py - a); |
947 | grid_face_set_dot(g, d, 1); |
948 | d = grid_get_dot(g, points, px + a + b, py + a); |
949 | grid_face_set_dot(g, d, 2); |
950 | } else { |
951 | d = grid_get_dot(g, points, px, py - a); |
952 | grid_face_set_dot(g, d, 0); |
953 | d = grid_get_dot(g, points, px + b, py); |
954 | grid_face_set_dot(g, d, 1); |
955 | d = grid_get_dot(g, points, px, py + a); |
956 | grid_face_set_dot(g, d, 2); |
957 | } |
958 | } |
959 | } |
960 | } |
961 | |
962 | freetree234(points); |
963 | assert(g->num_faces <= max_faces); |
964 | assert(g->num_dots <= max_dots); |
965 | g->middle_face = g->faces + (height/2) * width + (width/2); |
966 | |
967 | grid_make_consistent(g); |
968 | return g; |
969 | } |
970 | |
971 | grid *grid_new_cairo(int width, int height) |
972 | { |
973 | int x, y; |
974 | /* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */ |
975 | int a = 14; |
976 | int b = 31; |
977 | |
978 | /* Upper bounds - don't have to be exact */ |
979 | int max_faces = 2 * width * height; |
980 | int max_dots = 3 * (width + 1) * (height + 1); |
981 | |
982 | tree234 *points; |
983 | |
984 | grid *g = grid_new(); |
985 | g->tilesize = 40; |
986 | g->faces = snewn(max_faces, grid_face); |
987 | g->dots = snewn(max_dots, grid_dot); |
988 | |
989 | points = newtree234(grid_point_cmp_fn); |
990 | |
991 | for (y = 0; y < height; y++) { |
992 | for (x = 0; x < width; x++) { |
993 | grid_dot *d; |
994 | /* cell position */ |
995 | int px = 2 * b * x; |
996 | int py = 2 * b * y; |
997 | |
998 | /* horizontal pentagons */ |
999 | if (y > 0) { |
1000 | grid_face_add_new(g, 5); |
1001 | if ((x + y) % 2) { |
1002 | d = grid_get_dot(g, points, px + a, py - b); |
1003 | grid_face_set_dot(g, d, 0); |
1004 | d = grid_get_dot(g, points, px + 2*b - a, py - b); |
1005 | grid_face_set_dot(g, d, 1); |
1006 | d = grid_get_dot(g, points, px + 2*b, py); |
1007 | grid_face_set_dot(g, d, 2); |
1008 | d = grid_get_dot(g, points, px + b, py + a); |
1009 | grid_face_set_dot(g, d, 3); |
1010 | d = grid_get_dot(g, points, px, py); |
1011 | grid_face_set_dot(g, d, 4); |
1012 | } else { |
1013 | d = grid_get_dot(g, points, px, py); |
1014 | grid_face_set_dot(g, d, 0); |
1015 | d = grid_get_dot(g, points, px + b, py - a); |
1016 | grid_face_set_dot(g, d, 1); |
1017 | d = grid_get_dot(g, points, px + 2*b, py); |
1018 | grid_face_set_dot(g, d, 2); |
1019 | d = grid_get_dot(g, points, px + 2*b - a, py + b); |
1020 | grid_face_set_dot(g, d, 3); |
1021 | d = grid_get_dot(g, points, px + a, py + b); |
1022 | grid_face_set_dot(g, d, 4); |
1023 | } |
1024 | } |
1025 | /* vertical pentagons */ |
1026 | if (x > 0) { |
1027 | grid_face_add_new(g, 5); |
1028 | if ((x + y) % 2) { |
1029 | d = grid_get_dot(g, points, px, py); |
1030 | grid_face_set_dot(g, d, 0); |
1031 | d = grid_get_dot(g, points, px + b, py + a); |
1032 | grid_face_set_dot(g, d, 1); |
1033 | d = grid_get_dot(g, points, px + b, py + 2*b - a); |
1034 | grid_face_set_dot(g, d, 2); |
1035 | d = grid_get_dot(g, points, px, py + 2*b); |
1036 | grid_face_set_dot(g, d, 3); |
1037 | d = grid_get_dot(g, points, px - a, py + b); |
1038 | grid_face_set_dot(g, d, 4); |
1039 | } else { |
1040 | d = grid_get_dot(g, points, px, py); |
1041 | grid_face_set_dot(g, d, 0); |
1042 | d = grid_get_dot(g, points, px + a, py + b); |
1043 | grid_face_set_dot(g, d, 1); |
1044 | d = grid_get_dot(g, points, px, py + 2*b); |
1045 | grid_face_set_dot(g, d, 2); |
1046 | d = grid_get_dot(g, points, px - b, py + 2*b - a); |
1047 | grid_face_set_dot(g, d, 3); |
1048 | d = grid_get_dot(g, points, px - b, py + a); |
1049 | grid_face_set_dot(g, d, 4); |
1050 | } |
1051 | } |
1052 | } |
1053 | } |
1054 | |
1055 | freetree234(points); |
1056 | assert(g->num_faces <= max_faces); |
1057 | assert(g->num_dots <= max_dots); |
1058 | g->middle_face = g->faces + (height/2) * width + (width/2); |
1059 | |
1060 | grid_make_consistent(g); |
1061 | return g; |
1062 | } |
1063 | |
1064 | grid *grid_new_greathexagonal(int width, int height) |
1065 | { |
1066 | int x, y; |
1067 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
1068 | int a = 15; |
1069 | int b = 26; |
1070 | |
1071 | /* Upper bounds - don't have to be exact */ |
1072 | int max_faces = 6 * (width + 1) * (height + 1); |
1073 | int max_dots = 6 * width * height; |
1074 | |
1075 | tree234 *points; |
1076 | |
1077 | grid *g = grid_new(); |
1078 | g->tilesize = 18; |
1079 | g->faces = snewn(max_faces, grid_face); |
1080 | g->dots = snewn(max_dots, grid_dot); |
1081 | |
1082 | points = newtree234(grid_point_cmp_fn); |
1083 | |
1084 | for (y = 0; y < height; y++) { |
1085 | for (x = 0; x < width; x++) { |
1086 | grid_dot *d; |
1087 | /* centre of hexagon */ |
1088 | int px = (3*a + b) * x; |
1089 | int py = (2*a + 2*b) * y; |
1090 | if (x % 2) |
1091 | py += a + b; |
1092 | |
1093 | /* hexagon */ |
1094 | grid_face_add_new(g, 6); |
1095 | d = grid_get_dot(g, points, px - a, py - b); |
1096 | grid_face_set_dot(g, d, 0); |
1097 | d = grid_get_dot(g, points, px + a, py - b); |
1098 | grid_face_set_dot(g, d, 1); |
1099 | d = grid_get_dot(g, points, px + 2*a, py); |
1100 | grid_face_set_dot(g, d, 2); |
1101 | d = grid_get_dot(g, points, px + a, py + b); |
1102 | grid_face_set_dot(g, d, 3); |
1103 | d = grid_get_dot(g, points, px - a, py + b); |
1104 | grid_face_set_dot(g, d, 4); |
1105 | d = grid_get_dot(g, points, px - 2*a, py); |
1106 | grid_face_set_dot(g, d, 5); |
1107 | |
1108 | /* square below hexagon */ |
1109 | if (y < height - 1) { |
1110 | grid_face_add_new(g, 4); |
1111 | d = grid_get_dot(g, points, px - a, py + b); |
1112 | grid_face_set_dot(g, d, 0); |
1113 | d = grid_get_dot(g, points, px + a, py + b); |
1114 | grid_face_set_dot(g, d, 1); |
1115 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
1116 | grid_face_set_dot(g, d, 2); |
1117 | d = grid_get_dot(g, points, px - a, py + 2*a + b); |
1118 | grid_face_set_dot(g, d, 3); |
1119 | } |
1120 | |
1121 | /* square below right */ |
1122 | if ((x < width - 1) && (((x % 2) == 0) || (y < height - 1))) { |
1123 | grid_face_add_new(g, 4); |
1124 | d = grid_get_dot(g, points, px + 2*a, py); |
1125 | grid_face_set_dot(g, d, 0); |
1126 | d = grid_get_dot(g, points, px + 2*a + b, py + a); |
1127 | grid_face_set_dot(g, d, 1); |
1128 | d = grid_get_dot(g, points, px + a + b, py + a + b); |
1129 | grid_face_set_dot(g, d, 2); |
1130 | d = grid_get_dot(g, points, px + a, py + b); |
1131 | grid_face_set_dot(g, d, 3); |
1132 | } |
1133 | |
1134 | /* square below left */ |
1135 | if ((x > 0) && (((x % 2) == 0) || (y < height - 1))) { |
1136 | grid_face_add_new(g, 4); |
1137 | d = grid_get_dot(g, points, px - 2*a, py); |
1138 | grid_face_set_dot(g, d, 0); |
1139 | d = grid_get_dot(g, points, px - a, py + b); |
1140 | grid_face_set_dot(g, d, 1); |
1141 | d = grid_get_dot(g, points, px - a - b, py + a + b); |
1142 | grid_face_set_dot(g, d, 2); |
1143 | d = grid_get_dot(g, points, px - 2*a - b, py + a); |
1144 | grid_face_set_dot(g, d, 3); |
1145 | } |
1146 | |
1147 | /* Triangle below right */ |
1148 | if ((x < width - 1) && (y < height - 1)) { |
1149 | grid_face_add_new(g, 3); |
1150 | d = grid_get_dot(g, points, px + a, py + b); |
1151 | grid_face_set_dot(g, d, 0); |
1152 | d = grid_get_dot(g, points, px + a + b, py + a + b); |
1153 | grid_face_set_dot(g, d, 1); |
1154 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
1155 | grid_face_set_dot(g, d, 2); |
1156 | } |
1157 | |
1158 | /* Triangle below left */ |
1159 | if ((x > 0) && (y < height - 1)) { |
1160 | grid_face_add_new(g, 3); |
1161 | d = grid_get_dot(g, points, px - a, py + b); |
1162 | grid_face_set_dot(g, d, 0); |
1163 | d = grid_get_dot(g, points, px - a, py + 2*a + b); |
1164 | grid_face_set_dot(g, d, 1); |
1165 | d = grid_get_dot(g, points, px - a - b, py + a + b); |
1166 | grid_face_set_dot(g, d, 2); |
1167 | } |
1168 | } |
1169 | } |
1170 | |
1171 | freetree234(points); |
1172 | assert(g->num_faces <= max_faces); |
1173 | assert(g->num_dots <= max_dots); |
1174 | g->middle_face = g->faces + (height/2) * width + (width/2); |
1175 | |
1176 | grid_make_consistent(g); |
1177 | return g; |
1178 | } |
1179 | |
1180 | grid *grid_new_octagonal(int width, int height) |
1181 | { |
1182 | int x, y; |
1183 | /* b/a approx sqrt(2) */ |
1184 | int a = 29; |
1185 | int b = 41; |
1186 | |
1187 | /* Upper bounds - don't have to be exact */ |
1188 | int max_faces = 2 * width * height; |
1189 | int max_dots = 4 * (width + 1) * (height + 1); |
1190 | |
1191 | tree234 *points; |
1192 | |
1193 | grid *g = grid_new(); |
1194 | g->tilesize = 40; |
1195 | g->faces = snewn(max_faces, grid_face); |
1196 | g->dots = snewn(max_dots, grid_dot); |
1197 | |
1198 | points = newtree234(grid_point_cmp_fn); |
1199 | |
1200 | for (y = 0; y < height; y++) { |
1201 | for (x = 0; x < width; x++) { |
1202 | grid_dot *d; |
1203 | /* cell position */ |
1204 | int px = (2*a + b) * x; |
1205 | int py = (2*a + b) * y; |
1206 | /* octagon */ |
1207 | grid_face_add_new(g, 8); |
1208 | d = grid_get_dot(g, points, px + a, py); |
1209 | grid_face_set_dot(g, d, 0); |
1210 | d = grid_get_dot(g, points, px + a + b, py); |
1211 | grid_face_set_dot(g, d, 1); |
1212 | d = grid_get_dot(g, points, px + 2*a + b, py + a); |
1213 | grid_face_set_dot(g, d, 2); |
1214 | d = grid_get_dot(g, points, px + 2*a + b, py + a + b); |
1215 | grid_face_set_dot(g, d, 3); |
1216 | d = grid_get_dot(g, points, px + a + b, py + 2*a + b); |
1217 | grid_face_set_dot(g, d, 4); |
1218 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
1219 | grid_face_set_dot(g, d, 5); |
1220 | d = grid_get_dot(g, points, px, py + a + b); |
1221 | grid_face_set_dot(g, d, 6); |
1222 | d = grid_get_dot(g, points, px, py + a); |
1223 | grid_face_set_dot(g, d, 7); |
1224 | |
1225 | /* diamond */ |
1226 | if ((x > 0) && (y > 0)) { |
1227 | grid_face_add_new(g, 4); |
1228 | d = grid_get_dot(g, points, px, py - a); |
1229 | grid_face_set_dot(g, d, 0); |
1230 | d = grid_get_dot(g, points, px + a, py); |
1231 | grid_face_set_dot(g, d, 1); |
1232 | d = grid_get_dot(g, points, px, py + a); |
1233 | grid_face_set_dot(g, d, 2); |
1234 | d = grid_get_dot(g, points, px - a, py); |
1235 | grid_face_set_dot(g, d, 3); |
1236 | } |
1237 | } |
1238 | } |
1239 | |
1240 | freetree234(points); |
1241 | assert(g->num_faces <= max_faces); |
1242 | assert(g->num_dots <= max_dots); |
1243 | g->middle_face = g->faces + (height/2) * width + (width/2); |
1244 | |
1245 | grid_make_consistent(g); |
1246 | return g; |
1247 | } |
1248 | |
1249 | grid *grid_new_kites(int width, int height) |
1250 | { |
1251 | int x, y; |
1252 | /* b/a approx sqrt(3) */ |
1253 | int a = 15; |
1254 | int b = 26; |
1255 | |
1256 | /* Upper bounds - don't have to be exact */ |
1257 | int max_faces = 6 * width * height; |
1258 | int max_dots = 6 * (width + 1) * (height + 1); |
1259 | |
1260 | tree234 *points; |
1261 | |
1262 | grid *g = grid_new(); |
1263 | g->tilesize = 40; |
1264 | g->faces = snewn(max_faces, grid_face); |
1265 | g->dots = snewn(max_dots, grid_dot); |
1266 | |
1267 | points = newtree234(grid_point_cmp_fn); |
1268 | |
1269 | for (y = 0; y < height; y++) { |
1270 | for (x = 0; x < width; x++) { |
1271 | grid_dot *d; |
1272 | /* position of order-6 dot */ |
1273 | int px = 4*b * x; |
1274 | int py = 6*a * y; |
1275 | if (y % 2) |
1276 | px += 2*b; |
1277 | |
1278 | /* kite pointing up-left */ |
1279 | grid_face_add_new(g, 4); |
1280 | d = grid_get_dot(g, points, px, py); |
1281 | grid_face_set_dot(g, d, 0); |
1282 | d = grid_get_dot(g, points, px + 2*b, py); |
1283 | grid_face_set_dot(g, d, 1); |
1284 | d = grid_get_dot(g, points, px + 2*b, py + 2*a); |
1285 | grid_face_set_dot(g, d, 2); |
1286 | d = grid_get_dot(g, points, px + b, py + 3*a); |
1287 | grid_face_set_dot(g, d, 3); |
1288 | |
1289 | /* kite pointing up */ |
1290 | grid_face_add_new(g, 4); |
1291 | d = grid_get_dot(g, points, px, py); |
1292 | grid_face_set_dot(g, d, 0); |
1293 | d = grid_get_dot(g, points, px + b, py + 3*a); |
1294 | grid_face_set_dot(g, d, 1); |
1295 | d = grid_get_dot(g, points, px, py + 4*a); |
1296 | grid_face_set_dot(g, d, 2); |
1297 | d = grid_get_dot(g, points, px - b, py + 3*a); |
1298 | grid_face_set_dot(g, d, 3); |
1299 | |
1300 | /* kite pointing up-right */ |
1301 | grid_face_add_new(g, 4); |
1302 | d = grid_get_dot(g, points, px, py); |
1303 | grid_face_set_dot(g, d, 0); |
1304 | d = grid_get_dot(g, points, px - b, py + 3*a); |
1305 | grid_face_set_dot(g, d, 1); |
1306 | d = grid_get_dot(g, points, px - 2*b, py + 2*a); |
1307 | grid_face_set_dot(g, d, 2); |
1308 | d = grid_get_dot(g, points, px - 2*b, py); |
1309 | grid_face_set_dot(g, d, 3); |
1310 | |
1311 | /* kite pointing down-right */ |
1312 | grid_face_add_new(g, 4); |
1313 | d = grid_get_dot(g, points, px, py); |
1314 | grid_face_set_dot(g, d, 0); |
1315 | d = grid_get_dot(g, points, px - 2*b, py); |
1316 | grid_face_set_dot(g, d, 1); |
1317 | d = grid_get_dot(g, points, px - 2*b, py - 2*a); |
1318 | grid_face_set_dot(g, d, 2); |
1319 | d = grid_get_dot(g, points, px - b, py - 3*a); |
1320 | grid_face_set_dot(g, d, 3); |
1321 | |
1322 | /* kite pointing down */ |
1323 | grid_face_add_new(g, 4); |
1324 | d = grid_get_dot(g, points, px, py); |
1325 | grid_face_set_dot(g, d, 0); |
1326 | d = grid_get_dot(g, points, px - b, py - 3*a); |
1327 | grid_face_set_dot(g, d, 1); |
1328 | d = grid_get_dot(g, points, px, py - 4*a); |
1329 | grid_face_set_dot(g, d, 2); |
1330 | d = grid_get_dot(g, points, px + b, py - 3*a); |
1331 | grid_face_set_dot(g, d, 3); |
1332 | |
1333 | /* kite pointing down-left */ |
1334 | grid_face_add_new(g, 4); |
1335 | d = grid_get_dot(g, points, px, py); |
1336 | grid_face_set_dot(g, d, 0); |
1337 | d = grid_get_dot(g, points, px + b, py - 3*a); |
1338 | grid_face_set_dot(g, d, 1); |
1339 | d = grid_get_dot(g, points, px + 2*b, py - 2*a); |
1340 | grid_face_set_dot(g, d, 2); |
1341 | d = grid_get_dot(g, points, px + 2*b, py); |
1342 | grid_face_set_dot(g, d, 3); |
1343 | } |
1344 | } |
1345 | |
1346 | freetree234(points); |
1347 | assert(g->num_faces <= max_faces); |
1348 | assert(g->num_dots <= max_dots); |
1349 | g->middle_face = g->faces + 6 * ((height/2) * width + (width/2)); |
1350 | |
1351 | grid_make_consistent(g); |
1352 | return g; |
1353 | } |
1354 | |
1355 | /* ----------- End of grid generators ------------- */ |