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