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; |
7c95608a |
60 | g->refcount = 1; |
61 | g->lowest_x = g->lowest_y = g->highest_x = g->highest_y = 0; |
62 | return g; |
63 | } |
64 | |
65 | /* Helper function to calculate perpendicular distance from |
66 | * a point P to a line AB. A and B mustn't be equal here. |
67 | * |
68 | * Well-known formula for area A of a triangle: |
69 | * / 1 1 1 \ |
70 | * 2A = determinant of matrix | px ax bx | |
71 | * \ py ay by / |
72 | * |
73 | * Also well-known: 2A = base * height |
74 | * = perpendicular distance * line-length. |
75 | * |
76 | * Combining gives: distance = determinant / line-length(a,b) |
77 | */ |
b1535c90 |
78 | static double point_line_distance(long px, long py, |
79 | long ax, long ay, |
80 | long bx, long by) |
7c95608a |
81 | { |
b1535c90 |
82 | long det = ax*by - bx*ay + bx*py - px*by + px*ay - ax*py; |
1515b973 |
83 | double len; |
7c95608a |
84 | det = max(det, -det); |
1515b973 |
85 | len = sqrt(SQ(ax - bx) + SQ(ay - by)); |
7c95608a |
86 | return det / len; |
87 | } |
88 | |
89 | /* Determine nearest edge to where the user clicked. |
90 | * (x, y) is the clicked location, converted to grid coordinates. |
91 | * Returns the nearest edge, or NULL if no edge is reasonably |
92 | * near the position. |
93 | * |
f839ef77 |
94 | * Just judging edges by perpendicular distance is not quite right - |
95 | * the edge might be "off to one side". So we insist that the triangle |
96 | * with (x,y) has acute angles at the edge's dots. |
7c95608a |
97 | * |
98 | * edge1 |
99 | * *---------*------ |
100 | * | |
101 | * | *(x,y) |
102 | * edge2 | |
103 | * | edge2 is OK, but edge1 is not, even though |
104 | * | edge1 is perpendicularly closer to (x,y) |
105 | * * |
106 | * |
107 | */ |
108 | grid_edge *grid_nearest_edge(grid *g, int x, int y) |
109 | { |
7c95608a |
110 | grid_edge *best_edge; |
111 | double best_distance = 0; |
112 | int i; |
113 | |
7c95608a |
114 | best_edge = NULL; |
115 | |
f839ef77 |
116 | for (i = 0; i < g->num_edges; i++) { |
117 | grid_edge *e = &g->edges[i]; |
b1535c90 |
118 | long e2; /* squared length of edge */ |
119 | long a2, b2; /* squared lengths of other sides */ |
7c95608a |
120 | double dist; |
121 | |
122 | /* See if edge e is eligible - the triangle must have acute angles |
123 | * at the edge's dots. |
124 | * Pythagoras formula h^2 = a^2 + b^2 detects right-angles, |
125 | * so detect acute angles by testing for h^2 < a^2 + b^2 */ |
b1535c90 |
126 | e2 = SQ((long)e->dot1->x - (long)e->dot2->x) + SQ((long)e->dot1->y - (long)e->dot2->y); |
127 | a2 = SQ((long)e->dot1->x - (long)x) + SQ((long)e->dot1->y - (long)y); |
128 | b2 = SQ((long)e->dot2->x - (long)x) + SQ((long)e->dot2->y - (long)y); |
7c95608a |
129 | if (a2 >= e2 + b2) continue; |
130 | if (b2 >= e2 + a2) continue; |
131 | |
132 | /* e is eligible so far. Now check the edge is reasonably close |
133 | * to where the user clicked. Don't want to toggle an edge if the |
134 | * click was way off the grid. |
135 | * There is room for experimentation here. We could check the |
136 | * perpendicular distance is within a certain fraction of the length |
137 | * of the edge. That amounts to testing a rectangular region around |
138 | * the edge. |
139 | * Alternatively, we could check that the angle at the point is obtuse. |
140 | * That would amount to testing a circular region with the edge as |
141 | * diameter. */ |
b1535c90 |
142 | dist = point_line_distance((long)x, (long)y, |
143 | (long)e->dot1->x, (long)e->dot1->y, |
144 | (long)e->dot2->x, (long)e->dot2->y); |
7c95608a |
145 | /* Is dist more than half edge length ? */ |
146 | if (4 * SQ(dist) > e2) |
147 | continue; |
148 | |
149 | if (best_edge == NULL || dist < best_distance) { |
150 | best_edge = e; |
151 | best_distance = dist; |
152 | } |
153 | } |
154 | return best_edge; |
155 | } |
156 | |
157 | /* ---------------------------------------------------------------------- |
158 | * Grid generation |
159 | */ |
160 | |
161 | #ifdef DEBUG_GRID |
162 | /* Show the basic grid information, before doing grid_make_consistent */ |
163 | static void grid_print_basic(grid *g) |
164 | { |
165 | /* TODO: Maybe we should generate an SVG image of the dots and lines |
166 | * of the grid here, before grid_make_consistent. |
167 | * Would help with debugging grid generation. */ |
168 | int i; |
169 | printf("--- Basic Grid Data ---\n"); |
170 | for (i = 0; i < g->num_faces; i++) { |
171 | grid_face *f = g->faces + i; |
172 | printf("Face %d: dots[", i); |
173 | int j; |
174 | for (j = 0; j < f->order; j++) { |
175 | grid_dot *d = f->dots[j]; |
176 | printf("%s%d", j ? "," : "", (int)(d - g->dots)); |
177 | } |
178 | printf("]\n"); |
179 | } |
7c95608a |
180 | } |
181 | /* Show the derived grid information, computed by grid_make_consistent */ |
182 | static void grid_print_derived(grid *g) |
183 | { |
184 | /* edges */ |
185 | int i; |
186 | printf("--- Derived Grid Data ---\n"); |
187 | for (i = 0; i < g->num_edges; i++) { |
188 | grid_edge *e = g->edges + i; |
189 | printf("Edge %d: dots[%d,%d] faces[%d,%d]\n", |
190 | i, (int)(e->dot1 - g->dots), (int)(e->dot2 - g->dots), |
191 | e->face1 ? (int)(e->face1 - g->faces) : -1, |
192 | e->face2 ? (int)(e->face2 - g->faces) : -1); |
193 | } |
194 | /* faces */ |
195 | for (i = 0; i < g->num_faces; i++) { |
196 | grid_face *f = g->faces + i; |
197 | int j; |
198 | printf("Face %d: faces[", i); |
199 | for (j = 0; j < f->order; j++) { |
200 | grid_edge *e = f->edges[j]; |
201 | grid_face *f2 = (e->face1 == f) ? e->face2 : e->face1; |
202 | printf("%s%d", j ? "," : "", f2 ? (int)(f2 - g->faces) : -1); |
203 | } |
204 | printf("]\n"); |
205 | } |
206 | /* dots */ |
207 | for (i = 0; i < g->num_dots; i++) { |
208 | grid_dot *d = g->dots + i; |
209 | int j; |
210 | printf("Dot %d: dots[", i); |
211 | for (j = 0; j < d->order; j++) { |
212 | grid_edge *e = d->edges[j]; |
213 | grid_dot *d2 = (e->dot1 == d) ? e->dot2 : e->dot1; |
214 | printf("%s%d", j ? "," : "", (int)(d2 - g->dots)); |
215 | } |
216 | printf("] faces["); |
217 | for (j = 0; j < d->order; j++) { |
218 | grid_face *f = d->faces[j]; |
219 | printf("%s%d", j ? "," : "", f ? (int)(f - g->faces) : -1); |
220 | } |
221 | printf("]\n"); |
222 | } |
223 | } |
224 | #endif /* DEBUG_GRID */ |
225 | |
226 | /* Helper function for building incomplete-edges list in |
227 | * grid_make_consistent() */ |
228 | static int grid_edge_bydots_cmpfn(void *v1, void *v2) |
229 | { |
230 | grid_edge *a = v1; |
231 | grid_edge *b = v2; |
232 | grid_dot *da, *db; |
233 | |
234 | /* Pointer subtraction is valid here, because all dots point into the |
235 | * same dot-list (g->dots). |
236 | * Edges are not "normalised" - the 2 dots could be stored in any order, |
237 | * so we need to take this into account when comparing edges. */ |
238 | |
239 | /* Compare first dots */ |
240 | da = (a->dot1 < a->dot2) ? a->dot1 : a->dot2; |
241 | db = (b->dot1 < b->dot2) ? b->dot1 : b->dot2; |
242 | if (da != db) |
243 | return db - da; |
244 | /* Compare last dots */ |
245 | da = (a->dot1 < a->dot2) ? a->dot2 : a->dot1; |
246 | db = (b->dot1 < b->dot2) ? b->dot2 : b->dot1; |
247 | if (da != db) |
248 | return db - da; |
249 | |
250 | return 0; |
251 | } |
252 | |
253 | /* Input: grid has its dots and faces initialised: |
254 | * - dots have (optionally) x and y coordinates, but no edges or faces |
255 | * (pointers are NULL). |
256 | * - edges not initialised at all |
257 | * - faces initialised and know which dots they have (but no edges yet). The |
258 | * dots around each face are assumed to be clockwise. |
259 | * |
260 | * Output: grid is complete and valid with all relationships defined. |
261 | */ |
262 | static void grid_make_consistent(grid *g) |
263 | { |
264 | int i; |
265 | tree234 *incomplete_edges; |
266 | grid_edge *next_new_edge; /* Where new edge will go into g->edges */ |
267 | |
268 | #ifdef DEBUG_GRID |
269 | grid_print_basic(g); |
270 | #endif |
271 | |
272 | /* ====== Stage 1 ====== |
273 | * Generate edges |
274 | */ |
275 | |
276 | /* We know how many dots and faces there are, so we can find the exact |
277 | * number of edges from Euler's polyhedral formula: F + V = E + 2 . |
278 | * We use "-1", not "-2" here, because Euler's formula includes the |
279 | * infinite face, which we don't count. */ |
280 | g->num_edges = g->num_faces + g->num_dots - 1; |
281 | g->edges = snewn(g->num_edges, grid_edge); |
282 | next_new_edge = g->edges; |
283 | |
284 | /* Iterate over faces, and over each face's dots, generating edges as we |
285 | * go. As we find each new edge, we can immediately fill in the edge's |
286 | * dots, but only one of the edge's faces. Later on in the iteration, we |
287 | * will find the same edge again (unless it's on the border), but we will |
288 | * know the other face. |
289 | * For efficiency, maintain a list of the incomplete edges, sorted by |
290 | * their dots. */ |
291 | incomplete_edges = newtree234(grid_edge_bydots_cmpfn); |
292 | for (i = 0; i < g->num_faces; i++) { |
293 | grid_face *f = g->faces + i; |
294 | int j; |
295 | for (j = 0; j < f->order; j++) { |
296 | grid_edge e; /* fake edge for searching */ |
297 | grid_edge *edge_found; |
298 | int j2 = j + 1; |
299 | if (j2 == f->order) |
300 | j2 = 0; |
301 | e.dot1 = f->dots[j]; |
302 | e.dot2 = f->dots[j2]; |
303 | /* Use del234 instead of find234, because we always want to |
304 | * remove the edge if found */ |
305 | edge_found = del234(incomplete_edges, &e); |
306 | if (edge_found) { |
307 | /* This edge already added, so fill out missing face. |
308 | * Edge is already removed from incomplete_edges. */ |
309 | edge_found->face2 = f; |
310 | } else { |
311 | assert(next_new_edge - g->edges < g->num_edges); |
312 | next_new_edge->dot1 = e.dot1; |
313 | next_new_edge->dot2 = e.dot2; |
314 | next_new_edge->face1 = f; |
315 | next_new_edge->face2 = NULL; /* potentially infinite face */ |
316 | add234(incomplete_edges, next_new_edge); |
317 | ++next_new_edge; |
318 | } |
319 | } |
320 | } |
321 | freetree234(incomplete_edges); |
322 | |
323 | /* ====== Stage 2 ====== |
324 | * For each face, build its edge list. |
325 | */ |
326 | |
327 | /* Allocate space for each edge list. Can do this, because each face's |
328 | * edge-list is the same size as its dot-list. */ |
329 | for (i = 0; i < g->num_faces; i++) { |
330 | grid_face *f = g->faces + i; |
331 | int j; |
332 | f->edges = snewn(f->order, grid_edge*); |
333 | /* Preload with NULLs, to help detect potential bugs. */ |
334 | for (j = 0; j < f->order; j++) |
335 | f->edges[j] = NULL; |
336 | } |
337 | |
338 | /* Iterate over each edge, and over both its faces. Add this edge to |
339 | * the face's edge-list, after finding where it should go in the |
340 | * sequence. */ |
341 | for (i = 0; i < g->num_edges; i++) { |
342 | grid_edge *e = g->edges + i; |
343 | int j; |
344 | for (j = 0; j < 2; j++) { |
345 | grid_face *f = j ? e->face2 : e->face1; |
346 | int k, k2; |
347 | if (f == NULL) continue; |
348 | /* Find one of the dots around the face */ |
349 | for (k = 0; k < f->order; k++) { |
350 | if (f->dots[k] == e->dot1) |
351 | break; /* found dot1 */ |
352 | } |
353 | assert(k != f->order); /* Must find the dot around this face */ |
354 | |
355 | /* Labelling scheme: as we walk clockwise around the face, |
356 | * starting at dot0 (f->dots[0]), we hit: |
357 | * (dot0), edge0, dot1, edge1, dot2,... |
358 | * |
359 | * 0 |
360 | * 0-----1 |
361 | * | |
362 | * |1 |
363 | * | |
364 | * 3-----2 |
365 | * 2 |
366 | * |
367 | * Therefore, edgeK joins dotK and dot{K+1} |
368 | */ |
369 | |
370 | /* Around this face, either the next dot or the previous dot |
371 | * must be e->dot2. Otherwise the edge is wrong. */ |
372 | k2 = k + 1; |
373 | if (k2 == f->order) |
374 | k2 = 0; |
375 | if (f->dots[k2] == e->dot2) { |
376 | /* dot1(k) and dot2(k2) go clockwise around this face, so add |
377 | * this edge at position k (see diagram). */ |
378 | assert(f->edges[k] == NULL); |
379 | f->edges[k] = e; |
380 | continue; |
381 | } |
382 | /* Try previous dot */ |
383 | k2 = k - 1; |
384 | if (k2 == -1) |
385 | k2 = f->order - 1; |
386 | if (f->dots[k2] == e->dot2) { |
387 | /* dot1(k) and dot2(k2) go anticlockwise around this face. */ |
388 | assert(f->edges[k2] == NULL); |
389 | f->edges[k2] = e; |
390 | continue; |
391 | } |
392 | assert(!"Grid broken: bad edge-face relationship"); |
393 | } |
394 | } |
395 | |
396 | /* ====== Stage 3 ====== |
397 | * For each dot, build its edge-list and face-list. |
398 | */ |
399 | |
400 | /* We don't know how many edges/faces go around each dot, so we can't |
401 | * allocate the right space for these lists. Pre-compute the sizes by |
402 | * iterating over each edge and recording a tally against each dot. */ |
403 | for (i = 0; i < g->num_dots; i++) { |
404 | g->dots[i].order = 0; |
405 | } |
406 | for (i = 0; i < g->num_edges; i++) { |
407 | grid_edge *e = g->edges + i; |
408 | ++(e->dot1->order); |
409 | ++(e->dot2->order); |
410 | } |
411 | /* Now we have the sizes, pre-allocate the edge and face lists. */ |
412 | for (i = 0; i < g->num_dots; i++) { |
413 | grid_dot *d = g->dots + i; |
414 | int j; |
415 | assert(d->order >= 2); /* sanity check */ |
416 | d->edges = snewn(d->order, grid_edge*); |
417 | d->faces = snewn(d->order, grid_face*); |
418 | for (j = 0; j < d->order; j++) { |
419 | d->edges[j] = NULL; |
420 | d->faces[j] = NULL; |
421 | } |
422 | } |
423 | /* For each dot, need to find a face that touches it, so we can seed |
424 | * the edge-face-edge-face process around each dot. */ |
425 | for (i = 0; i < g->num_faces; i++) { |
426 | grid_face *f = g->faces + i; |
427 | int j; |
428 | for (j = 0; j < f->order; j++) { |
429 | grid_dot *d = f->dots[j]; |
430 | d->faces[0] = f; |
431 | } |
432 | } |
433 | /* Each dot now has a face in its first slot. Generate the remaining |
434 | * faces and edges around the dot, by searching both clockwise and |
435 | * anticlockwise from the first face. Need to do both directions, |
436 | * because of the possibility of hitting the infinite face, which |
437 | * blocks progress. But there's only one such face, so we will |
438 | * succeed in finding every edge and face this way. */ |
439 | for (i = 0; i < g->num_dots; i++) { |
440 | grid_dot *d = g->dots + i; |
441 | int current_face1 = 0; /* ascends clockwise */ |
442 | int current_face2 = 0; /* descends anticlockwise */ |
443 | |
444 | /* Labelling scheme: as we walk clockwise around the dot, starting |
445 | * at face0 (d->faces[0]), we hit: |
446 | * (face0), edge0, face1, edge1, face2,... |
447 | * |
448 | * 0 |
449 | * | |
450 | * 0 | 1 |
451 | * | |
452 | * -----d-----1 |
453 | * | |
454 | * | 2 |
455 | * | |
456 | * 2 |
457 | * |
458 | * So, for example, face1 should be joined to edge0 and edge1, |
459 | * and those edges should appear in an anticlockwise sense around |
460 | * that face (see diagram). */ |
461 | |
462 | /* clockwise search */ |
463 | while (TRUE) { |
464 | grid_face *f = d->faces[current_face1]; |
465 | grid_edge *e; |
466 | int j; |
467 | assert(f != NULL); |
468 | /* find dot around this face */ |
469 | for (j = 0; j < f->order; j++) { |
470 | if (f->dots[j] == d) |
471 | break; |
472 | } |
473 | assert(j != f->order); /* must find dot */ |
474 | |
475 | /* Around f, required edge is anticlockwise from the dot. See |
476 | * the other labelling scheme higher up, for why we subtract 1 |
477 | * from j. */ |
478 | j--; |
479 | if (j == -1) |
480 | j = f->order - 1; |
481 | e = f->edges[j]; |
482 | d->edges[current_face1] = e; /* set edge */ |
483 | current_face1++; |
484 | if (current_face1 == d->order) |
485 | break; |
486 | else { |
487 | /* set face */ |
488 | d->faces[current_face1] = |
489 | (e->face1 == f) ? e->face2 : e->face1; |
490 | if (d->faces[current_face1] == NULL) |
491 | break; /* cannot progress beyond infinite face */ |
492 | } |
493 | } |
494 | /* If the clockwise search made it all the way round, don't need to |
495 | * bother with the anticlockwise search. */ |
496 | if (current_face1 == d->order) |
497 | continue; /* this dot is complete, move on to next dot */ |
498 | |
499 | /* anticlockwise search */ |
500 | while (TRUE) { |
501 | grid_face *f = d->faces[current_face2]; |
502 | grid_edge *e; |
503 | int j; |
504 | assert(f != NULL); |
505 | /* find dot around this face */ |
506 | for (j = 0; j < f->order; j++) { |
507 | if (f->dots[j] == d) |
508 | break; |
509 | } |
510 | assert(j != f->order); /* must find dot */ |
511 | |
512 | /* Around f, required edge is clockwise from the dot. */ |
513 | e = f->edges[j]; |
514 | |
515 | current_face2--; |
516 | if (current_face2 == -1) |
517 | current_face2 = d->order - 1; |
518 | d->edges[current_face2] = e; /* set edge */ |
519 | |
520 | /* set face */ |
521 | if (current_face2 == current_face1) |
522 | break; |
523 | d->faces[current_face2] = |
524 | (e->face1 == f) ? e->face2 : e->face1; |
525 | /* There's only 1 infinite face, so we must get all the way |
526 | * to current_face1 before we hit it. */ |
527 | assert(d->faces[current_face2]); |
528 | } |
529 | } |
530 | |
531 | /* ====== Stage 4 ====== |
532 | * Compute other grid settings |
533 | */ |
534 | |
535 | /* Bounding rectangle */ |
536 | for (i = 0; i < g->num_dots; i++) { |
537 | grid_dot *d = g->dots + i; |
538 | if (i == 0) { |
539 | g->lowest_x = g->highest_x = d->x; |
540 | g->lowest_y = g->highest_y = d->y; |
541 | } else { |
542 | g->lowest_x = min(g->lowest_x, d->x); |
543 | g->highest_x = max(g->highest_x, d->x); |
544 | g->lowest_y = min(g->lowest_y, d->y); |
545 | g->highest_y = max(g->highest_y, d->y); |
546 | } |
547 | } |
548 | |
549 | #ifdef DEBUG_GRID |
550 | grid_print_derived(g); |
551 | #endif |
552 | } |
553 | |
554 | /* Helpers for making grid-generation easier. These functions are only |
555 | * intended for use during grid generation. */ |
556 | |
557 | /* Comparison function for the (tree234) sorted dot list */ |
558 | static int grid_point_cmp_fn(void *v1, void *v2) |
559 | { |
560 | grid_dot *p1 = v1; |
561 | grid_dot *p2 = v2; |
562 | if (p1->y != p2->y) |
563 | return p2->y - p1->y; |
564 | else |
565 | return p2->x - p1->x; |
566 | } |
567 | /* Add a new face to the grid, with its dot list allocated. |
568 | * Assumes there's enough space allocated for the new face in grid->faces */ |
569 | static void grid_face_add_new(grid *g, int face_size) |
570 | { |
571 | int i; |
572 | grid_face *new_face = g->faces + g->num_faces; |
573 | new_face->order = face_size; |
574 | new_face->dots = snewn(face_size, grid_dot*); |
575 | for (i = 0; i < face_size; i++) |
576 | new_face->dots[i] = NULL; |
577 | new_face->edges = NULL; |
578 | g->num_faces++; |
579 | } |
580 | /* Assumes dot list has enough space */ |
581 | static grid_dot *grid_dot_add_new(grid *g, int x, int y) |
582 | { |
583 | grid_dot *new_dot = g->dots + g->num_dots; |
584 | new_dot->order = 0; |
585 | new_dot->edges = NULL; |
586 | new_dot->faces = NULL; |
587 | new_dot->x = x; |
588 | new_dot->y = y; |
589 | g->num_dots++; |
590 | return new_dot; |
591 | } |
592 | /* Retrieve a dot with these (x,y) coordinates. Either return an existing dot |
593 | * in the dot_list, or add a new dot to the grid (and the dot_list) and |
594 | * return that. |
595 | * Assumes g->dots has enough capacity allocated */ |
596 | static grid_dot *grid_get_dot(grid *g, tree234 *dot_list, int x, int y) |
597 | { |
3466f373 |
598 | grid_dot test, *ret; |
599 | |
600 | test.order = 0; |
601 | test.edges = NULL; |
602 | test.faces = NULL; |
603 | test.x = x; |
604 | test.y = y; |
605 | ret = find234(dot_list, &test, NULL); |
7c95608a |
606 | if (ret) |
607 | return ret; |
608 | |
609 | ret = grid_dot_add_new(g, x, y); |
610 | add234(dot_list, ret); |
611 | return ret; |
612 | } |
613 | |
614 | /* Sets the last face of the grid to include this dot, at this position |
615 | * around the face. Assumes num_faces is at least 1 (a new face has |
616 | * previously been added, with the required number of dots allocated) */ |
617 | static void grid_face_set_dot(grid *g, grid_dot *d, int position) |
618 | { |
619 | grid_face *last_face = g->faces + g->num_faces - 1; |
620 | last_face->dots[position] = d; |
621 | } |
622 | |
623 | /* ------ Generate various types of grid ------ */ |
624 | |
625 | /* General method is to generate faces, by calculating their dot coordinates. |
626 | * As new faces are added, we keep track of all the dots so we can tell when |
627 | * a new face reuses an existing dot. For example, two squares touching at an |
628 | * edge would generate six unique dots: four dots from the first face, then |
629 | * two additional dots for the second face, because we detect the other two |
630 | * dots have already been taken up. This list is stored in a tree234 |
631 | * called "points". No extra memory-allocation needed here - we store the |
632 | * actual grid_dot* pointers, which all point into the g->dots list. |
633 | * For this reason, we have to calculate coordinates in such a way as to |
634 | * eliminate any rounding errors, so we can detect when a dot on one |
635 | * face precisely lands on a dot of a different face. No floating-point |
636 | * arithmetic here! |
637 | */ |
638 | |
639 | grid *grid_new_square(int width, int height) |
640 | { |
641 | int x, y; |
642 | /* Side length */ |
643 | int a = 20; |
644 | |
645 | /* Upper bounds - don't have to be exact */ |
646 | int max_faces = width * height; |
647 | int max_dots = (width + 1) * (height + 1); |
648 | |
649 | tree234 *points; |
650 | |
651 | grid *g = grid_new(); |
652 | g->tilesize = a; |
653 | g->faces = snewn(max_faces, grid_face); |
654 | g->dots = snewn(max_dots, grid_dot); |
655 | |
656 | points = newtree234(grid_point_cmp_fn); |
657 | |
658 | /* generate square faces */ |
659 | for (y = 0; y < height; y++) { |
660 | for (x = 0; x < width; x++) { |
661 | grid_dot *d; |
662 | /* face position */ |
663 | int px = a * x; |
664 | int py = a * y; |
665 | |
666 | grid_face_add_new(g, 4); |
667 | d = grid_get_dot(g, points, px, py); |
668 | grid_face_set_dot(g, d, 0); |
669 | d = grid_get_dot(g, points, px + a, py); |
670 | grid_face_set_dot(g, d, 1); |
671 | d = grid_get_dot(g, points, px + a, py + a); |
672 | grid_face_set_dot(g, d, 2); |
673 | d = grid_get_dot(g, points, px, py + a); |
674 | grid_face_set_dot(g, d, 3); |
675 | } |
676 | } |
677 | |
678 | freetree234(points); |
679 | assert(g->num_faces <= max_faces); |
680 | assert(g->num_dots <= max_dots); |
7c95608a |
681 | |
682 | grid_make_consistent(g); |
683 | return g; |
684 | } |
685 | |
686 | grid *grid_new_honeycomb(int width, int height) |
687 | { |
688 | int x, y; |
689 | /* Vector for side of hexagon - ratio is close to sqrt(3) */ |
690 | int a = 15; |
691 | int b = 26; |
692 | |
693 | /* Upper bounds - don't have to be exact */ |
694 | int max_faces = width * height; |
695 | int max_dots = 2 * (width + 1) * (height + 1); |
696 | |
697 | tree234 *points; |
698 | |
699 | grid *g = grid_new(); |
700 | g->tilesize = 3 * 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 hexagonal faces */ |
707 | for (y = 0; y < height; y++) { |
708 | for (x = 0; x < width; x++) { |
709 | grid_dot *d; |
710 | /* face centre */ |
711 | int cx = 3 * a * x; |
712 | int cy = 2 * b * y; |
713 | if (x % 2) |
714 | cy += b; |
715 | grid_face_add_new(g, 6); |
716 | |
717 | d = grid_get_dot(g, points, cx - a, cy - b); |
718 | grid_face_set_dot(g, d, 0); |
719 | d = grid_get_dot(g, points, cx + a, cy - b); |
720 | grid_face_set_dot(g, d, 1); |
721 | d = grid_get_dot(g, points, cx + 2*a, cy); |
722 | grid_face_set_dot(g, d, 2); |
723 | d = grid_get_dot(g, points, cx + a, cy + b); |
724 | grid_face_set_dot(g, d, 3); |
725 | d = grid_get_dot(g, points, cx - a, cy + b); |
726 | grid_face_set_dot(g, d, 4); |
727 | d = grid_get_dot(g, points, cx - 2*a, cy); |
728 | grid_face_set_dot(g, d, 5); |
729 | } |
730 | } |
731 | |
732 | freetree234(points); |
733 | assert(g->num_faces <= max_faces); |
734 | assert(g->num_dots <= max_dots); |
7c95608a |
735 | |
736 | grid_make_consistent(g); |
737 | return g; |
738 | } |
739 | |
740 | /* Doesn't use the previous method of generation, it pre-dates it! |
741 | * A triangular grid is just about simple enough to do by "brute force" */ |
742 | grid *grid_new_triangular(int width, int height) |
743 | { |
744 | int x,y; |
745 | |
746 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
747 | int vec_x = 15; |
748 | int vec_y = 26; |
749 | |
750 | int index; |
751 | |
752 | /* convenient alias */ |
753 | int w = width + 1; |
754 | |
755 | grid *g = grid_new(); |
756 | g->tilesize = 18; /* adjust to your taste */ |
757 | |
758 | g->num_faces = width * height * 2; |
759 | g->num_dots = (width + 1) * (height + 1); |
760 | g->faces = snewn(g->num_faces, grid_face); |
761 | g->dots = snewn(g->num_dots, grid_dot); |
762 | |
763 | /* generate dots */ |
764 | index = 0; |
765 | for (y = 0; y <= height; y++) { |
766 | for (x = 0; x <= width; x++) { |
767 | grid_dot *d = g->dots + index; |
768 | /* odd rows are offset to the right */ |
769 | d->order = 0; |
770 | d->edges = NULL; |
771 | d->faces = NULL; |
772 | d->x = x * 2 * vec_x + ((y % 2) ? vec_x : 0); |
773 | d->y = y * vec_y; |
774 | index++; |
775 | } |
776 | } |
777 | |
778 | /* generate faces */ |
779 | index = 0; |
780 | for (y = 0; y < height; y++) { |
781 | for (x = 0; x < width; x++) { |
782 | /* initialise two faces for this (x,y) */ |
783 | grid_face *f1 = g->faces + index; |
784 | grid_face *f2 = f1 + 1; |
785 | f1->edges = NULL; |
786 | f1->order = 3; |
787 | f1->dots = snewn(f1->order, grid_dot*); |
788 | f2->edges = NULL; |
789 | f2->order = 3; |
790 | f2->dots = snewn(f2->order, grid_dot*); |
791 | |
792 | /* face descriptions depend on whether the row-number is |
793 | * odd or even */ |
794 | if (y % 2) { |
795 | f1->dots[0] = g->dots + y * w + x; |
796 | f1->dots[1] = g->dots + (y + 1) * w + x + 1; |
797 | f1->dots[2] = g->dots + (y + 1) * w + x; |
798 | f2->dots[0] = g->dots + y * w + x; |
799 | f2->dots[1] = g->dots + y * w + x + 1; |
800 | f2->dots[2] = g->dots + (y + 1) * w + x + 1; |
801 | } else { |
802 | f1->dots[0] = g->dots + y * w + x; |
803 | f1->dots[1] = g->dots + y * w + x + 1; |
804 | f1->dots[2] = g->dots + (y + 1) * w + x; |
805 | f2->dots[0] = g->dots + y * w + x + 1; |
806 | f2->dots[1] = g->dots + (y + 1) * w + x + 1; |
807 | f2->dots[2] = g->dots + (y + 1) * w + x; |
808 | } |
809 | index += 2; |
810 | } |
811 | } |
812 | |
7c95608a |
813 | grid_make_consistent(g); |
814 | return g; |
815 | } |
816 | |
817 | grid *grid_new_snubsquare(int width, int height) |
818 | { |
819 | int x, y; |
820 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
821 | int a = 15; |
822 | int b = 26; |
823 | |
824 | /* Upper bounds - don't have to be exact */ |
825 | int max_faces = 3 * width * height; |
826 | int max_dots = 2 * (width + 1) * (height + 1); |
827 | |
828 | tree234 *points; |
829 | |
830 | grid *g = grid_new(); |
831 | g->tilesize = 18; |
832 | g->faces = snewn(max_faces, grid_face); |
833 | g->dots = snewn(max_dots, grid_dot); |
834 | |
835 | points = newtree234(grid_point_cmp_fn); |
836 | |
837 | for (y = 0; y < height; y++) { |
838 | for (x = 0; x < width; x++) { |
839 | grid_dot *d; |
840 | /* face position */ |
841 | int px = (a + b) * x; |
842 | int py = (a + b) * y; |
843 | |
844 | /* generate square faces */ |
845 | grid_face_add_new(g, 4); |
846 | if ((x + y) % 2) { |
847 | d = grid_get_dot(g, points, px + a, py); |
848 | grid_face_set_dot(g, d, 0); |
849 | d = grid_get_dot(g, points, px + a + b, py + a); |
850 | grid_face_set_dot(g, d, 1); |
851 | d = grid_get_dot(g, points, px + b, py + a + b); |
852 | grid_face_set_dot(g, d, 2); |
853 | d = grid_get_dot(g, points, px, py + b); |
854 | grid_face_set_dot(g, d, 3); |
855 | } else { |
856 | d = grid_get_dot(g, points, px + b, py); |
857 | grid_face_set_dot(g, d, 0); |
858 | d = grid_get_dot(g, points, px + a + b, py + b); |
859 | grid_face_set_dot(g, d, 1); |
860 | d = grid_get_dot(g, points, px + a, py + a + b); |
861 | grid_face_set_dot(g, d, 2); |
862 | d = grid_get_dot(g, points, px, py + a); |
863 | grid_face_set_dot(g, d, 3); |
864 | } |
865 | |
866 | /* generate up/down triangles */ |
867 | if (x > 0) { |
868 | grid_face_add_new(g, 3); |
869 | if ((x + y) % 2) { |
870 | d = grid_get_dot(g, points, px + a, py); |
871 | grid_face_set_dot(g, d, 0); |
872 | d = grid_get_dot(g, points, px, py + b); |
873 | grid_face_set_dot(g, d, 1); |
874 | d = grid_get_dot(g, points, px - a, py); |
875 | grid_face_set_dot(g, d, 2); |
876 | } else { |
877 | d = grid_get_dot(g, points, px, py + a); |
878 | grid_face_set_dot(g, d, 0); |
879 | d = grid_get_dot(g, points, px + a, py + a + b); |
880 | grid_face_set_dot(g, d, 1); |
881 | d = grid_get_dot(g, points, px - a, py + a + b); |
882 | grid_face_set_dot(g, d, 2); |
883 | } |
884 | } |
885 | |
886 | /* generate left/right triangles */ |
887 | if (y > 0) { |
888 | grid_face_add_new(g, 3); |
889 | if ((x + y) % 2) { |
890 | d = grid_get_dot(g, points, px + a, py); |
891 | grid_face_set_dot(g, d, 0); |
892 | d = grid_get_dot(g, points, px + a + b, py - a); |
893 | grid_face_set_dot(g, d, 1); |
894 | d = grid_get_dot(g, points, px + a + b, py + a); |
895 | grid_face_set_dot(g, d, 2); |
896 | } else { |
897 | d = grid_get_dot(g, points, px, py - a); |
898 | grid_face_set_dot(g, d, 0); |
899 | d = grid_get_dot(g, points, px + b, py); |
900 | grid_face_set_dot(g, d, 1); |
901 | d = grid_get_dot(g, points, px, py + a); |
902 | grid_face_set_dot(g, d, 2); |
903 | } |
904 | } |
905 | } |
906 | } |
907 | |
908 | freetree234(points); |
909 | assert(g->num_faces <= max_faces); |
910 | assert(g->num_dots <= max_dots); |
7c95608a |
911 | |
912 | grid_make_consistent(g); |
913 | return g; |
914 | } |
915 | |
916 | grid *grid_new_cairo(int width, int height) |
917 | { |
918 | int x, y; |
919 | /* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */ |
920 | int a = 14; |
921 | int b = 31; |
922 | |
923 | /* Upper bounds - don't have to be exact */ |
924 | int max_faces = 2 * width * height; |
925 | int max_dots = 3 * (width + 1) * (height + 1); |
926 | |
927 | tree234 *points; |
928 | |
929 | grid *g = grid_new(); |
930 | g->tilesize = 40; |
931 | g->faces = snewn(max_faces, grid_face); |
932 | g->dots = snewn(max_dots, grid_dot); |
933 | |
934 | points = newtree234(grid_point_cmp_fn); |
935 | |
936 | for (y = 0; y < height; y++) { |
937 | for (x = 0; x < width; x++) { |
938 | grid_dot *d; |
939 | /* cell position */ |
940 | int px = 2 * b * x; |
941 | int py = 2 * b * y; |
942 | |
943 | /* horizontal pentagons */ |
944 | if (y > 0) { |
945 | grid_face_add_new(g, 5); |
946 | if ((x + y) % 2) { |
947 | d = grid_get_dot(g, points, px + a, py - b); |
948 | grid_face_set_dot(g, d, 0); |
949 | d = grid_get_dot(g, points, px + 2*b - a, py - b); |
950 | grid_face_set_dot(g, d, 1); |
951 | d = grid_get_dot(g, points, px + 2*b, py); |
952 | grid_face_set_dot(g, d, 2); |
953 | d = grid_get_dot(g, points, px + b, py + a); |
954 | grid_face_set_dot(g, d, 3); |
955 | d = grid_get_dot(g, points, px, py); |
956 | grid_face_set_dot(g, d, 4); |
957 | } else { |
958 | d = grid_get_dot(g, points, px, py); |
959 | grid_face_set_dot(g, d, 0); |
960 | d = grid_get_dot(g, points, px + b, py - a); |
961 | grid_face_set_dot(g, d, 1); |
962 | d = grid_get_dot(g, points, px + 2*b, py); |
963 | grid_face_set_dot(g, d, 2); |
964 | d = grid_get_dot(g, points, px + 2*b - a, py + b); |
965 | grid_face_set_dot(g, d, 3); |
966 | d = grid_get_dot(g, points, px + a, py + b); |
967 | grid_face_set_dot(g, d, 4); |
968 | } |
969 | } |
970 | /* vertical pentagons */ |
971 | if (x > 0) { |
972 | grid_face_add_new(g, 5); |
973 | if ((x + y) % 2) { |
974 | d = grid_get_dot(g, points, px, py); |
975 | grid_face_set_dot(g, d, 0); |
976 | d = grid_get_dot(g, points, px + b, py + a); |
977 | grid_face_set_dot(g, d, 1); |
978 | d = grid_get_dot(g, points, px + b, py + 2*b - a); |
979 | grid_face_set_dot(g, d, 2); |
980 | d = grid_get_dot(g, points, px, py + 2*b); |
981 | grid_face_set_dot(g, d, 3); |
982 | d = grid_get_dot(g, points, px - a, py + b); |
983 | grid_face_set_dot(g, d, 4); |
984 | } else { |
985 | d = grid_get_dot(g, points, px, py); |
986 | grid_face_set_dot(g, d, 0); |
987 | d = grid_get_dot(g, points, px + a, py + b); |
988 | grid_face_set_dot(g, d, 1); |
989 | d = grid_get_dot(g, points, px, py + 2*b); |
990 | grid_face_set_dot(g, d, 2); |
991 | d = grid_get_dot(g, points, px - b, py + 2*b - a); |
992 | grid_face_set_dot(g, d, 3); |
993 | d = grid_get_dot(g, points, px - b, py + a); |
994 | grid_face_set_dot(g, d, 4); |
995 | } |
996 | } |
997 | } |
998 | } |
999 | |
1000 | freetree234(points); |
1001 | assert(g->num_faces <= max_faces); |
1002 | assert(g->num_dots <= max_dots); |
7c95608a |
1003 | |
1004 | grid_make_consistent(g); |
1005 | return g; |
1006 | } |
1007 | |
1008 | grid *grid_new_greathexagonal(int width, int height) |
1009 | { |
1010 | int x, y; |
1011 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
1012 | int a = 15; |
1013 | int b = 26; |
1014 | |
1015 | /* Upper bounds - don't have to be exact */ |
1016 | int max_faces = 6 * (width + 1) * (height + 1); |
1017 | int max_dots = 6 * width * height; |
1018 | |
1019 | tree234 *points; |
1020 | |
1021 | grid *g = grid_new(); |
1022 | g->tilesize = 18; |
1023 | g->faces = snewn(max_faces, grid_face); |
1024 | g->dots = snewn(max_dots, grid_dot); |
1025 | |
1026 | points = newtree234(grid_point_cmp_fn); |
1027 | |
1028 | for (y = 0; y < height; y++) { |
1029 | for (x = 0; x < width; x++) { |
1030 | grid_dot *d; |
1031 | /* centre of hexagon */ |
1032 | int px = (3*a + b) * x; |
1033 | int py = (2*a + 2*b) * y; |
1034 | if (x % 2) |
1035 | py += a + b; |
1036 | |
1037 | /* hexagon */ |
1038 | grid_face_add_new(g, 6); |
1039 | d = grid_get_dot(g, points, px - a, py - b); |
1040 | grid_face_set_dot(g, d, 0); |
1041 | d = grid_get_dot(g, points, px + a, py - b); |
1042 | grid_face_set_dot(g, d, 1); |
1043 | d = grid_get_dot(g, points, px + 2*a, py); |
1044 | grid_face_set_dot(g, d, 2); |
1045 | d = grid_get_dot(g, points, px + a, py + b); |
1046 | grid_face_set_dot(g, d, 3); |
1047 | d = grid_get_dot(g, points, px - a, py + b); |
1048 | grid_face_set_dot(g, d, 4); |
1049 | d = grid_get_dot(g, points, px - 2*a, py); |
1050 | grid_face_set_dot(g, d, 5); |
1051 | |
1052 | /* square below hexagon */ |
1053 | if (y < height - 1) { |
1054 | grid_face_add_new(g, 4); |
1055 | d = grid_get_dot(g, points, px - a, py + b); |
1056 | grid_face_set_dot(g, d, 0); |
1057 | d = grid_get_dot(g, points, px + a, py + b); |
1058 | grid_face_set_dot(g, d, 1); |
1059 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
1060 | grid_face_set_dot(g, d, 2); |
1061 | d = grid_get_dot(g, points, px - a, py + 2*a + b); |
1062 | grid_face_set_dot(g, d, 3); |
1063 | } |
1064 | |
1065 | /* square below right */ |
1066 | if ((x < width - 1) && (((x % 2) == 0) || (y < height - 1))) { |
1067 | grid_face_add_new(g, 4); |
1068 | d = grid_get_dot(g, points, px + 2*a, py); |
1069 | grid_face_set_dot(g, d, 0); |
1070 | d = grid_get_dot(g, points, px + 2*a + b, py + a); |
1071 | grid_face_set_dot(g, d, 1); |
1072 | d = grid_get_dot(g, points, px + a + b, py + a + b); |
1073 | grid_face_set_dot(g, d, 2); |
1074 | d = grid_get_dot(g, points, px + a, py + b); |
1075 | grid_face_set_dot(g, d, 3); |
1076 | } |
1077 | |
1078 | /* square below left */ |
1079 | if ((x > 0) && (((x % 2) == 0) || (y < height - 1))) { |
1080 | grid_face_add_new(g, 4); |
1081 | d = grid_get_dot(g, points, px - 2*a, py); |
1082 | grid_face_set_dot(g, d, 0); |
1083 | d = grid_get_dot(g, points, px - a, py + b); |
1084 | grid_face_set_dot(g, d, 1); |
1085 | d = grid_get_dot(g, points, px - a - b, py + a + b); |
1086 | grid_face_set_dot(g, d, 2); |
1087 | d = grid_get_dot(g, points, px - 2*a - b, py + a); |
1088 | grid_face_set_dot(g, d, 3); |
1089 | } |
1090 | |
1091 | /* Triangle below right */ |
1092 | if ((x < width - 1) && (y < height - 1)) { |
1093 | grid_face_add_new(g, 3); |
1094 | d = grid_get_dot(g, points, px + a, py + b); |
1095 | grid_face_set_dot(g, d, 0); |
1096 | d = grid_get_dot(g, points, px + a + b, py + a + b); |
1097 | grid_face_set_dot(g, d, 1); |
1098 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
1099 | grid_face_set_dot(g, d, 2); |
1100 | } |
1101 | |
1102 | /* Triangle below left */ |
1103 | if ((x > 0) && (y < height - 1)) { |
1104 | grid_face_add_new(g, 3); |
1105 | d = grid_get_dot(g, points, px - a, py + b); |
1106 | grid_face_set_dot(g, d, 0); |
1107 | d = grid_get_dot(g, points, px - a, py + 2*a + b); |
1108 | grid_face_set_dot(g, d, 1); |
1109 | d = grid_get_dot(g, points, px - a - b, py + a + b); |
1110 | grid_face_set_dot(g, d, 2); |
1111 | } |
1112 | } |
1113 | } |
1114 | |
1115 | freetree234(points); |
1116 | assert(g->num_faces <= max_faces); |
1117 | assert(g->num_dots <= max_dots); |
7c95608a |
1118 | |
1119 | grid_make_consistent(g); |
1120 | return g; |
1121 | } |
1122 | |
1123 | grid *grid_new_octagonal(int width, int height) |
1124 | { |
1125 | int x, y; |
1126 | /* b/a approx sqrt(2) */ |
1127 | int a = 29; |
1128 | int b = 41; |
1129 | |
1130 | /* Upper bounds - don't have to be exact */ |
1131 | int max_faces = 2 * width * height; |
1132 | int max_dots = 4 * (width + 1) * (height + 1); |
1133 | |
1134 | tree234 *points; |
1135 | |
1136 | grid *g = grid_new(); |
1137 | g->tilesize = 40; |
1138 | g->faces = snewn(max_faces, grid_face); |
1139 | g->dots = snewn(max_dots, grid_dot); |
1140 | |
1141 | points = newtree234(grid_point_cmp_fn); |
1142 | |
1143 | for (y = 0; y < height; y++) { |
1144 | for (x = 0; x < width; x++) { |
1145 | grid_dot *d; |
1146 | /* cell position */ |
1147 | int px = (2*a + b) * x; |
1148 | int py = (2*a + b) * y; |
1149 | /* octagon */ |
1150 | grid_face_add_new(g, 8); |
1151 | d = grid_get_dot(g, points, px + a, py); |
1152 | grid_face_set_dot(g, d, 0); |
1153 | d = grid_get_dot(g, points, px + a + b, py); |
1154 | grid_face_set_dot(g, d, 1); |
1155 | d = grid_get_dot(g, points, px + 2*a + b, py + a); |
1156 | grid_face_set_dot(g, d, 2); |
1157 | d = grid_get_dot(g, points, px + 2*a + b, py + a + b); |
1158 | grid_face_set_dot(g, d, 3); |
1159 | d = grid_get_dot(g, points, px + a + b, py + 2*a + b); |
1160 | grid_face_set_dot(g, d, 4); |
1161 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
1162 | grid_face_set_dot(g, d, 5); |
1163 | d = grid_get_dot(g, points, px, py + a + b); |
1164 | grid_face_set_dot(g, d, 6); |
1165 | d = grid_get_dot(g, points, px, py + a); |
1166 | grid_face_set_dot(g, d, 7); |
1167 | |
1168 | /* diamond */ |
1169 | if ((x > 0) && (y > 0)) { |
1170 | grid_face_add_new(g, 4); |
1171 | d = grid_get_dot(g, points, px, py - a); |
1172 | grid_face_set_dot(g, d, 0); |
1173 | d = grid_get_dot(g, points, px + a, py); |
1174 | grid_face_set_dot(g, d, 1); |
1175 | d = grid_get_dot(g, points, px, py + a); |
1176 | grid_face_set_dot(g, d, 2); |
1177 | d = grid_get_dot(g, points, px - a, py); |
1178 | grid_face_set_dot(g, d, 3); |
1179 | } |
1180 | } |
1181 | } |
1182 | |
1183 | freetree234(points); |
1184 | assert(g->num_faces <= max_faces); |
1185 | assert(g->num_dots <= max_dots); |
7c95608a |
1186 | |
1187 | grid_make_consistent(g); |
1188 | return g; |
1189 | } |
1190 | |
1191 | grid *grid_new_kites(int width, int height) |
1192 | { |
1193 | int x, y; |
1194 | /* b/a approx sqrt(3) */ |
1195 | int a = 15; |
1196 | int b = 26; |
1197 | |
1198 | /* Upper bounds - don't have to be exact */ |
1199 | int max_faces = 6 * width * height; |
1200 | int max_dots = 6 * (width + 1) * (height + 1); |
1201 | |
1202 | tree234 *points; |
1203 | |
1204 | grid *g = grid_new(); |
1205 | g->tilesize = 40; |
1206 | g->faces = snewn(max_faces, grid_face); |
1207 | g->dots = snewn(max_dots, grid_dot); |
1208 | |
1209 | points = newtree234(grid_point_cmp_fn); |
1210 | |
1211 | for (y = 0; y < height; y++) { |
1212 | for (x = 0; x < width; x++) { |
1213 | grid_dot *d; |
1214 | /* position of order-6 dot */ |
1215 | int px = 4*b * x; |
1216 | int py = 6*a * y; |
1217 | if (y % 2) |
1218 | px += 2*b; |
1219 | |
1220 | /* kite pointing up-left */ |
1221 | grid_face_add_new(g, 4); |
1222 | d = grid_get_dot(g, points, px, py); |
1223 | grid_face_set_dot(g, d, 0); |
1224 | d = grid_get_dot(g, points, px + 2*b, py); |
1225 | grid_face_set_dot(g, d, 1); |
1226 | d = grid_get_dot(g, points, px + 2*b, py + 2*a); |
1227 | grid_face_set_dot(g, d, 2); |
1228 | d = grid_get_dot(g, points, px + b, py + 3*a); |
1229 | grid_face_set_dot(g, d, 3); |
1230 | |
1231 | /* kite pointing up */ |
1232 | grid_face_add_new(g, 4); |
1233 | d = grid_get_dot(g, points, px, py); |
1234 | grid_face_set_dot(g, d, 0); |
1235 | d = grid_get_dot(g, points, px + b, py + 3*a); |
1236 | grid_face_set_dot(g, d, 1); |
1237 | d = grid_get_dot(g, points, px, py + 4*a); |
1238 | grid_face_set_dot(g, d, 2); |
1239 | d = grid_get_dot(g, points, px - b, py + 3*a); |
1240 | grid_face_set_dot(g, d, 3); |
1241 | |
1242 | /* kite pointing up-right */ |
1243 | grid_face_add_new(g, 4); |
1244 | d = grid_get_dot(g, points, px, py); |
1245 | grid_face_set_dot(g, d, 0); |
1246 | d = grid_get_dot(g, points, px - b, py + 3*a); |
1247 | grid_face_set_dot(g, d, 1); |
1248 | d = grid_get_dot(g, points, px - 2*b, py + 2*a); |
1249 | grid_face_set_dot(g, d, 2); |
1250 | d = grid_get_dot(g, points, px - 2*b, py); |
1251 | grid_face_set_dot(g, d, 3); |
1252 | |
1253 | /* kite pointing down-right */ |
1254 | grid_face_add_new(g, 4); |
1255 | d = grid_get_dot(g, points, px, py); |
1256 | grid_face_set_dot(g, d, 0); |
1257 | d = grid_get_dot(g, points, px - 2*b, py); |
1258 | grid_face_set_dot(g, d, 1); |
1259 | d = grid_get_dot(g, points, px - 2*b, py - 2*a); |
1260 | grid_face_set_dot(g, d, 2); |
1261 | d = grid_get_dot(g, points, px - b, py - 3*a); |
1262 | grid_face_set_dot(g, d, 3); |
1263 | |
1264 | /* kite pointing down */ |
1265 | grid_face_add_new(g, 4); |
1266 | d = grid_get_dot(g, points, px, py); |
1267 | grid_face_set_dot(g, d, 0); |
1268 | d = grid_get_dot(g, points, px - b, py - 3*a); |
1269 | grid_face_set_dot(g, d, 1); |
1270 | d = grid_get_dot(g, points, px, py - 4*a); |
1271 | grid_face_set_dot(g, d, 2); |
1272 | d = grid_get_dot(g, points, px + b, py - 3*a); |
1273 | grid_face_set_dot(g, d, 3); |
1274 | |
1275 | /* kite pointing down-left */ |
1276 | grid_face_add_new(g, 4); |
1277 | d = grid_get_dot(g, points, px, py); |
1278 | grid_face_set_dot(g, d, 0); |
1279 | d = grid_get_dot(g, points, px + b, py - 3*a); |
1280 | grid_face_set_dot(g, d, 1); |
1281 | d = grid_get_dot(g, points, px + 2*b, py - 2*a); |
1282 | grid_face_set_dot(g, d, 2); |
1283 | d = grid_get_dot(g, points, px + 2*b, py); |
1284 | grid_face_set_dot(g, d, 3); |
1285 | } |
1286 | } |
1287 | |
1288 | freetree234(points); |
1289 | assert(g->num_faces <= max_faces); |
1290 | assert(g->num_dots <= max_dots); |
7c95608a |
1291 | |
1292 | grid_make_consistent(g); |
1293 | return g; |
1294 | } |
1295 | |
e30d39f6 |
1296 | grid *grid_new_floret(int width, int height) |
1297 | { |
1298 | int x, y; |
1299 | /* Vectors for sides; weird numbers needed to keep puzzle aligned with window |
1300 | * -py/px is close to tan(30 - atan(sqrt(3)/9)) |
1301 | * using py=26 makes everything lean to the left, rather than right |
1302 | */ |
1303 | int px = 75, py = -26; /* |( 75, -26)| = 79.43 */ |
1304 | int qx = 4*px/5, qy = -py*2; /* |( 60, 52)| = 79.40 */ |
1305 | int rx = qx-px, ry = qy-py; /* |(-15, 78)| = 79.38 */ |
1306 | |
1307 | /* Upper bounds - don't have to be exact */ |
1308 | int max_faces = 6 * width * height; |
1309 | int max_dots = 9 * (width + 1) * (height + 1); |
1310 | |
1311 | tree234 *points; |
1312 | |
1313 | grid *g = grid_new(); |
1314 | g->tilesize = 2 * px; |
1315 | g->faces = snewn(max_faces, grid_face); |
1316 | g->dots = snewn(max_dots, grid_dot); |
1317 | |
1318 | points = newtree234(grid_point_cmp_fn); |
1319 | |
1320 | /* generate pentagonal faces */ |
1321 | for (y = 0; y < height; y++) { |
1322 | for (x = 0; x < width; x++) { |
1323 | grid_dot *d; |
1324 | /* face centre */ |
1325 | int cx = (6*px+3*qx)/2 * x; |
1326 | int cy = (4*py-5*qy) * y; |
1327 | if (x % 2) |
1328 | cy -= (4*py-5*qy)/2; |
1329 | else if (y && y == height-1) |
1330 | continue; /* make better looking grids? try 3x3 for instance */ |
1331 | |
1332 | grid_face_add_new(g, 5); |
1333 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
1334 | d = grid_get_dot(g, points, cx+2*rx , cy+2*ry ); grid_face_set_dot(g, d, 1); |
1335 | d = grid_get_dot(g, points, cx+2*rx+qx, cy+2*ry+qy); grid_face_set_dot(g, d, 2); |
1336 | d = grid_get_dot(g, points, cx+2*qx+rx, cy+2*qy+ry); grid_face_set_dot(g, d, 3); |
1337 | d = grid_get_dot(g, points, cx+2*qx , cy+2*qy ); grid_face_set_dot(g, d, 4); |
1338 | |
1339 | grid_face_add_new(g, 5); |
1340 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
1341 | d = grid_get_dot(g, points, cx+2*qx , cy+2*qy ); grid_face_set_dot(g, d, 1); |
1342 | d = grid_get_dot(g, points, cx+2*qx+px, cy+2*qy+py); grid_face_set_dot(g, d, 2); |
1343 | d = grid_get_dot(g, points, cx+2*px+qx, cy+2*py+qy); grid_face_set_dot(g, d, 3); |
1344 | d = grid_get_dot(g, points, cx+2*px , cy+2*py ); grid_face_set_dot(g, d, 4); |
1345 | |
1346 | grid_face_add_new(g, 5); |
1347 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
1348 | d = grid_get_dot(g, points, cx+2*px , cy+2*py ); grid_face_set_dot(g, d, 1); |
1349 | d = grid_get_dot(g, points, cx+2*px-rx, cy+2*py-ry); grid_face_set_dot(g, d, 2); |
1350 | d = grid_get_dot(g, points, cx-2*rx+px, cy-2*ry+py); grid_face_set_dot(g, d, 3); |
1351 | d = grid_get_dot(g, points, cx-2*rx , cy-2*ry ); grid_face_set_dot(g, d, 4); |
1352 | |
1353 | grid_face_add_new(g, 5); |
1354 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
1355 | d = grid_get_dot(g, points, cx-2*rx , cy-2*ry ); grid_face_set_dot(g, d, 1); |
1356 | d = grid_get_dot(g, points, cx-2*rx-qx, cy-2*ry-qy); grid_face_set_dot(g, d, 2); |
1357 | d = grid_get_dot(g, points, cx-2*qx-rx, cy-2*qy-ry); grid_face_set_dot(g, d, 3); |
1358 | d = grid_get_dot(g, points, cx-2*qx , cy-2*qy ); grid_face_set_dot(g, d, 4); |
1359 | |
1360 | grid_face_add_new(g, 5); |
1361 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
1362 | d = grid_get_dot(g, points, cx-2*qx , cy-2*qy ); grid_face_set_dot(g, d, 1); |
1363 | d = grid_get_dot(g, points, cx-2*qx-px, cy-2*qy-py); grid_face_set_dot(g, d, 2); |
1364 | d = grid_get_dot(g, points, cx-2*px-qx, cy-2*py-qy); grid_face_set_dot(g, d, 3); |
1365 | d = grid_get_dot(g, points, cx-2*px , cy-2*py ); grid_face_set_dot(g, d, 4); |
1366 | |
1367 | grid_face_add_new(g, 5); |
1368 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
1369 | d = grid_get_dot(g, points, cx-2*px , cy-2*py ); grid_face_set_dot(g, d, 1); |
1370 | d = grid_get_dot(g, points, cx-2*px+rx, cy-2*py+ry); grid_face_set_dot(g, d, 2); |
1371 | d = grid_get_dot(g, points, cx+2*rx-px, cy+2*ry-py); grid_face_set_dot(g, d, 3); |
1372 | d = grid_get_dot(g, points, cx+2*rx , cy+2*ry ); grid_face_set_dot(g, d, 4); |
1373 | } |
1374 | } |
1375 | |
1376 | freetree234(points); |
1377 | assert(g->num_faces <= max_faces); |
1378 | assert(g->num_dots <= max_dots); |
e30d39f6 |
1379 | |
1380 | grid_make_consistent(g); |
1381 | return g; |
1382 | } |
1383 | |
918a098a |
1384 | grid *grid_new_dodecagonal(int width, int height) |
1385 | { |
1386 | int x, y; |
1387 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
1388 | int a = 15; |
1389 | int b = 26; |
1390 | |
1391 | /* Upper bounds - don't have to be exact */ |
1392 | int max_faces = 3 * width * height; |
1393 | int max_dots = 14 * width * height; |
1394 | |
1395 | tree234 *points; |
1396 | |
1397 | grid *g = grid_new(); |
1398 | g->tilesize = b; |
1399 | g->faces = snewn(max_faces, grid_face); |
1400 | g->dots = snewn(max_dots, grid_dot); |
1401 | |
1402 | points = newtree234(grid_point_cmp_fn); |
1403 | |
1404 | for (y = 0; y < height; y++) { |
1405 | for (x = 0; x < width; x++) { |
1406 | grid_dot *d; |
1407 | /* centre of dodecagon */ |
1408 | int px = (4*a + 2*b) * x; |
1409 | int py = (3*a + 2*b) * y; |
1410 | if (y % 2) |
1411 | px += 2*a + b; |
1412 | |
1413 | /* dodecagon */ |
1414 | grid_face_add_new(g, 12); |
1415 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); |
1416 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 1); |
1417 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a )); grid_face_set_dot(g, d, 2); |
1418 | d = grid_get_dot(g, points, px + (2*a + b), py + ( a )); grid_face_set_dot(g, d, 3); |
1419 | d = grid_get_dot(g, points, px + ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 4); |
1420 | d = grid_get_dot(g, points, px + ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 5); |
1421 | d = grid_get_dot(g, points, px - ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 6); |
1422 | d = grid_get_dot(g, points, px - ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 7); |
1423 | d = grid_get_dot(g, points, px - (2*a + b), py + ( a )); grid_face_set_dot(g, d, 8); |
1424 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a )); grid_face_set_dot(g, d, 9); |
1425 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 10); |
1426 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 11); |
1427 | |
1428 | /* triangle below dodecagon */ |
1429 | if ((y < height - 1 && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2)))) { |
1430 | grid_face_add_new(g, 3); |
1431 | d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0); |
1432 | d = grid_get_dot(g, points, px , py + (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
1433 | d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 2); |
1434 | } |
1435 | |
1436 | /* triangle above dodecagon */ |
1437 | if ((y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2)))) { |
1438 | grid_face_add_new(g, 3); |
1439 | d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 0); |
1440 | d = grid_get_dot(g, points, px , py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
1441 | d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 2); |
1442 | } |
1443 | } |
1444 | } |
1445 | |
1446 | freetree234(points); |
1447 | assert(g->num_faces <= max_faces); |
1448 | assert(g->num_dots <= max_dots); |
1449 | |
1450 | grid_make_consistent(g); |
1451 | return g; |
1452 | } |
1453 | |
1454 | grid *grid_new_greatdodecagonal(int width, int height) |
1455 | { |
1456 | int x, y; |
1457 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
1458 | int a = 15; |
1459 | int b = 26; |
1460 | |
1461 | /* Upper bounds - don't have to be exact */ |
1462 | int max_faces = 30 * width * height; |
1463 | int max_dots = 200 * width * height; |
1464 | |
1465 | tree234 *points; |
1466 | |
1467 | grid *g = grid_new(); |
1468 | g->tilesize = b; |
1469 | g->faces = snewn(max_faces, grid_face); |
1470 | g->dots = snewn(max_dots, grid_dot); |
1471 | |
1472 | points = newtree234(grid_point_cmp_fn); |
1473 | |
1474 | for (y = 0; y < height; y++) { |
1475 | for (x = 0; x < width; x++) { |
1476 | grid_dot *d; |
1477 | /* centre of dodecagon */ |
1478 | int px = (6*a + 2*b) * x; |
1479 | int py = (3*a + 3*b) * y; |
1480 | if (y % 2) |
1481 | px += 3*a + b; |
1482 | |
1483 | /* dodecagon */ |
1484 | grid_face_add_new(g, 12); |
1485 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); |
1486 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 1); |
1487 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a )); grid_face_set_dot(g, d, 2); |
1488 | d = grid_get_dot(g, points, px + (2*a + b), py + ( a )); grid_face_set_dot(g, d, 3); |
1489 | d = grid_get_dot(g, points, px + ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 4); |
1490 | d = grid_get_dot(g, points, px + ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 5); |
1491 | d = grid_get_dot(g, points, px - ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 6); |
1492 | d = grid_get_dot(g, points, px - ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 7); |
1493 | d = grid_get_dot(g, points, px - (2*a + b), py + ( a )); grid_face_set_dot(g, d, 8); |
1494 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a )); grid_face_set_dot(g, d, 9); |
1495 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 10); |
1496 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 11); |
1497 | |
1498 | /* hexagon below dodecagon */ |
1499 | if (y < height - 1 && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) { |
1500 | grid_face_add_new(g, 6); |
1501 | d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0); |
1502 | d = grid_get_dot(g, points, px + 2*a, py + (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
1503 | d = grid_get_dot(g, points, px + a, py + (2*a + 3*b)); grid_face_set_dot(g, d, 2); |
1504 | d = grid_get_dot(g, points, px - a, py + (2*a + 3*b)); grid_face_set_dot(g, d, 3); |
1505 | d = grid_get_dot(g, points, px - 2*a, py + (2*a + 2*b)); grid_face_set_dot(g, d, 4); |
1506 | d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 5); |
1507 | } |
1508 | |
1509 | /* hexagon above dodecagon */ |
1510 | if (y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) { |
1511 | grid_face_add_new(g, 6); |
1512 | d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 0); |
1513 | d = grid_get_dot(g, points, px - 2*a, py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
1514 | d = grid_get_dot(g, points, px - a, py - (2*a + 3*b)); grid_face_set_dot(g, d, 2); |
1515 | d = grid_get_dot(g, points, px + a, py - (2*a + 3*b)); grid_face_set_dot(g, d, 3); |
1516 | d = grid_get_dot(g, points, px + 2*a, py - (2*a + 2*b)); grid_face_set_dot(g, d, 4); |
1517 | d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 5); |
1518 | } |
1519 | |
1520 | /* square on right of dodecagon */ |
1521 | if (x < width - 1) { |
1522 | grid_face_add_new(g, 4); |
1523 | d = grid_get_dot(g, points, px + 2*a + b, py - a); grid_face_set_dot(g, d, 0); |
1524 | d = grid_get_dot(g, points, px + 4*a + b, py - a); grid_face_set_dot(g, d, 1); |
1525 | d = grid_get_dot(g, points, px + 4*a + b, py + a); grid_face_set_dot(g, d, 2); |
1526 | d = grid_get_dot(g, points, px + 2*a + b, py + a); grid_face_set_dot(g, d, 3); |
1527 | } |
1528 | |
1529 | /* square on top right of dodecagon */ |
1530 | if (y && (x < width - 1 || !(y % 2))) { |
1531 | grid_face_add_new(g, 4); |
1532 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); |
1533 | d = grid_get_dot(g, points, px + (2*a ), py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
1534 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a + 2*b)); grid_face_set_dot(g, d, 2); |
1535 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 3); |
1536 | } |
1537 | |
1538 | /* square on top left of dodecagon */ |
1539 | if (y && (x || (y % 2))) { |
1540 | grid_face_add_new(g, 4); |
1541 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 0); |
1542 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a + 2*b)); grid_face_set_dot(g, d, 1); |
1543 | d = grid_get_dot(g, points, px - (2*a ), py - (2*a + 2*b)); grid_face_set_dot(g, d, 2); |
1544 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 3); |
1545 | } |
1546 | } |
1547 | } |
1548 | |
1549 | freetree234(points); |
1550 | assert(g->num_faces <= max_faces); |
1551 | assert(g->num_dots <= max_dots); |
1552 | |
1553 | grid_make_consistent(g); |
1554 | return g; |
1555 | } |
1556 | |
7c95608a |
1557 | /* ----------- End of grid generators ------------- */ |