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 | |
e64991db |
623 | /* |
624 | * Helper routines for grid_find_incentre. |
625 | */ |
626 | static int solve_2x2_matrix(double mx[4], double vin[2], double vout[2]) |
627 | { |
628 | double inv[4]; |
629 | double det; |
630 | det = (mx[0]*mx[3] - mx[1]*mx[2]); |
631 | if (det == 0) |
632 | return FALSE; |
633 | |
634 | inv[0] = mx[3] / det; |
635 | inv[1] = -mx[1] / det; |
636 | inv[2] = -mx[2] / det; |
637 | inv[3] = mx[0] / det; |
638 | |
639 | vout[0] = inv[0]*vin[0] + inv[1]*vin[1]; |
640 | vout[1] = inv[2]*vin[0] + inv[3]*vin[1]; |
641 | |
642 | return TRUE; |
643 | } |
644 | static int solve_3x3_matrix(double mx[9], double vin[3], double vout[3]) |
645 | { |
646 | double inv[9]; |
647 | double det; |
648 | |
649 | det = (mx[0]*mx[4]*mx[8] + mx[1]*mx[5]*mx[6] + mx[2]*mx[3]*mx[7] - |
650 | mx[0]*mx[5]*mx[7] - mx[1]*mx[3]*mx[8] - mx[2]*mx[4]*mx[6]); |
651 | if (det == 0) |
652 | return FALSE; |
653 | |
654 | inv[0] = (mx[4]*mx[8] - mx[5]*mx[7]) / det; |
655 | inv[1] = (mx[2]*mx[7] - mx[1]*mx[8]) / det; |
656 | inv[2] = (mx[1]*mx[5] - mx[2]*mx[4]) / det; |
657 | inv[3] = (mx[5]*mx[6] - mx[3]*mx[8]) / det; |
658 | inv[4] = (mx[0]*mx[8] - mx[2]*mx[6]) / det; |
659 | inv[5] = (mx[2]*mx[3] - mx[0]*mx[5]) / det; |
660 | inv[6] = (mx[3]*mx[7] - mx[4]*mx[6]) / det; |
661 | inv[7] = (mx[1]*mx[6] - mx[0]*mx[7]) / det; |
662 | inv[8] = (mx[0]*mx[4] - mx[1]*mx[3]) / det; |
663 | |
664 | vout[0] = inv[0]*vin[0] + inv[1]*vin[1] + inv[2]*vin[2]; |
665 | vout[1] = inv[3]*vin[0] + inv[4]*vin[1] + inv[5]*vin[2]; |
666 | vout[2] = inv[6]*vin[0] + inv[7]*vin[1] + inv[8]*vin[2]; |
667 | |
668 | return TRUE; |
669 | } |
670 | |
671 | void grid_find_incentre(grid_face *f) |
672 | { |
673 | double xbest, ybest, bestdist; |
674 | int i, j, k, m; |
675 | grid_dot *edgedot1[3], *edgedot2[3]; |
676 | grid_dot *dots[3]; |
677 | int nedges, ndots; |
678 | |
679 | if (f->has_incentre) |
680 | return; |
681 | |
682 | /* |
683 | * Find the point in the polygon with the maximum distance to any |
684 | * edge or corner. |
685 | * |
686 | * Such a point must exist which is in contact with at least three |
687 | * edges and/or vertices. (Proof: if it's only in contact with two |
688 | * edges and/or vertices, it can't even be at a _local_ maximum - |
689 | * any such circle can always be expanded in some direction.) So |
690 | * we iterate through all 3-subsets of the combined set of edges |
691 | * and vertices; for each subset we generate one or two candidate |
692 | * points that might be the incentre, and then we vet each one to |
693 | * see if it's inside the polygon and what its maximum radius is. |
694 | * |
695 | * (There's one case which this algorithm will get noticeably |
696 | * wrong, and that's when a continuum of equally good answers |
697 | * exists due to parallel edges. Consider a long thin rectangle, |
698 | * for instance, or a parallelogram. This algorithm will pick a |
699 | * point near one end, and choose the end arbitrarily; obviously a |
700 | * nicer point to choose would be in the centre. To fix this I |
701 | * would have to introduce a special-case system which detected |
702 | * parallel edges in advance, set aside all candidate points |
703 | * generated using both edges in a parallel pair, and generated |
704 | * some additional candidate points half way between them. Also, |
705 | * of course, I'd have to cope with rounding error making such a |
706 | * point look worse than one of its endpoints. So I haven't done |
707 | * this for the moment, and will cross it if necessary when I come |
708 | * to it.) |
709 | * |
710 | * We don't actually iterate literally over _edges_, in the sense |
711 | * of grid_edge structures. Instead, we fill in edgedot1[] and |
712 | * edgedot2[] with a pair of dots adjacent in the face's list of |
713 | * vertices. This ensures that we get the edges in consistent |
714 | * orientation, which we could not do from the grid structure |
715 | * alone. (A moment's consideration of an order-3 vertex should |
716 | * make it clear that if a notional arrow was written on each |
717 | * edge, _at least one_ of the three faces bordering that vertex |
718 | * would have to have the two arrows tip-to-tip or tail-to-tail |
719 | * rather than tip-to-tail.) |
720 | */ |
721 | nedges = ndots = 0; |
722 | bestdist = 0; |
723 | xbest = ybest = 0; |
724 | |
725 | for (i = 0; i+2 < 2*f->order; i++) { |
726 | if (i < f->order) { |
727 | edgedot1[nedges] = f->dots[i]; |
728 | edgedot2[nedges++] = f->dots[(i+1)%f->order]; |
729 | } else |
730 | dots[ndots++] = f->dots[i - f->order]; |
731 | |
732 | for (j = i+1; j+1 < 2*f->order; j++) { |
733 | if (j < f->order) { |
734 | edgedot1[nedges] = f->dots[j]; |
735 | edgedot2[nedges++] = f->dots[(j+1)%f->order]; |
736 | } else |
737 | dots[ndots++] = f->dots[j - f->order]; |
738 | |
739 | for (k = j+1; k < 2*f->order; k++) { |
740 | double cx[2], cy[2]; /* candidate positions */ |
741 | int cn = 0; /* number of candidates */ |
742 | |
743 | if (k < f->order) { |
744 | edgedot1[nedges] = f->dots[k]; |
745 | edgedot2[nedges++] = f->dots[(k+1)%f->order]; |
746 | } else |
747 | dots[ndots++] = f->dots[k - f->order]; |
748 | |
749 | /* |
750 | * Find a point, or pair of points, equidistant from |
751 | * all the specified edges and/or vertices. |
752 | */ |
753 | if (nedges == 3) { |
754 | /* |
755 | * Three edges. This is a linear matrix equation: |
756 | * each row of the matrix represents the fact that |
757 | * the point (x,y) we seek is at distance r from |
758 | * that edge, and we solve three of those |
759 | * simultaneously to obtain x,y,r. (We ignore r.) |
760 | */ |
761 | double matrix[9], vector[3], vector2[3]; |
762 | int m; |
763 | |
764 | for (m = 0; m < 3; m++) { |
765 | int x1 = edgedot1[m]->x, x2 = edgedot2[m]->x; |
766 | int y1 = edgedot1[m]->y, y2 = edgedot2[m]->y; |
767 | int dx = x2-x1, dy = y2-y1; |
768 | |
769 | /* |
770 | * ((x,y) - (x1,y1)) . (dy,-dx) = r |(dx,dy)| |
771 | * |
772 | * => x dy - y dx - r |(dx,dy)| = (x1 dy - y1 dx) |
773 | */ |
774 | matrix[3*m+0] = dy; |
775 | matrix[3*m+1] = -dx; |
776 | matrix[3*m+2] = -sqrt((double)dx*dx+(double)dy*dy); |
777 | vector[m] = (double)x1*dy - (double)y1*dx; |
778 | } |
779 | |
780 | if (solve_3x3_matrix(matrix, vector, vector2)) { |
781 | cx[cn] = vector2[0]; |
782 | cy[cn] = vector2[1]; |
783 | cn++; |
784 | } |
785 | } else if (nedges == 2) { |
786 | /* |
787 | * Two edges and a dot. This will end up in a |
788 | * quadratic equation. |
789 | * |
790 | * First, look at the two edges. Having our point |
791 | * be some distance r from both of them gives rise |
792 | * to a pair of linear equations in x,y,r of the |
793 | * form |
794 | * |
795 | * (x-x1) dy - (y-y1) dx = r sqrt(dx^2+dy^2) |
796 | * |
797 | * We eliminate r between those equations to give |
798 | * us a single linear equation in x,y describing |
799 | * the locus of points equidistant from both lines |
800 | * - i.e. the angle bisector. |
801 | * |
802 | * We then choose one of x,y to be a parameter t, |
803 | * and derive linear formulae for x,y,r in terms |
804 | * of t. This enables us to write down the |
805 | * circular equation (x-xd)^2+(y-yd)^2=r^2 as a |
806 | * quadratic in t; solving that and substituting |
807 | * in for x,y gives us two candidate points. |
808 | */ |
809 | double eqs[2][4]; /* a,b,c,d : ax+by+cr=d */ |
810 | double eq[3]; /* a,b,c: ax+by=c */ |
811 | double xt[2], yt[2], rt[2]; /* a,b: {x,y,r}=at+b */ |
812 | double q[3]; /* a,b,c: at^2+bt+c=0 */ |
813 | double disc; |
814 | |
815 | /* Find equations of the two input lines. */ |
816 | for (m = 0; m < 2; m++) { |
817 | int x1 = edgedot1[m]->x, x2 = edgedot2[m]->x; |
818 | int y1 = edgedot1[m]->y, y2 = edgedot2[m]->y; |
819 | int dx = x2-x1, dy = y2-y1; |
820 | |
821 | eqs[m][0] = dy; |
822 | eqs[m][1] = -dx; |
823 | eqs[m][2] = -sqrt(dx*dx+dy*dy); |
824 | eqs[m][3] = x1*dy - y1*dx; |
825 | } |
826 | |
827 | /* Derive the angle bisector by eliminating r. */ |
828 | eq[0] = eqs[0][0]*eqs[1][2] - eqs[1][0]*eqs[0][2]; |
829 | eq[1] = eqs[0][1]*eqs[1][2] - eqs[1][1]*eqs[0][2]; |
830 | eq[2] = eqs[0][3]*eqs[1][2] - eqs[1][3]*eqs[0][2]; |
831 | |
832 | /* Parametrise x and y in terms of some t. */ |
833 | if (abs(eq[0]) < abs(eq[1])) { |
834 | /* Parameter is x. */ |
835 | xt[0] = 1; xt[1] = 0; |
836 | yt[0] = -eq[0]/eq[1]; yt[1] = eq[2]/eq[1]; |
837 | } else { |
838 | /* Parameter is y. */ |
839 | yt[0] = 1; yt[1] = 0; |
840 | xt[0] = -eq[1]/eq[0]; xt[1] = eq[2]/eq[0]; |
841 | } |
842 | |
843 | /* Find a linear representation of r using eqs[0]. */ |
844 | rt[0] = -(eqs[0][0]*xt[0] + eqs[0][1]*yt[0])/eqs[0][2]; |
845 | rt[1] = (eqs[0][3] - eqs[0][0]*xt[1] - |
846 | eqs[0][1]*yt[1])/eqs[0][2]; |
847 | |
848 | /* Construct the quadratic equation. */ |
849 | q[0] = -rt[0]*rt[0]; |
850 | q[1] = -2*rt[0]*rt[1]; |
851 | q[2] = -rt[1]*rt[1]; |
852 | q[0] += xt[0]*xt[0]; |
853 | q[1] += 2*xt[0]*(xt[1]-dots[0]->x); |
854 | q[2] += (xt[1]-dots[0]->x)*(xt[1]-dots[0]->x); |
855 | q[0] += yt[0]*yt[0]; |
856 | q[1] += 2*yt[0]*(yt[1]-dots[0]->y); |
857 | q[2] += (yt[1]-dots[0]->y)*(yt[1]-dots[0]->y); |
858 | |
859 | /* And solve it. */ |
860 | disc = q[1]*q[1] - 4*q[0]*q[2]; |
861 | if (disc >= 0) { |
862 | double t; |
863 | |
864 | disc = sqrt(disc); |
865 | |
866 | t = (-q[1] + disc) / (2*q[0]); |
867 | cx[cn] = xt[0]*t + xt[1]; |
868 | cy[cn] = yt[0]*t + yt[1]; |
869 | cn++; |
870 | |
871 | t = (-q[1] - disc) / (2*q[0]); |
872 | cx[cn] = xt[0]*t + xt[1]; |
873 | cy[cn] = yt[0]*t + yt[1]; |
874 | cn++; |
875 | } |
876 | } else if (nedges == 1) { |
877 | /* |
878 | * Two dots and an edge. This one's another |
879 | * quadratic equation. |
880 | * |
881 | * The point we want must lie on the perpendicular |
882 | * bisector of the two dots; that much is obvious. |
883 | * So we can construct a parametrisation of that |
884 | * bisecting line, giving linear formulae for x,y |
885 | * in terms of t. We can also express the distance |
886 | * from the edge as such a linear formula. |
887 | * |
888 | * Then we set that equal to the radius of the |
889 | * circle passing through the two points, which is |
890 | * a Pythagoras exercise; that gives rise to a |
891 | * quadratic in t, which we solve. |
892 | */ |
893 | double xt[2], yt[2], rt[2]; /* a,b: {x,y,r}=at+b */ |
894 | double q[3]; /* a,b,c: at^2+bt+c=0 */ |
895 | double disc; |
896 | double halfsep; |
897 | |
898 | /* Find parametric formulae for x,y. */ |
899 | { |
900 | int x1 = dots[0]->x, x2 = dots[1]->x; |
901 | int y1 = dots[0]->y, y2 = dots[1]->y; |
902 | int dx = x2-x1, dy = y2-y1; |
903 | double d = sqrt((double)dx*dx + (double)dy*dy); |
904 | |
905 | xt[1] = (x1+x2)/2.0; |
906 | yt[1] = (y1+y2)/2.0; |
907 | /* It's convenient if we have t at standard scale. */ |
908 | xt[0] = -dy/d; |
909 | yt[0] = dx/d; |
910 | |
911 | /* Also note down half the separation between |
912 | * the dots, for use in computing the circle radius. */ |
913 | halfsep = 0.5*d; |
914 | } |
915 | |
916 | /* Find a parametric formula for r. */ |
917 | { |
918 | int x1 = edgedot1[0]->x, x2 = edgedot2[0]->x; |
919 | int y1 = edgedot1[0]->y, y2 = edgedot2[0]->y; |
920 | int dx = x2-x1, dy = y2-y1; |
921 | double d = sqrt((double)dx*dx + (double)dy*dy); |
922 | rt[0] = (xt[0]*dy - yt[0]*dx) / d; |
923 | rt[1] = ((xt[1]-x1)*dy - (yt[1]-y1)*dx) / d; |
924 | } |
925 | |
926 | /* Construct the quadratic equation. */ |
927 | q[0] = rt[0]*rt[0]; |
928 | q[1] = 2*rt[0]*rt[1]; |
929 | q[2] = rt[1]*rt[1]; |
930 | q[0] -= 1; |
931 | q[2] -= halfsep*halfsep; |
932 | |
933 | /* And solve it. */ |
934 | disc = q[1]*q[1] - 4*q[0]*q[2]; |
935 | if (disc >= 0) { |
936 | double t; |
937 | |
938 | disc = sqrt(disc); |
939 | |
940 | t = (-q[1] + disc) / (2*q[0]); |
941 | cx[cn] = xt[0]*t + xt[1]; |
942 | cy[cn] = yt[0]*t + yt[1]; |
943 | cn++; |
944 | |
945 | t = (-q[1] - disc) / (2*q[0]); |
946 | cx[cn] = xt[0]*t + xt[1]; |
947 | cy[cn] = yt[0]*t + yt[1]; |
948 | cn++; |
949 | } |
950 | } else if (nedges == 0) { |
951 | /* |
952 | * Three dots. This is another linear matrix |
953 | * equation, this time with each row of the matrix |
954 | * representing the perpendicular bisector between |
955 | * two of the points. Of course we only need two |
956 | * such lines to find their intersection, so we |
957 | * need only solve a 2x2 matrix equation. |
958 | */ |
959 | |
960 | double matrix[4], vector[2], vector2[2]; |
961 | int m; |
962 | |
963 | for (m = 0; m < 2; m++) { |
964 | int x1 = dots[m]->x, x2 = dots[m+1]->x; |
965 | int y1 = dots[m]->y, y2 = dots[m+1]->y; |
966 | int dx = x2-x1, dy = y2-y1; |
967 | |
968 | /* |
969 | * ((x,y) - (x1,y1)) . (dx,dy) = 1/2 |(dx,dy)|^2 |
970 | * |
971 | * => 2x dx + 2y dy = dx^2+dy^2 + (2 x1 dx + 2 y1 dy) |
972 | */ |
973 | matrix[2*m+0] = 2*dx; |
974 | matrix[2*m+1] = 2*dy; |
975 | vector[m] = ((double)dx*dx + (double)dy*dy + |
976 | 2.0*x1*dx + 2.0*y1*dy); |
977 | } |
978 | |
979 | if (solve_2x2_matrix(matrix, vector, vector2)) { |
980 | cx[cn] = vector2[0]; |
981 | cy[cn] = vector2[1]; |
982 | cn++; |
983 | } |
984 | } |
985 | |
986 | /* |
987 | * Now go through our candidate points and see if any |
988 | * of them are better than what we've got so far. |
989 | */ |
990 | for (m = 0; m < cn; m++) { |
991 | double x = cx[m], y = cy[m]; |
992 | |
993 | /* |
994 | * First, disqualify the point if it's not inside |
995 | * the polygon, which we work out by counting the |
996 | * edges to the right of the point. (For |
997 | * tiebreaking purposes when edges start or end on |
998 | * our y-coordinate or go right through it, we |
999 | * consider our point to be offset by a small |
1000 | * _positive_ epsilon in both the x- and |
1001 | * y-direction.) |
1002 | */ |
1003 | int e, in = 0; |
1004 | for (e = 0; e < f->order; e++) { |
1005 | int xs = f->edges[e]->dot1->x; |
1006 | int xe = f->edges[e]->dot2->x; |
1007 | int ys = f->edges[e]->dot1->y; |
1008 | int ye = f->edges[e]->dot2->y; |
1009 | if ((y >= ys && y < ye) || (y >= ye && y < ys)) { |
1010 | /* |
1011 | * The line goes past our y-position. Now we need |
1012 | * to know if its x-coordinate when it does so is |
1013 | * to our right. |
1014 | * |
1015 | * The x-coordinate in question is mathematically |
1016 | * (y - ys) * (xe - xs) / (ye - ys), and we want |
1017 | * to know whether (x - xs) >= that. Of course we |
1018 | * avoid the division, so we can work in integers; |
1019 | * to do this we must multiply both sides of the |
1020 | * inequality by ye - ys, which means we must |
1021 | * first check that's not negative. |
1022 | */ |
1023 | int num = xe - xs, denom = ye - ys; |
1024 | if (denom < 0) { |
1025 | num = -num; |
1026 | denom = -denom; |
1027 | } |
1028 | if ((x - xs) * denom >= (y - ys) * num) |
1029 | in ^= 1; |
1030 | } |
1031 | } |
1032 | |
1033 | if (in) { |
1034 | double mindist = HUGE_VAL; |
1035 | int e, d; |
1036 | |
1037 | /* |
1038 | * This point is inside the polygon, so now we check |
1039 | * its minimum distance to every edge and corner. |
1040 | * First the corners ... |
1041 | */ |
1042 | for (d = 0; d < f->order; d++) { |
1043 | int xp = f->dots[d]->x; |
1044 | int yp = f->dots[d]->y; |
1045 | double dx = x - xp, dy = y - yp; |
1046 | double dist = dx*dx + dy*dy; |
1047 | if (mindist > dist) |
1048 | mindist = dist; |
1049 | } |
1050 | |
1051 | /* |
1052 | * ... and now also check the perpendicular distance |
1053 | * to every edge, if the perpendicular lies between |
1054 | * the edge's endpoints. |
1055 | */ |
1056 | for (e = 0; e < f->order; e++) { |
1057 | int xs = f->edges[e]->dot1->x; |
1058 | int xe = f->edges[e]->dot2->x; |
1059 | int ys = f->edges[e]->dot1->y; |
1060 | int ye = f->edges[e]->dot2->y; |
1061 | |
1062 | /* |
1063 | * If s and e are our endpoints, and p our |
1064 | * candidate circle centre, the foot of a |
1065 | * perpendicular from p to the line se lies |
1066 | * between s and e if and only if (p-s).(e-s) lies |
1067 | * strictly between 0 and (e-s).(e-s). |
1068 | */ |
1069 | int edx = xe - xs, edy = ye - ys; |
1070 | double pdx = x - xs, pdy = y - ys; |
1071 | double pde = pdx * edx + pdy * edy; |
1072 | long ede = (long)edx * edx + (long)edy * edy; |
1073 | if (0 < pde && pde < ede) { |
1074 | /* |
1075 | * Yes, the nearest point on this edge is |
1076 | * closer than either endpoint, so we must |
1077 | * take it into account by measuring the |
1078 | * perpendicular distance to the edge and |
1079 | * checking its square against mindist. |
1080 | */ |
1081 | |
1082 | double pdre = pdx * edy - pdy * edx; |
1083 | double sqlen = pdre * pdre / ede; |
1084 | |
1085 | if (mindist > sqlen) |
1086 | mindist = sqlen; |
1087 | } |
1088 | } |
1089 | |
1090 | /* |
1091 | * Right. Now we know the biggest circle around this |
1092 | * point, so we can check it against bestdist. |
1093 | */ |
1094 | if (bestdist < mindist) { |
1095 | bestdist = mindist; |
1096 | xbest = x; |
1097 | ybest = y; |
1098 | } |
1099 | } |
1100 | } |
1101 | |
1102 | if (k < f->order) |
1103 | nedges--; |
1104 | else |
1105 | ndots--; |
1106 | } |
1107 | if (j < f->order) |
1108 | nedges--; |
1109 | else |
1110 | ndots--; |
1111 | } |
1112 | if (i < f->order) |
1113 | nedges--; |
1114 | else |
1115 | ndots--; |
1116 | } |
1117 | |
1118 | assert(bestdist > 0); |
1119 | |
1120 | f->has_incentre = TRUE; |
1121 | f->ix = xbest + 0.5; /* round to nearest */ |
1122 | f->iy = ybest + 0.5; |
1123 | } |
1124 | |
7c95608a |
1125 | /* ------ Generate various types of grid ------ */ |
1126 | |
1127 | /* General method is to generate faces, by calculating their dot coordinates. |
1128 | * As new faces are added, we keep track of all the dots so we can tell when |
1129 | * a new face reuses an existing dot. For example, two squares touching at an |
1130 | * edge would generate six unique dots: four dots from the first face, then |
1131 | * two additional dots for the second face, because we detect the other two |
1132 | * dots have already been taken up. This list is stored in a tree234 |
1133 | * called "points". No extra memory-allocation needed here - we store the |
1134 | * actual grid_dot* pointers, which all point into the g->dots list. |
1135 | * For this reason, we have to calculate coordinates in such a way as to |
1136 | * eliminate any rounding errors, so we can detect when a dot on one |
1137 | * face precisely lands on a dot of a different face. No floating-point |
1138 | * arithmetic here! |
1139 | */ |
1140 | |
1141 | grid *grid_new_square(int width, int height) |
1142 | { |
1143 | int x, y; |
1144 | /* Side length */ |
1145 | int a = 20; |
1146 | |
1147 | /* Upper bounds - don't have to be exact */ |
1148 | int max_faces = width * height; |
1149 | int max_dots = (width + 1) * (height + 1); |
1150 | |
1151 | tree234 *points; |
1152 | |
1153 | grid *g = grid_new(); |
1154 | g->tilesize = a; |
1155 | g->faces = snewn(max_faces, grid_face); |
1156 | g->dots = snewn(max_dots, grid_dot); |
1157 | |
1158 | points = newtree234(grid_point_cmp_fn); |
1159 | |
1160 | /* generate square faces */ |
1161 | for (y = 0; y < height; y++) { |
1162 | for (x = 0; x < width; x++) { |
1163 | grid_dot *d; |
1164 | /* face position */ |
1165 | int px = a * x; |
1166 | int py = a * y; |
1167 | |
1168 | grid_face_add_new(g, 4); |
1169 | d = grid_get_dot(g, points, px, py); |
1170 | grid_face_set_dot(g, d, 0); |
1171 | d = grid_get_dot(g, points, px + a, py); |
1172 | grid_face_set_dot(g, d, 1); |
1173 | d = grid_get_dot(g, points, px + a, py + a); |
1174 | grid_face_set_dot(g, d, 2); |
1175 | d = grid_get_dot(g, points, px, py + a); |
1176 | grid_face_set_dot(g, d, 3); |
1177 | } |
1178 | } |
1179 | |
1180 | freetree234(points); |
1181 | assert(g->num_faces <= max_faces); |
1182 | assert(g->num_dots <= max_dots); |
7c95608a |
1183 | |
1184 | grid_make_consistent(g); |
1185 | return g; |
1186 | } |
1187 | |
1188 | grid *grid_new_honeycomb(int width, int height) |
1189 | { |
1190 | int x, y; |
1191 | /* Vector for side of hexagon - ratio is close to sqrt(3) */ |
1192 | int a = 15; |
1193 | int b = 26; |
1194 | |
1195 | /* Upper bounds - don't have to be exact */ |
1196 | int max_faces = width * height; |
1197 | int max_dots = 2 * (width + 1) * (height + 1); |
1198 | |
1199 | tree234 *points; |
1200 | |
1201 | grid *g = grid_new(); |
1202 | g->tilesize = 3 * a; |
1203 | g->faces = snewn(max_faces, grid_face); |
1204 | g->dots = snewn(max_dots, grid_dot); |
1205 | |
1206 | points = newtree234(grid_point_cmp_fn); |
1207 | |
1208 | /* generate hexagonal faces */ |
1209 | for (y = 0; y < height; y++) { |
1210 | for (x = 0; x < width; x++) { |
1211 | grid_dot *d; |
1212 | /* face centre */ |
1213 | int cx = 3 * a * x; |
1214 | int cy = 2 * b * y; |
1215 | if (x % 2) |
1216 | cy += b; |
1217 | grid_face_add_new(g, 6); |
1218 | |
1219 | d = grid_get_dot(g, points, cx - a, cy - b); |
1220 | grid_face_set_dot(g, d, 0); |
1221 | d = grid_get_dot(g, points, cx + a, cy - b); |
1222 | grid_face_set_dot(g, d, 1); |
1223 | d = grid_get_dot(g, points, cx + 2*a, cy); |
1224 | grid_face_set_dot(g, d, 2); |
1225 | d = grid_get_dot(g, points, cx + a, cy + b); |
1226 | grid_face_set_dot(g, d, 3); |
1227 | d = grid_get_dot(g, points, cx - a, cy + b); |
1228 | grid_face_set_dot(g, d, 4); |
1229 | d = grid_get_dot(g, points, cx - 2*a, cy); |
1230 | grid_face_set_dot(g, d, 5); |
1231 | } |
1232 | } |
1233 | |
1234 | freetree234(points); |
1235 | assert(g->num_faces <= max_faces); |
1236 | assert(g->num_dots <= max_dots); |
7c95608a |
1237 | |
1238 | grid_make_consistent(g); |
1239 | return g; |
1240 | } |
1241 | |
1242 | /* Doesn't use the previous method of generation, it pre-dates it! |
1243 | * A triangular grid is just about simple enough to do by "brute force" */ |
1244 | grid *grid_new_triangular(int width, int height) |
1245 | { |
1246 | int x,y; |
1247 | |
1248 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
1249 | int vec_x = 15; |
1250 | int vec_y = 26; |
1251 | |
1252 | int index; |
1253 | |
1254 | /* convenient alias */ |
1255 | int w = width + 1; |
1256 | |
1257 | grid *g = grid_new(); |
1258 | g->tilesize = 18; /* adjust to your taste */ |
1259 | |
1260 | g->num_faces = width * height * 2; |
1261 | g->num_dots = (width + 1) * (height + 1); |
1262 | g->faces = snewn(g->num_faces, grid_face); |
1263 | g->dots = snewn(g->num_dots, grid_dot); |
1264 | |
1265 | /* generate dots */ |
1266 | index = 0; |
1267 | for (y = 0; y <= height; y++) { |
1268 | for (x = 0; x <= width; x++) { |
1269 | grid_dot *d = g->dots + index; |
1270 | /* odd rows are offset to the right */ |
1271 | d->order = 0; |
1272 | d->edges = NULL; |
1273 | d->faces = NULL; |
1274 | d->x = x * 2 * vec_x + ((y % 2) ? vec_x : 0); |
1275 | d->y = y * vec_y; |
1276 | index++; |
1277 | } |
1278 | } |
1279 | |
1280 | /* generate faces */ |
1281 | index = 0; |
1282 | for (y = 0; y < height; y++) { |
1283 | for (x = 0; x < width; x++) { |
1284 | /* initialise two faces for this (x,y) */ |
1285 | grid_face *f1 = g->faces + index; |
1286 | grid_face *f2 = f1 + 1; |
1287 | f1->edges = NULL; |
1288 | f1->order = 3; |
1289 | f1->dots = snewn(f1->order, grid_dot*); |
1290 | f2->edges = NULL; |
1291 | f2->order = 3; |
1292 | f2->dots = snewn(f2->order, grid_dot*); |
1293 | |
1294 | /* face descriptions depend on whether the row-number is |
1295 | * odd or even */ |
1296 | if (y % 2) { |
1297 | f1->dots[0] = g->dots + y * w + x; |
1298 | f1->dots[1] = g->dots + (y + 1) * w + x + 1; |
1299 | f1->dots[2] = g->dots + (y + 1) * w + x; |
1300 | f2->dots[0] = g->dots + y * w + x; |
1301 | f2->dots[1] = g->dots + y * w + x + 1; |
1302 | f2->dots[2] = g->dots + (y + 1) * w + x + 1; |
1303 | } else { |
1304 | f1->dots[0] = g->dots + y * w + x; |
1305 | f1->dots[1] = g->dots + y * w + x + 1; |
1306 | f1->dots[2] = g->dots + (y + 1) * w + x; |
1307 | f2->dots[0] = g->dots + y * w + x + 1; |
1308 | f2->dots[1] = g->dots + (y + 1) * w + x + 1; |
1309 | f2->dots[2] = g->dots + (y + 1) * w + x; |
1310 | } |
1311 | index += 2; |
1312 | } |
1313 | } |
1314 | |
7c95608a |
1315 | grid_make_consistent(g); |
1316 | return g; |
1317 | } |
1318 | |
1319 | grid *grid_new_snubsquare(int width, int height) |
1320 | { |
1321 | int x, y; |
1322 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
1323 | int a = 15; |
1324 | int b = 26; |
1325 | |
1326 | /* Upper bounds - don't have to be exact */ |
1327 | int max_faces = 3 * width * height; |
1328 | int max_dots = 2 * (width + 1) * (height + 1); |
1329 | |
1330 | tree234 *points; |
1331 | |
1332 | grid *g = grid_new(); |
1333 | g->tilesize = 18; |
1334 | g->faces = snewn(max_faces, grid_face); |
1335 | g->dots = snewn(max_dots, grid_dot); |
1336 | |
1337 | points = newtree234(grid_point_cmp_fn); |
1338 | |
1339 | for (y = 0; y < height; y++) { |
1340 | for (x = 0; x < width; x++) { |
1341 | grid_dot *d; |
1342 | /* face position */ |
1343 | int px = (a + b) * x; |
1344 | int py = (a + b) * y; |
1345 | |
1346 | /* generate square faces */ |
1347 | grid_face_add_new(g, 4); |
1348 | if ((x + y) % 2) { |
1349 | d = grid_get_dot(g, points, px + a, py); |
1350 | grid_face_set_dot(g, d, 0); |
1351 | d = grid_get_dot(g, points, px + a + b, py + a); |
1352 | grid_face_set_dot(g, d, 1); |
1353 | d = grid_get_dot(g, points, px + b, py + a + b); |
1354 | grid_face_set_dot(g, d, 2); |
1355 | d = grid_get_dot(g, points, px, py + b); |
1356 | grid_face_set_dot(g, d, 3); |
1357 | } else { |
1358 | d = grid_get_dot(g, points, px + b, py); |
1359 | grid_face_set_dot(g, d, 0); |
1360 | d = grid_get_dot(g, points, px + a + b, py + b); |
1361 | grid_face_set_dot(g, d, 1); |
1362 | d = grid_get_dot(g, points, px + a, py + a + b); |
1363 | grid_face_set_dot(g, d, 2); |
1364 | d = grid_get_dot(g, points, px, py + a); |
1365 | grid_face_set_dot(g, d, 3); |
1366 | } |
1367 | |
1368 | /* generate up/down triangles */ |
1369 | if (x > 0) { |
1370 | grid_face_add_new(g, 3); |
1371 | if ((x + y) % 2) { |
1372 | d = grid_get_dot(g, points, px + a, py); |
1373 | grid_face_set_dot(g, d, 0); |
1374 | d = grid_get_dot(g, points, px, py + b); |
1375 | grid_face_set_dot(g, d, 1); |
1376 | d = grid_get_dot(g, points, px - a, py); |
1377 | grid_face_set_dot(g, d, 2); |
1378 | } else { |
1379 | d = grid_get_dot(g, points, px, py + a); |
1380 | grid_face_set_dot(g, d, 0); |
1381 | d = grid_get_dot(g, points, px + a, py + a + b); |
1382 | grid_face_set_dot(g, d, 1); |
1383 | d = grid_get_dot(g, points, px - a, py + a + b); |
1384 | grid_face_set_dot(g, d, 2); |
1385 | } |
1386 | } |
1387 | |
1388 | /* generate left/right triangles */ |
1389 | if (y > 0) { |
1390 | grid_face_add_new(g, 3); |
1391 | if ((x + y) % 2) { |
1392 | d = grid_get_dot(g, points, px + a, py); |
1393 | grid_face_set_dot(g, d, 0); |
1394 | d = grid_get_dot(g, points, px + a + b, py - a); |
1395 | grid_face_set_dot(g, d, 1); |
1396 | d = grid_get_dot(g, points, px + a + b, py + a); |
1397 | grid_face_set_dot(g, d, 2); |
1398 | } else { |
1399 | d = grid_get_dot(g, points, px, py - a); |
1400 | grid_face_set_dot(g, d, 0); |
1401 | d = grid_get_dot(g, points, px + b, py); |
1402 | grid_face_set_dot(g, d, 1); |
1403 | d = grid_get_dot(g, points, px, py + a); |
1404 | grid_face_set_dot(g, d, 2); |
1405 | } |
1406 | } |
1407 | } |
1408 | } |
1409 | |
1410 | freetree234(points); |
1411 | assert(g->num_faces <= max_faces); |
1412 | assert(g->num_dots <= max_dots); |
7c95608a |
1413 | |
1414 | grid_make_consistent(g); |
1415 | return g; |
1416 | } |
1417 | |
1418 | grid *grid_new_cairo(int width, int height) |
1419 | { |
1420 | int x, y; |
1421 | /* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */ |
1422 | int a = 14; |
1423 | int b = 31; |
1424 | |
1425 | /* Upper bounds - don't have to be exact */ |
1426 | int max_faces = 2 * width * height; |
1427 | int max_dots = 3 * (width + 1) * (height + 1); |
1428 | |
1429 | tree234 *points; |
1430 | |
1431 | grid *g = grid_new(); |
1432 | g->tilesize = 40; |
1433 | g->faces = snewn(max_faces, grid_face); |
1434 | g->dots = snewn(max_dots, grid_dot); |
1435 | |
1436 | points = newtree234(grid_point_cmp_fn); |
1437 | |
1438 | for (y = 0; y < height; y++) { |
1439 | for (x = 0; x < width; x++) { |
1440 | grid_dot *d; |
1441 | /* cell position */ |
1442 | int px = 2 * b * x; |
1443 | int py = 2 * b * y; |
1444 | |
1445 | /* horizontal pentagons */ |
1446 | if (y > 0) { |
1447 | grid_face_add_new(g, 5); |
1448 | if ((x + y) % 2) { |
1449 | d = grid_get_dot(g, points, px + a, py - b); |
1450 | grid_face_set_dot(g, d, 0); |
1451 | d = grid_get_dot(g, points, px + 2*b - a, py - b); |
1452 | grid_face_set_dot(g, d, 1); |
1453 | d = grid_get_dot(g, points, px + 2*b, py); |
1454 | grid_face_set_dot(g, d, 2); |
1455 | d = grid_get_dot(g, points, px + b, py + a); |
1456 | grid_face_set_dot(g, d, 3); |
1457 | d = grid_get_dot(g, points, px, py); |
1458 | grid_face_set_dot(g, d, 4); |
1459 | } else { |
1460 | d = grid_get_dot(g, points, px, py); |
1461 | grid_face_set_dot(g, d, 0); |
1462 | d = grid_get_dot(g, points, px + b, py - a); |
1463 | grid_face_set_dot(g, d, 1); |
1464 | d = grid_get_dot(g, points, px + 2*b, py); |
1465 | grid_face_set_dot(g, d, 2); |
1466 | d = grid_get_dot(g, points, px + 2*b - a, py + b); |
1467 | grid_face_set_dot(g, d, 3); |
1468 | d = grid_get_dot(g, points, px + a, py + b); |
1469 | grid_face_set_dot(g, d, 4); |
1470 | } |
1471 | } |
1472 | /* vertical pentagons */ |
1473 | if (x > 0) { |
1474 | grid_face_add_new(g, 5); |
1475 | if ((x + y) % 2) { |
1476 | d = grid_get_dot(g, points, px, py); |
1477 | grid_face_set_dot(g, d, 0); |
1478 | d = grid_get_dot(g, points, px + b, py + a); |
1479 | grid_face_set_dot(g, d, 1); |
1480 | d = grid_get_dot(g, points, px + b, py + 2*b - a); |
1481 | grid_face_set_dot(g, d, 2); |
1482 | d = grid_get_dot(g, points, px, py + 2*b); |
1483 | grid_face_set_dot(g, d, 3); |
1484 | d = grid_get_dot(g, points, px - a, py + b); |
1485 | grid_face_set_dot(g, d, 4); |
1486 | } else { |
1487 | d = grid_get_dot(g, points, px, py); |
1488 | grid_face_set_dot(g, d, 0); |
1489 | d = grid_get_dot(g, points, px + a, py + b); |
1490 | grid_face_set_dot(g, d, 1); |
1491 | d = grid_get_dot(g, points, px, py + 2*b); |
1492 | grid_face_set_dot(g, d, 2); |
1493 | d = grid_get_dot(g, points, px - b, py + 2*b - a); |
1494 | grid_face_set_dot(g, d, 3); |
1495 | d = grid_get_dot(g, points, px - b, py + a); |
1496 | grid_face_set_dot(g, d, 4); |
1497 | } |
1498 | } |
1499 | } |
1500 | } |
1501 | |
1502 | freetree234(points); |
1503 | assert(g->num_faces <= max_faces); |
1504 | assert(g->num_dots <= max_dots); |
7c95608a |
1505 | |
1506 | grid_make_consistent(g); |
1507 | return g; |
1508 | } |
1509 | |
1510 | grid *grid_new_greathexagonal(int width, int height) |
1511 | { |
1512 | int x, y; |
1513 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
1514 | int a = 15; |
1515 | int b = 26; |
1516 | |
1517 | /* Upper bounds - don't have to be exact */ |
1518 | int max_faces = 6 * (width + 1) * (height + 1); |
1519 | int max_dots = 6 * width * height; |
1520 | |
1521 | tree234 *points; |
1522 | |
1523 | grid *g = grid_new(); |
1524 | g->tilesize = 18; |
1525 | g->faces = snewn(max_faces, grid_face); |
1526 | g->dots = snewn(max_dots, grid_dot); |
1527 | |
1528 | points = newtree234(grid_point_cmp_fn); |
1529 | |
1530 | for (y = 0; y < height; y++) { |
1531 | for (x = 0; x < width; x++) { |
1532 | grid_dot *d; |
1533 | /* centre of hexagon */ |
1534 | int px = (3*a + b) * x; |
1535 | int py = (2*a + 2*b) * y; |
1536 | if (x % 2) |
1537 | py += a + b; |
1538 | |
1539 | /* hexagon */ |
1540 | grid_face_add_new(g, 6); |
1541 | d = grid_get_dot(g, points, px - a, py - b); |
1542 | grid_face_set_dot(g, d, 0); |
1543 | d = grid_get_dot(g, points, px + a, py - b); |
1544 | grid_face_set_dot(g, d, 1); |
1545 | d = grid_get_dot(g, points, px + 2*a, py); |
1546 | grid_face_set_dot(g, d, 2); |
1547 | d = grid_get_dot(g, points, px + a, py + b); |
1548 | grid_face_set_dot(g, d, 3); |
1549 | d = grid_get_dot(g, points, px - a, py + b); |
1550 | grid_face_set_dot(g, d, 4); |
1551 | d = grid_get_dot(g, points, px - 2*a, py); |
1552 | grid_face_set_dot(g, d, 5); |
1553 | |
1554 | /* square below hexagon */ |
1555 | if (y < height - 1) { |
1556 | grid_face_add_new(g, 4); |
1557 | d = grid_get_dot(g, points, px - a, py + b); |
1558 | grid_face_set_dot(g, d, 0); |
1559 | d = grid_get_dot(g, points, px + a, py + b); |
1560 | grid_face_set_dot(g, d, 1); |
1561 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
1562 | grid_face_set_dot(g, d, 2); |
1563 | d = grid_get_dot(g, points, px - a, py + 2*a + b); |
1564 | grid_face_set_dot(g, d, 3); |
1565 | } |
1566 | |
1567 | /* square below right */ |
1568 | if ((x < width - 1) && (((x % 2) == 0) || (y < height - 1))) { |
1569 | grid_face_add_new(g, 4); |
1570 | d = grid_get_dot(g, points, px + 2*a, py); |
1571 | grid_face_set_dot(g, d, 0); |
1572 | d = grid_get_dot(g, points, px + 2*a + b, py + a); |
1573 | grid_face_set_dot(g, d, 1); |
1574 | d = grid_get_dot(g, points, px + a + b, py + a + b); |
1575 | grid_face_set_dot(g, d, 2); |
1576 | d = grid_get_dot(g, points, px + a, py + b); |
1577 | grid_face_set_dot(g, d, 3); |
1578 | } |
1579 | |
1580 | /* square below left */ |
1581 | if ((x > 0) && (((x % 2) == 0) || (y < height - 1))) { |
1582 | grid_face_add_new(g, 4); |
1583 | d = grid_get_dot(g, points, px - 2*a, py); |
1584 | grid_face_set_dot(g, d, 0); |
1585 | d = grid_get_dot(g, points, px - a, py + b); |
1586 | grid_face_set_dot(g, d, 1); |
1587 | d = grid_get_dot(g, points, px - a - b, py + a + b); |
1588 | grid_face_set_dot(g, d, 2); |
1589 | d = grid_get_dot(g, points, px - 2*a - b, py + a); |
1590 | grid_face_set_dot(g, d, 3); |
1591 | } |
1592 | |
1593 | /* Triangle below right */ |
1594 | if ((x < width - 1) && (y < height - 1)) { |
1595 | grid_face_add_new(g, 3); |
1596 | d = grid_get_dot(g, points, px + a, py + b); |
1597 | grid_face_set_dot(g, d, 0); |
1598 | d = grid_get_dot(g, points, px + a + b, py + a + b); |
1599 | grid_face_set_dot(g, d, 1); |
1600 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
1601 | grid_face_set_dot(g, d, 2); |
1602 | } |
1603 | |
1604 | /* Triangle below left */ |
1605 | if ((x > 0) && (y < height - 1)) { |
1606 | grid_face_add_new(g, 3); |
1607 | d = grid_get_dot(g, points, px - a, py + b); |
1608 | grid_face_set_dot(g, d, 0); |
1609 | d = grid_get_dot(g, points, px - a, py + 2*a + b); |
1610 | grid_face_set_dot(g, d, 1); |
1611 | d = grid_get_dot(g, points, px - a - b, py + a + b); |
1612 | grid_face_set_dot(g, d, 2); |
1613 | } |
1614 | } |
1615 | } |
1616 | |
1617 | freetree234(points); |
1618 | assert(g->num_faces <= max_faces); |
1619 | assert(g->num_dots <= max_dots); |
7c95608a |
1620 | |
1621 | grid_make_consistent(g); |
1622 | return g; |
1623 | } |
1624 | |
1625 | grid *grid_new_octagonal(int width, int height) |
1626 | { |
1627 | int x, y; |
1628 | /* b/a approx sqrt(2) */ |
1629 | int a = 29; |
1630 | int b = 41; |
1631 | |
1632 | /* Upper bounds - don't have to be exact */ |
1633 | int max_faces = 2 * width * height; |
1634 | int max_dots = 4 * (width + 1) * (height + 1); |
1635 | |
1636 | tree234 *points; |
1637 | |
1638 | grid *g = grid_new(); |
1639 | g->tilesize = 40; |
1640 | g->faces = snewn(max_faces, grid_face); |
1641 | g->dots = snewn(max_dots, grid_dot); |
1642 | |
1643 | points = newtree234(grid_point_cmp_fn); |
1644 | |
1645 | for (y = 0; y < height; y++) { |
1646 | for (x = 0; x < width; x++) { |
1647 | grid_dot *d; |
1648 | /* cell position */ |
1649 | int px = (2*a + b) * x; |
1650 | int py = (2*a + b) * y; |
1651 | /* octagon */ |
1652 | grid_face_add_new(g, 8); |
1653 | d = grid_get_dot(g, points, px + a, py); |
1654 | grid_face_set_dot(g, d, 0); |
1655 | d = grid_get_dot(g, points, px + a + b, py); |
1656 | grid_face_set_dot(g, d, 1); |
1657 | d = grid_get_dot(g, points, px + 2*a + b, py + a); |
1658 | grid_face_set_dot(g, d, 2); |
1659 | d = grid_get_dot(g, points, px + 2*a + b, py + a + b); |
1660 | grid_face_set_dot(g, d, 3); |
1661 | d = grid_get_dot(g, points, px + a + b, py + 2*a + b); |
1662 | grid_face_set_dot(g, d, 4); |
1663 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
1664 | grid_face_set_dot(g, d, 5); |
1665 | d = grid_get_dot(g, points, px, py + a + b); |
1666 | grid_face_set_dot(g, d, 6); |
1667 | d = grid_get_dot(g, points, px, py + a); |
1668 | grid_face_set_dot(g, d, 7); |
1669 | |
1670 | /* diamond */ |
1671 | if ((x > 0) && (y > 0)) { |
1672 | grid_face_add_new(g, 4); |
1673 | d = grid_get_dot(g, points, px, py - a); |
1674 | grid_face_set_dot(g, d, 0); |
1675 | d = grid_get_dot(g, points, px + a, py); |
1676 | grid_face_set_dot(g, d, 1); |
1677 | d = grid_get_dot(g, points, px, py + a); |
1678 | grid_face_set_dot(g, d, 2); |
1679 | d = grid_get_dot(g, points, px - a, py); |
1680 | grid_face_set_dot(g, d, 3); |
1681 | } |
1682 | } |
1683 | } |
1684 | |
1685 | freetree234(points); |
1686 | assert(g->num_faces <= max_faces); |
1687 | assert(g->num_dots <= max_dots); |
7c95608a |
1688 | |
1689 | grid_make_consistent(g); |
1690 | return g; |
1691 | } |
1692 | |
1693 | grid *grid_new_kites(int width, int height) |
1694 | { |
1695 | int x, y; |
1696 | /* b/a approx sqrt(3) */ |
1697 | int a = 15; |
1698 | int b = 26; |
1699 | |
1700 | /* Upper bounds - don't have to be exact */ |
1701 | int max_faces = 6 * width * height; |
1702 | int max_dots = 6 * (width + 1) * (height + 1); |
1703 | |
1704 | tree234 *points; |
1705 | |
1706 | grid *g = grid_new(); |
1707 | g->tilesize = 40; |
1708 | g->faces = snewn(max_faces, grid_face); |
1709 | g->dots = snewn(max_dots, grid_dot); |
1710 | |
1711 | points = newtree234(grid_point_cmp_fn); |
1712 | |
1713 | for (y = 0; y < height; y++) { |
1714 | for (x = 0; x < width; x++) { |
1715 | grid_dot *d; |
1716 | /* position of order-6 dot */ |
1717 | int px = 4*b * x; |
1718 | int py = 6*a * y; |
1719 | if (y % 2) |
1720 | px += 2*b; |
1721 | |
1722 | /* kite pointing up-left */ |
1723 | grid_face_add_new(g, 4); |
1724 | d = grid_get_dot(g, points, px, py); |
1725 | grid_face_set_dot(g, d, 0); |
1726 | d = grid_get_dot(g, points, px + 2*b, py); |
1727 | grid_face_set_dot(g, d, 1); |
1728 | d = grid_get_dot(g, points, px + 2*b, py + 2*a); |
1729 | grid_face_set_dot(g, d, 2); |
1730 | d = grid_get_dot(g, points, px + b, py + 3*a); |
1731 | grid_face_set_dot(g, d, 3); |
1732 | |
1733 | /* kite pointing up */ |
1734 | grid_face_add_new(g, 4); |
1735 | d = grid_get_dot(g, points, px, py); |
1736 | grid_face_set_dot(g, d, 0); |
1737 | d = grid_get_dot(g, points, px + b, py + 3*a); |
1738 | grid_face_set_dot(g, d, 1); |
1739 | d = grid_get_dot(g, points, px, py + 4*a); |
1740 | grid_face_set_dot(g, d, 2); |
1741 | d = grid_get_dot(g, points, px - b, py + 3*a); |
1742 | grid_face_set_dot(g, d, 3); |
1743 | |
1744 | /* kite pointing up-right */ |
1745 | grid_face_add_new(g, 4); |
1746 | d = grid_get_dot(g, points, px, py); |
1747 | grid_face_set_dot(g, d, 0); |
1748 | d = grid_get_dot(g, points, px - b, py + 3*a); |
1749 | grid_face_set_dot(g, d, 1); |
1750 | d = grid_get_dot(g, points, px - 2*b, py + 2*a); |
1751 | grid_face_set_dot(g, d, 2); |
1752 | d = grid_get_dot(g, points, px - 2*b, py); |
1753 | grid_face_set_dot(g, d, 3); |
1754 | |
1755 | /* kite pointing down-right */ |
1756 | grid_face_add_new(g, 4); |
1757 | d = grid_get_dot(g, points, px, py); |
1758 | grid_face_set_dot(g, d, 0); |
1759 | d = grid_get_dot(g, points, px - 2*b, py); |
1760 | grid_face_set_dot(g, d, 1); |
1761 | d = grid_get_dot(g, points, px - 2*b, py - 2*a); |
1762 | grid_face_set_dot(g, d, 2); |
1763 | d = grid_get_dot(g, points, px - b, py - 3*a); |
1764 | grid_face_set_dot(g, d, 3); |
1765 | |
1766 | /* kite pointing down */ |
1767 | grid_face_add_new(g, 4); |
1768 | d = grid_get_dot(g, points, px, py); |
1769 | grid_face_set_dot(g, d, 0); |
1770 | d = grid_get_dot(g, points, px - b, py - 3*a); |
1771 | grid_face_set_dot(g, d, 1); |
1772 | d = grid_get_dot(g, points, px, py - 4*a); |
1773 | grid_face_set_dot(g, d, 2); |
1774 | d = grid_get_dot(g, points, px + b, py - 3*a); |
1775 | grid_face_set_dot(g, d, 3); |
1776 | |
1777 | /* kite pointing down-left */ |
1778 | grid_face_add_new(g, 4); |
1779 | d = grid_get_dot(g, points, px, py); |
1780 | grid_face_set_dot(g, d, 0); |
1781 | d = grid_get_dot(g, points, px + b, py - 3*a); |
1782 | grid_face_set_dot(g, d, 1); |
1783 | d = grid_get_dot(g, points, px + 2*b, py - 2*a); |
1784 | grid_face_set_dot(g, d, 2); |
1785 | d = grid_get_dot(g, points, px + 2*b, py); |
1786 | grid_face_set_dot(g, d, 3); |
1787 | } |
1788 | } |
1789 | |
1790 | freetree234(points); |
1791 | assert(g->num_faces <= max_faces); |
1792 | assert(g->num_dots <= max_dots); |
7c95608a |
1793 | |
1794 | grid_make_consistent(g); |
1795 | return g; |
1796 | } |
1797 | |
e30d39f6 |
1798 | grid *grid_new_floret(int width, int height) |
1799 | { |
1800 | int x, y; |
1801 | /* Vectors for sides; weird numbers needed to keep puzzle aligned with window |
1802 | * -py/px is close to tan(30 - atan(sqrt(3)/9)) |
1803 | * using py=26 makes everything lean to the left, rather than right |
1804 | */ |
1805 | int px = 75, py = -26; /* |( 75, -26)| = 79.43 */ |
1806 | int qx = 4*px/5, qy = -py*2; /* |( 60, 52)| = 79.40 */ |
1807 | int rx = qx-px, ry = qy-py; /* |(-15, 78)| = 79.38 */ |
1808 | |
1809 | /* Upper bounds - don't have to be exact */ |
1810 | int max_faces = 6 * width * height; |
1811 | int max_dots = 9 * (width + 1) * (height + 1); |
1812 | |
1813 | tree234 *points; |
1814 | |
1815 | grid *g = grid_new(); |
1816 | g->tilesize = 2 * px; |
1817 | g->faces = snewn(max_faces, grid_face); |
1818 | g->dots = snewn(max_dots, grid_dot); |
1819 | |
1820 | points = newtree234(grid_point_cmp_fn); |
1821 | |
1822 | /* generate pentagonal faces */ |
1823 | for (y = 0; y < height; y++) { |
1824 | for (x = 0; x < width; x++) { |
1825 | grid_dot *d; |
1826 | /* face centre */ |
1827 | int cx = (6*px+3*qx)/2 * x; |
1828 | int cy = (4*py-5*qy) * y; |
1829 | if (x % 2) |
1830 | cy -= (4*py-5*qy)/2; |
1831 | else if (y && y == height-1) |
1832 | continue; /* make better looking grids? try 3x3 for instance */ |
1833 | |
1834 | grid_face_add_new(g, 5); |
1835 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
1836 | d = grid_get_dot(g, points, cx+2*rx , cy+2*ry ); grid_face_set_dot(g, d, 1); |
1837 | d = grid_get_dot(g, points, cx+2*rx+qx, cy+2*ry+qy); grid_face_set_dot(g, d, 2); |
1838 | d = grid_get_dot(g, points, cx+2*qx+rx, cy+2*qy+ry); grid_face_set_dot(g, d, 3); |
1839 | d = grid_get_dot(g, points, cx+2*qx , cy+2*qy ); grid_face_set_dot(g, d, 4); |
1840 | |
1841 | grid_face_add_new(g, 5); |
1842 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
1843 | d = grid_get_dot(g, points, cx+2*qx , cy+2*qy ); grid_face_set_dot(g, d, 1); |
1844 | d = grid_get_dot(g, points, cx+2*qx+px, cy+2*qy+py); grid_face_set_dot(g, d, 2); |
1845 | d = grid_get_dot(g, points, cx+2*px+qx, cy+2*py+qy); grid_face_set_dot(g, d, 3); |
1846 | d = grid_get_dot(g, points, cx+2*px , cy+2*py ); grid_face_set_dot(g, d, 4); |
1847 | |
1848 | grid_face_add_new(g, 5); |
1849 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
1850 | d = grid_get_dot(g, points, cx+2*px , cy+2*py ); grid_face_set_dot(g, d, 1); |
1851 | d = grid_get_dot(g, points, cx+2*px-rx, cy+2*py-ry); grid_face_set_dot(g, d, 2); |
1852 | d = grid_get_dot(g, points, cx-2*rx+px, cy-2*ry+py); grid_face_set_dot(g, d, 3); |
1853 | d = grid_get_dot(g, points, cx-2*rx , cy-2*ry ); grid_face_set_dot(g, d, 4); |
1854 | |
1855 | grid_face_add_new(g, 5); |
1856 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
1857 | d = grid_get_dot(g, points, cx-2*rx , cy-2*ry ); grid_face_set_dot(g, d, 1); |
1858 | d = grid_get_dot(g, points, cx-2*rx-qx, cy-2*ry-qy); grid_face_set_dot(g, d, 2); |
1859 | d = grid_get_dot(g, points, cx-2*qx-rx, cy-2*qy-ry); grid_face_set_dot(g, d, 3); |
1860 | d = grid_get_dot(g, points, cx-2*qx , cy-2*qy ); grid_face_set_dot(g, d, 4); |
1861 | |
1862 | grid_face_add_new(g, 5); |
1863 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
1864 | d = grid_get_dot(g, points, cx-2*qx , cy-2*qy ); grid_face_set_dot(g, d, 1); |
1865 | d = grid_get_dot(g, points, cx-2*qx-px, cy-2*qy-py); grid_face_set_dot(g, d, 2); |
1866 | d = grid_get_dot(g, points, cx-2*px-qx, cy-2*py-qy); grid_face_set_dot(g, d, 3); |
1867 | d = grid_get_dot(g, points, cx-2*px , cy-2*py ); grid_face_set_dot(g, d, 4); |
1868 | |
1869 | grid_face_add_new(g, 5); |
1870 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
1871 | d = grid_get_dot(g, points, cx-2*px , cy-2*py ); grid_face_set_dot(g, d, 1); |
1872 | d = grid_get_dot(g, points, cx-2*px+rx, cy-2*py+ry); grid_face_set_dot(g, d, 2); |
1873 | d = grid_get_dot(g, points, cx+2*rx-px, cy+2*ry-py); grid_face_set_dot(g, d, 3); |
1874 | d = grid_get_dot(g, points, cx+2*rx , cy+2*ry ); grid_face_set_dot(g, d, 4); |
1875 | } |
1876 | } |
1877 | |
1878 | freetree234(points); |
1879 | assert(g->num_faces <= max_faces); |
1880 | assert(g->num_dots <= max_dots); |
e30d39f6 |
1881 | |
1882 | grid_make_consistent(g); |
1883 | return g; |
1884 | } |
1885 | |
918a098a |
1886 | grid *grid_new_dodecagonal(int width, int height) |
1887 | { |
1888 | int x, y; |
1889 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
1890 | int a = 15; |
1891 | int b = 26; |
1892 | |
1893 | /* Upper bounds - don't have to be exact */ |
1894 | int max_faces = 3 * width * height; |
1895 | int max_dots = 14 * width * height; |
1896 | |
1897 | tree234 *points; |
1898 | |
1899 | grid *g = grid_new(); |
1900 | g->tilesize = b; |
1901 | g->faces = snewn(max_faces, grid_face); |
1902 | g->dots = snewn(max_dots, grid_dot); |
1903 | |
1904 | points = newtree234(grid_point_cmp_fn); |
1905 | |
1906 | for (y = 0; y < height; y++) { |
1907 | for (x = 0; x < width; x++) { |
1908 | grid_dot *d; |
1909 | /* centre of dodecagon */ |
1910 | int px = (4*a + 2*b) * x; |
1911 | int py = (3*a + 2*b) * y; |
1912 | if (y % 2) |
1913 | px += 2*a + b; |
1914 | |
1915 | /* dodecagon */ |
1916 | grid_face_add_new(g, 12); |
1917 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); |
1918 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 1); |
1919 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a )); grid_face_set_dot(g, d, 2); |
1920 | d = grid_get_dot(g, points, px + (2*a + b), py + ( a )); grid_face_set_dot(g, d, 3); |
1921 | d = grid_get_dot(g, points, px + ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 4); |
1922 | d = grid_get_dot(g, points, px + ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 5); |
1923 | d = grid_get_dot(g, points, px - ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 6); |
1924 | d = grid_get_dot(g, points, px - ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 7); |
1925 | d = grid_get_dot(g, points, px - (2*a + b), py + ( a )); grid_face_set_dot(g, d, 8); |
1926 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a )); grid_face_set_dot(g, d, 9); |
1927 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 10); |
1928 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 11); |
1929 | |
1930 | /* triangle below dodecagon */ |
1931 | if ((y < height - 1 && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2)))) { |
1932 | grid_face_add_new(g, 3); |
1933 | d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0); |
1934 | d = grid_get_dot(g, points, px , py + (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
1935 | d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 2); |
1936 | } |
1937 | |
1938 | /* triangle above dodecagon */ |
1939 | if ((y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2)))) { |
1940 | grid_face_add_new(g, 3); |
1941 | d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 0); |
1942 | d = grid_get_dot(g, points, px , py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
1943 | d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 2); |
1944 | } |
1945 | } |
1946 | } |
1947 | |
1948 | freetree234(points); |
1949 | assert(g->num_faces <= max_faces); |
1950 | assert(g->num_dots <= max_dots); |
1951 | |
1952 | grid_make_consistent(g); |
1953 | return g; |
1954 | } |
1955 | |
1956 | grid *grid_new_greatdodecagonal(int width, int height) |
1957 | { |
1958 | int x, y; |
1959 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
1960 | int a = 15; |
1961 | int b = 26; |
1962 | |
1963 | /* Upper bounds - don't have to be exact */ |
1964 | int max_faces = 30 * width * height; |
1965 | int max_dots = 200 * width * height; |
1966 | |
1967 | tree234 *points; |
1968 | |
1969 | grid *g = grid_new(); |
1970 | g->tilesize = b; |
1971 | g->faces = snewn(max_faces, grid_face); |
1972 | g->dots = snewn(max_dots, grid_dot); |
1973 | |
1974 | points = newtree234(grid_point_cmp_fn); |
1975 | |
1976 | for (y = 0; y < height; y++) { |
1977 | for (x = 0; x < width; x++) { |
1978 | grid_dot *d; |
1979 | /* centre of dodecagon */ |
1980 | int px = (6*a + 2*b) * x; |
1981 | int py = (3*a + 3*b) * y; |
1982 | if (y % 2) |
1983 | px += 3*a + b; |
1984 | |
1985 | /* dodecagon */ |
1986 | grid_face_add_new(g, 12); |
1987 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); |
1988 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 1); |
1989 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a )); grid_face_set_dot(g, d, 2); |
1990 | d = grid_get_dot(g, points, px + (2*a + b), py + ( a )); grid_face_set_dot(g, d, 3); |
1991 | d = grid_get_dot(g, points, px + ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 4); |
1992 | d = grid_get_dot(g, points, px + ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 5); |
1993 | d = grid_get_dot(g, points, px - ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 6); |
1994 | d = grid_get_dot(g, points, px - ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 7); |
1995 | d = grid_get_dot(g, points, px - (2*a + b), py + ( a )); grid_face_set_dot(g, d, 8); |
1996 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a )); grid_face_set_dot(g, d, 9); |
1997 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 10); |
1998 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 11); |
1999 | |
2000 | /* hexagon below dodecagon */ |
2001 | if (y < height - 1 && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) { |
2002 | grid_face_add_new(g, 6); |
2003 | d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0); |
2004 | d = grid_get_dot(g, points, px + 2*a, py + (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
2005 | d = grid_get_dot(g, points, px + a, py + (2*a + 3*b)); grid_face_set_dot(g, d, 2); |
2006 | d = grid_get_dot(g, points, px - a, py + (2*a + 3*b)); grid_face_set_dot(g, d, 3); |
2007 | d = grid_get_dot(g, points, px - 2*a, py + (2*a + 2*b)); grid_face_set_dot(g, d, 4); |
2008 | d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 5); |
2009 | } |
2010 | |
2011 | /* hexagon above dodecagon */ |
2012 | if (y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) { |
2013 | grid_face_add_new(g, 6); |
2014 | d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 0); |
2015 | d = grid_get_dot(g, points, px - 2*a, py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
2016 | d = grid_get_dot(g, points, px - a, py - (2*a + 3*b)); grid_face_set_dot(g, d, 2); |
2017 | d = grid_get_dot(g, points, px + a, py - (2*a + 3*b)); grid_face_set_dot(g, d, 3); |
2018 | d = grid_get_dot(g, points, px + 2*a, py - (2*a + 2*b)); grid_face_set_dot(g, d, 4); |
2019 | d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 5); |
2020 | } |
2021 | |
2022 | /* square on right of dodecagon */ |
2023 | if (x < width - 1) { |
2024 | grid_face_add_new(g, 4); |
2025 | d = grid_get_dot(g, points, px + 2*a + b, py - a); grid_face_set_dot(g, d, 0); |
2026 | d = grid_get_dot(g, points, px + 4*a + b, py - a); grid_face_set_dot(g, d, 1); |
2027 | d = grid_get_dot(g, points, px + 4*a + b, py + a); grid_face_set_dot(g, d, 2); |
2028 | d = grid_get_dot(g, points, px + 2*a + b, py + a); grid_face_set_dot(g, d, 3); |
2029 | } |
2030 | |
2031 | /* square on top right of dodecagon */ |
2032 | if (y && (x < width - 1 || !(y % 2))) { |
2033 | grid_face_add_new(g, 4); |
2034 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); |
2035 | d = grid_get_dot(g, points, px + (2*a ), py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
2036 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a + 2*b)); grid_face_set_dot(g, d, 2); |
2037 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 3); |
2038 | } |
2039 | |
2040 | /* square on top left of dodecagon */ |
2041 | if (y && (x || (y % 2))) { |
2042 | grid_face_add_new(g, 4); |
2043 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 0); |
2044 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a + 2*b)); grid_face_set_dot(g, d, 1); |
2045 | d = grid_get_dot(g, points, px - (2*a ), py - (2*a + 2*b)); grid_face_set_dot(g, d, 2); |
2046 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 3); |
2047 | } |
2048 | } |
2049 | } |
2050 | |
2051 | freetree234(points); |
2052 | assert(g->num_faces <= max_faces); |
2053 | assert(g->num_dots <= max_dots); |
2054 | |
2055 | grid_make_consistent(g); |
2056 | return g; |
2057 | } |
2058 | |
7c95608a |
2059 | /* ----------- End of grid generators ------------- */ |