| 1 | /* |
| 2 | * (c) Lambros Lambrou 2008 |
| 3 | * |
| 4 | * Code for working with general grids, which can be any planar graph |
| 5 | * with faces, edges and vertices (dots). Includes generators for a few |
| 6 | * types of grid, including square, hexagonal, triangular and others. |
| 7 | */ |
| 8 | |
| 9 | #include <stdio.h> |
| 10 | #include <stdlib.h> |
| 11 | #include <string.h> |
| 12 | #include <assert.h> |
| 13 | #include <ctype.h> |
| 14 | #include <math.h> |
| 15 | |
| 16 | #include "puzzles.h" |
| 17 | #include "tree234.h" |
| 18 | #include "grid.h" |
| 19 | |
| 20 | /* Debugging options */ |
| 21 | |
| 22 | /* |
| 23 | #define DEBUG_GRID |
| 24 | */ |
| 25 | |
| 26 | /* ---------------------------------------------------------------------- |
| 27 | * Deallocate or dereference a grid |
| 28 | */ |
| 29 | void grid_free(grid *g) |
| 30 | { |
| 31 | assert(g->refcount); |
| 32 | |
| 33 | g->refcount--; |
| 34 | if (g->refcount == 0) { |
| 35 | int i; |
| 36 | for (i = 0; i < g->num_faces; i++) { |
| 37 | sfree(g->faces[i].dots); |
| 38 | sfree(g->faces[i].edges); |
| 39 | } |
| 40 | for (i = 0; i < g->num_dots; i++) { |
| 41 | sfree(g->dots[i].faces); |
| 42 | sfree(g->dots[i].edges); |
| 43 | } |
| 44 | sfree(g->faces); |
| 45 | sfree(g->edges); |
| 46 | sfree(g->dots); |
| 47 | sfree(g); |
| 48 | } |
| 49 | } |
| 50 | |
| 51 | /* Used by the other grid generators. Create a brand new grid with nothing |
| 52 | * initialised (all lists are NULL) */ |
| 53 | static grid *grid_new(void) |
| 54 | { |
| 55 | grid *g = snew(grid); |
| 56 | g->faces = NULL; |
| 57 | g->edges = NULL; |
| 58 | g->dots = NULL; |
| 59 | g->num_faces = g->num_edges = g->num_dots = 0; |
| 60 | g->middle_face = NULL; |
| 61 | g->refcount = 1; |
| 62 | g->lowest_x = g->lowest_y = g->highest_x = g->highest_y = 0; |
| 63 | return g; |
| 64 | } |
| 65 | |
| 66 | /* Helper function to calculate perpendicular distance from |
| 67 | * a point P to a line AB. A and B mustn't be equal here. |
| 68 | * |
| 69 | * Well-known formula for area A of a triangle: |
| 70 | * / 1 1 1 \ |
| 71 | * 2A = determinant of matrix | px ax bx | |
| 72 | * \ py ay by / |
| 73 | * |
| 74 | * Also well-known: 2A = base * height |
| 75 | * = perpendicular distance * line-length. |
| 76 | * |
| 77 | * Combining gives: distance = determinant / line-length(a,b) |
| 78 | */ |
| 79 | static double point_line_distance(long px, long py, |
| 80 | long ax, long ay, |
| 81 | long bx, long by) |
| 82 | { |
| 83 | long det = ax*by - bx*ay + bx*py - px*by + px*ay - ax*py; |
| 84 | double len; |
| 85 | det = max(det, -det); |
| 86 | len = sqrt(SQ(ax - bx) + SQ(ay - by)); |
| 87 | return det / len; |
| 88 | } |
| 89 | |
| 90 | /* Determine nearest edge to where the user clicked. |
| 91 | * (x, y) is the clicked location, converted to grid coordinates. |
| 92 | * Returns the nearest edge, or NULL if no edge is reasonably |
| 93 | * near the position. |
| 94 | * |
| 95 | * This algorithm is nice and generic, and doesn't depend on any particular |
| 96 | * geometric layout of the grid: |
| 97 | * Start at any dot (pick one next to middle_face). |
| 98 | * Walk along a path by choosing, from all nearby dots, the one that is |
| 99 | * nearest the target (x,y). Hopefully end up at the dot which is closest |
| 100 | * to (x,y). Should work, as long as faces aren't too badly shaped. |
| 101 | * Then examine each edge around this dot, and pick whichever one is |
| 102 | * closest (perpendicular distance) to (x,y). |
| 103 | * Using perpendicular distance is not quite right - the edge might be |
| 104 | * "off to one side". So we insist that the triangle with (x,y) has |
| 105 | * acute angles at the edge's dots. |
| 106 | * |
| 107 | * edge1 |
| 108 | * *---------*------ |
| 109 | * | |
| 110 | * | *(x,y) |
| 111 | * edge2 | |
| 112 | * | edge2 is OK, but edge1 is not, even though |
| 113 | * | edge1 is perpendicularly closer to (x,y) |
| 114 | * * |
| 115 | * |
| 116 | */ |
| 117 | grid_edge *grid_nearest_edge(grid *g, int x, int y) |
| 118 | { |
| 119 | grid_dot *cur; |
| 120 | grid_edge *best_edge; |
| 121 | double best_distance = 0; |
| 122 | int i; |
| 123 | |
| 124 | cur = g->middle_face->dots[0]; |
| 125 | |
| 126 | for (;;) { |
| 127 | /* Target to beat */ |
| 128 | long dist = SQ((long)cur->x - (long)x) + SQ((long)cur->y - (long)y); |
| 129 | /* Look for nearer dot - if found, store in 'new'. */ |
| 130 | grid_dot *new = cur; |
| 131 | int i; |
| 132 | /* Search all dots in all faces touching this dot. Some shapes |
| 133 | * (such as in Cairo) don't quite work properly if we only search |
| 134 | * the dot's immediate neighbours. */ |
| 135 | for (i = 0; i < cur->order; i++) { |
| 136 | grid_face *f = cur->faces[i]; |
| 137 | int j; |
| 138 | if (!f) continue; |
| 139 | for (j = 0; j < f->order; j++) { |
| 140 | long new_dist; |
| 141 | grid_dot *d = f->dots[j]; |
| 142 | if (d == cur) continue; |
| 143 | new_dist = SQ((long)d->x - (long)x) + SQ((long)d->y - (long)y); |
| 144 | if (new_dist < dist) { |
| 145 | new = d; |
| 146 | break; /* found closer dot */ |
| 147 | } |
| 148 | } |
| 149 | if (new != cur) |
| 150 | break; /* found closer dot */ |
| 151 | } |
| 152 | |
| 153 | if (new == cur) { |
| 154 | /* Didn't find a closer dot among the neighbours of 'cur' */ |
| 155 | break; |
| 156 | } else { |
| 157 | cur = new; |
| 158 | } |
| 159 | } |
| 160 | /* 'cur' is nearest dot, so find which of the dot's edges is closest. */ |
| 161 | best_edge = NULL; |
| 162 | |
| 163 | for (i = 0; i < cur->order; i++) { |
| 164 | grid_edge *e = cur->edges[i]; |
| 165 | long e2; /* squared length of edge */ |
| 166 | long a2, b2; /* squared lengths of other sides */ |
| 167 | double dist; |
| 168 | |
| 169 | /* See if edge e is eligible - the triangle must have acute angles |
| 170 | * at the edge's dots. |
| 171 | * Pythagoras formula h^2 = a^2 + b^2 detects right-angles, |
| 172 | * so detect acute angles by testing for h^2 < a^2 + b^2 */ |
| 173 | e2 = SQ((long)e->dot1->x - (long)e->dot2->x) + SQ((long)e->dot1->y - (long)e->dot2->y); |
| 174 | a2 = SQ((long)e->dot1->x - (long)x) + SQ((long)e->dot1->y - (long)y); |
| 175 | b2 = SQ((long)e->dot2->x - (long)x) + SQ((long)e->dot2->y - (long)y); |
| 176 | if (a2 >= e2 + b2) continue; |
| 177 | if (b2 >= e2 + a2) continue; |
| 178 | |
| 179 | /* e is eligible so far. Now check the edge is reasonably close |
| 180 | * to where the user clicked. Don't want to toggle an edge if the |
| 181 | * click was way off the grid. |
| 182 | * There is room for experimentation here. We could check the |
| 183 | * perpendicular distance is within a certain fraction of the length |
| 184 | * of the edge. That amounts to testing a rectangular region around |
| 185 | * the edge. |
| 186 | * Alternatively, we could check that the angle at the point is obtuse. |
| 187 | * That would amount to testing a circular region with the edge as |
| 188 | * diameter. */ |
| 189 | dist = point_line_distance((long)x, (long)y, |
| 190 | (long)e->dot1->x, (long)e->dot1->y, |
| 191 | (long)e->dot2->x, (long)e->dot2->y); |
| 192 | /* Is dist more than half edge length ? */ |
| 193 | if (4 * SQ(dist) > e2) |
| 194 | continue; |
| 195 | |
| 196 | if (best_edge == NULL || dist < best_distance) { |
| 197 | best_edge = e; |
| 198 | best_distance = dist; |
| 199 | } |
| 200 | } |
| 201 | return best_edge; |
| 202 | } |
| 203 | |
| 204 | /* ---------------------------------------------------------------------- |
| 205 | * Grid generation |
| 206 | */ |
| 207 | |
| 208 | #ifdef DEBUG_GRID |
| 209 | /* Show the basic grid information, before doing grid_make_consistent */ |
| 210 | static void grid_print_basic(grid *g) |
| 211 | { |
| 212 | /* TODO: Maybe we should generate an SVG image of the dots and lines |
| 213 | * of the grid here, before grid_make_consistent. |
| 214 | * Would help with debugging grid generation. */ |
| 215 | int i; |
| 216 | printf("--- Basic Grid Data ---\n"); |
| 217 | for (i = 0; i < g->num_faces; i++) { |
| 218 | grid_face *f = g->faces + i; |
| 219 | printf("Face %d: dots[", i); |
| 220 | int j; |
| 221 | for (j = 0; j < f->order; j++) { |
| 222 | grid_dot *d = f->dots[j]; |
| 223 | printf("%s%d", j ? "," : "", (int)(d - g->dots)); |
| 224 | } |
| 225 | printf("]\n"); |
| 226 | } |
| 227 | printf("Middle face: %d\n", (int)(g->middle_face - g->faces)); |
| 228 | } |
| 229 | /* Show the derived grid information, computed by grid_make_consistent */ |
| 230 | static void grid_print_derived(grid *g) |
| 231 | { |
| 232 | /* edges */ |
| 233 | int i; |
| 234 | printf("--- Derived Grid Data ---\n"); |
| 235 | for (i = 0; i < g->num_edges; i++) { |
| 236 | grid_edge *e = g->edges + i; |
| 237 | printf("Edge %d: dots[%d,%d] faces[%d,%d]\n", |
| 238 | i, (int)(e->dot1 - g->dots), (int)(e->dot2 - g->dots), |
| 239 | e->face1 ? (int)(e->face1 - g->faces) : -1, |
| 240 | e->face2 ? (int)(e->face2 - g->faces) : -1); |
| 241 | } |
| 242 | /* faces */ |
| 243 | for (i = 0; i < g->num_faces; i++) { |
| 244 | grid_face *f = g->faces + i; |
| 245 | int j; |
| 246 | printf("Face %d: faces[", i); |
| 247 | for (j = 0; j < f->order; j++) { |
| 248 | grid_edge *e = f->edges[j]; |
| 249 | grid_face *f2 = (e->face1 == f) ? e->face2 : e->face1; |
| 250 | printf("%s%d", j ? "," : "", f2 ? (int)(f2 - g->faces) : -1); |
| 251 | } |
| 252 | printf("]\n"); |
| 253 | } |
| 254 | /* dots */ |
| 255 | for (i = 0; i < g->num_dots; i++) { |
| 256 | grid_dot *d = g->dots + i; |
| 257 | int j; |
| 258 | printf("Dot %d: dots[", i); |
| 259 | for (j = 0; j < d->order; j++) { |
| 260 | grid_edge *e = d->edges[j]; |
| 261 | grid_dot *d2 = (e->dot1 == d) ? e->dot2 : e->dot1; |
| 262 | printf("%s%d", j ? "," : "", (int)(d2 - g->dots)); |
| 263 | } |
| 264 | printf("] faces["); |
| 265 | for (j = 0; j < d->order; j++) { |
| 266 | grid_face *f = d->faces[j]; |
| 267 | printf("%s%d", j ? "," : "", f ? (int)(f - g->faces) : -1); |
| 268 | } |
| 269 | printf("]\n"); |
| 270 | } |
| 271 | } |
| 272 | #endif /* DEBUG_GRID */ |
| 273 | |
| 274 | /* Helper function for building incomplete-edges list in |
| 275 | * grid_make_consistent() */ |
| 276 | static int grid_edge_bydots_cmpfn(void *v1, void *v2) |
| 277 | { |
| 278 | grid_edge *a = v1; |
| 279 | grid_edge *b = v2; |
| 280 | grid_dot *da, *db; |
| 281 | |
| 282 | /* Pointer subtraction is valid here, because all dots point into the |
| 283 | * same dot-list (g->dots). |
| 284 | * Edges are not "normalised" - the 2 dots could be stored in any order, |
| 285 | * so we need to take this into account when comparing edges. */ |
| 286 | |
| 287 | /* Compare first dots */ |
| 288 | da = (a->dot1 < a->dot2) ? a->dot1 : a->dot2; |
| 289 | db = (b->dot1 < b->dot2) ? b->dot1 : b->dot2; |
| 290 | if (da != db) |
| 291 | return db - da; |
| 292 | /* Compare last dots */ |
| 293 | da = (a->dot1 < a->dot2) ? a->dot2 : a->dot1; |
| 294 | db = (b->dot1 < b->dot2) ? b->dot2 : b->dot1; |
| 295 | if (da != db) |
| 296 | return db - da; |
| 297 | |
| 298 | return 0; |
| 299 | } |
| 300 | |
| 301 | /* Input: grid has its dots and faces initialised: |
| 302 | * - dots have (optionally) x and y coordinates, but no edges or faces |
| 303 | * (pointers are NULL). |
| 304 | * - edges not initialised at all |
| 305 | * - faces initialised and know which dots they have (but no edges yet). The |
| 306 | * dots around each face are assumed to be clockwise. |
| 307 | * |
| 308 | * Output: grid is complete and valid with all relationships defined. |
| 309 | */ |
| 310 | static void grid_make_consistent(grid *g) |
| 311 | { |
| 312 | int i; |
| 313 | tree234 *incomplete_edges; |
| 314 | grid_edge *next_new_edge; /* Where new edge will go into g->edges */ |
| 315 | |
| 316 | #ifdef DEBUG_GRID |
| 317 | grid_print_basic(g); |
| 318 | #endif |
| 319 | |
| 320 | /* ====== Stage 1 ====== |
| 321 | * Generate edges |
| 322 | */ |
| 323 | |
| 324 | /* We know how many dots and faces there are, so we can find the exact |
| 325 | * number of edges from Euler's polyhedral formula: F + V = E + 2 . |
| 326 | * We use "-1", not "-2" here, because Euler's formula includes the |
| 327 | * infinite face, which we don't count. */ |
| 328 | g->num_edges = g->num_faces + g->num_dots - 1; |
| 329 | g->edges = snewn(g->num_edges, grid_edge); |
| 330 | next_new_edge = g->edges; |
| 331 | |
| 332 | /* Iterate over faces, and over each face's dots, generating edges as we |
| 333 | * go. As we find each new edge, we can immediately fill in the edge's |
| 334 | * dots, but only one of the edge's faces. Later on in the iteration, we |
| 335 | * will find the same edge again (unless it's on the border), but we will |
| 336 | * know the other face. |
| 337 | * For efficiency, maintain a list of the incomplete edges, sorted by |
| 338 | * their dots. */ |
| 339 | incomplete_edges = newtree234(grid_edge_bydots_cmpfn); |
| 340 | for (i = 0; i < g->num_faces; i++) { |
| 341 | grid_face *f = g->faces + i; |
| 342 | int j; |
| 343 | for (j = 0; j < f->order; j++) { |
| 344 | grid_edge e; /* fake edge for searching */ |
| 345 | grid_edge *edge_found; |
| 346 | int j2 = j + 1; |
| 347 | if (j2 == f->order) |
| 348 | j2 = 0; |
| 349 | e.dot1 = f->dots[j]; |
| 350 | e.dot2 = f->dots[j2]; |
| 351 | /* Use del234 instead of find234, because we always want to |
| 352 | * remove the edge if found */ |
| 353 | edge_found = del234(incomplete_edges, &e); |
| 354 | if (edge_found) { |
| 355 | /* This edge already added, so fill out missing face. |
| 356 | * Edge is already removed from incomplete_edges. */ |
| 357 | edge_found->face2 = f; |
| 358 | } else { |
| 359 | assert(next_new_edge - g->edges < g->num_edges); |
| 360 | next_new_edge->dot1 = e.dot1; |
| 361 | next_new_edge->dot2 = e.dot2; |
| 362 | next_new_edge->face1 = f; |
| 363 | next_new_edge->face2 = NULL; /* potentially infinite face */ |
| 364 | add234(incomplete_edges, next_new_edge); |
| 365 | ++next_new_edge; |
| 366 | } |
| 367 | } |
| 368 | } |
| 369 | freetree234(incomplete_edges); |
| 370 | |
| 371 | /* ====== Stage 2 ====== |
| 372 | * For each face, build its edge list. |
| 373 | */ |
| 374 | |
| 375 | /* Allocate space for each edge list. Can do this, because each face's |
| 376 | * edge-list is the same size as its dot-list. */ |
| 377 | for (i = 0; i < g->num_faces; i++) { |
| 378 | grid_face *f = g->faces + i; |
| 379 | int j; |
| 380 | f->edges = snewn(f->order, grid_edge*); |
| 381 | /* Preload with NULLs, to help detect potential bugs. */ |
| 382 | for (j = 0; j < f->order; j++) |
| 383 | f->edges[j] = NULL; |
| 384 | } |
| 385 | |
| 386 | /* Iterate over each edge, and over both its faces. Add this edge to |
| 387 | * the face's edge-list, after finding where it should go in the |
| 388 | * sequence. */ |
| 389 | for (i = 0; i < g->num_edges; i++) { |
| 390 | grid_edge *e = g->edges + i; |
| 391 | int j; |
| 392 | for (j = 0; j < 2; j++) { |
| 393 | grid_face *f = j ? e->face2 : e->face1; |
| 394 | int k, k2; |
| 395 | if (f == NULL) continue; |
| 396 | /* Find one of the dots around the face */ |
| 397 | for (k = 0; k < f->order; k++) { |
| 398 | if (f->dots[k] == e->dot1) |
| 399 | break; /* found dot1 */ |
| 400 | } |
| 401 | assert(k != f->order); /* Must find the dot around this face */ |
| 402 | |
| 403 | /* Labelling scheme: as we walk clockwise around the face, |
| 404 | * starting at dot0 (f->dots[0]), we hit: |
| 405 | * (dot0), edge0, dot1, edge1, dot2,... |
| 406 | * |
| 407 | * 0 |
| 408 | * 0-----1 |
| 409 | * | |
| 410 | * |1 |
| 411 | * | |
| 412 | * 3-----2 |
| 413 | * 2 |
| 414 | * |
| 415 | * Therefore, edgeK joins dotK and dot{K+1} |
| 416 | */ |
| 417 | |
| 418 | /* Around this face, either the next dot or the previous dot |
| 419 | * must be e->dot2. Otherwise the edge is wrong. */ |
| 420 | k2 = k + 1; |
| 421 | if (k2 == f->order) |
| 422 | k2 = 0; |
| 423 | if (f->dots[k2] == e->dot2) { |
| 424 | /* dot1(k) and dot2(k2) go clockwise around this face, so add |
| 425 | * this edge at position k (see diagram). */ |
| 426 | assert(f->edges[k] == NULL); |
| 427 | f->edges[k] = e; |
| 428 | continue; |
| 429 | } |
| 430 | /* Try previous dot */ |
| 431 | k2 = k - 1; |
| 432 | if (k2 == -1) |
| 433 | k2 = f->order - 1; |
| 434 | if (f->dots[k2] == e->dot2) { |
| 435 | /* dot1(k) and dot2(k2) go anticlockwise around this face. */ |
| 436 | assert(f->edges[k2] == NULL); |
| 437 | f->edges[k2] = e; |
| 438 | continue; |
| 439 | } |
| 440 | assert(!"Grid broken: bad edge-face relationship"); |
| 441 | } |
| 442 | } |
| 443 | |
| 444 | /* ====== Stage 3 ====== |
| 445 | * For each dot, build its edge-list and face-list. |
| 446 | */ |
| 447 | |
| 448 | /* We don't know how many edges/faces go around each dot, so we can't |
| 449 | * allocate the right space for these lists. Pre-compute the sizes by |
| 450 | * iterating over each edge and recording a tally against each dot. */ |
| 451 | for (i = 0; i < g->num_dots; i++) { |
| 452 | g->dots[i].order = 0; |
| 453 | } |
| 454 | for (i = 0; i < g->num_edges; i++) { |
| 455 | grid_edge *e = g->edges + i; |
| 456 | ++(e->dot1->order); |
| 457 | ++(e->dot2->order); |
| 458 | } |
| 459 | /* Now we have the sizes, pre-allocate the edge and face lists. */ |
| 460 | for (i = 0; i < g->num_dots; i++) { |
| 461 | grid_dot *d = g->dots + i; |
| 462 | int j; |
| 463 | assert(d->order >= 2); /* sanity check */ |
| 464 | d->edges = snewn(d->order, grid_edge*); |
| 465 | d->faces = snewn(d->order, grid_face*); |
| 466 | for (j = 0; j < d->order; j++) { |
| 467 | d->edges[j] = NULL; |
| 468 | d->faces[j] = NULL; |
| 469 | } |
| 470 | } |
| 471 | /* For each dot, need to find a face that touches it, so we can seed |
| 472 | * the edge-face-edge-face process around each dot. */ |
| 473 | for (i = 0; i < g->num_faces; i++) { |
| 474 | grid_face *f = g->faces + i; |
| 475 | int j; |
| 476 | for (j = 0; j < f->order; j++) { |
| 477 | grid_dot *d = f->dots[j]; |
| 478 | d->faces[0] = f; |
| 479 | } |
| 480 | } |
| 481 | /* Each dot now has a face in its first slot. Generate the remaining |
| 482 | * faces and edges around the dot, by searching both clockwise and |
| 483 | * anticlockwise from the first face. Need to do both directions, |
| 484 | * because of the possibility of hitting the infinite face, which |
| 485 | * blocks progress. But there's only one such face, so we will |
| 486 | * succeed in finding every edge and face this way. */ |
| 487 | for (i = 0; i < g->num_dots; i++) { |
| 488 | grid_dot *d = g->dots + i; |
| 489 | int current_face1 = 0; /* ascends clockwise */ |
| 490 | int current_face2 = 0; /* descends anticlockwise */ |
| 491 | |
| 492 | /* Labelling scheme: as we walk clockwise around the dot, starting |
| 493 | * at face0 (d->faces[0]), we hit: |
| 494 | * (face0), edge0, face1, edge1, face2,... |
| 495 | * |
| 496 | * 0 |
| 497 | * | |
| 498 | * 0 | 1 |
| 499 | * | |
| 500 | * -----d-----1 |
| 501 | * | |
| 502 | * | 2 |
| 503 | * | |
| 504 | * 2 |
| 505 | * |
| 506 | * So, for example, face1 should be joined to edge0 and edge1, |
| 507 | * and those edges should appear in an anticlockwise sense around |
| 508 | * that face (see diagram). */ |
| 509 | |
| 510 | /* clockwise search */ |
| 511 | while (TRUE) { |
| 512 | grid_face *f = d->faces[current_face1]; |
| 513 | grid_edge *e; |
| 514 | int j; |
| 515 | assert(f != NULL); |
| 516 | /* find dot around this face */ |
| 517 | for (j = 0; j < f->order; j++) { |
| 518 | if (f->dots[j] == d) |
| 519 | break; |
| 520 | } |
| 521 | assert(j != f->order); /* must find dot */ |
| 522 | |
| 523 | /* Around f, required edge is anticlockwise from the dot. See |
| 524 | * the other labelling scheme higher up, for why we subtract 1 |
| 525 | * from j. */ |
| 526 | j--; |
| 527 | if (j == -1) |
| 528 | j = f->order - 1; |
| 529 | e = f->edges[j]; |
| 530 | d->edges[current_face1] = e; /* set edge */ |
| 531 | current_face1++; |
| 532 | if (current_face1 == d->order) |
| 533 | break; |
| 534 | else { |
| 535 | /* set face */ |
| 536 | d->faces[current_face1] = |
| 537 | (e->face1 == f) ? e->face2 : e->face1; |
| 538 | if (d->faces[current_face1] == NULL) |
| 539 | break; /* cannot progress beyond infinite face */ |
| 540 | } |
| 541 | } |
| 542 | /* If the clockwise search made it all the way round, don't need to |
| 543 | * bother with the anticlockwise search. */ |
| 544 | if (current_face1 == d->order) |
| 545 | continue; /* this dot is complete, move on to next dot */ |
| 546 | |
| 547 | /* anticlockwise search */ |
| 548 | while (TRUE) { |
| 549 | grid_face *f = d->faces[current_face2]; |
| 550 | grid_edge *e; |
| 551 | int j; |
| 552 | assert(f != NULL); |
| 553 | /* find dot around this face */ |
| 554 | for (j = 0; j < f->order; j++) { |
| 555 | if (f->dots[j] == d) |
| 556 | break; |
| 557 | } |
| 558 | assert(j != f->order); /* must find dot */ |
| 559 | |
| 560 | /* Around f, required edge is clockwise from the dot. */ |
| 561 | e = f->edges[j]; |
| 562 | |
| 563 | current_face2--; |
| 564 | if (current_face2 == -1) |
| 565 | current_face2 = d->order - 1; |
| 566 | d->edges[current_face2] = e; /* set edge */ |
| 567 | |
| 568 | /* set face */ |
| 569 | if (current_face2 == current_face1) |
| 570 | break; |
| 571 | d->faces[current_face2] = |
| 572 | (e->face1 == f) ? e->face2 : e->face1; |
| 573 | /* There's only 1 infinite face, so we must get all the way |
| 574 | * to current_face1 before we hit it. */ |
| 575 | assert(d->faces[current_face2]); |
| 576 | } |
| 577 | } |
| 578 | |
| 579 | /* ====== Stage 4 ====== |
| 580 | * Compute other grid settings |
| 581 | */ |
| 582 | |
| 583 | /* Bounding rectangle */ |
| 584 | for (i = 0; i < g->num_dots; i++) { |
| 585 | grid_dot *d = g->dots + i; |
| 586 | if (i == 0) { |
| 587 | g->lowest_x = g->highest_x = d->x; |
| 588 | g->lowest_y = g->highest_y = d->y; |
| 589 | } else { |
| 590 | g->lowest_x = min(g->lowest_x, d->x); |
| 591 | g->highest_x = max(g->highest_x, d->x); |
| 592 | g->lowest_y = min(g->lowest_y, d->y); |
| 593 | g->highest_y = max(g->highest_y, d->y); |
| 594 | } |
| 595 | } |
| 596 | |
| 597 | #ifdef DEBUG_GRID |
| 598 | grid_print_derived(g); |
| 599 | #endif |
| 600 | } |
| 601 | |
| 602 | /* Helpers for making grid-generation easier. These functions are only |
| 603 | * intended for use during grid generation. */ |
| 604 | |
| 605 | /* Comparison function for the (tree234) sorted dot list */ |
| 606 | static int grid_point_cmp_fn(void *v1, void *v2) |
| 607 | { |
| 608 | grid_dot *p1 = v1; |
| 609 | grid_dot *p2 = v2; |
| 610 | if (p1->y != p2->y) |
| 611 | return p2->y - p1->y; |
| 612 | else |
| 613 | return p2->x - p1->x; |
| 614 | } |
| 615 | /* Add a new face to the grid, with its dot list allocated. |
| 616 | * Assumes there's enough space allocated for the new face in grid->faces */ |
| 617 | static void grid_face_add_new(grid *g, int face_size) |
| 618 | { |
| 619 | int i; |
| 620 | grid_face *new_face = g->faces + g->num_faces; |
| 621 | new_face->order = face_size; |
| 622 | new_face->dots = snewn(face_size, grid_dot*); |
| 623 | for (i = 0; i < face_size; i++) |
| 624 | new_face->dots[i] = NULL; |
| 625 | new_face->edges = NULL; |
| 626 | g->num_faces++; |
| 627 | } |
| 628 | /* Assumes dot list has enough space */ |
| 629 | static grid_dot *grid_dot_add_new(grid *g, int x, int y) |
| 630 | { |
| 631 | grid_dot *new_dot = g->dots + g->num_dots; |
| 632 | new_dot->order = 0; |
| 633 | new_dot->edges = NULL; |
| 634 | new_dot->faces = NULL; |
| 635 | new_dot->x = x; |
| 636 | new_dot->y = y; |
| 637 | g->num_dots++; |
| 638 | return new_dot; |
| 639 | } |
| 640 | /* Retrieve a dot with these (x,y) coordinates. Either return an existing dot |
| 641 | * in the dot_list, or add a new dot to the grid (and the dot_list) and |
| 642 | * return that. |
| 643 | * Assumes g->dots has enough capacity allocated */ |
| 644 | static grid_dot *grid_get_dot(grid *g, tree234 *dot_list, int x, int y) |
| 645 | { |
| 646 | grid_dot test, *ret; |
| 647 | |
| 648 | test.order = 0; |
| 649 | test.edges = NULL; |
| 650 | test.faces = NULL; |
| 651 | test.x = x; |
| 652 | test.y = y; |
| 653 | ret = find234(dot_list, &test, NULL); |
| 654 | if (ret) |
| 655 | return ret; |
| 656 | |
| 657 | ret = grid_dot_add_new(g, x, y); |
| 658 | add234(dot_list, ret); |
| 659 | return ret; |
| 660 | } |
| 661 | |
| 662 | /* Sets the last face of the grid to include this dot, at this position |
| 663 | * around the face. Assumes num_faces is at least 1 (a new face has |
| 664 | * previously been added, with the required number of dots allocated) */ |
| 665 | static void grid_face_set_dot(grid *g, grid_dot *d, int position) |
| 666 | { |
| 667 | grid_face *last_face = g->faces + g->num_faces - 1; |
| 668 | last_face->dots[position] = d; |
| 669 | } |
| 670 | |
| 671 | /* ------ Generate various types of grid ------ */ |
| 672 | |
| 673 | /* General method is to generate faces, by calculating their dot coordinates. |
| 674 | * As new faces are added, we keep track of all the dots so we can tell when |
| 675 | * a new face reuses an existing dot. For example, two squares touching at an |
| 676 | * edge would generate six unique dots: four dots from the first face, then |
| 677 | * two additional dots for the second face, because we detect the other two |
| 678 | * dots have already been taken up. This list is stored in a tree234 |
| 679 | * called "points". No extra memory-allocation needed here - we store the |
| 680 | * actual grid_dot* pointers, which all point into the g->dots list. |
| 681 | * For this reason, we have to calculate coordinates in such a way as to |
| 682 | * eliminate any rounding errors, so we can detect when a dot on one |
| 683 | * face precisely lands on a dot of a different face. No floating-point |
| 684 | * arithmetic here! |
| 685 | */ |
| 686 | |
| 687 | grid *grid_new_square(int width, int height) |
| 688 | { |
| 689 | int x, y; |
| 690 | /* Side length */ |
| 691 | int a = 20; |
| 692 | |
| 693 | /* Upper bounds - don't have to be exact */ |
| 694 | int max_faces = width * height; |
| 695 | int max_dots = (width + 1) * (height + 1); |
| 696 | |
| 697 | tree234 *points; |
| 698 | |
| 699 | grid *g = grid_new(); |
| 700 | g->tilesize = a; |
| 701 | g->faces = snewn(max_faces, grid_face); |
| 702 | g->dots = snewn(max_dots, grid_dot); |
| 703 | |
| 704 | points = newtree234(grid_point_cmp_fn); |
| 705 | |
| 706 | /* generate square faces */ |
| 707 | for (y = 0; y < height; y++) { |
| 708 | for (x = 0; x < width; x++) { |
| 709 | grid_dot *d; |
| 710 | /* face position */ |
| 711 | int px = a * x; |
| 712 | int py = a * y; |
| 713 | |
| 714 | grid_face_add_new(g, 4); |
| 715 | d = grid_get_dot(g, points, px, py); |
| 716 | grid_face_set_dot(g, d, 0); |
| 717 | d = grid_get_dot(g, points, px + a, py); |
| 718 | grid_face_set_dot(g, d, 1); |
| 719 | d = grid_get_dot(g, points, px + a, py + a); |
| 720 | grid_face_set_dot(g, d, 2); |
| 721 | d = grid_get_dot(g, points, px, py + a); |
| 722 | grid_face_set_dot(g, d, 3); |
| 723 | } |
| 724 | } |
| 725 | |
| 726 | freetree234(points); |
| 727 | assert(g->num_faces <= max_faces); |
| 728 | assert(g->num_dots <= max_dots); |
| 729 | g->middle_face = g->faces + (height/2) * width + (width/2); |
| 730 | |
| 731 | grid_make_consistent(g); |
| 732 | return g; |
| 733 | } |
| 734 | |
| 735 | grid *grid_new_honeycomb(int width, int height) |
| 736 | { |
| 737 | int x, y; |
| 738 | /* Vector for side of hexagon - ratio is close to sqrt(3) */ |
| 739 | int a = 15; |
| 740 | int b = 26; |
| 741 | |
| 742 | /* Upper bounds - don't have to be exact */ |
| 743 | int max_faces = width * height; |
| 744 | int max_dots = 2 * (width + 1) * (height + 1); |
| 745 | |
| 746 | tree234 *points; |
| 747 | |
| 748 | grid *g = grid_new(); |
| 749 | g->tilesize = 3 * a; |
| 750 | g->faces = snewn(max_faces, grid_face); |
| 751 | g->dots = snewn(max_dots, grid_dot); |
| 752 | |
| 753 | points = newtree234(grid_point_cmp_fn); |
| 754 | |
| 755 | /* generate hexagonal faces */ |
| 756 | for (y = 0; y < height; y++) { |
| 757 | for (x = 0; x < width; x++) { |
| 758 | grid_dot *d; |
| 759 | /* face centre */ |
| 760 | int cx = 3 * a * x; |
| 761 | int cy = 2 * b * y; |
| 762 | if (x % 2) |
| 763 | cy += b; |
| 764 | grid_face_add_new(g, 6); |
| 765 | |
| 766 | d = grid_get_dot(g, points, cx - a, cy - b); |
| 767 | grid_face_set_dot(g, d, 0); |
| 768 | d = grid_get_dot(g, points, cx + a, cy - b); |
| 769 | grid_face_set_dot(g, d, 1); |
| 770 | d = grid_get_dot(g, points, cx + 2*a, cy); |
| 771 | grid_face_set_dot(g, d, 2); |
| 772 | d = grid_get_dot(g, points, cx + a, cy + b); |
| 773 | grid_face_set_dot(g, d, 3); |
| 774 | d = grid_get_dot(g, points, cx - a, cy + b); |
| 775 | grid_face_set_dot(g, d, 4); |
| 776 | d = grid_get_dot(g, points, cx - 2*a, cy); |
| 777 | grid_face_set_dot(g, d, 5); |
| 778 | } |
| 779 | } |
| 780 | |
| 781 | freetree234(points); |
| 782 | assert(g->num_faces <= max_faces); |
| 783 | assert(g->num_dots <= max_dots); |
| 784 | g->middle_face = g->faces + (height/2) * width + (width/2); |
| 785 | |
| 786 | grid_make_consistent(g); |
| 787 | return g; |
| 788 | } |
| 789 | |
| 790 | /* Doesn't use the previous method of generation, it pre-dates it! |
| 791 | * A triangular grid is just about simple enough to do by "brute force" */ |
| 792 | grid *grid_new_triangular(int width, int height) |
| 793 | { |
| 794 | int x,y; |
| 795 | |
| 796 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
| 797 | int vec_x = 15; |
| 798 | int vec_y = 26; |
| 799 | |
| 800 | int index; |
| 801 | |
| 802 | /* convenient alias */ |
| 803 | int w = width + 1; |
| 804 | |
| 805 | grid *g = grid_new(); |
| 806 | g->tilesize = 18; /* adjust to your taste */ |
| 807 | |
| 808 | g->num_faces = width * height * 2; |
| 809 | g->num_dots = (width + 1) * (height + 1); |
| 810 | g->faces = snewn(g->num_faces, grid_face); |
| 811 | g->dots = snewn(g->num_dots, grid_dot); |
| 812 | |
| 813 | /* generate dots */ |
| 814 | index = 0; |
| 815 | for (y = 0; y <= height; y++) { |
| 816 | for (x = 0; x <= width; x++) { |
| 817 | grid_dot *d = g->dots + index; |
| 818 | /* odd rows are offset to the right */ |
| 819 | d->order = 0; |
| 820 | d->edges = NULL; |
| 821 | d->faces = NULL; |
| 822 | d->x = x * 2 * vec_x + ((y % 2) ? vec_x : 0); |
| 823 | d->y = y * vec_y; |
| 824 | index++; |
| 825 | } |
| 826 | } |
| 827 | |
| 828 | /* generate faces */ |
| 829 | index = 0; |
| 830 | for (y = 0; y < height; y++) { |
| 831 | for (x = 0; x < width; x++) { |
| 832 | /* initialise two faces for this (x,y) */ |
| 833 | grid_face *f1 = g->faces + index; |
| 834 | grid_face *f2 = f1 + 1; |
| 835 | f1->edges = NULL; |
| 836 | f1->order = 3; |
| 837 | f1->dots = snewn(f1->order, grid_dot*); |
| 838 | f2->edges = NULL; |
| 839 | f2->order = 3; |
| 840 | f2->dots = snewn(f2->order, grid_dot*); |
| 841 | |
| 842 | /* face descriptions depend on whether the row-number is |
| 843 | * odd or even */ |
| 844 | if (y % 2) { |
| 845 | f1->dots[0] = g->dots + y * w + x; |
| 846 | f1->dots[1] = g->dots + (y + 1) * w + x + 1; |
| 847 | f1->dots[2] = g->dots + (y + 1) * w + x; |
| 848 | f2->dots[0] = g->dots + y * w + x; |
| 849 | f2->dots[1] = g->dots + y * w + x + 1; |
| 850 | f2->dots[2] = g->dots + (y + 1) * w + x + 1; |
| 851 | } else { |
| 852 | f1->dots[0] = g->dots + y * w + x; |
| 853 | f1->dots[1] = g->dots + y * w + x + 1; |
| 854 | f1->dots[2] = g->dots + (y + 1) * w + x; |
| 855 | f2->dots[0] = g->dots + y * w + x + 1; |
| 856 | f2->dots[1] = g->dots + (y + 1) * w + x + 1; |
| 857 | f2->dots[2] = g->dots + (y + 1) * w + x; |
| 858 | } |
| 859 | index += 2; |
| 860 | } |
| 861 | } |
| 862 | |
| 863 | /* "+ width" takes us to the middle of the row, because each row has |
| 864 | * (2*width) faces. */ |
| 865 | g->middle_face = g->faces + (height / 2) * 2 * width + width; |
| 866 | |
| 867 | grid_make_consistent(g); |
| 868 | return g; |
| 869 | } |
| 870 | |
| 871 | grid *grid_new_snubsquare(int width, int height) |
| 872 | { |
| 873 | int x, y; |
| 874 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
| 875 | int a = 15; |
| 876 | int b = 26; |
| 877 | |
| 878 | /* Upper bounds - don't have to be exact */ |
| 879 | int max_faces = 3 * width * height; |
| 880 | int max_dots = 2 * (width + 1) * (height + 1); |
| 881 | |
| 882 | tree234 *points; |
| 883 | |
| 884 | grid *g = grid_new(); |
| 885 | g->tilesize = 18; |
| 886 | g->faces = snewn(max_faces, grid_face); |
| 887 | g->dots = snewn(max_dots, grid_dot); |
| 888 | |
| 889 | points = newtree234(grid_point_cmp_fn); |
| 890 | |
| 891 | for (y = 0; y < height; y++) { |
| 892 | for (x = 0; x < width; x++) { |
| 893 | grid_dot *d; |
| 894 | /* face position */ |
| 895 | int px = (a + b) * x; |
| 896 | int py = (a + b) * y; |
| 897 | |
| 898 | /* generate square faces */ |
| 899 | grid_face_add_new(g, 4); |
| 900 | if ((x + y) % 2) { |
| 901 | d = grid_get_dot(g, points, px + a, py); |
| 902 | grid_face_set_dot(g, d, 0); |
| 903 | d = grid_get_dot(g, points, px + a + b, py + a); |
| 904 | grid_face_set_dot(g, d, 1); |
| 905 | d = grid_get_dot(g, points, px + b, py + a + b); |
| 906 | grid_face_set_dot(g, d, 2); |
| 907 | d = grid_get_dot(g, points, px, py + b); |
| 908 | grid_face_set_dot(g, d, 3); |
| 909 | } else { |
| 910 | d = grid_get_dot(g, points, px + b, py); |
| 911 | grid_face_set_dot(g, d, 0); |
| 912 | d = grid_get_dot(g, points, px + a + b, py + b); |
| 913 | grid_face_set_dot(g, d, 1); |
| 914 | d = grid_get_dot(g, points, px + a, py + a + b); |
| 915 | grid_face_set_dot(g, d, 2); |
| 916 | d = grid_get_dot(g, points, px, py + a); |
| 917 | grid_face_set_dot(g, d, 3); |
| 918 | } |
| 919 | |
| 920 | /* generate up/down triangles */ |
| 921 | if (x > 0) { |
| 922 | grid_face_add_new(g, 3); |
| 923 | if ((x + y) % 2) { |
| 924 | d = grid_get_dot(g, points, px + a, py); |
| 925 | grid_face_set_dot(g, d, 0); |
| 926 | d = grid_get_dot(g, points, px, py + b); |
| 927 | grid_face_set_dot(g, d, 1); |
| 928 | d = grid_get_dot(g, points, px - a, py); |
| 929 | grid_face_set_dot(g, d, 2); |
| 930 | } else { |
| 931 | d = grid_get_dot(g, points, px, py + a); |
| 932 | grid_face_set_dot(g, d, 0); |
| 933 | d = grid_get_dot(g, points, px + a, py + a + b); |
| 934 | grid_face_set_dot(g, d, 1); |
| 935 | d = grid_get_dot(g, points, px - a, py + a + b); |
| 936 | grid_face_set_dot(g, d, 2); |
| 937 | } |
| 938 | } |
| 939 | |
| 940 | /* generate left/right triangles */ |
| 941 | if (y > 0) { |
| 942 | grid_face_add_new(g, 3); |
| 943 | if ((x + y) % 2) { |
| 944 | d = grid_get_dot(g, points, px + a, py); |
| 945 | grid_face_set_dot(g, d, 0); |
| 946 | d = grid_get_dot(g, points, px + a + b, py - a); |
| 947 | grid_face_set_dot(g, d, 1); |
| 948 | d = grid_get_dot(g, points, px + a + b, py + a); |
| 949 | grid_face_set_dot(g, d, 2); |
| 950 | } else { |
| 951 | d = grid_get_dot(g, points, px, py - a); |
| 952 | grid_face_set_dot(g, d, 0); |
| 953 | d = grid_get_dot(g, points, px + b, py); |
| 954 | grid_face_set_dot(g, d, 1); |
| 955 | d = grid_get_dot(g, points, px, py + a); |
| 956 | grid_face_set_dot(g, d, 2); |
| 957 | } |
| 958 | } |
| 959 | } |
| 960 | } |
| 961 | |
| 962 | freetree234(points); |
| 963 | assert(g->num_faces <= max_faces); |
| 964 | assert(g->num_dots <= max_dots); |
| 965 | g->middle_face = g->faces + (height/2) * width + (width/2); |
| 966 | |
| 967 | grid_make_consistent(g); |
| 968 | return g; |
| 969 | } |
| 970 | |
| 971 | grid *grid_new_cairo(int width, int height) |
| 972 | { |
| 973 | int x, y; |
| 974 | /* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */ |
| 975 | int a = 14; |
| 976 | int b = 31; |
| 977 | |
| 978 | /* Upper bounds - don't have to be exact */ |
| 979 | int max_faces = 2 * width * height; |
| 980 | int max_dots = 3 * (width + 1) * (height + 1); |
| 981 | |
| 982 | tree234 *points; |
| 983 | |
| 984 | grid *g = grid_new(); |
| 985 | g->tilesize = 40; |
| 986 | g->faces = snewn(max_faces, grid_face); |
| 987 | g->dots = snewn(max_dots, grid_dot); |
| 988 | |
| 989 | points = newtree234(grid_point_cmp_fn); |
| 990 | |
| 991 | for (y = 0; y < height; y++) { |
| 992 | for (x = 0; x < width; x++) { |
| 993 | grid_dot *d; |
| 994 | /* cell position */ |
| 995 | int px = 2 * b * x; |
| 996 | int py = 2 * b * y; |
| 997 | |
| 998 | /* horizontal pentagons */ |
| 999 | if (y > 0) { |
| 1000 | grid_face_add_new(g, 5); |
| 1001 | if ((x + y) % 2) { |
| 1002 | d = grid_get_dot(g, points, px + a, py - b); |
| 1003 | grid_face_set_dot(g, d, 0); |
| 1004 | d = grid_get_dot(g, points, px + 2*b - a, py - b); |
| 1005 | grid_face_set_dot(g, d, 1); |
| 1006 | d = grid_get_dot(g, points, px + 2*b, py); |
| 1007 | grid_face_set_dot(g, d, 2); |
| 1008 | d = grid_get_dot(g, points, px + b, py + a); |
| 1009 | grid_face_set_dot(g, d, 3); |
| 1010 | d = grid_get_dot(g, points, px, py); |
| 1011 | grid_face_set_dot(g, d, 4); |
| 1012 | } else { |
| 1013 | d = grid_get_dot(g, points, px, py); |
| 1014 | grid_face_set_dot(g, d, 0); |
| 1015 | d = grid_get_dot(g, points, px + b, py - a); |
| 1016 | grid_face_set_dot(g, d, 1); |
| 1017 | d = grid_get_dot(g, points, px + 2*b, py); |
| 1018 | grid_face_set_dot(g, d, 2); |
| 1019 | d = grid_get_dot(g, points, px + 2*b - a, py + b); |
| 1020 | grid_face_set_dot(g, d, 3); |
| 1021 | d = grid_get_dot(g, points, px + a, py + b); |
| 1022 | grid_face_set_dot(g, d, 4); |
| 1023 | } |
| 1024 | } |
| 1025 | /* vertical pentagons */ |
| 1026 | if (x > 0) { |
| 1027 | grid_face_add_new(g, 5); |
| 1028 | if ((x + y) % 2) { |
| 1029 | d = grid_get_dot(g, points, px, py); |
| 1030 | grid_face_set_dot(g, d, 0); |
| 1031 | d = grid_get_dot(g, points, px + b, py + a); |
| 1032 | grid_face_set_dot(g, d, 1); |
| 1033 | d = grid_get_dot(g, points, px + b, py + 2*b - a); |
| 1034 | grid_face_set_dot(g, d, 2); |
| 1035 | d = grid_get_dot(g, points, px, py + 2*b); |
| 1036 | grid_face_set_dot(g, d, 3); |
| 1037 | d = grid_get_dot(g, points, px - a, py + b); |
| 1038 | grid_face_set_dot(g, d, 4); |
| 1039 | } else { |
| 1040 | d = grid_get_dot(g, points, px, py); |
| 1041 | grid_face_set_dot(g, d, 0); |
| 1042 | d = grid_get_dot(g, points, px + a, py + b); |
| 1043 | grid_face_set_dot(g, d, 1); |
| 1044 | d = grid_get_dot(g, points, px, py + 2*b); |
| 1045 | grid_face_set_dot(g, d, 2); |
| 1046 | d = grid_get_dot(g, points, px - b, py + 2*b - a); |
| 1047 | grid_face_set_dot(g, d, 3); |
| 1048 | d = grid_get_dot(g, points, px - b, py + a); |
| 1049 | grid_face_set_dot(g, d, 4); |
| 1050 | } |
| 1051 | } |
| 1052 | } |
| 1053 | } |
| 1054 | |
| 1055 | freetree234(points); |
| 1056 | assert(g->num_faces <= max_faces); |
| 1057 | assert(g->num_dots <= max_dots); |
| 1058 | g->middle_face = g->faces + (height/2) * width + (width/2); |
| 1059 | |
| 1060 | grid_make_consistent(g); |
| 1061 | return g; |
| 1062 | } |
| 1063 | |
| 1064 | grid *grid_new_greathexagonal(int width, int height) |
| 1065 | { |
| 1066 | int x, y; |
| 1067 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
| 1068 | int a = 15; |
| 1069 | int b = 26; |
| 1070 | |
| 1071 | /* Upper bounds - don't have to be exact */ |
| 1072 | int max_faces = 6 * (width + 1) * (height + 1); |
| 1073 | int max_dots = 6 * width * height; |
| 1074 | |
| 1075 | tree234 *points; |
| 1076 | |
| 1077 | grid *g = grid_new(); |
| 1078 | g->tilesize = 18; |
| 1079 | g->faces = snewn(max_faces, grid_face); |
| 1080 | g->dots = snewn(max_dots, grid_dot); |
| 1081 | |
| 1082 | points = newtree234(grid_point_cmp_fn); |
| 1083 | |
| 1084 | for (y = 0; y < height; y++) { |
| 1085 | for (x = 0; x < width; x++) { |
| 1086 | grid_dot *d; |
| 1087 | /* centre of hexagon */ |
| 1088 | int px = (3*a + b) * x; |
| 1089 | int py = (2*a + 2*b) * y; |
| 1090 | if (x % 2) |
| 1091 | py += a + b; |
| 1092 | |
| 1093 | /* hexagon */ |
| 1094 | grid_face_add_new(g, 6); |
| 1095 | d = grid_get_dot(g, points, px - a, py - b); |
| 1096 | grid_face_set_dot(g, d, 0); |
| 1097 | d = grid_get_dot(g, points, px + a, py - b); |
| 1098 | grid_face_set_dot(g, d, 1); |
| 1099 | d = grid_get_dot(g, points, px + 2*a, py); |
| 1100 | grid_face_set_dot(g, d, 2); |
| 1101 | d = grid_get_dot(g, points, px + a, py + b); |
| 1102 | grid_face_set_dot(g, d, 3); |
| 1103 | d = grid_get_dot(g, points, px - a, py + b); |
| 1104 | grid_face_set_dot(g, d, 4); |
| 1105 | d = grid_get_dot(g, points, px - 2*a, py); |
| 1106 | grid_face_set_dot(g, d, 5); |
| 1107 | |
| 1108 | /* square below hexagon */ |
| 1109 | if (y < height - 1) { |
| 1110 | grid_face_add_new(g, 4); |
| 1111 | d = grid_get_dot(g, points, px - a, py + b); |
| 1112 | grid_face_set_dot(g, d, 0); |
| 1113 | d = grid_get_dot(g, points, px + a, py + b); |
| 1114 | grid_face_set_dot(g, d, 1); |
| 1115 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
| 1116 | grid_face_set_dot(g, d, 2); |
| 1117 | d = grid_get_dot(g, points, px - a, py + 2*a + b); |
| 1118 | grid_face_set_dot(g, d, 3); |
| 1119 | } |
| 1120 | |
| 1121 | /* square below right */ |
| 1122 | if ((x < width - 1) && (((x % 2) == 0) || (y < height - 1))) { |
| 1123 | grid_face_add_new(g, 4); |
| 1124 | d = grid_get_dot(g, points, px + 2*a, py); |
| 1125 | grid_face_set_dot(g, d, 0); |
| 1126 | d = grid_get_dot(g, points, px + 2*a + b, py + a); |
| 1127 | grid_face_set_dot(g, d, 1); |
| 1128 | d = grid_get_dot(g, points, px + a + b, py + a + b); |
| 1129 | grid_face_set_dot(g, d, 2); |
| 1130 | d = grid_get_dot(g, points, px + a, py + b); |
| 1131 | grid_face_set_dot(g, d, 3); |
| 1132 | } |
| 1133 | |
| 1134 | /* square below left */ |
| 1135 | if ((x > 0) && (((x % 2) == 0) || (y < height - 1))) { |
| 1136 | grid_face_add_new(g, 4); |
| 1137 | d = grid_get_dot(g, points, px - 2*a, py); |
| 1138 | grid_face_set_dot(g, d, 0); |
| 1139 | d = grid_get_dot(g, points, px - a, py + b); |
| 1140 | grid_face_set_dot(g, d, 1); |
| 1141 | d = grid_get_dot(g, points, px - a - b, py + a + b); |
| 1142 | grid_face_set_dot(g, d, 2); |
| 1143 | d = grid_get_dot(g, points, px - 2*a - b, py + a); |
| 1144 | grid_face_set_dot(g, d, 3); |
| 1145 | } |
| 1146 | |
| 1147 | /* Triangle below right */ |
| 1148 | if ((x < width - 1) && (y < height - 1)) { |
| 1149 | grid_face_add_new(g, 3); |
| 1150 | d = grid_get_dot(g, points, px + a, py + b); |
| 1151 | grid_face_set_dot(g, d, 0); |
| 1152 | d = grid_get_dot(g, points, px + a + b, py + a + b); |
| 1153 | grid_face_set_dot(g, d, 1); |
| 1154 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
| 1155 | grid_face_set_dot(g, d, 2); |
| 1156 | } |
| 1157 | |
| 1158 | /* Triangle below left */ |
| 1159 | if ((x > 0) && (y < height - 1)) { |
| 1160 | grid_face_add_new(g, 3); |
| 1161 | d = grid_get_dot(g, points, px - a, py + b); |
| 1162 | grid_face_set_dot(g, d, 0); |
| 1163 | d = grid_get_dot(g, points, px - a, py + 2*a + b); |
| 1164 | grid_face_set_dot(g, d, 1); |
| 1165 | d = grid_get_dot(g, points, px - a - b, py + a + b); |
| 1166 | grid_face_set_dot(g, d, 2); |
| 1167 | } |
| 1168 | } |
| 1169 | } |
| 1170 | |
| 1171 | freetree234(points); |
| 1172 | assert(g->num_faces <= max_faces); |
| 1173 | assert(g->num_dots <= max_dots); |
| 1174 | g->middle_face = g->faces + (height/2) * width + (width/2); |
| 1175 | |
| 1176 | grid_make_consistent(g); |
| 1177 | return g; |
| 1178 | } |
| 1179 | |
| 1180 | grid *grid_new_octagonal(int width, int height) |
| 1181 | { |
| 1182 | int x, y; |
| 1183 | /* b/a approx sqrt(2) */ |
| 1184 | int a = 29; |
| 1185 | int b = 41; |
| 1186 | |
| 1187 | /* Upper bounds - don't have to be exact */ |
| 1188 | int max_faces = 2 * width * height; |
| 1189 | int max_dots = 4 * (width + 1) * (height + 1); |
| 1190 | |
| 1191 | tree234 *points; |
| 1192 | |
| 1193 | grid *g = grid_new(); |
| 1194 | g->tilesize = 40; |
| 1195 | g->faces = snewn(max_faces, grid_face); |
| 1196 | g->dots = snewn(max_dots, grid_dot); |
| 1197 | |
| 1198 | points = newtree234(grid_point_cmp_fn); |
| 1199 | |
| 1200 | for (y = 0; y < height; y++) { |
| 1201 | for (x = 0; x < width; x++) { |
| 1202 | grid_dot *d; |
| 1203 | /* cell position */ |
| 1204 | int px = (2*a + b) * x; |
| 1205 | int py = (2*a + b) * y; |
| 1206 | /* octagon */ |
| 1207 | grid_face_add_new(g, 8); |
| 1208 | d = grid_get_dot(g, points, px + a, py); |
| 1209 | grid_face_set_dot(g, d, 0); |
| 1210 | d = grid_get_dot(g, points, px + a + b, py); |
| 1211 | grid_face_set_dot(g, d, 1); |
| 1212 | d = grid_get_dot(g, points, px + 2*a + b, py + a); |
| 1213 | grid_face_set_dot(g, d, 2); |
| 1214 | d = grid_get_dot(g, points, px + 2*a + b, py + a + b); |
| 1215 | grid_face_set_dot(g, d, 3); |
| 1216 | d = grid_get_dot(g, points, px + a + b, py + 2*a + b); |
| 1217 | grid_face_set_dot(g, d, 4); |
| 1218 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
| 1219 | grid_face_set_dot(g, d, 5); |
| 1220 | d = grid_get_dot(g, points, px, py + a + b); |
| 1221 | grid_face_set_dot(g, d, 6); |
| 1222 | d = grid_get_dot(g, points, px, py + a); |
| 1223 | grid_face_set_dot(g, d, 7); |
| 1224 | |
| 1225 | /* diamond */ |
| 1226 | if ((x > 0) && (y > 0)) { |
| 1227 | grid_face_add_new(g, 4); |
| 1228 | d = grid_get_dot(g, points, px, py - a); |
| 1229 | grid_face_set_dot(g, d, 0); |
| 1230 | d = grid_get_dot(g, points, px + a, py); |
| 1231 | grid_face_set_dot(g, d, 1); |
| 1232 | d = grid_get_dot(g, points, px, py + a); |
| 1233 | grid_face_set_dot(g, d, 2); |
| 1234 | d = grid_get_dot(g, points, px - a, py); |
| 1235 | grid_face_set_dot(g, d, 3); |
| 1236 | } |
| 1237 | } |
| 1238 | } |
| 1239 | |
| 1240 | freetree234(points); |
| 1241 | assert(g->num_faces <= max_faces); |
| 1242 | assert(g->num_dots <= max_dots); |
| 1243 | g->middle_face = g->faces + (height/2) * width + (width/2); |
| 1244 | |
| 1245 | grid_make_consistent(g); |
| 1246 | return g; |
| 1247 | } |
| 1248 | |
| 1249 | grid *grid_new_kites(int width, int height) |
| 1250 | { |
| 1251 | int x, y; |
| 1252 | /* b/a approx sqrt(3) */ |
| 1253 | int a = 15; |
| 1254 | int b = 26; |
| 1255 | |
| 1256 | /* Upper bounds - don't have to be exact */ |
| 1257 | int max_faces = 6 * width * height; |
| 1258 | int max_dots = 6 * (width + 1) * (height + 1); |
| 1259 | |
| 1260 | tree234 *points; |
| 1261 | |
| 1262 | grid *g = grid_new(); |
| 1263 | g->tilesize = 40; |
| 1264 | g->faces = snewn(max_faces, grid_face); |
| 1265 | g->dots = snewn(max_dots, grid_dot); |
| 1266 | |
| 1267 | points = newtree234(grid_point_cmp_fn); |
| 1268 | |
| 1269 | for (y = 0; y < height; y++) { |
| 1270 | for (x = 0; x < width; x++) { |
| 1271 | grid_dot *d; |
| 1272 | /* position of order-6 dot */ |
| 1273 | int px = 4*b * x; |
| 1274 | int py = 6*a * y; |
| 1275 | if (y % 2) |
| 1276 | px += 2*b; |
| 1277 | |
| 1278 | /* kite pointing up-left */ |
| 1279 | grid_face_add_new(g, 4); |
| 1280 | d = grid_get_dot(g, points, px, py); |
| 1281 | grid_face_set_dot(g, d, 0); |
| 1282 | d = grid_get_dot(g, points, px + 2*b, py); |
| 1283 | grid_face_set_dot(g, d, 1); |
| 1284 | d = grid_get_dot(g, points, px + 2*b, py + 2*a); |
| 1285 | grid_face_set_dot(g, d, 2); |
| 1286 | d = grid_get_dot(g, points, px + b, py + 3*a); |
| 1287 | grid_face_set_dot(g, d, 3); |
| 1288 | |
| 1289 | /* kite pointing up */ |
| 1290 | grid_face_add_new(g, 4); |
| 1291 | d = grid_get_dot(g, points, px, py); |
| 1292 | grid_face_set_dot(g, d, 0); |
| 1293 | d = grid_get_dot(g, points, px + b, py + 3*a); |
| 1294 | grid_face_set_dot(g, d, 1); |
| 1295 | d = grid_get_dot(g, points, px, py + 4*a); |
| 1296 | grid_face_set_dot(g, d, 2); |
| 1297 | d = grid_get_dot(g, points, px - b, py + 3*a); |
| 1298 | grid_face_set_dot(g, d, 3); |
| 1299 | |
| 1300 | /* kite pointing up-right */ |
| 1301 | grid_face_add_new(g, 4); |
| 1302 | d = grid_get_dot(g, points, px, py); |
| 1303 | grid_face_set_dot(g, d, 0); |
| 1304 | d = grid_get_dot(g, points, px - b, py + 3*a); |
| 1305 | grid_face_set_dot(g, d, 1); |
| 1306 | d = grid_get_dot(g, points, px - 2*b, py + 2*a); |
| 1307 | grid_face_set_dot(g, d, 2); |
| 1308 | d = grid_get_dot(g, points, px - 2*b, py); |
| 1309 | grid_face_set_dot(g, d, 3); |
| 1310 | |
| 1311 | /* kite pointing down-right */ |
| 1312 | grid_face_add_new(g, 4); |
| 1313 | d = grid_get_dot(g, points, px, py); |
| 1314 | grid_face_set_dot(g, d, 0); |
| 1315 | d = grid_get_dot(g, points, px - 2*b, py); |
| 1316 | grid_face_set_dot(g, d, 1); |
| 1317 | d = grid_get_dot(g, points, px - 2*b, py - 2*a); |
| 1318 | grid_face_set_dot(g, d, 2); |
| 1319 | d = grid_get_dot(g, points, px - b, py - 3*a); |
| 1320 | grid_face_set_dot(g, d, 3); |
| 1321 | |
| 1322 | /* kite pointing down */ |
| 1323 | grid_face_add_new(g, 4); |
| 1324 | d = grid_get_dot(g, points, px, py); |
| 1325 | grid_face_set_dot(g, d, 0); |
| 1326 | d = grid_get_dot(g, points, px - b, py - 3*a); |
| 1327 | grid_face_set_dot(g, d, 1); |
| 1328 | d = grid_get_dot(g, points, px, py - 4*a); |
| 1329 | grid_face_set_dot(g, d, 2); |
| 1330 | d = grid_get_dot(g, points, px + b, py - 3*a); |
| 1331 | grid_face_set_dot(g, d, 3); |
| 1332 | |
| 1333 | /* kite pointing down-left */ |
| 1334 | grid_face_add_new(g, 4); |
| 1335 | d = grid_get_dot(g, points, px, py); |
| 1336 | grid_face_set_dot(g, d, 0); |
| 1337 | d = grid_get_dot(g, points, px + b, py - 3*a); |
| 1338 | grid_face_set_dot(g, d, 1); |
| 1339 | d = grid_get_dot(g, points, px + 2*b, py - 2*a); |
| 1340 | grid_face_set_dot(g, d, 2); |
| 1341 | d = grid_get_dot(g, points, px + 2*b, py); |
| 1342 | grid_face_set_dot(g, d, 3); |
| 1343 | } |
| 1344 | } |
| 1345 | |
| 1346 | freetree234(points); |
| 1347 | assert(g->num_faces <= max_faces); |
| 1348 | assert(g->num_dots <= max_dots); |
| 1349 | g->middle_face = g->faces + 6 * ((height/2) * width + (width/2)); |
| 1350 | |
| 1351 | grid_make_consistent(g); |
| 1352 | return g; |
| 1353 | } |
| 1354 | |
| 1355 | /* ----------- End of grid generators ------------- */ |