| 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> |
| cebf0b0d |
15 | #include <errno.h> |
| 7c95608a |
16 | |
| 17 | #include "puzzles.h" |
| 18 | #include "tree234.h" |
| 19 | #include "grid.h" |
| cebf0b0d |
20 | #include "penrose.h" |
| 7c95608a |
21 | |
| 22 | /* Debugging options */ |
| 23 | |
| 24 | /* |
| 25 | #define DEBUG_GRID |
| 26 | */ |
| 27 | |
| 28 | /* ---------------------------------------------------------------------- |
| 29 | * Deallocate or dereference a grid |
| 30 | */ |
| 31 | void grid_free(grid *g) |
| 32 | { |
| 33 | assert(g->refcount); |
| 34 | |
| 35 | g->refcount--; |
| 36 | if (g->refcount == 0) { |
| 37 | int i; |
| 38 | for (i = 0; i < g->num_faces; i++) { |
| 39 | sfree(g->faces[i].dots); |
| 40 | sfree(g->faces[i].edges); |
| 41 | } |
| 42 | for (i = 0; i < g->num_dots; i++) { |
| 43 | sfree(g->dots[i].faces); |
| 44 | sfree(g->dots[i].edges); |
| 45 | } |
| 46 | sfree(g->faces); |
| 47 | sfree(g->edges); |
| 48 | sfree(g->dots); |
| 49 | sfree(g); |
| 50 | } |
| 51 | } |
| 52 | |
| 53 | /* Used by the other grid generators. Create a brand new grid with nothing |
| 54 | * initialised (all lists are NULL) */ |
| cebf0b0d |
55 | static grid *grid_empty() |
| 7c95608a |
56 | { |
| 57 | grid *g = snew(grid); |
| 58 | g->faces = NULL; |
| 59 | g->edges = NULL; |
| 60 | g->dots = NULL; |
| 61 | g->num_faces = g->num_edges = g->num_dots = 0; |
| 7c95608a |
62 | g->refcount = 1; |
| 63 | g->lowest_x = g->lowest_y = g->highest_x = g->highest_y = 0; |
| 64 | return g; |
| 65 | } |
| 66 | |
| 67 | /* Helper function to calculate perpendicular distance from |
| 68 | * a point P to a line AB. A and B mustn't be equal here. |
| 69 | * |
| 70 | * Well-known formula for area A of a triangle: |
| 71 | * / 1 1 1 \ |
| 72 | * 2A = determinant of matrix | px ax bx | |
| 73 | * \ py ay by / |
| 74 | * |
| 75 | * Also well-known: 2A = base * height |
| 76 | * = perpendicular distance * line-length. |
| 77 | * |
| 78 | * Combining gives: distance = determinant / line-length(a,b) |
| 79 | */ |
| b1535c90 |
80 | static double point_line_distance(long px, long py, |
| 81 | long ax, long ay, |
| 82 | long bx, long by) |
| 7c95608a |
83 | { |
| b1535c90 |
84 | long det = ax*by - bx*ay + bx*py - px*by + px*ay - ax*py; |
| 1515b973 |
85 | double len; |
| 7c95608a |
86 | det = max(det, -det); |
| 1515b973 |
87 | len = sqrt(SQ(ax - bx) + SQ(ay - by)); |
| 7c95608a |
88 | return det / len; |
| 89 | } |
| 90 | |
| 91 | /* Determine nearest edge to where the user clicked. |
| 92 | * (x, y) is the clicked location, converted to grid coordinates. |
| 93 | * Returns the nearest edge, or NULL if no edge is reasonably |
| 94 | * near the position. |
| 95 | * |
| f839ef77 |
96 | * Just judging edges by perpendicular distance is not quite right - |
| 97 | * the edge might be "off to one side". So we insist that the triangle |
| 98 | * with (x,y) has acute angles at the edge's dots. |
| 7c95608a |
99 | * |
| 100 | * edge1 |
| 101 | * *---------*------ |
| 102 | * | |
| 103 | * | *(x,y) |
| 104 | * edge2 | |
| 105 | * | edge2 is OK, but edge1 is not, even though |
| 106 | * | edge1 is perpendicularly closer to (x,y) |
| 107 | * * |
| 108 | * |
| 109 | */ |
| 110 | grid_edge *grid_nearest_edge(grid *g, int x, int y) |
| 111 | { |
| 7c95608a |
112 | grid_edge *best_edge; |
| 113 | double best_distance = 0; |
| 114 | int i; |
| 115 | |
| 7c95608a |
116 | best_edge = NULL; |
| 117 | |
| f839ef77 |
118 | for (i = 0; i < g->num_edges; i++) { |
| 119 | grid_edge *e = &g->edges[i]; |
| b1535c90 |
120 | long e2; /* squared length of edge */ |
| 121 | long a2, b2; /* squared lengths of other sides */ |
| 7c95608a |
122 | double dist; |
| 123 | |
| 124 | /* See if edge e is eligible - the triangle must have acute angles |
| 125 | * at the edge's dots. |
| 126 | * Pythagoras formula h^2 = a^2 + b^2 detects right-angles, |
| 127 | * so detect acute angles by testing for h^2 < a^2 + b^2 */ |
| b1535c90 |
128 | e2 = SQ((long)e->dot1->x - (long)e->dot2->x) + SQ((long)e->dot1->y - (long)e->dot2->y); |
| 129 | a2 = SQ((long)e->dot1->x - (long)x) + SQ((long)e->dot1->y - (long)y); |
| 130 | b2 = SQ((long)e->dot2->x - (long)x) + SQ((long)e->dot2->y - (long)y); |
| 7c95608a |
131 | if (a2 >= e2 + b2) continue; |
| 132 | if (b2 >= e2 + a2) continue; |
| 133 | |
| 134 | /* e is eligible so far. Now check the edge is reasonably close |
| 135 | * to where the user clicked. Don't want to toggle an edge if the |
| 136 | * click was way off the grid. |
| 137 | * There is room for experimentation here. We could check the |
| 138 | * perpendicular distance is within a certain fraction of the length |
| 139 | * of the edge. That amounts to testing a rectangular region around |
| 140 | * the edge. |
| 141 | * Alternatively, we could check that the angle at the point is obtuse. |
| 142 | * That would amount to testing a circular region with the edge as |
| 143 | * diameter. */ |
| b1535c90 |
144 | dist = point_line_distance((long)x, (long)y, |
| 145 | (long)e->dot1->x, (long)e->dot1->y, |
| 146 | (long)e->dot2->x, (long)e->dot2->y); |
| 7c95608a |
147 | /* Is dist more than half edge length ? */ |
| 148 | if (4 * SQ(dist) > e2) |
| 149 | continue; |
| 150 | |
| 151 | if (best_edge == NULL || dist < best_distance) { |
| 152 | best_edge = e; |
| 153 | best_distance = dist; |
| 154 | } |
| 155 | } |
| 156 | return best_edge; |
| 157 | } |
| 158 | |
| 159 | /* ---------------------------------------------------------------------- |
| 160 | * Grid generation |
| 161 | */ |
| 162 | |
| cebf0b0d |
163 | #ifdef SVG_GRID |
| 164 | |
| 165 | #define SVG_DOTS 1 |
| 166 | #define SVG_EDGES 2 |
| 167 | #define SVG_FACES 4 |
| 168 | |
| 169 | #define FACE_COLOUR "red" |
| 170 | #define EDGE_COLOUR "blue" |
| 171 | #define DOT_COLOUR "black" |
| 172 | |
| 173 | static void grid_output_svg(FILE *fp, grid *g, int which) |
| 174 | { |
| 175 | int i, j; |
| 176 | |
| 177 | fprintf(fp,"\ |
| 178 | <?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n\ |
| 179 | <!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 20010904//EN\"\n\ |
| 180 | \"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd\">\n\ |
| 181 | \n\ |
| 182 | <svg xmlns=\"http://www.w3.org/2000/svg\"\n\ |
| 183 | xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n\n"); |
| 184 | |
| 185 | if (which & SVG_FACES) { |
| 186 | fprintf(fp, "<g>\n"); |
| 187 | for (i = 0; i < g->num_faces; i++) { |
| 188 | grid_face *f = g->faces + i; |
| 189 | fprintf(fp, "<polygon points=\""); |
| 190 | for (j = 0; j < f->order; j++) { |
| 191 | grid_dot *d = f->dots[j]; |
| 192 | fprintf(fp, "%s%d,%d", (j == 0) ? "" : " ", |
| 193 | d->x, d->y); |
| 194 | } |
| 195 | fprintf(fp, "\" style=\"fill: %s; fill-opacity: 0.2; stroke: %s\" />\n", |
| 196 | FACE_COLOUR, FACE_COLOUR); |
| 197 | } |
| 198 | fprintf(fp, "</g>\n"); |
| 199 | } |
| 200 | if (which & SVG_EDGES) { |
| 201 | fprintf(fp, "<g>\n"); |
| 202 | for (i = 0; i < g->num_edges; i++) { |
| 203 | grid_edge *e = g->edges + i; |
| 204 | grid_dot *d1 = e->dot1, *d2 = e->dot2; |
| 205 | |
| 206 | fprintf(fp, "<line x1=\"%d\" y1=\"%d\" x2=\"%d\" y2=\"%d\" " |
| 207 | "style=\"stroke: %s\" />\n", |
| 208 | d1->x, d1->y, d2->x, d2->y, EDGE_COLOUR); |
| 209 | } |
| 210 | fprintf(fp, "</g>\n"); |
| 211 | } |
| 212 | |
| 213 | if (which & SVG_DOTS) { |
| 214 | fprintf(fp, "<g>\n"); |
| 215 | for (i = 0; i < g->num_dots; i++) { |
| 216 | grid_dot *d = g->dots + i; |
| 217 | fprintf(fp, "<ellipse cx=\"%d\" cy=\"%d\" rx=\"%d\" ry=\"%d\" fill=\"%s\" />", |
| 218 | d->x, d->y, g->tilesize/20, g->tilesize/20, DOT_COLOUR); |
| 219 | } |
| 220 | fprintf(fp, "</g>\n"); |
| 221 | } |
| 222 | |
| 223 | fprintf(fp, "</svg>\n"); |
| 224 | } |
| 225 | #endif |
| 226 | |
| 227 | #ifdef SVG_GRID |
| 228 | static void grid_try_svg(grid *g, int which) |
| 229 | { |
| 230 | char *svg = getenv("PUZZLES_SVG_GRID"); |
| 231 | if (svg) { |
| 232 | FILE *svgf = fopen(svg, "w"); |
| 233 | if (svgf) { |
| 234 | grid_output_svg(svgf, g, which); |
| 235 | fclose(svgf); |
| 236 | } else { |
| 237 | fprintf(stderr, "Unable to open file `%s': %s", svg, strerror(errno)); |
| 238 | } |
| 239 | } |
| 240 | } |
| 241 | #endif |
| 242 | |
| 7c95608a |
243 | /* Show the basic grid information, before doing grid_make_consistent */ |
| cebf0b0d |
244 | static void grid_debug_basic(grid *g) |
| 7c95608a |
245 | { |
| 246 | /* TODO: Maybe we should generate an SVG image of the dots and lines |
| 247 | * of the grid here, before grid_make_consistent. |
| 248 | * Would help with debugging grid generation. */ |
| cebf0b0d |
249 | #ifdef DEBUG_GRID |
| 7c95608a |
250 | int i; |
| 251 | printf("--- Basic Grid Data ---\n"); |
| 252 | for (i = 0; i < g->num_faces; i++) { |
| 253 | grid_face *f = g->faces + i; |
| 254 | printf("Face %d: dots[", i); |
| 255 | int j; |
| 256 | for (j = 0; j < f->order; j++) { |
| 257 | grid_dot *d = f->dots[j]; |
| 258 | printf("%s%d", j ? "," : "", (int)(d - g->dots)); |
| 259 | } |
| 260 | printf("]\n"); |
| 261 | } |
| cebf0b0d |
262 | #endif |
| 263 | #ifdef SVG_GRID |
| 264 | grid_try_svg(g, SVG_FACES); |
| 265 | #endif |
| 7c95608a |
266 | } |
| cebf0b0d |
267 | |
| 7c95608a |
268 | /* Show the derived grid information, computed by grid_make_consistent */ |
| cebf0b0d |
269 | static void grid_debug_derived(grid *g) |
| 7c95608a |
270 | { |
| cebf0b0d |
271 | #ifdef DEBUG_GRID |
| 7c95608a |
272 | /* edges */ |
| 273 | int i; |
| 274 | printf("--- Derived Grid Data ---\n"); |
| 275 | for (i = 0; i < g->num_edges; i++) { |
| 276 | grid_edge *e = g->edges + i; |
| 277 | printf("Edge %d: dots[%d,%d] faces[%d,%d]\n", |
| 278 | i, (int)(e->dot1 - g->dots), (int)(e->dot2 - g->dots), |
| 279 | e->face1 ? (int)(e->face1 - g->faces) : -1, |
| 280 | e->face2 ? (int)(e->face2 - g->faces) : -1); |
| 281 | } |
| 282 | /* faces */ |
| 283 | for (i = 0; i < g->num_faces; i++) { |
| 284 | grid_face *f = g->faces + i; |
| 285 | int j; |
| 286 | printf("Face %d: faces[", i); |
| 287 | for (j = 0; j < f->order; j++) { |
| 288 | grid_edge *e = f->edges[j]; |
| 289 | grid_face *f2 = (e->face1 == f) ? e->face2 : e->face1; |
| 290 | printf("%s%d", j ? "," : "", f2 ? (int)(f2 - g->faces) : -1); |
| 291 | } |
| 292 | printf("]\n"); |
| 293 | } |
| 294 | /* dots */ |
| 295 | for (i = 0; i < g->num_dots; i++) { |
| 296 | grid_dot *d = g->dots + i; |
| 297 | int j; |
| 298 | printf("Dot %d: dots[", i); |
| 299 | for (j = 0; j < d->order; j++) { |
| 300 | grid_edge *e = d->edges[j]; |
| 301 | grid_dot *d2 = (e->dot1 == d) ? e->dot2 : e->dot1; |
| 302 | printf("%s%d", j ? "," : "", (int)(d2 - g->dots)); |
| 303 | } |
| 304 | printf("] faces["); |
| 305 | for (j = 0; j < d->order; j++) { |
| 306 | grid_face *f = d->faces[j]; |
| 307 | printf("%s%d", j ? "," : "", f ? (int)(f - g->faces) : -1); |
| 308 | } |
| 309 | printf("]\n"); |
| 310 | } |
| cebf0b0d |
311 | #endif |
| 312 | #ifdef SVG_GRID |
| 313 | grid_try_svg(g, SVG_DOTS | SVG_EDGES | SVG_FACES); |
| 314 | #endif |
| 7c95608a |
315 | } |
| 7c95608a |
316 | |
| 317 | /* Helper function for building incomplete-edges list in |
| 318 | * grid_make_consistent() */ |
| 319 | static int grid_edge_bydots_cmpfn(void *v1, void *v2) |
| 320 | { |
| 321 | grid_edge *a = v1; |
| 322 | grid_edge *b = v2; |
| 323 | grid_dot *da, *db; |
| 324 | |
| 325 | /* Pointer subtraction is valid here, because all dots point into the |
| 326 | * same dot-list (g->dots). |
| 327 | * Edges are not "normalised" - the 2 dots could be stored in any order, |
| 328 | * so we need to take this into account when comparing edges. */ |
| 329 | |
| 330 | /* Compare first dots */ |
| 331 | da = (a->dot1 < a->dot2) ? a->dot1 : a->dot2; |
| 332 | db = (b->dot1 < b->dot2) ? b->dot1 : b->dot2; |
| 333 | if (da != db) |
| 334 | return db - da; |
| 335 | /* Compare last dots */ |
| 336 | da = (a->dot1 < a->dot2) ? a->dot2 : a->dot1; |
| 337 | db = (b->dot1 < b->dot2) ? b->dot2 : b->dot1; |
| 338 | if (da != db) |
| 339 | return db - da; |
| 340 | |
| 341 | return 0; |
| 342 | } |
| 343 | |
| cebf0b0d |
344 | /* |
| 345 | * 'Vigorously trim' a grid, by which I mean deleting any isolated or |
| 346 | * uninteresting faces. By which, in turn, I mean: ensure that the |
| 347 | * grid is composed solely of faces adjacent to at least one |
| 348 | * 'landlocked' dot (i.e. one not in contact with the infinite |
| 349 | * exterior face), and that all those dots are in a single connected |
| 350 | * component. |
| 351 | * |
| 352 | * This function operates on, and returns, a grid satisfying the |
| 353 | * preconditions to grid_make_consistent() rather than the |
| 354 | * postconditions. (So call it first.) |
| 355 | */ |
| 356 | static void grid_trim_vigorously(grid *g) |
| 357 | { |
| 358 | int *dotpairs, *faces, *dots; |
| 359 | int *dsf; |
| 360 | int i, j, k, size, newfaces, newdots; |
| 361 | |
| 362 | /* |
| 363 | * First construct a matrix in which each ordered pair of dots is |
| 364 | * mapped to the index of the face in which those dots occur in |
| 365 | * that order. |
| 366 | */ |
| 367 | dotpairs = snewn(g->num_dots * g->num_dots, int); |
| 368 | for (i = 0; i < g->num_dots; i++) |
| 369 | for (j = 0; j < g->num_dots; j++) |
| 370 | dotpairs[i*g->num_dots+j] = -1; |
| 371 | for (i = 0; i < g->num_faces; i++) { |
| 372 | grid_face *f = g->faces + i; |
| 373 | int dot0 = f->dots[f->order-1] - g->dots; |
| 374 | for (j = 0; j < f->order; j++) { |
| 375 | int dot1 = f->dots[j] - g->dots; |
| 376 | dotpairs[dot0 * g->num_dots + dot1] = i; |
| 377 | dot0 = dot1; |
| 378 | } |
| 379 | } |
| 380 | |
| 381 | /* |
| 382 | * Now we can identify landlocked dots: they're the ones all of |
| 383 | * whose edges have a mirror-image counterpart in this matrix. |
| 384 | */ |
| 385 | dots = snewn(g->num_dots, int); |
| 386 | for (i = 0; i < g->num_dots; i++) { |
| 387 | dots[i] = TRUE; |
| 388 | for (j = 0; j < g->num_dots; j++) { |
| 389 | if ((dotpairs[i*g->num_dots+j] >= 0) ^ |
| 390 | (dotpairs[j*g->num_dots+i] >= 0)) |
| 391 | dots[i] = FALSE; /* non-duplicated edge: coastal dot */ |
| 392 | } |
| 393 | } |
| 394 | |
| 395 | /* |
| 396 | * Now identify connected pairs of landlocked dots, and form a dsf |
| 397 | * unifying them. |
| 398 | */ |
| 399 | dsf = snew_dsf(g->num_dots); |
| 400 | for (i = 0; i < g->num_dots; i++) |
| 401 | for (j = 0; j < i; j++) |
| 402 | if (dots[i] && dots[j] && |
| 403 | dotpairs[i*g->num_dots+j] >= 0 && |
| 404 | dotpairs[j*g->num_dots+i] >= 0) |
| 405 | dsf_merge(dsf, i, j); |
| 406 | |
| 407 | /* |
| 408 | * Now look for the largest component. |
| 409 | */ |
| 410 | size = 0; |
| 411 | j = -1; |
| 412 | for (i = 0; i < g->num_dots; i++) { |
| 413 | int newsize; |
| 414 | if (dots[i] && dsf_canonify(dsf, i) == i && |
| 415 | (newsize = dsf_size(dsf, i)) > size) { |
| 416 | j = i; |
| 417 | size = newsize; |
| 418 | } |
| 419 | } |
| 420 | |
| 421 | /* |
| 422 | * Work out which faces we're going to keep (precisely those with |
| 423 | * at least one dot in the same connected component as j) and |
| 424 | * which dots (those required by any face we're keeping). |
| 425 | * |
| 426 | * At this point we reuse the 'dots' array to indicate the dots |
| 427 | * we're keeping, rather than the ones that are landlocked. |
| 428 | */ |
| 429 | faces = snewn(g->num_faces, int); |
| 430 | for (i = 0; i < g->num_faces; i++) |
| 431 | faces[i] = 0; |
| 432 | for (i = 0; i < g->num_dots; i++) |
| 433 | dots[i] = 0; |
| 434 | for (i = 0; i < g->num_faces; i++) { |
| 435 | grid_face *f = g->faces + i; |
| 436 | int keep = FALSE; |
| 437 | for (k = 0; k < f->order; k++) |
| 438 | if (dsf_canonify(dsf, f->dots[k] - g->dots) == j) |
| 439 | keep = TRUE; |
| 440 | if (keep) { |
| 441 | faces[i] = TRUE; |
| 442 | for (k = 0; k < f->order; k++) |
| 443 | dots[f->dots[k]-g->dots] = TRUE; |
| 444 | } |
| 445 | } |
| 446 | |
| 447 | /* |
| 448 | * Work out the new indices of those faces and dots, when we |
| 449 | * compact the arrays containing them. |
| 450 | */ |
| 451 | for (i = newfaces = 0; i < g->num_faces; i++) |
| 452 | faces[i] = (faces[i] ? newfaces++ : -1); |
| 453 | for (i = newdots = 0; i < g->num_dots; i++) |
| 454 | dots[i] = (dots[i] ? newdots++ : -1); |
| 455 | |
| 456 | /* |
| a6bd4b9c |
457 | * Free the dynamically allocated 'dots' pointer lists in faces |
| 458 | * we're going to discard. |
| 459 | */ |
| 460 | for (i = 0; i < g->num_faces; i++) |
| 461 | if (faces[i] < 0) |
| 462 | sfree(g->faces[i].dots); |
| 463 | |
| 464 | /* |
| cebf0b0d |
465 | * Go through and compact the arrays. |
| 466 | */ |
| 467 | for (i = 0; i < g->num_dots; i++) |
| 468 | if (dots[i] >= 0) { |
| 469 | grid_dot *dnew = g->dots + dots[i], *dold = g->dots + i; |
| 470 | *dnew = *dold; /* structure copy */ |
| 471 | } |
| 472 | for (i = 0; i < g->num_faces; i++) |
| 473 | if (faces[i] >= 0) { |
| 474 | grid_face *fnew = g->faces + faces[i], *fold = g->faces + i; |
| 475 | *fnew = *fold; /* structure copy */ |
| 476 | for (j = 0; j < fnew->order; j++) { |
| 477 | /* |
| 478 | * Reindex the dots in this face. |
| 479 | */ |
| 480 | k = fnew->dots[j] - g->dots; |
| 481 | fnew->dots[j] = g->dots + dots[k]; |
| 482 | } |
| 483 | } |
| 484 | g->num_faces = newfaces; |
| 485 | g->num_dots = newdots; |
| 486 | |
| 487 | sfree(dotpairs); |
| 488 | sfree(dsf); |
| 489 | sfree(dots); |
| 490 | sfree(faces); |
| 491 | } |
| 492 | |
| 7c95608a |
493 | /* Input: grid has its dots and faces initialised: |
| 494 | * - dots have (optionally) x and y coordinates, but no edges or faces |
| 495 | * (pointers are NULL). |
| 496 | * - edges not initialised at all |
| 497 | * - faces initialised and know which dots they have (but no edges yet). The |
| 498 | * dots around each face are assumed to be clockwise. |
| 499 | * |
| 500 | * Output: grid is complete and valid with all relationships defined. |
| 501 | */ |
| 502 | static void grid_make_consistent(grid *g) |
| 503 | { |
| 504 | int i; |
| 505 | tree234 *incomplete_edges; |
| 506 | grid_edge *next_new_edge; /* Where new edge will go into g->edges */ |
| 507 | |
| cebf0b0d |
508 | grid_debug_basic(g); |
| 7c95608a |
509 | |
| 510 | /* ====== Stage 1 ====== |
| 511 | * Generate edges |
| 512 | */ |
| 513 | |
| 514 | /* We know how many dots and faces there are, so we can find the exact |
| 515 | * number of edges from Euler's polyhedral formula: F + V = E + 2 . |
| 516 | * We use "-1", not "-2" here, because Euler's formula includes the |
| 517 | * infinite face, which we don't count. */ |
| 518 | g->num_edges = g->num_faces + g->num_dots - 1; |
| 519 | g->edges = snewn(g->num_edges, grid_edge); |
| 520 | next_new_edge = g->edges; |
| 521 | |
| 522 | /* Iterate over faces, and over each face's dots, generating edges as we |
| 523 | * go. As we find each new edge, we can immediately fill in the edge's |
| 524 | * dots, but only one of the edge's faces. Later on in the iteration, we |
| 525 | * will find the same edge again (unless it's on the border), but we will |
| 526 | * know the other face. |
| 527 | * For efficiency, maintain a list of the incomplete edges, sorted by |
| 528 | * their dots. */ |
| 529 | incomplete_edges = newtree234(grid_edge_bydots_cmpfn); |
| 530 | for (i = 0; i < g->num_faces; i++) { |
| 531 | grid_face *f = g->faces + i; |
| 532 | int j; |
| 533 | for (j = 0; j < f->order; j++) { |
| 534 | grid_edge e; /* fake edge for searching */ |
| 535 | grid_edge *edge_found; |
| 536 | int j2 = j + 1; |
| 537 | if (j2 == f->order) |
| 538 | j2 = 0; |
| 539 | e.dot1 = f->dots[j]; |
| 540 | e.dot2 = f->dots[j2]; |
| 541 | /* Use del234 instead of find234, because we always want to |
| 542 | * remove the edge if found */ |
| 543 | edge_found = del234(incomplete_edges, &e); |
| 544 | if (edge_found) { |
| 545 | /* This edge already added, so fill out missing face. |
| 546 | * Edge is already removed from incomplete_edges. */ |
| 547 | edge_found->face2 = f; |
| 548 | } else { |
| 549 | assert(next_new_edge - g->edges < g->num_edges); |
| 550 | next_new_edge->dot1 = e.dot1; |
| 551 | next_new_edge->dot2 = e.dot2; |
| 552 | next_new_edge->face1 = f; |
| 553 | next_new_edge->face2 = NULL; /* potentially infinite face */ |
| 554 | add234(incomplete_edges, next_new_edge); |
| 555 | ++next_new_edge; |
| 556 | } |
| 557 | } |
| 558 | } |
| 559 | freetree234(incomplete_edges); |
| 560 | |
| 561 | /* ====== Stage 2 ====== |
| 562 | * For each face, build its edge list. |
| 563 | */ |
| 564 | |
| 565 | /* Allocate space for each edge list. Can do this, because each face's |
| 566 | * edge-list is the same size as its dot-list. */ |
| 567 | for (i = 0; i < g->num_faces; i++) { |
| 568 | grid_face *f = g->faces + i; |
| 569 | int j; |
| 570 | f->edges = snewn(f->order, grid_edge*); |
| 571 | /* Preload with NULLs, to help detect potential bugs. */ |
| 572 | for (j = 0; j < f->order; j++) |
| 573 | f->edges[j] = NULL; |
| 574 | } |
| 575 | |
| 576 | /* Iterate over each edge, and over both its faces. Add this edge to |
| 577 | * the face's edge-list, after finding where it should go in the |
| 578 | * sequence. */ |
| 579 | for (i = 0; i < g->num_edges; i++) { |
| 580 | grid_edge *e = g->edges + i; |
| 581 | int j; |
| 582 | for (j = 0; j < 2; j++) { |
| 583 | grid_face *f = j ? e->face2 : e->face1; |
| 584 | int k, k2; |
| 585 | if (f == NULL) continue; |
| 586 | /* Find one of the dots around the face */ |
| 587 | for (k = 0; k < f->order; k++) { |
| 588 | if (f->dots[k] == e->dot1) |
| 589 | break; /* found dot1 */ |
| 590 | } |
| 591 | assert(k != f->order); /* Must find the dot around this face */ |
| 592 | |
| 593 | /* Labelling scheme: as we walk clockwise around the face, |
| 594 | * starting at dot0 (f->dots[0]), we hit: |
| 595 | * (dot0), edge0, dot1, edge1, dot2,... |
| 596 | * |
| 597 | * 0 |
| 598 | * 0-----1 |
| 599 | * | |
| 600 | * |1 |
| 601 | * | |
| 602 | * 3-----2 |
| 603 | * 2 |
| 604 | * |
| 605 | * Therefore, edgeK joins dotK and dot{K+1} |
| 606 | */ |
| 607 | |
| 608 | /* Around this face, either the next dot or the previous dot |
| 609 | * must be e->dot2. Otherwise the edge is wrong. */ |
| 610 | k2 = k + 1; |
| 611 | if (k2 == f->order) |
| 612 | k2 = 0; |
| 613 | if (f->dots[k2] == e->dot2) { |
| 614 | /* dot1(k) and dot2(k2) go clockwise around this face, so add |
| 615 | * this edge at position k (see diagram). */ |
| 616 | assert(f->edges[k] == NULL); |
| 617 | f->edges[k] = e; |
| 618 | continue; |
| 619 | } |
| 620 | /* Try previous dot */ |
| 621 | k2 = k - 1; |
| 622 | if (k2 == -1) |
| 623 | k2 = f->order - 1; |
| 624 | if (f->dots[k2] == e->dot2) { |
| 625 | /* dot1(k) and dot2(k2) go anticlockwise around this face. */ |
| 626 | assert(f->edges[k2] == NULL); |
| 627 | f->edges[k2] = e; |
| 628 | continue; |
| 629 | } |
| 630 | assert(!"Grid broken: bad edge-face relationship"); |
| 631 | } |
| 632 | } |
| 633 | |
| 634 | /* ====== Stage 3 ====== |
| 635 | * For each dot, build its edge-list and face-list. |
| 636 | */ |
| 637 | |
| 638 | /* We don't know how many edges/faces go around each dot, so we can't |
| 639 | * allocate the right space for these lists. Pre-compute the sizes by |
| 640 | * iterating over each edge and recording a tally against each dot. */ |
| 641 | for (i = 0; i < g->num_dots; i++) { |
| 642 | g->dots[i].order = 0; |
| 643 | } |
| 644 | for (i = 0; i < g->num_edges; i++) { |
| 645 | grid_edge *e = g->edges + i; |
| 646 | ++(e->dot1->order); |
| 647 | ++(e->dot2->order); |
| 648 | } |
| 649 | /* Now we have the sizes, pre-allocate the edge and face lists. */ |
| 650 | for (i = 0; i < g->num_dots; i++) { |
| 651 | grid_dot *d = g->dots + i; |
| 652 | int j; |
| 653 | assert(d->order >= 2); /* sanity check */ |
| 654 | d->edges = snewn(d->order, grid_edge*); |
| 655 | d->faces = snewn(d->order, grid_face*); |
| 656 | for (j = 0; j < d->order; j++) { |
| 657 | d->edges[j] = NULL; |
| 658 | d->faces[j] = NULL; |
| 659 | } |
| 660 | } |
| 661 | /* For each dot, need to find a face that touches it, so we can seed |
| 662 | * the edge-face-edge-face process around each dot. */ |
| 663 | for (i = 0; i < g->num_faces; i++) { |
| 664 | grid_face *f = g->faces + i; |
| 665 | int j; |
| 666 | for (j = 0; j < f->order; j++) { |
| 667 | grid_dot *d = f->dots[j]; |
| 668 | d->faces[0] = f; |
| 669 | } |
| 670 | } |
| 671 | /* Each dot now has a face in its first slot. Generate the remaining |
| 672 | * faces and edges around the dot, by searching both clockwise and |
| 673 | * anticlockwise from the first face. Need to do both directions, |
| 674 | * because of the possibility of hitting the infinite face, which |
| 675 | * blocks progress. But there's only one such face, so we will |
| 676 | * succeed in finding every edge and face this way. */ |
| 677 | for (i = 0; i < g->num_dots; i++) { |
| 678 | grid_dot *d = g->dots + i; |
| 679 | int current_face1 = 0; /* ascends clockwise */ |
| 680 | int current_face2 = 0; /* descends anticlockwise */ |
| 681 | |
| 682 | /* Labelling scheme: as we walk clockwise around the dot, starting |
| 683 | * at face0 (d->faces[0]), we hit: |
| 684 | * (face0), edge0, face1, edge1, face2,... |
| 685 | * |
| 686 | * 0 |
| 687 | * | |
| 688 | * 0 | 1 |
| 689 | * | |
| 690 | * -----d-----1 |
| 691 | * | |
| 692 | * | 2 |
| 693 | * | |
| 694 | * 2 |
| 695 | * |
| 696 | * So, for example, face1 should be joined to edge0 and edge1, |
| 697 | * and those edges should appear in an anticlockwise sense around |
| 698 | * that face (see diagram). */ |
| 699 | |
| 700 | /* clockwise search */ |
| 701 | while (TRUE) { |
| 702 | grid_face *f = d->faces[current_face1]; |
| 703 | grid_edge *e; |
| 704 | int j; |
| 705 | assert(f != NULL); |
| 706 | /* find dot around this face */ |
| 707 | for (j = 0; j < f->order; j++) { |
| 708 | if (f->dots[j] == d) |
| 709 | break; |
| 710 | } |
| 711 | assert(j != f->order); /* must find dot */ |
| 712 | |
| 713 | /* Around f, required edge is anticlockwise from the dot. See |
| 714 | * the other labelling scheme higher up, for why we subtract 1 |
| 715 | * from j. */ |
| 716 | j--; |
| 717 | if (j == -1) |
| 718 | j = f->order - 1; |
| 719 | e = f->edges[j]; |
| 720 | d->edges[current_face1] = e; /* set edge */ |
| 721 | current_face1++; |
| 722 | if (current_face1 == d->order) |
| 723 | break; |
| 724 | else { |
| 725 | /* set face */ |
| 726 | d->faces[current_face1] = |
| 727 | (e->face1 == f) ? e->face2 : e->face1; |
| 728 | if (d->faces[current_face1] == NULL) |
| 729 | break; /* cannot progress beyond infinite face */ |
| 730 | } |
| 731 | } |
| 732 | /* If the clockwise search made it all the way round, don't need to |
| 733 | * bother with the anticlockwise search. */ |
| 734 | if (current_face1 == d->order) |
| 735 | continue; /* this dot is complete, move on to next dot */ |
| 736 | |
| 737 | /* anticlockwise search */ |
| 738 | while (TRUE) { |
| 739 | grid_face *f = d->faces[current_face2]; |
| 740 | grid_edge *e; |
| 741 | int j; |
| 742 | assert(f != NULL); |
| 743 | /* find dot around this face */ |
| 744 | for (j = 0; j < f->order; j++) { |
| 745 | if (f->dots[j] == d) |
| 746 | break; |
| 747 | } |
| 748 | assert(j != f->order); /* must find dot */ |
| 749 | |
| 750 | /* Around f, required edge is clockwise from the dot. */ |
| 751 | e = f->edges[j]; |
| 752 | |
| 753 | current_face2--; |
| 754 | if (current_face2 == -1) |
| 755 | current_face2 = d->order - 1; |
| 756 | d->edges[current_face2] = e; /* set edge */ |
| 757 | |
| 758 | /* set face */ |
| 759 | if (current_face2 == current_face1) |
| 760 | break; |
| 761 | d->faces[current_face2] = |
| 762 | (e->face1 == f) ? e->face2 : e->face1; |
| 763 | /* There's only 1 infinite face, so we must get all the way |
| 764 | * to current_face1 before we hit it. */ |
| 765 | assert(d->faces[current_face2]); |
| 766 | } |
| 767 | } |
| 768 | |
| 769 | /* ====== Stage 4 ====== |
| 770 | * Compute other grid settings |
| 771 | */ |
| 772 | |
| 773 | /* Bounding rectangle */ |
| 774 | for (i = 0; i < g->num_dots; i++) { |
| 775 | grid_dot *d = g->dots + i; |
| 776 | if (i == 0) { |
| 777 | g->lowest_x = g->highest_x = d->x; |
| 778 | g->lowest_y = g->highest_y = d->y; |
| 779 | } else { |
| 780 | g->lowest_x = min(g->lowest_x, d->x); |
| 781 | g->highest_x = max(g->highest_x, d->x); |
| 782 | g->lowest_y = min(g->lowest_y, d->y); |
| 783 | g->highest_y = max(g->highest_y, d->y); |
| 784 | } |
| 785 | } |
| cebf0b0d |
786 | |
| 787 | grid_debug_derived(g); |
| 7c95608a |
788 | } |
| 789 | |
| 790 | /* Helpers for making grid-generation easier. These functions are only |
| 791 | * intended for use during grid generation. */ |
| 792 | |
| 793 | /* Comparison function for the (tree234) sorted dot list */ |
| 794 | static int grid_point_cmp_fn(void *v1, void *v2) |
| 795 | { |
| 796 | grid_dot *p1 = v1; |
| 797 | grid_dot *p2 = v2; |
| 798 | if (p1->y != p2->y) |
| 799 | return p2->y - p1->y; |
| 800 | else |
| 801 | return p2->x - p1->x; |
| 802 | } |
| 803 | /* Add a new face to the grid, with its dot list allocated. |
| 804 | * Assumes there's enough space allocated for the new face in grid->faces */ |
| 805 | static void grid_face_add_new(grid *g, int face_size) |
| 806 | { |
| 807 | int i; |
| 808 | grid_face *new_face = g->faces + g->num_faces; |
| 809 | new_face->order = face_size; |
| 810 | new_face->dots = snewn(face_size, grid_dot*); |
| 811 | for (i = 0; i < face_size; i++) |
| 812 | new_face->dots[i] = NULL; |
| 813 | new_face->edges = NULL; |
| a10bec21 |
814 | new_face->has_incentre = FALSE; |
| 7c95608a |
815 | g->num_faces++; |
| 816 | } |
| 817 | /* Assumes dot list has enough space */ |
| 818 | static grid_dot *grid_dot_add_new(grid *g, int x, int y) |
| 819 | { |
| 820 | grid_dot *new_dot = g->dots + g->num_dots; |
| 821 | new_dot->order = 0; |
| 822 | new_dot->edges = NULL; |
| 823 | new_dot->faces = NULL; |
| 824 | new_dot->x = x; |
| 825 | new_dot->y = y; |
| 826 | g->num_dots++; |
| 827 | return new_dot; |
| 828 | } |
| 829 | /* Retrieve a dot with these (x,y) coordinates. Either return an existing dot |
| 830 | * in the dot_list, or add a new dot to the grid (and the dot_list) and |
| 831 | * return that. |
| 832 | * Assumes g->dots has enough capacity allocated */ |
| 833 | static grid_dot *grid_get_dot(grid *g, tree234 *dot_list, int x, int y) |
| 834 | { |
| 3466f373 |
835 | grid_dot test, *ret; |
| 836 | |
| 837 | test.order = 0; |
| 838 | test.edges = NULL; |
| 839 | test.faces = NULL; |
| 840 | test.x = x; |
| 841 | test.y = y; |
| 842 | ret = find234(dot_list, &test, NULL); |
| 7c95608a |
843 | if (ret) |
| 844 | return ret; |
| 845 | |
| 846 | ret = grid_dot_add_new(g, x, y); |
| 847 | add234(dot_list, ret); |
| 848 | return ret; |
| 849 | } |
| 850 | |
| 851 | /* Sets the last face of the grid to include this dot, at this position |
| 852 | * around the face. Assumes num_faces is at least 1 (a new face has |
| 853 | * previously been added, with the required number of dots allocated) */ |
| 854 | static void grid_face_set_dot(grid *g, grid_dot *d, int position) |
| 855 | { |
| 856 | grid_face *last_face = g->faces + g->num_faces - 1; |
| 857 | last_face->dots[position] = d; |
| 858 | } |
| 859 | |
| e64991db |
860 | /* |
| 861 | * Helper routines for grid_find_incentre. |
| 862 | */ |
| 863 | static int solve_2x2_matrix(double mx[4], double vin[2], double vout[2]) |
| 864 | { |
| 865 | double inv[4]; |
| 866 | double det; |
| 867 | det = (mx[0]*mx[3] - mx[1]*mx[2]); |
| 868 | if (det == 0) |
| 869 | return FALSE; |
| 870 | |
| 871 | inv[0] = mx[3] / det; |
| 872 | inv[1] = -mx[1] / det; |
| 873 | inv[2] = -mx[2] / det; |
| 874 | inv[3] = mx[0] / det; |
| 875 | |
| 876 | vout[0] = inv[0]*vin[0] + inv[1]*vin[1]; |
| 877 | vout[1] = inv[2]*vin[0] + inv[3]*vin[1]; |
| 878 | |
| 879 | return TRUE; |
| 880 | } |
| 881 | static int solve_3x3_matrix(double mx[9], double vin[3], double vout[3]) |
| 882 | { |
| 883 | double inv[9]; |
| 884 | double det; |
| 885 | |
| 886 | det = (mx[0]*mx[4]*mx[8] + mx[1]*mx[5]*mx[6] + mx[2]*mx[3]*mx[7] - |
| 887 | mx[0]*mx[5]*mx[7] - mx[1]*mx[3]*mx[8] - mx[2]*mx[4]*mx[6]); |
| 888 | if (det == 0) |
| 889 | return FALSE; |
| 890 | |
| 891 | inv[0] = (mx[4]*mx[8] - mx[5]*mx[7]) / det; |
| 892 | inv[1] = (mx[2]*mx[7] - mx[1]*mx[8]) / det; |
| 893 | inv[2] = (mx[1]*mx[5] - mx[2]*mx[4]) / det; |
| 894 | inv[3] = (mx[5]*mx[6] - mx[3]*mx[8]) / det; |
| 895 | inv[4] = (mx[0]*mx[8] - mx[2]*mx[6]) / det; |
| 896 | inv[5] = (mx[2]*mx[3] - mx[0]*mx[5]) / det; |
| 897 | inv[6] = (mx[3]*mx[7] - mx[4]*mx[6]) / det; |
| 898 | inv[7] = (mx[1]*mx[6] - mx[0]*mx[7]) / det; |
| 899 | inv[8] = (mx[0]*mx[4] - mx[1]*mx[3]) / det; |
| 900 | |
| 901 | vout[0] = inv[0]*vin[0] + inv[1]*vin[1] + inv[2]*vin[2]; |
| 902 | vout[1] = inv[3]*vin[0] + inv[4]*vin[1] + inv[5]*vin[2]; |
| 903 | vout[2] = inv[6]*vin[0] + inv[7]*vin[1] + inv[8]*vin[2]; |
| 904 | |
| 905 | return TRUE; |
| 906 | } |
| 907 | |
| 908 | void grid_find_incentre(grid_face *f) |
| 909 | { |
| 910 | double xbest, ybest, bestdist; |
| 911 | int i, j, k, m; |
| 912 | grid_dot *edgedot1[3], *edgedot2[3]; |
| 913 | grid_dot *dots[3]; |
| 914 | int nedges, ndots; |
| 915 | |
| 916 | if (f->has_incentre) |
| 917 | return; |
| 918 | |
| 919 | /* |
| 920 | * Find the point in the polygon with the maximum distance to any |
| 921 | * edge or corner. |
| 922 | * |
| 923 | * Such a point must exist which is in contact with at least three |
| 924 | * edges and/or vertices. (Proof: if it's only in contact with two |
| 925 | * edges and/or vertices, it can't even be at a _local_ maximum - |
| 926 | * any such circle can always be expanded in some direction.) So |
| 927 | * we iterate through all 3-subsets of the combined set of edges |
| 928 | * and vertices; for each subset we generate one or two candidate |
| 929 | * points that might be the incentre, and then we vet each one to |
| 930 | * see if it's inside the polygon and what its maximum radius is. |
| 931 | * |
| 932 | * (There's one case which this algorithm will get noticeably |
| 933 | * wrong, and that's when a continuum of equally good answers |
| 934 | * exists due to parallel edges. Consider a long thin rectangle, |
| 935 | * for instance, or a parallelogram. This algorithm will pick a |
| 936 | * point near one end, and choose the end arbitrarily; obviously a |
| 937 | * nicer point to choose would be in the centre. To fix this I |
| 938 | * would have to introduce a special-case system which detected |
| 939 | * parallel edges in advance, set aside all candidate points |
| 940 | * generated using both edges in a parallel pair, and generated |
| 941 | * some additional candidate points half way between them. Also, |
| 942 | * of course, I'd have to cope with rounding error making such a |
| 943 | * point look worse than one of its endpoints. So I haven't done |
| 944 | * this for the moment, and will cross it if necessary when I come |
| 945 | * to it.) |
| 946 | * |
| 947 | * We don't actually iterate literally over _edges_, in the sense |
| 948 | * of grid_edge structures. Instead, we fill in edgedot1[] and |
| 949 | * edgedot2[] with a pair of dots adjacent in the face's list of |
| 950 | * vertices. This ensures that we get the edges in consistent |
| 951 | * orientation, which we could not do from the grid structure |
| 952 | * alone. (A moment's consideration of an order-3 vertex should |
| 953 | * make it clear that if a notional arrow was written on each |
| 954 | * edge, _at least one_ of the three faces bordering that vertex |
| 955 | * would have to have the two arrows tip-to-tip or tail-to-tail |
| 956 | * rather than tip-to-tail.) |
| 957 | */ |
| 958 | nedges = ndots = 0; |
| 959 | bestdist = 0; |
| 960 | xbest = ybest = 0; |
| 961 | |
| 962 | for (i = 0; i+2 < 2*f->order; i++) { |
| 963 | if (i < f->order) { |
| 964 | edgedot1[nedges] = f->dots[i]; |
| 965 | edgedot2[nedges++] = f->dots[(i+1)%f->order]; |
| 966 | } else |
| 967 | dots[ndots++] = f->dots[i - f->order]; |
| 968 | |
| 969 | for (j = i+1; j+1 < 2*f->order; j++) { |
| 970 | if (j < f->order) { |
| 971 | edgedot1[nedges] = f->dots[j]; |
| 972 | edgedot2[nedges++] = f->dots[(j+1)%f->order]; |
| 973 | } else |
| 974 | dots[ndots++] = f->dots[j - f->order]; |
| 975 | |
| 976 | for (k = j+1; k < 2*f->order; k++) { |
| 977 | double cx[2], cy[2]; /* candidate positions */ |
| 978 | int cn = 0; /* number of candidates */ |
| 979 | |
| 980 | if (k < f->order) { |
| 981 | edgedot1[nedges] = f->dots[k]; |
| 982 | edgedot2[nedges++] = f->dots[(k+1)%f->order]; |
| 983 | } else |
| 984 | dots[ndots++] = f->dots[k - f->order]; |
| 985 | |
| 986 | /* |
| 987 | * Find a point, or pair of points, equidistant from |
| 988 | * all the specified edges and/or vertices. |
| 989 | */ |
| 990 | if (nedges == 3) { |
| 991 | /* |
| 992 | * Three edges. This is a linear matrix equation: |
| 993 | * each row of the matrix represents the fact that |
| 994 | * the point (x,y) we seek is at distance r from |
| 995 | * that edge, and we solve three of those |
| 996 | * simultaneously to obtain x,y,r. (We ignore r.) |
| 997 | */ |
| 998 | double matrix[9], vector[3], vector2[3]; |
| 999 | int m; |
| 1000 | |
| 1001 | for (m = 0; m < 3; m++) { |
| 1002 | int x1 = edgedot1[m]->x, x2 = edgedot2[m]->x; |
| 1003 | int y1 = edgedot1[m]->y, y2 = edgedot2[m]->y; |
| 1004 | int dx = x2-x1, dy = y2-y1; |
| 1005 | |
| 1006 | /* |
| 1007 | * ((x,y) - (x1,y1)) . (dy,-dx) = r |(dx,dy)| |
| 1008 | * |
| 1009 | * => x dy - y dx - r |(dx,dy)| = (x1 dy - y1 dx) |
| 1010 | */ |
| 1011 | matrix[3*m+0] = dy; |
| 1012 | matrix[3*m+1] = -dx; |
| 1013 | matrix[3*m+2] = -sqrt((double)dx*dx+(double)dy*dy); |
| 1014 | vector[m] = (double)x1*dy - (double)y1*dx; |
| 1015 | } |
| 1016 | |
| 1017 | if (solve_3x3_matrix(matrix, vector, vector2)) { |
| 1018 | cx[cn] = vector2[0]; |
| 1019 | cy[cn] = vector2[1]; |
| 1020 | cn++; |
| 1021 | } |
| 1022 | } else if (nedges == 2) { |
| 1023 | /* |
| 1024 | * Two edges and a dot. This will end up in a |
| 1025 | * quadratic equation. |
| 1026 | * |
| 1027 | * First, look at the two edges. Having our point |
| 1028 | * be some distance r from both of them gives rise |
| 1029 | * to a pair of linear equations in x,y,r of the |
| 1030 | * form |
| 1031 | * |
| 1032 | * (x-x1) dy - (y-y1) dx = r sqrt(dx^2+dy^2) |
| 1033 | * |
| 1034 | * We eliminate r between those equations to give |
| 1035 | * us a single linear equation in x,y describing |
| 1036 | * the locus of points equidistant from both lines |
| 1037 | * - i.e. the angle bisector. |
| 1038 | * |
| 1039 | * We then choose one of x,y to be a parameter t, |
| 1040 | * and derive linear formulae for x,y,r in terms |
| 1041 | * of t. This enables us to write down the |
| 1042 | * circular equation (x-xd)^2+(y-yd)^2=r^2 as a |
| 1043 | * quadratic in t; solving that and substituting |
| 1044 | * in for x,y gives us two candidate points. |
| 1045 | */ |
| 1046 | double eqs[2][4]; /* a,b,c,d : ax+by+cr=d */ |
| 1047 | double eq[3]; /* a,b,c: ax+by=c */ |
| 1048 | double xt[2], yt[2], rt[2]; /* a,b: {x,y,r}=at+b */ |
| 1049 | double q[3]; /* a,b,c: at^2+bt+c=0 */ |
| 1050 | double disc; |
| 1051 | |
| 1052 | /* Find equations of the two input lines. */ |
| 1053 | for (m = 0; m < 2; m++) { |
| 1054 | int x1 = edgedot1[m]->x, x2 = edgedot2[m]->x; |
| 1055 | int y1 = edgedot1[m]->y, y2 = edgedot2[m]->y; |
| 1056 | int dx = x2-x1, dy = y2-y1; |
| 1057 | |
| 1058 | eqs[m][0] = dy; |
| 1059 | eqs[m][1] = -dx; |
| 1060 | eqs[m][2] = -sqrt(dx*dx+dy*dy); |
| 1061 | eqs[m][3] = x1*dy - y1*dx; |
| 1062 | } |
| 1063 | |
| 1064 | /* Derive the angle bisector by eliminating r. */ |
| 1065 | eq[0] = eqs[0][0]*eqs[1][2] - eqs[1][0]*eqs[0][2]; |
| 1066 | eq[1] = eqs[0][1]*eqs[1][2] - eqs[1][1]*eqs[0][2]; |
| 1067 | eq[2] = eqs[0][3]*eqs[1][2] - eqs[1][3]*eqs[0][2]; |
| 1068 | |
| 1069 | /* Parametrise x and y in terms of some t. */ |
| 1070 | if (abs(eq[0]) < abs(eq[1])) { |
| 1071 | /* Parameter is x. */ |
| 1072 | xt[0] = 1; xt[1] = 0; |
| 1073 | yt[0] = -eq[0]/eq[1]; yt[1] = eq[2]/eq[1]; |
| 1074 | } else { |
| 1075 | /* Parameter is y. */ |
| 1076 | yt[0] = 1; yt[1] = 0; |
| 1077 | xt[0] = -eq[1]/eq[0]; xt[1] = eq[2]/eq[0]; |
| 1078 | } |
| 1079 | |
| 1080 | /* Find a linear representation of r using eqs[0]. */ |
| 1081 | rt[0] = -(eqs[0][0]*xt[0] + eqs[0][1]*yt[0])/eqs[0][2]; |
| 1082 | rt[1] = (eqs[0][3] - eqs[0][0]*xt[1] - |
| 1083 | eqs[0][1]*yt[1])/eqs[0][2]; |
| 1084 | |
| 1085 | /* Construct the quadratic equation. */ |
| 1086 | q[0] = -rt[0]*rt[0]; |
| 1087 | q[1] = -2*rt[0]*rt[1]; |
| 1088 | q[2] = -rt[1]*rt[1]; |
| 1089 | q[0] += xt[0]*xt[0]; |
| 1090 | q[1] += 2*xt[0]*(xt[1]-dots[0]->x); |
| 1091 | q[2] += (xt[1]-dots[0]->x)*(xt[1]-dots[0]->x); |
| 1092 | q[0] += yt[0]*yt[0]; |
| 1093 | q[1] += 2*yt[0]*(yt[1]-dots[0]->y); |
| 1094 | q[2] += (yt[1]-dots[0]->y)*(yt[1]-dots[0]->y); |
| 1095 | |
| 1096 | /* And solve it. */ |
| 1097 | disc = q[1]*q[1] - 4*q[0]*q[2]; |
| 1098 | if (disc >= 0) { |
| 1099 | double t; |
| 1100 | |
| 1101 | disc = sqrt(disc); |
| 1102 | |
| 1103 | t = (-q[1] + disc) / (2*q[0]); |
| 1104 | cx[cn] = xt[0]*t + xt[1]; |
| 1105 | cy[cn] = yt[0]*t + yt[1]; |
| 1106 | cn++; |
| 1107 | |
| 1108 | t = (-q[1] - disc) / (2*q[0]); |
| 1109 | cx[cn] = xt[0]*t + xt[1]; |
| 1110 | cy[cn] = yt[0]*t + yt[1]; |
| 1111 | cn++; |
| 1112 | } |
| 1113 | } else if (nedges == 1) { |
| 1114 | /* |
| 1115 | * Two dots and an edge. This one's another |
| 1116 | * quadratic equation. |
| 1117 | * |
| 1118 | * The point we want must lie on the perpendicular |
| 1119 | * bisector of the two dots; that much is obvious. |
| 1120 | * So we can construct a parametrisation of that |
| 1121 | * bisecting line, giving linear formulae for x,y |
| 1122 | * in terms of t. We can also express the distance |
| 1123 | * from the edge as such a linear formula. |
| 1124 | * |
| 1125 | * Then we set that equal to the radius of the |
| 1126 | * circle passing through the two points, which is |
| 1127 | * a Pythagoras exercise; that gives rise to a |
| 1128 | * quadratic in t, which we solve. |
| 1129 | */ |
| 1130 | double xt[2], yt[2], rt[2]; /* a,b: {x,y,r}=at+b */ |
| 1131 | double q[3]; /* a,b,c: at^2+bt+c=0 */ |
| 1132 | double disc; |
| 1133 | double halfsep; |
| 1134 | |
| 1135 | /* Find parametric formulae for x,y. */ |
| 1136 | { |
| 1137 | int x1 = dots[0]->x, x2 = dots[1]->x; |
| 1138 | int y1 = dots[0]->y, y2 = dots[1]->y; |
| 1139 | int dx = x2-x1, dy = y2-y1; |
| 1140 | double d = sqrt((double)dx*dx + (double)dy*dy); |
| 1141 | |
| 1142 | xt[1] = (x1+x2)/2.0; |
| 1143 | yt[1] = (y1+y2)/2.0; |
| 1144 | /* It's convenient if we have t at standard scale. */ |
| 1145 | xt[0] = -dy/d; |
| 1146 | yt[0] = dx/d; |
| 1147 | |
| 1148 | /* Also note down half the separation between |
| 1149 | * the dots, for use in computing the circle radius. */ |
| 1150 | halfsep = 0.5*d; |
| 1151 | } |
| 1152 | |
| 1153 | /* Find a parametric formula for r. */ |
| 1154 | { |
| 1155 | int x1 = edgedot1[0]->x, x2 = edgedot2[0]->x; |
| 1156 | int y1 = edgedot1[0]->y, y2 = edgedot2[0]->y; |
| 1157 | int dx = x2-x1, dy = y2-y1; |
| 1158 | double d = sqrt((double)dx*dx + (double)dy*dy); |
| 1159 | rt[0] = (xt[0]*dy - yt[0]*dx) / d; |
| 1160 | rt[1] = ((xt[1]-x1)*dy - (yt[1]-y1)*dx) / d; |
| 1161 | } |
| 1162 | |
| 1163 | /* Construct the quadratic equation. */ |
| 1164 | q[0] = rt[0]*rt[0]; |
| 1165 | q[1] = 2*rt[0]*rt[1]; |
| 1166 | q[2] = rt[1]*rt[1]; |
| 1167 | q[0] -= 1; |
| 1168 | q[2] -= halfsep*halfsep; |
| 1169 | |
| 1170 | /* And solve it. */ |
| 1171 | disc = q[1]*q[1] - 4*q[0]*q[2]; |
| 1172 | if (disc >= 0) { |
| 1173 | double t; |
| 1174 | |
| 1175 | disc = sqrt(disc); |
| 1176 | |
| 1177 | t = (-q[1] + disc) / (2*q[0]); |
| 1178 | cx[cn] = xt[0]*t + xt[1]; |
| 1179 | cy[cn] = yt[0]*t + yt[1]; |
| 1180 | cn++; |
| 1181 | |
| 1182 | t = (-q[1] - disc) / (2*q[0]); |
| 1183 | cx[cn] = xt[0]*t + xt[1]; |
| 1184 | cy[cn] = yt[0]*t + yt[1]; |
| 1185 | cn++; |
| 1186 | } |
| 1187 | } else if (nedges == 0) { |
| 1188 | /* |
| 1189 | * Three dots. This is another linear matrix |
| 1190 | * equation, this time with each row of the matrix |
| 1191 | * representing the perpendicular bisector between |
| 1192 | * two of the points. Of course we only need two |
| 1193 | * such lines to find their intersection, so we |
| 1194 | * need only solve a 2x2 matrix equation. |
| 1195 | */ |
| 1196 | |
| 1197 | double matrix[4], vector[2], vector2[2]; |
| 1198 | int m; |
| 1199 | |
| 1200 | for (m = 0; m < 2; m++) { |
| 1201 | int x1 = dots[m]->x, x2 = dots[m+1]->x; |
| 1202 | int y1 = dots[m]->y, y2 = dots[m+1]->y; |
| 1203 | int dx = x2-x1, dy = y2-y1; |
| 1204 | |
| 1205 | /* |
| 1206 | * ((x,y) - (x1,y1)) . (dx,dy) = 1/2 |(dx,dy)|^2 |
| 1207 | * |
| 1208 | * => 2x dx + 2y dy = dx^2+dy^2 + (2 x1 dx + 2 y1 dy) |
| 1209 | */ |
| 1210 | matrix[2*m+0] = 2*dx; |
| 1211 | matrix[2*m+1] = 2*dy; |
| 1212 | vector[m] = ((double)dx*dx + (double)dy*dy + |
| 1213 | 2.0*x1*dx + 2.0*y1*dy); |
| 1214 | } |
| 1215 | |
| 1216 | if (solve_2x2_matrix(matrix, vector, vector2)) { |
| 1217 | cx[cn] = vector2[0]; |
| 1218 | cy[cn] = vector2[1]; |
| 1219 | cn++; |
| 1220 | } |
| 1221 | } |
| 1222 | |
| 1223 | /* |
| 1224 | * Now go through our candidate points and see if any |
| 1225 | * of them are better than what we've got so far. |
| 1226 | */ |
| 1227 | for (m = 0; m < cn; m++) { |
| 1228 | double x = cx[m], y = cy[m]; |
| 1229 | |
| 1230 | /* |
| 1231 | * First, disqualify the point if it's not inside |
| 1232 | * the polygon, which we work out by counting the |
| 1233 | * edges to the right of the point. (For |
| 1234 | * tiebreaking purposes when edges start or end on |
| 1235 | * our y-coordinate or go right through it, we |
| 1236 | * consider our point to be offset by a small |
| 1237 | * _positive_ epsilon in both the x- and |
| 1238 | * y-direction.) |
| 1239 | */ |
| 1240 | int e, in = 0; |
| 1241 | for (e = 0; e < f->order; e++) { |
| 1242 | int xs = f->edges[e]->dot1->x; |
| 1243 | int xe = f->edges[e]->dot2->x; |
| 1244 | int ys = f->edges[e]->dot1->y; |
| 1245 | int ye = f->edges[e]->dot2->y; |
| 1246 | if ((y >= ys && y < ye) || (y >= ye && y < ys)) { |
| 1247 | /* |
| 1248 | * The line goes past our y-position. Now we need |
| 1249 | * to know if its x-coordinate when it does so is |
| 1250 | * to our right. |
| 1251 | * |
| 1252 | * The x-coordinate in question is mathematically |
| 1253 | * (y - ys) * (xe - xs) / (ye - ys), and we want |
| 1254 | * to know whether (x - xs) >= that. Of course we |
| 1255 | * avoid the division, so we can work in integers; |
| 1256 | * to do this we must multiply both sides of the |
| 1257 | * inequality by ye - ys, which means we must |
| 1258 | * first check that's not negative. |
| 1259 | */ |
| 1260 | int num = xe - xs, denom = ye - ys; |
| 1261 | if (denom < 0) { |
| 1262 | num = -num; |
| 1263 | denom = -denom; |
| 1264 | } |
| 1265 | if ((x - xs) * denom >= (y - ys) * num) |
| 1266 | in ^= 1; |
| 1267 | } |
| 1268 | } |
| 1269 | |
| 1270 | if (in) { |
| 1271 | double mindist = HUGE_VAL; |
| 1272 | int e, d; |
| 1273 | |
| 1274 | /* |
| 1275 | * This point is inside the polygon, so now we check |
| 1276 | * its minimum distance to every edge and corner. |
| 1277 | * First the corners ... |
| 1278 | */ |
| 1279 | for (d = 0; d < f->order; d++) { |
| 1280 | int xp = f->dots[d]->x; |
| 1281 | int yp = f->dots[d]->y; |
| 1282 | double dx = x - xp, dy = y - yp; |
| 1283 | double dist = dx*dx + dy*dy; |
| 1284 | if (mindist > dist) |
| 1285 | mindist = dist; |
| 1286 | } |
| 1287 | |
| 1288 | /* |
| 1289 | * ... and now also check the perpendicular distance |
| 1290 | * to every edge, if the perpendicular lies between |
| 1291 | * the edge's endpoints. |
| 1292 | */ |
| 1293 | for (e = 0; e < f->order; e++) { |
| 1294 | int xs = f->edges[e]->dot1->x; |
| 1295 | int xe = f->edges[e]->dot2->x; |
| 1296 | int ys = f->edges[e]->dot1->y; |
| 1297 | int ye = f->edges[e]->dot2->y; |
| 1298 | |
| 1299 | /* |
| 1300 | * If s and e are our endpoints, and p our |
| 1301 | * candidate circle centre, the foot of a |
| 1302 | * perpendicular from p to the line se lies |
| 1303 | * between s and e if and only if (p-s).(e-s) lies |
| 1304 | * strictly between 0 and (e-s).(e-s). |
| 1305 | */ |
| 1306 | int edx = xe - xs, edy = ye - ys; |
| 1307 | double pdx = x - xs, pdy = y - ys; |
| 1308 | double pde = pdx * edx + pdy * edy; |
| 1309 | long ede = (long)edx * edx + (long)edy * edy; |
| 1310 | if (0 < pde && pde < ede) { |
| 1311 | /* |
| 1312 | * Yes, the nearest point on this edge is |
| 1313 | * closer than either endpoint, so we must |
| 1314 | * take it into account by measuring the |
| 1315 | * perpendicular distance to the edge and |
| 1316 | * checking its square against mindist. |
| 1317 | */ |
| 1318 | |
| 1319 | double pdre = pdx * edy - pdy * edx; |
| 1320 | double sqlen = pdre * pdre / ede; |
| 1321 | |
| 1322 | if (mindist > sqlen) |
| 1323 | mindist = sqlen; |
| 1324 | } |
| 1325 | } |
| 1326 | |
| 1327 | /* |
| 1328 | * Right. Now we know the biggest circle around this |
| 1329 | * point, so we can check it against bestdist. |
| 1330 | */ |
| 1331 | if (bestdist < mindist) { |
| 1332 | bestdist = mindist; |
| 1333 | xbest = x; |
| 1334 | ybest = y; |
| 1335 | } |
| 1336 | } |
| 1337 | } |
| 1338 | |
| 1339 | if (k < f->order) |
| 1340 | nedges--; |
| 1341 | else |
| 1342 | ndots--; |
| 1343 | } |
| 1344 | if (j < f->order) |
| 1345 | nedges--; |
| 1346 | else |
| 1347 | ndots--; |
| 1348 | } |
| 1349 | if (i < f->order) |
| 1350 | nedges--; |
| 1351 | else |
| 1352 | ndots--; |
| 1353 | } |
| 1354 | |
| 1355 | assert(bestdist > 0); |
| 1356 | |
| 1357 | f->has_incentre = TRUE; |
| 1358 | f->ix = xbest + 0.5; /* round to nearest */ |
| 1359 | f->iy = ybest + 0.5; |
| 1360 | } |
| 1361 | |
| 7c95608a |
1362 | /* ------ Generate various types of grid ------ */ |
| 1363 | |
| 1364 | /* General method is to generate faces, by calculating their dot coordinates. |
| 1365 | * As new faces are added, we keep track of all the dots so we can tell when |
| 1366 | * a new face reuses an existing dot. For example, two squares touching at an |
| 1367 | * edge would generate six unique dots: four dots from the first face, then |
| 1368 | * two additional dots for the second face, because we detect the other two |
| 1369 | * dots have already been taken up. This list is stored in a tree234 |
| 1370 | * called "points". No extra memory-allocation needed here - we store the |
| 1371 | * actual grid_dot* pointers, which all point into the g->dots list. |
| 1372 | * For this reason, we have to calculate coordinates in such a way as to |
| 1373 | * eliminate any rounding errors, so we can detect when a dot on one |
| 1374 | * face precisely lands on a dot of a different face. No floating-point |
| 1375 | * arithmetic here! |
| 1376 | */ |
| 1377 | |
| cebf0b0d |
1378 | #define SQUARE_TILESIZE 20 |
| 1379 | |
| 1380 | void grid_size_square(int width, int height, |
| 1381 | int *tilesize, int *xextent, int *yextent) |
| 1382 | { |
| 1383 | int a = SQUARE_TILESIZE; |
| 1384 | |
| 1385 | *tilesize = a; |
| 1386 | *xextent = width * a; |
| 1387 | *yextent = height * a; |
| 1388 | } |
| 1389 | |
| 1390 | grid *grid_new_square(int width, int height, char *desc) |
| 7c95608a |
1391 | { |
| 1392 | int x, y; |
| 1393 | /* Side length */ |
| cebf0b0d |
1394 | int a = SQUARE_TILESIZE; |
| 7c95608a |
1395 | |
| 1396 | /* Upper bounds - don't have to be exact */ |
| 1397 | int max_faces = width * height; |
| 1398 | int max_dots = (width + 1) * (height + 1); |
| 1399 | |
| 1400 | tree234 *points; |
| 1401 | |
| cebf0b0d |
1402 | grid *g = grid_empty(); |
| 7c95608a |
1403 | g->tilesize = a; |
| 1404 | g->faces = snewn(max_faces, grid_face); |
| 1405 | g->dots = snewn(max_dots, grid_dot); |
| 1406 | |
| 1407 | points = newtree234(grid_point_cmp_fn); |
| 1408 | |
| 1409 | /* generate square faces */ |
| 1410 | for (y = 0; y < height; y++) { |
| 1411 | for (x = 0; x < width; x++) { |
| 1412 | grid_dot *d; |
| 1413 | /* face position */ |
| 1414 | int px = a * x; |
| 1415 | int py = a * y; |
| 1416 | |
| 1417 | grid_face_add_new(g, 4); |
| 1418 | d = grid_get_dot(g, points, px, py); |
| 1419 | grid_face_set_dot(g, d, 0); |
| 1420 | d = grid_get_dot(g, points, px + a, py); |
| 1421 | grid_face_set_dot(g, d, 1); |
| 1422 | d = grid_get_dot(g, points, px + a, py + a); |
| 1423 | grid_face_set_dot(g, d, 2); |
| 1424 | d = grid_get_dot(g, points, px, py + a); |
| 1425 | grid_face_set_dot(g, d, 3); |
| 1426 | } |
| 1427 | } |
| 1428 | |
| 1429 | freetree234(points); |
| 1430 | assert(g->num_faces <= max_faces); |
| 1431 | assert(g->num_dots <= max_dots); |
| 7c95608a |
1432 | |
| 1433 | grid_make_consistent(g); |
| 1434 | return g; |
| 1435 | } |
| 1436 | |
| cebf0b0d |
1437 | #define HONEY_TILESIZE 45 |
| 1438 | /* Vector for side of hexagon - ratio is close to sqrt(3) */ |
| 1439 | #define HONEY_A 15 |
| 1440 | #define HONEY_B 26 |
| 1441 | |
| 1442 | void grid_size_honeycomb(int width, int height, |
| 1443 | int *tilesize, int *xextent, int *yextent) |
| 1444 | { |
| 1445 | int a = HONEY_A; |
| 1446 | int b = HONEY_B; |
| 1447 | |
| 1448 | *tilesize = HONEY_TILESIZE; |
| 1449 | *xextent = (3 * a * (width-1)) + 4*a; |
| 1450 | *yextent = (2 * b * (height-1)) + 3*b; |
| 1451 | } |
| 1452 | |
| 1453 | grid *grid_new_honeycomb(int width, int height, char *desc) |
| 7c95608a |
1454 | { |
| 1455 | int x, y; |
| cebf0b0d |
1456 | int a = HONEY_A; |
| 1457 | int b = HONEY_B; |
| 7c95608a |
1458 | |
| 1459 | /* Upper bounds - don't have to be exact */ |
| 1460 | int max_faces = width * height; |
| 1461 | int max_dots = 2 * (width + 1) * (height + 1); |
| cebf0b0d |
1462 | |
| 7c95608a |
1463 | tree234 *points; |
| 1464 | |
| cebf0b0d |
1465 | grid *g = grid_empty(); |
| 1466 | g->tilesize = HONEY_TILESIZE; |
| 7c95608a |
1467 | g->faces = snewn(max_faces, grid_face); |
| 1468 | g->dots = snewn(max_dots, grid_dot); |
| 1469 | |
| 1470 | points = newtree234(grid_point_cmp_fn); |
| 1471 | |
| 1472 | /* generate hexagonal faces */ |
| 1473 | for (y = 0; y < height; y++) { |
| 1474 | for (x = 0; x < width; x++) { |
| 1475 | grid_dot *d; |
| 1476 | /* face centre */ |
| 1477 | int cx = 3 * a * x; |
| 1478 | int cy = 2 * b * y; |
| 1479 | if (x % 2) |
| 1480 | cy += b; |
| 1481 | grid_face_add_new(g, 6); |
| 1482 | |
| 1483 | d = grid_get_dot(g, points, cx - a, cy - b); |
| 1484 | grid_face_set_dot(g, d, 0); |
| 1485 | d = grid_get_dot(g, points, cx + a, cy - b); |
| 1486 | grid_face_set_dot(g, d, 1); |
| 1487 | d = grid_get_dot(g, points, cx + 2*a, cy); |
| 1488 | grid_face_set_dot(g, d, 2); |
| 1489 | d = grid_get_dot(g, points, cx + a, cy + b); |
| 1490 | grid_face_set_dot(g, d, 3); |
| 1491 | d = grid_get_dot(g, points, cx - a, cy + b); |
| 1492 | grid_face_set_dot(g, d, 4); |
| 1493 | d = grid_get_dot(g, points, cx - 2*a, cy); |
| 1494 | grid_face_set_dot(g, d, 5); |
| 1495 | } |
| 1496 | } |
| 1497 | |
| 1498 | freetree234(points); |
| 1499 | assert(g->num_faces <= max_faces); |
| 1500 | assert(g->num_dots <= max_dots); |
| 7c95608a |
1501 | |
| 1502 | grid_make_consistent(g); |
| 1503 | return g; |
| 1504 | } |
| 1505 | |
| cebf0b0d |
1506 | #define TRIANGLE_TILESIZE 18 |
| 1507 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
| 1508 | #define TRIANGLE_VEC_X 15 |
| 1509 | #define TRIANGLE_VEC_Y 26 |
| 1510 | |
| 1511 | void grid_size_triangular(int width, int height, |
| 1512 | int *tilesize, int *xextent, int *yextent) |
| 1513 | { |
| 1514 | int vec_x = TRIANGLE_VEC_X; |
| 1515 | int vec_y = TRIANGLE_VEC_Y; |
| 1516 | |
| 1517 | *tilesize = TRIANGLE_TILESIZE; |
| 1518 | *xextent = width * 2 * vec_x + vec_x; |
| 1519 | *yextent = height * vec_y; |
| 1520 | } |
| 1521 | |
| 7c95608a |
1522 | /* Doesn't use the previous method of generation, it pre-dates it! |
| 1523 | * A triangular grid is just about simple enough to do by "brute force" */ |
| cebf0b0d |
1524 | grid *grid_new_triangular(int width, int height, char *desc) |
| 7c95608a |
1525 | { |
| 1526 | int x,y; |
| 1527 | |
| 1528 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
| cebf0b0d |
1529 | int vec_x = TRIANGLE_VEC_X; |
| 1530 | int vec_y = TRIANGLE_VEC_Y; |
| 7c95608a |
1531 | |
| 1532 | int index; |
| 1533 | |
| 1534 | /* convenient alias */ |
| 1535 | int w = width + 1; |
| 1536 | |
| cebf0b0d |
1537 | grid *g = grid_empty(); |
| 1538 | g->tilesize = TRIANGLE_TILESIZE; |
| 7c95608a |
1539 | |
| 1540 | g->num_faces = width * height * 2; |
| 1541 | g->num_dots = (width + 1) * (height + 1); |
| 1542 | g->faces = snewn(g->num_faces, grid_face); |
| 1543 | g->dots = snewn(g->num_dots, grid_dot); |
| 1544 | |
| 1545 | /* generate dots */ |
| 1546 | index = 0; |
| 1547 | for (y = 0; y <= height; y++) { |
| 1548 | for (x = 0; x <= width; x++) { |
| 1549 | grid_dot *d = g->dots + index; |
| 1550 | /* odd rows are offset to the right */ |
| 1551 | d->order = 0; |
| 1552 | d->edges = NULL; |
| 1553 | d->faces = NULL; |
| 1554 | d->x = x * 2 * vec_x + ((y % 2) ? vec_x : 0); |
| 1555 | d->y = y * vec_y; |
| 1556 | index++; |
| 1557 | } |
| 1558 | } |
| 1559 | |
| 1560 | /* generate faces */ |
| 1561 | index = 0; |
| 1562 | for (y = 0; y < height; y++) { |
| 1563 | for (x = 0; x < width; x++) { |
| 1564 | /* initialise two faces for this (x,y) */ |
| 1565 | grid_face *f1 = g->faces + index; |
| 1566 | grid_face *f2 = f1 + 1; |
| 1567 | f1->edges = NULL; |
| 1568 | f1->order = 3; |
| 1569 | f1->dots = snewn(f1->order, grid_dot*); |
| 18eb897f |
1570 | f1->has_incentre = FALSE; |
| 7c95608a |
1571 | f2->edges = NULL; |
| 1572 | f2->order = 3; |
| 1573 | f2->dots = snewn(f2->order, grid_dot*); |
| 18eb897f |
1574 | f2->has_incentre = FALSE; |
| 7c95608a |
1575 | |
| 1576 | /* face descriptions depend on whether the row-number is |
| 1577 | * odd or even */ |
| 1578 | if (y % 2) { |
| 1579 | f1->dots[0] = g->dots + y * w + x; |
| 1580 | f1->dots[1] = g->dots + (y + 1) * w + x + 1; |
| 1581 | f1->dots[2] = g->dots + (y + 1) * w + x; |
| 1582 | f2->dots[0] = g->dots + y * w + x; |
| 1583 | f2->dots[1] = g->dots + y * w + x + 1; |
| 1584 | f2->dots[2] = g->dots + (y + 1) * w + x + 1; |
| 1585 | } else { |
| 1586 | f1->dots[0] = g->dots + y * w + x; |
| 1587 | f1->dots[1] = g->dots + y * w + x + 1; |
| 1588 | f1->dots[2] = g->dots + (y + 1) * w + x; |
| 1589 | f2->dots[0] = g->dots + y * w + x + 1; |
| 1590 | f2->dots[1] = g->dots + (y + 1) * w + x + 1; |
| 1591 | f2->dots[2] = g->dots + (y + 1) * w + x; |
| 1592 | } |
| 1593 | index += 2; |
| 1594 | } |
| 1595 | } |
| 1596 | |
| 7c95608a |
1597 | grid_make_consistent(g); |
| 1598 | return g; |
| 1599 | } |
| 1600 | |
| cebf0b0d |
1601 | #define SNUBSQUARE_TILESIZE 18 |
| 1602 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
| 1603 | #define SNUBSQUARE_A 15 |
| 1604 | #define SNUBSQUARE_B 26 |
| 1605 | |
| 1606 | void grid_size_snubsquare(int width, int height, |
| 1607 | int *tilesize, int *xextent, int *yextent) |
| 1608 | { |
| 1609 | int a = SNUBSQUARE_A; |
| 1610 | int b = SNUBSQUARE_B; |
| 1611 | |
| 1612 | *tilesize = SNUBSQUARE_TILESIZE; |
| 1613 | *xextent = (a+b) * (width-1) + a + b; |
| 1614 | *yextent = (a+b) * (height-1) + a + b; |
| 1615 | } |
| 1616 | |
| 1617 | grid *grid_new_snubsquare(int width, int height, char *desc) |
| 7c95608a |
1618 | { |
| 1619 | int x, y; |
| cebf0b0d |
1620 | int a = SNUBSQUARE_A; |
| 1621 | int b = SNUBSQUARE_B; |
| 7c95608a |
1622 | |
| 1623 | /* Upper bounds - don't have to be exact */ |
| 1624 | int max_faces = 3 * width * height; |
| 1625 | int max_dots = 2 * (width + 1) * (height + 1); |
| cebf0b0d |
1626 | |
| 7c95608a |
1627 | tree234 *points; |
| 1628 | |
| cebf0b0d |
1629 | grid *g = grid_empty(); |
| 1630 | g->tilesize = SNUBSQUARE_TILESIZE; |
| 7c95608a |
1631 | g->faces = snewn(max_faces, grid_face); |
| 1632 | g->dots = snewn(max_dots, grid_dot); |
| 1633 | |
| 1634 | points = newtree234(grid_point_cmp_fn); |
| 1635 | |
| 1636 | for (y = 0; y < height; y++) { |
| 1637 | for (x = 0; x < width; x++) { |
| 1638 | grid_dot *d; |
| 1639 | /* face position */ |
| 1640 | int px = (a + b) * x; |
| 1641 | int py = (a + b) * y; |
| 1642 | |
| 1643 | /* generate square faces */ |
| 1644 | grid_face_add_new(g, 4); |
| 1645 | if ((x + y) % 2) { |
| 1646 | d = grid_get_dot(g, points, px + a, py); |
| 1647 | grid_face_set_dot(g, d, 0); |
| 1648 | d = grid_get_dot(g, points, px + a + b, py + a); |
| 1649 | grid_face_set_dot(g, d, 1); |
| 1650 | d = grid_get_dot(g, points, px + b, py + a + b); |
| 1651 | grid_face_set_dot(g, d, 2); |
| 1652 | d = grid_get_dot(g, points, px, py + b); |
| 1653 | grid_face_set_dot(g, d, 3); |
| 1654 | } else { |
| 1655 | d = grid_get_dot(g, points, px + b, py); |
| 1656 | grid_face_set_dot(g, d, 0); |
| 1657 | d = grid_get_dot(g, points, px + a + b, py + b); |
| 1658 | grid_face_set_dot(g, d, 1); |
| 1659 | d = grid_get_dot(g, points, px + a, py + a + b); |
| 1660 | grid_face_set_dot(g, d, 2); |
| 1661 | d = grid_get_dot(g, points, px, py + a); |
| 1662 | grid_face_set_dot(g, d, 3); |
| 1663 | } |
| 1664 | |
| 1665 | /* generate up/down triangles */ |
| 1666 | if (x > 0) { |
| 1667 | grid_face_add_new(g, 3); |
| 1668 | if ((x + y) % 2) { |
| 1669 | d = grid_get_dot(g, points, px + a, py); |
| 1670 | grid_face_set_dot(g, d, 0); |
| 1671 | d = grid_get_dot(g, points, px, py + b); |
| 1672 | grid_face_set_dot(g, d, 1); |
| 1673 | d = grid_get_dot(g, points, px - a, py); |
| 1674 | grid_face_set_dot(g, d, 2); |
| 1675 | } else { |
| 1676 | d = grid_get_dot(g, points, px, py + a); |
| 1677 | grid_face_set_dot(g, d, 0); |
| 1678 | d = grid_get_dot(g, points, px + a, py + a + b); |
| 1679 | grid_face_set_dot(g, d, 1); |
| 1680 | d = grid_get_dot(g, points, px - a, py + a + b); |
| 1681 | grid_face_set_dot(g, d, 2); |
| 1682 | } |
| 1683 | } |
| 1684 | |
| 1685 | /* generate left/right triangles */ |
| 1686 | if (y > 0) { |
| 1687 | grid_face_add_new(g, 3); |
| 1688 | if ((x + y) % 2) { |
| 1689 | d = grid_get_dot(g, points, px + a, py); |
| 1690 | grid_face_set_dot(g, d, 0); |
| 1691 | d = grid_get_dot(g, points, px + a + b, py - a); |
| 1692 | grid_face_set_dot(g, d, 1); |
| 1693 | d = grid_get_dot(g, points, px + a + b, py + a); |
| 1694 | grid_face_set_dot(g, d, 2); |
| 1695 | } else { |
| 1696 | d = grid_get_dot(g, points, px, py - a); |
| 1697 | grid_face_set_dot(g, d, 0); |
| 1698 | d = grid_get_dot(g, points, px + b, py); |
| 1699 | grid_face_set_dot(g, d, 1); |
| 1700 | d = grid_get_dot(g, points, px, py + a); |
| 1701 | grid_face_set_dot(g, d, 2); |
| 1702 | } |
| 1703 | } |
| 1704 | } |
| 1705 | } |
| 1706 | |
| 1707 | freetree234(points); |
| 1708 | assert(g->num_faces <= max_faces); |
| 1709 | assert(g->num_dots <= max_dots); |
| 7c95608a |
1710 | |
| 1711 | grid_make_consistent(g); |
| 1712 | return g; |
| 1713 | } |
| 1714 | |
| cebf0b0d |
1715 | #define CAIRO_TILESIZE 40 |
| 1716 | /* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */ |
| 1717 | #define CAIRO_A 14 |
| 1718 | #define CAIRO_B 31 |
| 1719 | |
| 1720 | void grid_size_cairo(int width, int height, |
| 1721 | int *tilesize, int *xextent, int *yextent) |
| 1722 | { |
| 1723 | int b = CAIRO_B; /* a unused in determining grid size. */ |
| 1724 | |
| 1725 | *tilesize = CAIRO_TILESIZE; |
| 1726 | *xextent = 2*b*(width-1) + 2*b; |
| 1727 | *yextent = 2*b*(height-1) + 2*b; |
| 1728 | } |
| 1729 | |
| 1730 | grid *grid_new_cairo(int width, int height, char *desc) |
| 7c95608a |
1731 | { |
| 1732 | int x, y; |
| cebf0b0d |
1733 | int a = CAIRO_A; |
| 1734 | int b = CAIRO_B; |
| 7c95608a |
1735 | |
| 1736 | /* Upper bounds - don't have to be exact */ |
| 1737 | int max_faces = 2 * width * height; |
| 1738 | int max_dots = 3 * (width + 1) * (height + 1); |
| cebf0b0d |
1739 | |
| 7c95608a |
1740 | tree234 *points; |
| 1741 | |
| cebf0b0d |
1742 | grid *g = grid_empty(); |
| 1743 | g->tilesize = CAIRO_TILESIZE; |
| 7c95608a |
1744 | g->faces = snewn(max_faces, grid_face); |
| 1745 | g->dots = snewn(max_dots, grid_dot); |
| 1746 | |
| 1747 | points = newtree234(grid_point_cmp_fn); |
| 1748 | |
| 1749 | for (y = 0; y < height; y++) { |
| 1750 | for (x = 0; x < width; x++) { |
| 1751 | grid_dot *d; |
| 1752 | /* cell position */ |
| 1753 | int px = 2 * b * x; |
| 1754 | int py = 2 * b * y; |
| 1755 | |
| 1756 | /* horizontal pentagons */ |
| 1757 | if (y > 0) { |
| 1758 | grid_face_add_new(g, 5); |
| 1759 | if ((x + y) % 2) { |
| 1760 | d = grid_get_dot(g, points, px + a, py - b); |
| 1761 | grid_face_set_dot(g, d, 0); |
| 1762 | d = grid_get_dot(g, points, px + 2*b - a, py - b); |
| 1763 | grid_face_set_dot(g, d, 1); |
| 1764 | d = grid_get_dot(g, points, px + 2*b, py); |
| 1765 | grid_face_set_dot(g, d, 2); |
| 1766 | d = grid_get_dot(g, points, px + b, py + a); |
| 1767 | grid_face_set_dot(g, d, 3); |
| 1768 | d = grid_get_dot(g, points, px, py); |
| 1769 | grid_face_set_dot(g, d, 4); |
| 1770 | } else { |
| 1771 | d = grid_get_dot(g, points, px, py); |
| 1772 | grid_face_set_dot(g, d, 0); |
| 1773 | d = grid_get_dot(g, points, px + b, py - a); |
| 1774 | grid_face_set_dot(g, d, 1); |
| 1775 | d = grid_get_dot(g, points, px + 2*b, py); |
| 1776 | grid_face_set_dot(g, d, 2); |
| 1777 | d = grid_get_dot(g, points, px + 2*b - a, py + b); |
| 1778 | grid_face_set_dot(g, d, 3); |
| 1779 | d = grid_get_dot(g, points, px + a, py + b); |
| 1780 | grid_face_set_dot(g, d, 4); |
| 1781 | } |
| 1782 | } |
| 1783 | /* vertical pentagons */ |
| 1784 | if (x > 0) { |
| 1785 | grid_face_add_new(g, 5); |
| 1786 | if ((x + y) % 2) { |
| 1787 | d = grid_get_dot(g, points, px, py); |
| 1788 | grid_face_set_dot(g, d, 0); |
| 1789 | d = grid_get_dot(g, points, px + b, py + a); |
| 1790 | grid_face_set_dot(g, d, 1); |
| 1791 | d = grid_get_dot(g, points, px + b, py + 2*b - a); |
| 1792 | grid_face_set_dot(g, d, 2); |
| 1793 | d = grid_get_dot(g, points, px, py + 2*b); |
| 1794 | grid_face_set_dot(g, d, 3); |
| 1795 | d = grid_get_dot(g, points, px - a, py + b); |
| 1796 | grid_face_set_dot(g, d, 4); |
| 1797 | } else { |
| 1798 | d = grid_get_dot(g, points, px, py); |
| 1799 | grid_face_set_dot(g, d, 0); |
| 1800 | d = grid_get_dot(g, points, px + a, py + b); |
| 1801 | grid_face_set_dot(g, d, 1); |
| 1802 | d = grid_get_dot(g, points, px, py + 2*b); |
| 1803 | grid_face_set_dot(g, d, 2); |
| 1804 | d = grid_get_dot(g, points, px - b, py + 2*b - a); |
| 1805 | grid_face_set_dot(g, d, 3); |
| 1806 | d = grid_get_dot(g, points, px - b, py + a); |
| 1807 | grid_face_set_dot(g, d, 4); |
| 1808 | } |
| 1809 | } |
| 1810 | } |
| 1811 | } |
| 1812 | |
| 1813 | freetree234(points); |
| 1814 | assert(g->num_faces <= max_faces); |
| 1815 | assert(g->num_dots <= max_dots); |
| 7c95608a |
1816 | |
| 1817 | grid_make_consistent(g); |
| 1818 | return g; |
| 1819 | } |
| 1820 | |
| cebf0b0d |
1821 | #define GREATHEX_TILESIZE 18 |
| 1822 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
| 1823 | #define GREATHEX_A 15 |
| 1824 | #define GREATHEX_B 26 |
| 1825 | |
| 1826 | void grid_size_greathexagonal(int width, int height, |
| 1827 | int *tilesize, int *xextent, int *yextent) |
| 1828 | { |
| 1829 | int a = GREATHEX_A; |
| 1830 | int b = GREATHEX_B; |
| 1831 | |
| 1832 | *tilesize = GREATHEX_TILESIZE; |
| 1833 | *xextent = (3*a + b) * (width-1) + 4*a; |
| 1834 | *yextent = (2*a + 2*b) * (height-1) + 3*b + a; |
| 1835 | } |
| 1836 | |
| 1837 | grid *grid_new_greathexagonal(int width, int height, char *desc) |
| 7c95608a |
1838 | { |
| 1839 | int x, y; |
| cebf0b0d |
1840 | int a = GREATHEX_A; |
| 1841 | int b = GREATHEX_B; |
| 7c95608a |
1842 | |
| 1843 | /* Upper bounds - don't have to be exact */ |
| 1844 | int max_faces = 6 * (width + 1) * (height + 1); |
| 1845 | int max_dots = 6 * width * height; |
| 1846 | |
| 1847 | tree234 *points; |
| 1848 | |
| cebf0b0d |
1849 | grid *g = grid_empty(); |
| 1850 | g->tilesize = GREATHEX_TILESIZE; |
| 7c95608a |
1851 | g->faces = snewn(max_faces, grid_face); |
| 1852 | g->dots = snewn(max_dots, grid_dot); |
| 1853 | |
| 1854 | points = newtree234(grid_point_cmp_fn); |
| 1855 | |
| 1856 | for (y = 0; y < height; y++) { |
| 1857 | for (x = 0; x < width; x++) { |
| 1858 | grid_dot *d; |
| 1859 | /* centre of hexagon */ |
| 1860 | int px = (3*a + b) * x; |
| 1861 | int py = (2*a + 2*b) * y; |
| 1862 | if (x % 2) |
| 1863 | py += a + b; |
| 1864 | |
| 1865 | /* hexagon */ |
| 1866 | grid_face_add_new(g, 6); |
| 1867 | d = grid_get_dot(g, points, px - a, py - b); |
| 1868 | grid_face_set_dot(g, d, 0); |
| 1869 | d = grid_get_dot(g, points, px + a, py - b); |
| 1870 | grid_face_set_dot(g, d, 1); |
| 1871 | d = grid_get_dot(g, points, px + 2*a, py); |
| 1872 | grid_face_set_dot(g, d, 2); |
| 1873 | d = grid_get_dot(g, points, px + a, py + b); |
| 1874 | grid_face_set_dot(g, d, 3); |
| 1875 | d = grid_get_dot(g, points, px - a, py + b); |
| 1876 | grid_face_set_dot(g, d, 4); |
| 1877 | d = grid_get_dot(g, points, px - 2*a, py); |
| 1878 | grid_face_set_dot(g, d, 5); |
| 1879 | |
| 1880 | /* square below hexagon */ |
| 1881 | if (y < height - 1) { |
| 1882 | grid_face_add_new(g, 4); |
| 1883 | d = grid_get_dot(g, points, px - a, py + b); |
| 1884 | grid_face_set_dot(g, d, 0); |
| 1885 | d = grid_get_dot(g, points, px + a, py + b); |
| 1886 | grid_face_set_dot(g, d, 1); |
| 1887 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
| 1888 | grid_face_set_dot(g, d, 2); |
| 1889 | d = grid_get_dot(g, points, px - a, py + 2*a + b); |
| 1890 | grid_face_set_dot(g, d, 3); |
| 1891 | } |
| 1892 | |
| 1893 | /* square below right */ |
| 1894 | if ((x < width - 1) && (((x % 2) == 0) || (y < height - 1))) { |
| 1895 | grid_face_add_new(g, 4); |
| 1896 | d = grid_get_dot(g, points, px + 2*a, py); |
| 1897 | grid_face_set_dot(g, d, 0); |
| 1898 | d = grid_get_dot(g, points, px + 2*a + b, py + a); |
| 1899 | grid_face_set_dot(g, d, 1); |
| 1900 | d = grid_get_dot(g, points, px + a + b, py + a + b); |
| 1901 | grid_face_set_dot(g, d, 2); |
| 1902 | d = grid_get_dot(g, points, px + a, py + b); |
| 1903 | grid_face_set_dot(g, d, 3); |
| 1904 | } |
| 1905 | |
| 1906 | /* square below left */ |
| 1907 | if ((x > 0) && (((x % 2) == 0) || (y < height - 1))) { |
| 1908 | grid_face_add_new(g, 4); |
| 1909 | d = grid_get_dot(g, points, px - 2*a, py); |
| 1910 | grid_face_set_dot(g, d, 0); |
| 1911 | d = grid_get_dot(g, points, px - a, py + b); |
| 1912 | grid_face_set_dot(g, d, 1); |
| 1913 | d = grid_get_dot(g, points, px - a - b, py + a + b); |
| 1914 | grid_face_set_dot(g, d, 2); |
| 1915 | d = grid_get_dot(g, points, px - 2*a - b, py + a); |
| 1916 | grid_face_set_dot(g, d, 3); |
| 1917 | } |
| 1918 | |
| 1919 | /* Triangle below right */ |
| 1920 | if ((x < width - 1) && (y < height - 1)) { |
| 1921 | grid_face_add_new(g, 3); |
| 1922 | d = grid_get_dot(g, points, px + a, py + b); |
| 1923 | grid_face_set_dot(g, d, 0); |
| 1924 | d = grid_get_dot(g, points, px + a + b, py + a + b); |
| 1925 | grid_face_set_dot(g, d, 1); |
| 1926 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
| 1927 | grid_face_set_dot(g, d, 2); |
| 1928 | } |
| 1929 | |
| 1930 | /* Triangle below left */ |
| 1931 | if ((x > 0) && (y < height - 1)) { |
| 1932 | grid_face_add_new(g, 3); |
| 1933 | d = grid_get_dot(g, points, px - a, py + b); |
| 1934 | grid_face_set_dot(g, d, 0); |
| 1935 | d = grid_get_dot(g, points, px - a, py + 2*a + b); |
| 1936 | grid_face_set_dot(g, d, 1); |
| 1937 | d = grid_get_dot(g, points, px - a - b, py + a + b); |
| 1938 | grid_face_set_dot(g, d, 2); |
| 1939 | } |
| 1940 | } |
| 1941 | } |
| 1942 | |
| 1943 | freetree234(points); |
| 1944 | assert(g->num_faces <= max_faces); |
| 1945 | assert(g->num_dots <= max_dots); |
| 7c95608a |
1946 | |
| 1947 | grid_make_consistent(g); |
| 1948 | return g; |
| 1949 | } |
| 1950 | |
| cebf0b0d |
1951 | #define OCTAGONAL_TILESIZE 40 |
| 1952 | /* b/a approx sqrt(2) */ |
| 1953 | #define OCTAGONAL_A 29 |
| 1954 | #define OCTAGONAL_B 41 |
| 1955 | |
| 1956 | void grid_size_octagonal(int width, int height, |
| 1957 | int *tilesize, int *xextent, int *yextent) |
| 1958 | { |
| 1959 | int a = OCTAGONAL_A; |
| 1960 | int b = OCTAGONAL_B; |
| 1961 | |
| 1962 | *tilesize = OCTAGONAL_TILESIZE; |
| 1963 | *xextent = (2*a + b) * width; |
| 1964 | *yextent = (2*a + b) * height; |
| 1965 | } |
| 1966 | |
| 1967 | grid *grid_new_octagonal(int width, int height, char *desc) |
| 7c95608a |
1968 | { |
| 1969 | int x, y; |
| cebf0b0d |
1970 | int a = OCTAGONAL_A; |
| 1971 | int b = OCTAGONAL_B; |
| 7c95608a |
1972 | |
| 1973 | /* Upper bounds - don't have to be exact */ |
| 1974 | int max_faces = 2 * width * height; |
| 1975 | int max_dots = 4 * (width + 1) * (height + 1); |
| 1976 | |
| 1977 | tree234 *points; |
| 1978 | |
| cebf0b0d |
1979 | grid *g = grid_empty(); |
| 1980 | g->tilesize = OCTAGONAL_TILESIZE; |
| 7c95608a |
1981 | g->faces = snewn(max_faces, grid_face); |
| 1982 | g->dots = snewn(max_dots, grid_dot); |
| 1983 | |
| 1984 | points = newtree234(grid_point_cmp_fn); |
| 1985 | |
| 1986 | for (y = 0; y < height; y++) { |
| 1987 | for (x = 0; x < width; x++) { |
| 1988 | grid_dot *d; |
| 1989 | /* cell position */ |
| 1990 | int px = (2*a + b) * x; |
| 1991 | int py = (2*a + b) * y; |
| 1992 | /* octagon */ |
| 1993 | grid_face_add_new(g, 8); |
| 1994 | d = grid_get_dot(g, points, px + a, py); |
| 1995 | grid_face_set_dot(g, d, 0); |
| 1996 | d = grid_get_dot(g, points, px + a + b, py); |
| 1997 | grid_face_set_dot(g, d, 1); |
| 1998 | d = grid_get_dot(g, points, px + 2*a + b, py + a); |
| 1999 | grid_face_set_dot(g, d, 2); |
| 2000 | d = grid_get_dot(g, points, px + 2*a + b, py + a + b); |
| 2001 | grid_face_set_dot(g, d, 3); |
| 2002 | d = grid_get_dot(g, points, px + a + b, py + 2*a + b); |
| 2003 | grid_face_set_dot(g, d, 4); |
| 2004 | d = grid_get_dot(g, points, px + a, py + 2*a + b); |
| 2005 | grid_face_set_dot(g, d, 5); |
| 2006 | d = grid_get_dot(g, points, px, py + a + b); |
| 2007 | grid_face_set_dot(g, d, 6); |
| 2008 | d = grid_get_dot(g, points, px, py + a); |
| 2009 | grid_face_set_dot(g, d, 7); |
| 2010 | |
| 2011 | /* diamond */ |
| 2012 | if ((x > 0) && (y > 0)) { |
| 2013 | grid_face_add_new(g, 4); |
| 2014 | d = grid_get_dot(g, points, px, py - a); |
| 2015 | grid_face_set_dot(g, d, 0); |
| 2016 | d = grid_get_dot(g, points, px + a, py); |
| 2017 | grid_face_set_dot(g, d, 1); |
| 2018 | d = grid_get_dot(g, points, px, py + a); |
| 2019 | grid_face_set_dot(g, d, 2); |
| 2020 | d = grid_get_dot(g, points, px - a, py); |
| 2021 | grid_face_set_dot(g, d, 3); |
| 2022 | } |
| 2023 | } |
| 2024 | } |
| 2025 | |
| 2026 | freetree234(points); |
| 2027 | assert(g->num_faces <= max_faces); |
| 2028 | assert(g->num_dots <= max_dots); |
| 7c95608a |
2029 | |
| 2030 | grid_make_consistent(g); |
| 2031 | return g; |
| 2032 | } |
| 2033 | |
| cebf0b0d |
2034 | #define KITE_TILESIZE 40 |
| 2035 | /* b/a approx sqrt(3) */ |
| 2036 | #define KITE_A 15 |
| 2037 | #define KITE_B 26 |
| 2038 | |
| 2039 | void grid_size_kites(int width, int height, |
| 2040 | int *tilesize, int *xextent, int *yextent) |
| 2041 | { |
| 2042 | int a = KITE_A; |
| 2043 | int b = KITE_B; |
| 2044 | |
| 2045 | *tilesize = KITE_TILESIZE; |
| 2046 | *xextent = 4*b * width + 2*b; |
| 2047 | *yextent = 6*a * (height-1) + 8*a; |
| 2048 | } |
| 2049 | |
| 2050 | grid *grid_new_kites(int width, int height, char *desc) |
| 7c95608a |
2051 | { |
| 2052 | int x, y; |
| cebf0b0d |
2053 | int a = KITE_A; |
| 2054 | int b = KITE_B; |
| 7c95608a |
2055 | |
| 2056 | /* Upper bounds - don't have to be exact */ |
| 2057 | int max_faces = 6 * width * height; |
| 2058 | int max_dots = 6 * (width + 1) * (height + 1); |
| 2059 | |
| 2060 | tree234 *points; |
| 2061 | |
| cebf0b0d |
2062 | grid *g = grid_empty(); |
| 2063 | g->tilesize = KITE_TILESIZE; |
| 7c95608a |
2064 | g->faces = snewn(max_faces, grid_face); |
| 2065 | g->dots = snewn(max_dots, grid_dot); |
| 2066 | |
| 2067 | points = newtree234(grid_point_cmp_fn); |
| 2068 | |
| 2069 | for (y = 0; y < height; y++) { |
| 2070 | for (x = 0; x < width; x++) { |
| 2071 | grid_dot *d; |
| 2072 | /* position of order-6 dot */ |
| 2073 | int px = 4*b * x; |
| 2074 | int py = 6*a * y; |
| 2075 | if (y % 2) |
| 2076 | px += 2*b; |
| 2077 | |
| 2078 | /* kite pointing up-left */ |
| 2079 | grid_face_add_new(g, 4); |
| 2080 | d = grid_get_dot(g, points, px, py); |
| 2081 | grid_face_set_dot(g, d, 0); |
| 2082 | d = grid_get_dot(g, points, px + 2*b, py); |
| 2083 | grid_face_set_dot(g, d, 1); |
| 2084 | d = grid_get_dot(g, points, px + 2*b, py + 2*a); |
| 2085 | grid_face_set_dot(g, d, 2); |
| 2086 | d = grid_get_dot(g, points, px + b, py + 3*a); |
| 2087 | grid_face_set_dot(g, d, 3); |
| 2088 | |
| 2089 | /* kite pointing up */ |
| 2090 | grid_face_add_new(g, 4); |
| 2091 | d = grid_get_dot(g, points, px, py); |
| 2092 | grid_face_set_dot(g, d, 0); |
| 2093 | d = grid_get_dot(g, points, px + b, py + 3*a); |
| 2094 | grid_face_set_dot(g, d, 1); |
| 2095 | d = grid_get_dot(g, points, px, py + 4*a); |
| 2096 | grid_face_set_dot(g, d, 2); |
| 2097 | d = grid_get_dot(g, points, px - b, py + 3*a); |
| 2098 | grid_face_set_dot(g, d, 3); |
| 2099 | |
| 2100 | /* kite pointing up-right */ |
| 2101 | grid_face_add_new(g, 4); |
| 2102 | d = grid_get_dot(g, points, px, py); |
| 2103 | grid_face_set_dot(g, d, 0); |
| 2104 | d = grid_get_dot(g, points, px - b, py + 3*a); |
| 2105 | grid_face_set_dot(g, d, 1); |
| 2106 | d = grid_get_dot(g, points, px - 2*b, py + 2*a); |
| 2107 | grid_face_set_dot(g, d, 2); |
| 2108 | d = grid_get_dot(g, points, px - 2*b, py); |
| 2109 | grid_face_set_dot(g, d, 3); |
| 2110 | |
| 2111 | /* kite pointing down-right */ |
| 2112 | grid_face_add_new(g, 4); |
| 2113 | d = grid_get_dot(g, points, px, py); |
| 2114 | grid_face_set_dot(g, d, 0); |
| 2115 | d = grid_get_dot(g, points, px - 2*b, py); |
| 2116 | grid_face_set_dot(g, d, 1); |
| 2117 | d = grid_get_dot(g, points, px - 2*b, py - 2*a); |
| 2118 | grid_face_set_dot(g, d, 2); |
| 2119 | d = grid_get_dot(g, points, px - b, py - 3*a); |
| 2120 | grid_face_set_dot(g, d, 3); |
| 2121 | |
| 2122 | /* kite pointing down */ |
| 2123 | grid_face_add_new(g, 4); |
| 2124 | d = grid_get_dot(g, points, px, py); |
| 2125 | grid_face_set_dot(g, d, 0); |
| 2126 | d = grid_get_dot(g, points, px - b, py - 3*a); |
| 2127 | grid_face_set_dot(g, d, 1); |
| 2128 | d = grid_get_dot(g, points, px, py - 4*a); |
| 2129 | grid_face_set_dot(g, d, 2); |
| 2130 | d = grid_get_dot(g, points, px + b, py - 3*a); |
| 2131 | grid_face_set_dot(g, d, 3); |
| 2132 | |
| 2133 | /* kite pointing down-left */ |
| 2134 | grid_face_add_new(g, 4); |
| 2135 | d = grid_get_dot(g, points, px, py); |
| 2136 | grid_face_set_dot(g, d, 0); |
| 2137 | d = grid_get_dot(g, points, px + b, py - 3*a); |
| 2138 | grid_face_set_dot(g, d, 1); |
| 2139 | d = grid_get_dot(g, points, px + 2*b, py - 2*a); |
| 2140 | grid_face_set_dot(g, d, 2); |
| 2141 | d = grid_get_dot(g, points, px + 2*b, py); |
| 2142 | grid_face_set_dot(g, d, 3); |
| 2143 | } |
| 2144 | } |
| 2145 | |
| 2146 | freetree234(points); |
| 2147 | assert(g->num_faces <= max_faces); |
| 2148 | assert(g->num_dots <= max_dots); |
| 7c95608a |
2149 | |
| 2150 | grid_make_consistent(g); |
| 2151 | return g; |
| 2152 | } |
| 2153 | |
| cebf0b0d |
2154 | #define FLORET_TILESIZE 150 |
| 2155 | /* -py/px is close to tan(30 - atan(sqrt(3)/9)) |
| 2156 | * using py=26 makes everything lean to the left, rather than right |
| 2157 | */ |
| 2158 | #define FLORET_PX 75 |
| 2159 | #define FLORET_PY -26 |
| 2160 | |
| 2161 | void grid_size_floret(int width, int height, |
| 2162 | int *tilesize, int *xextent, int *yextent) |
| 2163 | { |
| 2164 | int px = FLORET_PX, py = FLORET_PY; /* |( 75, -26)| = 79.43 */ |
| 2165 | int qx = 4*px/5, qy = -py*2; /* |( 60, 52)| = 79.40 */ |
| 2166 | int ry = qy-py; |
| 2167 | /* rx unused in determining grid size. */ |
| 2168 | |
| 2169 | *tilesize = FLORET_TILESIZE; |
| 2170 | *xextent = (6*px+3*qx)/2 * (width-1) + 4*qx + 2*px; |
| 2171 | *yextent = (5*qy-4*py) * (height-1) + 4*qy + 2*ry; |
| 2172 | } |
| 2173 | |
| 2174 | grid *grid_new_floret(int width, int height, char *desc) |
| e30d39f6 |
2175 | { |
| 2176 | int x, y; |
| 2177 | /* Vectors for sides; weird numbers needed to keep puzzle aligned with window |
| 2178 | * -py/px is close to tan(30 - atan(sqrt(3)/9)) |
| 2179 | * using py=26 makes everything lean to the left, rather than right |
| 2180 | */ |
| cebf0b0d |
2181 | int px = FLORET_PX, py = FLORET_PY; /* |( 75, -26)| = 79.43 */ |
| 2182 | int qx = 4*px/5, qy = -py*2; /* |( 60, 52)| = 79.40 */ |
| 2183 | int rx = qx-px, ry = qy-py; /* |(-15, 78)| = 79.38 */ |
| e30d39f6 |
2184 | |
| 2185 | /* Upper bounds - don't have to be exact */ |
| 2186 | int max_faces = 6 * width * height; |
| 2187 | int max_dots = 9 * (width + 1) * (height + 1); |
| cebf0b0d |
2188 | |
| e30d39f6 |
2189 | tree234 *points; |
| 2190 | |
| cebf0b0d |
2191 | grid *g = grid_empty(); |
| 2192 | g->tilesize = FLORET_TILESIZE; |
| e30d39f6 |
2193 | g->faces = snewn(max_faces, grid_face); |
| 2194 | g->dots = snewn(max_dots, grid_dot); |
| 2195 | |
| 2196 | points = newtree234(grid_point_cmp_fn); |
| 2197 | |
| 2198 | /* generate pentagonal faces */ |
| 2199 | for (y = 0; y < height; y++) { |
| 2200 | for (x = 0; x < width; x++) { |
| 2201 | grid_dot *d; |
| 2202 | /* face centre */ |
| 2203 | int cx = (6*px+3*qx)/2 * x; |
| 2204 | int cy = (4*py-5*qy) * y; |
| 2205 | if (x % 2) |
| 2206 | cy -= (4*py-5*qy)/2; |
| 2207 | else if (y && y == height-1) |
| 2208 | continue; /* make better looking grids? try 3x3 for instance */ |
| 2209 | |
| 2210 | grid_face_add_new(g, 5); |
| 2211 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
| 2212 | d = grid_get_dot(g, points, cx+2*rx , cy+2*ry ); grid_face_set_dot(g, d, 1); |
| 2213 | d = grid_get_dot(g, points, cx+2*rx+qx, cy+2*ry+qy); grid_face_set_dot(g, d, 2); |
| 2214 | d = grid_get_dot(g, points, cx+2*qx+rx, cy+2*qy+ry); grid_face_set_dot(g, d, 3); |
| 2215 | d = grid_get_dot(g, points, cx+2*qx , cy+2*qy ); grid_face_set_dot(g, d, 4); |
| 2216 | |
| 2217 | grid_face_add_new(g, 5); |
| 2218 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
| 2219 | d = grid_get_dot(g, points, cx+2*qx , cy+2*qy ); grid_face_set_dot(g, d, 1); |
| 2220 | d = grid_get_dot(g, points, cx+2*qx+px, cy+2*qy+py); grid_face_set_dot(g, d, 2); |
| 2221 | d = grid_get_dot(g, points, cx+2*px+qx, cy+2*py+qy); grid_face_set_dot(g, d, 3); |
| 2222 | d = grid_get_dot(g, points, cx+2*px , cy+2*py ); grid_face_set_dot(g, d, 4); |
| 2223 | |
| 2224 | grid_face_add_new(g, 5); |
| 2225 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
| 2226 | d = grid_get_dot(g, points, cx+2*px , cy+2*py ); grid_face_set_dot(g, d, 1); |
| 2227 | d = grid_get_dot(g, points, cx+2*px-rx, cy+2*py-ry); grid_face_set_dot(g, d, 2); |
| 2228 | d = grid_get_dot(g, points, cx-2*rx+px, cy-2*ry+py); grid_face_set_dot(g, d, 3); |
| 2229 | d = grid_get_dot(g, points, cx-2*rx , cy-2*ry ); grid_face_set_dot(g, d, 4); |
| 2230 | |
| 2231 | grid_face_add_new(g, 5); |
| 2232 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
| 2233 | d = grid_get_dot(g, points, cx-2*rx , cy-2*ry ); grid_face_set_dot(g, d, 1); |
| 2234 | d = grid_get_dot(g, points, cx-2*rx-qx, cy-2*ry-qy); grid_face_set_dot(g, d, 2); |
| 2235 | d = grid_get_dot(g, points, cx-2*qx-rx, cy-2*qy-ry); grid_face_set_dot(g, d, 3); |
| 2236 | d = grid_get_dot(g, points, cx-2*qx , cy-2*qy ); grid_face_set_dot(g, d, 4); |
| 2237 | |
| 2238 | grid_face_add_new(g, 5); |
| 2239 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
| 2240 | d = grid_get_dot(g, points, cx-2*qx , cy-2*qy ); grid_face_set_dot(g, d, 1); |
| 2241 | d = grid_get_dot(g, points, cx-2*qx-px, cy-2*qy-py); grid_face_set_dot(g, d, 2); |
| 2242 | d = grid_get_dot(g, points, cx-2*px-qx, cy-2*py-qy); grid_face_set_dot(g, d, 3); |
| 2243 | d = grid_get_dot(g, points, cx-2*px , cy-2*py ); grid_face_set_dot(g, d, 4); |
| 2244 | |
| 2245 | grid_face_add_new(g, 5); |
| 2246 | d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0); |
| 2247 | d = grid_get_dot(g, points, cx-2*px , cy-2*py ); grid_face_set_dot(g, d, 1); |
| 2248 | d = grid_get_dot(g, points, cx-2*px+rx, cy-2*py+ry); grid_face_set_dot(g, d, 2); |
| 2249 | d = grid_get_dot(g, points, cx+2*rx-px, cy+2*ry-py); grid_face_set_dot(g, d, 3); |
| 2250 | d = grid_get_dot(g, points, cx+2*rx , cy+2*ry ); grid_face_set_dot(g, d, 4); |
| 2251 | } |
| 2252 | } |
| 2253 | |
| 2254 | freetree234(points); |
| 2255 | assert(g->num_faces <= max_faces); |
| 2256 | assert(g->num_dots <= max_dots); |
| e30d39f6 |
2257 | |
| 2258 | grid_make_consistent(g); |
| 2259 | return g; |
| 2260 | } |
| 2261 | |
| cebf0b0d |
2262 | /* DODEC_* are used for dodecagonal and great-dodecagonal grids. */ |
| 2263 | #define DODEC_TILESIZE 26 |
| 2264 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
| 2265 | #define DODEC_A 15 |
| 2266 | #define DODEC_B 26 |
| 2267 | |
| 2268 | void grid_size_dodecagonal(int width, int height, |
| 2269 | int *tilesize, int *xextent, int *yextent) |
| 2270 | { |
| 2271 | int a = DODEC_A; |
| 2272 | int b = DODEC_B; |
| 2273 | |
| 2274 | *tilesize = DODEC_TILESIZE; |
| 2275 | *xextent = (4*a + 2*b) * (width-1) + 3*(2*a + b); |
| 2276 | *yextent = (3*a + 2*b) * (height-1) + 2*(2*a + b); |
| 2277 | } |
| 2278 | |
| 2279 | grid *grid_new_dodecagonal(int width, int height, char *desc) |
| 918a098a |
2280 | { |
| 2281 | int x, y; |
| cebf0b0d |
2282 | int a = DODEC_A; |
| 2283 | int b = DODEC_B; |
| 918a098a |
2284 | |
| 2285 | /* Upper bounds - don't have to be exact */ |
| 2286 | int max_faces = 3 * width * height; |
| 2287 | int max_dots = 14 * width * height; |
| 2288 | |
| 2289 | tree234 *points; |
| 2290 | |
| cebf0b0d |
2291 | grid *g = grid_empty(); |
| 2292 | g->tilesize = DODEC_TILESIZE; |
| 918a098a |
2293 | g->faces = snewn(max_faces, grid_face); |
| 2294 | g->dots = snewn(max_dots, grid_dot); |
| 2295 | |
| 2296 | points = newtree234(grid_point_cmp_fn); |
| 2297 | |
| 2298 | for (y = 0; y < height; y++) { |
| 2299 | for (x = 0; x < width; x++) { |
| 2300 | grid_dot *d; |
| 2301 | /* centre of dodecagon */ |
| 2302 | int px = (4*a + 2*b) * x; |
| 2303 | int py = (3*a + 2*b) * y; |
| 2304 | if (y % 2) |
| 2305 | px += 2*a + b; |
| 2306 | |
| 2307 | /* dodecagon */ |
| 2308 | grid_face_add_new(g, 12); |
| 2309 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); |
| 2310 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 1); |
| 2311 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a )); grid_face_set_dot(g, d, 2); |
| 2312 | d = grid_get_dot(g, points, px + (2*a + b), py + ( a )); grid_face_set_dot(g, d, 3); |
| 2313 | d = grid_get_dot(g, points, px + ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 4); |
| 2314 | d = grid_get_dot(g, points, px + ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 5); |
| 2315 | d = grid_get_dot(g, points, px - ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 6); |
| 2316 | d = grid_get_dot(g, points, px - ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 7); |
| 2317 | d = grid_get_dot(g, points, px - (2*a + b), py + ( a )); grid_face_set_dot(g, d, 8); |
| 2318 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a )); grid_face_set_dot(g, d, 9); |
| 2319 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 10); |
| 2320 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 11); |
| 2321 | |
| 2322 | /* triangle below dodecagon */ |
| 2323 | if ((y < height - 1 && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2)))) { |
| 2324 | grid_face_add_new(g, 3); |
| 2325 | d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0); |
| 2326 | d = grid_get_dot(g, points, px , py + (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
| 2327 | d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 2); |
| 2328 | } |
| 2329 | |
| 2330 | /* triangle above dodecagon */ |
| 2331 | if ((y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2)))) { |
| 2332 | grid_face_add_new(g, 3); |
| 2333 | d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 0); |
| 2334 | d = grid_get_dot(g, points, px , py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
| 2335 | d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 2); |
| 2336 | } |
| 2337 | } |
| 2338 | } |
| 2339 | |
| 2340 | freetree234(points); |
| 2341 | assert(g->num_faces <= max_faces); |
| 2342 | assert(g->num_dots <= max_dots); |
| 2343 | |
| 2344 | grid_make_consistent(g); |
| 2345 | return g; |
| 2346 | } |
| 2347 | |
| cebf0b0d |
2348 | void grid_size_greatdodecagonal(int width, int height, |
| 2349 | int *tilesize, int *xextent, int *yextent) |
| 2350 | { |
| 2351 | int a = DODEC_A; |
| 2352 | int b = DODEC_B; |
| 2353 | |
| 2354 | *tilesize = DODEC_TILESIZE; |
| 2355 | *xextent = (6*a + 2*b) * (width-1) + 2*(2*a + b) + 3*a + b; |
| 2356 | *yextent = (3*a + 3*b) * (height-1) + 2*(2*a + b); |
| 2357 | } |
| 2358 | |
| 2359 | grid *grid_new_greatdodecagonal(int width, int height, char *desc) |
| 918a098a |
2360 | { |
| 2361 | int x, y; |
| 2362 | /* Vector for side of triangle - ratio is close to sqrt(3) */ |
| cebf0b0d |
2363 | int a = DODEC_A; |
| 2364 | int b = DODEC_B; |
| 918a098a |
2365 | |
| 2366 | /* Upper bounds - don't have to be exact */ |
| 2367 | int max_faces = 30 * width * height; |
| 2368 | int max_dots = 200 * width * height; |
| 2369 | |
| 2370 | tree234 *points; |
| 2371 | |
| cebf0b0d |
2372 | grid *g = grid_empty(); |
| 2373 | g->tilesize = DODEC_TILESIZE; |
| 918a098a |
2374 | g->faces = snewn(max_faces, grid_face); |
| 2375 | g->dots = snewn(max_dots, grid_dot); |
| 2376 | |
| 2377 | points = newtree234(grid_point_cmp_fn); |
| 2378 | |
| 2379 | for (y = 0; y < height; y++) { |
| 2380 | for (x = 0; x < width; x++) { |
| 2381 | grid_dot *d; |
| 2382 | /* centre of dodecagon */ |
| 2383 | int px = (6*a + 2*b) * x; |
| 2384 | int py = (3*a + 3*b) * y; |
| 2385 | if (y % 2) |
| 2386 | px += 3*a + b; |
| 2387 | |
| 2388 | /* dodecagon */ |
| 2389 | grid_face_add_new(g, 12); |
| 2390 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); |
| 2391 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 1); |
| 2392 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a )); grid_face_set_dot(g, d, 2); |
| 2393 | d = grid_get_dot(g, points, px + (2*a + b), py + ( a )); grid_face_set_dot(g, d, 3); |
| 2394 | d = grid_get_dot(g, points, px + ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 4); |
| 2395 | d = grid_get_dot(g, points, px + ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 5); |
| 2396 | d = grid_get_dot(g, points, px - ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 6); |
| 2397 | d = grid_get_dot(g, points, px - ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 7); |
| 2398 | d = grid_get_dot(g, points, px - (2*a + b), py + ( a )); grid_face_set_dot(g, d, 8); |
| 2399 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a )); grid_face_set_dot(g, d, 9); |
| 2400 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 10); |
| 2401 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 11); |
| 2402 | |
| 2403 | /* hexagon below dodecagon */ |
| 2404 | if (y < height - 1 && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) { |
| 2405 | grid_face_add_new(g, 6); |
| 2406 | d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0); |
| 2407 | d = grid_get_dot(g, points, px + 2*a, py + (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
| 2408 | d = grid_get_dot(g, points, px + a, py + (2*a + 3*b)); grid_face_set_dot(g, d, 2); |
| 2409 | d = grid_get_dot(g, points, px - a, py + (2*a + 3*b)); grid_face_set_dot(g, d, 3); |
| 2410 | d = grid_get_dot(g, points, px - 2*a, py + (2*a + 2*b)); grid_face_set_dot(g, d, 4); |
| 2411 | d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 5); |
| 2412 | } |
| 2413 | |
| 2414 | /* hexagon above dodecagon */ |
| 2415 | if (y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) { |
| 2416 | grid_face_add_new(g, 6); |
| 2417 | d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 0); |
| 2418 | d = grid_get_dot(g, points, px - 2*a, py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
| 2419 | d = grid_get_dot(g, points, px - a, py - (2*a + 3*b)); grid_face_set_dot(g, d, 2); |
| 2420 | d = grid_get_dot(g, points, px + a, py - (2*a + 3*b)); grid_face_set_dot(g, d, 3); |
| 2421 | d = grid_get_dot(g, points, px + 2*a, py - (2*a + 2*b)); grid_face_set_dot(g, d, 4); |
| 2422 | d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 5); |
| 2423 | } |
| 2424 | |
| 2425 | /* square on right of dodecagon */ |
| 2426 | if (x < width - 1) { |
| 2427 | grid_face_add_new(g, 4); |
| 2428 | d = grid_get_dot(g, points, px + 2*a + b, py - a); grid_face_set_dot(g, d, 0); |
| 2429 | d = grid_get_dot(g, points, px + 4*a + b, py - a); grid_face_set_dot(g, d, 1); |
| 2430 | d = grid_get_dot(g, points, px + 4*a + b, py + a); grid_face_set_dot(g, d, 2); |
| 2431 | d = grid_get_dot(g, points, px + 2*a + b, py + a); grid_face_set_dot(g, d, 3); |
| 2432 | } |
| 2433 | |
| 2434 | /* square on top right of dodecagon */ |
| 2435 | if (y && (x < width - 1 || !(y % 2))) { |
| 2436 | grid_face_add_new(g, 4); |
| 2437 | d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0); |
| 2438 | d = grid_get_dot(g, points, px + (2*a ), py - (2*a + 2*b)); grid_face_set_dot(g, d, 1); |
| 2439 | d = grid_get_dot(g, points, px + (2*a + b), py - ( a + 2*b)); grid_face_set_dot(g, d, 2); |
| 2440 | d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 3); |
| 2441 | } |
| 2442 | |
| 2443 | /* square on top left of dodecagon */ |
| 2444 | if (y && (x || (y % 2))) { |
| 2445 | grid_face_add_new(g, 4); |
| 2446 | d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 0); |
| 2447 | d = grid_get_dot(g, points, px - (2*a + b), py - ( a + 2*b)); grid_face_set_dot(g, d, 1); |
| 2448 | d = grid_get_dot(g, points, px - (2*a ), py - (2*a + 2*b)); grid_face_set_dot(g, d, 2); |
| 2449 | d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 3); |
| 2450 | } |
| 2451 | } |
| 2452 | } |
| 2453 | |
| 2454 | freetree234(points); |
| 2455 | assert(g->num_faces <= max_faces); |
| 2456 | assert(g->num_dots <= max_dots); |
| 2457 | |
| 2458 | grid_make_consistent(g); |
| 2459 | return g; |
| 2460 | } |
| 2461 | |
| cebf0b0d |
2462 | typedef struct setface_ctx |
| 2463 | { |
| 2464 | int xmin, xmax, ymin, ymax; |
| 2465 | int aoff; |
| 2466 | |
| 2467 | grid *g; |
| 2468 | tree234 *points; |
| 2469 | } setface_ctx; |
| 2470 | |
| 2471 | double round(double r) |
| 2472 | { |
| 2473 | return (r > 0.0) ? floor(r + 0.5) : ceil(r - 0.5); |
| 2474 | } |
| 2475 | |
| 2476 | int set_faces(penrose_state *state, vector *vs, int n, int depth) |
| 2477 | { |
| 2478 | setface_ctx *sf_ctx = (setface_ctx *)state->ctx; |
| 2479 | int i; |
| 2480 | int xs[4], ys[4]; |
| 2481 | double cosa = cos(sf_ctx->aoff * PI / 180.0); |
| 2482 | double sina = sin(sf_ctx->aoff * PI / 180.0); |
| 2483 | |
| 2484 | if (depth < state->max_depth) return 0; |
| 2485 | #ifdef DEBUG_PENROSE |
| 2486 | if (n != 4) return 0; /* triangles are sent as debugging. */ |
| 2487 | #endif |
| 2488 | |
| 2489 | for (i = 0; i < n; i++) { |
| 2490 | double tx = v_x(vs, i), ty = v_y(vs, i); |
| 2491 | |
| 2492 | xs[i] = (int)round( tx*cosa + ty*sina); |
| 2493 | ys[i] = (int)round(-tx*sina + ty*cosa); |
| 2494 | |
| 2495 | if (xs[i] < sf_ctx->xmin || xs[i] > sf_ctx->xmax) return 0; |
| 2496 | if (ys[i] < sf_ctx->ymin || ys[i] > sf_ctx->ymax) return 0; |
| 2497 | } |
| 2498 | |
| 2499 | grid_face_add_new(sf_ctx->g, n); |
| 2500 | debug(("penrose: new face l=%f gen=%d...", |
| 2501 | penrose_side_length(state->start_size, depth), depth)); |
| 2502 | for (i = 0; i < n; i++) { |
| 2503 | grid_dot *d = grid_get_dot(sf_ctx->g, sf_ctx->points, |
| 2504 | xs[i], ys[i]); |
| 2505 | grid_face_set_dot(sf_ctx->g, d, i); |
| 2506 | debug((" ... dot 0x%x (%d,%d) (was %2.2f,%2.2f)", |
| 2507 | d, d->x, d->y, v_x(vs, i), v_y(vs, i))); |
| 2508 | } |
| 2509 | |
| 2510 | return 0; |
| 2511 | } |
| 2512 | |
| 2513 | #define PENROSE_TILESIZE 100 |
| 2514 | |
| 2515 | void grid_size_penrose(int width, int height, |
| 2516 | int *tilesize, int *xextent, int *yextent) |
| 2517 | { |
| 2518 | int l = PENROSE_TILESIZE; |
| 2519 | |
| 2520 | *tilesize = l; |
| 2521 | *xextent = l * width; |
| 2522 | *yextent = l * height; |
| 2523 | } |
| 2524 | |
| 2525 | static char *grid_new_desc_penrose(grid_type type, int width, int height, random_state *rs) |
| 2526 | { |
| 2527 | int tilesize = PENROSE_TILESIZE, startsz, depth, xoff, yoff, aoff; |
| 2528 | double outer_radius; |
| 2529 | int inner_radius; |
| 2530 | char gd[255]; |
| 2531 | int which = (type == GRID_PENROSE_P2 ? PENROSE_P2 : PENROSE_P3); |
| 2532 | |
| 2533 | /* We want to produce a random bit of penrose tiling, so we calculate |
| 2534 | * a random offset (within the patch that penrose.c calculates for us) |
| 2535 | * and an angle (multiple of 36) to rotate the patch. */ |
| 2536 | |
| 2537 | penrose_calculate_size(which, tilesize, width, height, |
| 2538 | &outer_radius, &startsz, &depth); |
| 2539 | |
| 2540 | /* Calculate radius of (circumcircle of) patch, subtract from |
| 2541 | * radius calculated. */ |
| 2542 | inner_radius = (int)(outer_radius - sqrt(width*width + height*height)); |
| 2543 | |
| 2544 | /* Pick a random offset (the easy way: choose within outer square, |
| 2545 | * discarding while it's outside the circle) */ |
| 2546 | do { |
| 2547 | xoff = random_upto(rs, 2*inner_radius) - inner_radius; |
| 2548 | yoff = random_upto(rs, 2*inner_radius) - inner_radius; |
| 2549 | } while (sqrt(xoff*xoff+yoff*yoff) > inner_radius); |
| 2550 | |
| 2551 | aoff = random_upto(rs, 360/36) * 36; |
| 2552 | |
| 2553 | debug(("grid_desc: ts %d, %dx%d patch, orad %2.2f irad %d", |
| 2554 | tilesize, width, height, outer_radius, inner_radius)); |
| 2555 | debug((" -> xoff %d yoff %d aoff %d", xoff, yoff, aoff)); |
| 2556 | |
| 2557 | sprintf(gd, "G%d,%d,%d", xoff, yoff, aoff); |
| 2558 | |
| 2559 | return dupstr(gd); |
| 2560 | } |
| 2561 | |
| 2562 | static char *grid_validate_desc_penrose(grid_type type, int width, int height, char *desc) |
| 2563 | { |
| 2564 | int tilesize = PENROSE_TILESIZE, startsz, depth, xoff, yoff, aoff, inner_radius; |
| 2565 | double outer_radius; |
| 2566 | int which = (type == GRID_PENROSE_P2 ? PENROSE_P2 : PENROSE_P3); |
| 2567 | |
| 2568 | if (!desc) |
| 2569 | return "Missing grid description string."; |
| 2570 | |
| 2571 | penrose_calculate_size(which, tilesize, width, height, |
| 2572 | &outer_radius, &startsz, &depth); |
| 2573 | inner_radius = (int)(outer_radius - sqrt(width*width + height*height)); |
| 2574 | |
| 2575 | if (sscanf(desc, "G%d,%d,%d", &xoff, &yoff, &aoff) != 3) |
| 2576 | return "Invalid format grid description string."; |
| 2577 | |
| 2578 | if (sqrt(xoff*xoff + yoff*yoff) > inner_radius) |
| 2579 | return "Patch offset out of bounds."; |
| 2580 | if ((aoff % 36) != 0 || aoff < 0 || aoff >= 360) |
| 2581 | return "Angle offset out of bounds."; |
| 2582 | |
| 2583 | return NULL; |
| 2584 | } |
| 2585 | |
| 2586 | /* |
| 2587 | * We're asked for a grid of a particular size, and we generate enough |
| 2588 | * of the tiling so we can be sure to have enough random grid from which |
| 2589 | * to pick. |
| 2590 | */ |
| 2591 | |
| 2592 | static grid *grid_new_penrose(int width, int height, int which, char *desc) |
| 2593 | { |
| 2594 | int max_faces, max_dots, tilesize = PENROSE_TILESIZE; |
| 2595 | int xsz, ysz, xoff, yoff; |
| 2596 | double rradius; |
| 2597 | |
| 2598 | tree234 *points; |
| 2599 | grid *g; |
| 2600 | |
| 2601 | penrose_state ps; |
| 2602 | setface_ctx sf_ctx; |
| 2603 | |
| 2604 | penrose_calculate_size(which, tilesize, width, height, |
| 2605 | &rradius, &ps.start_size, &ps.max_depth); |
| 2606 | |
| 2607 | debug(("penrose: w%d h%d, tile size %d, start size %d, depth %d", |
| 2608 | width, height, tilesize, ps.start_size, ps.max_depth)); |
| 2609 | |
| 2610 | ps.new_tile = set_faces; |
| 2611 | ps.ctx = &sf_ctx; |
| 2612 | |
| 2613 | max_faces = (width*3) * (height*3); /* somewhat paranoid... */ |
| 2614 | max_dots = max_faces * 4; /* ditto... */ |
| 2615 | |
| 2616 | g = grid_empty(); |
| 2617 | g->tilesize = tilesize; |
| 2618 | g->faces = snewn(max_faces, grid_face); |
| 2619 | g->dots = snewn(max_dots, grid_dot); |
| 2620 | |
| 2621 | points = newtree234(grid_point_cmp_fn); |
| 2622 | |
| 2623 | memset(&sf_ctx, 0, sizeof(sf_ctx)); |
| 2624 | sf_ctx.g = g; |
| 2625 | sf_ctx.points = points; |
| 2626 | |
| 2627 | if (desc != NULL) { |
| 2628 | if (sscanf(desc, "G%d,%d,%d", &xoff, &yoff, &sf_ctx.aoff) != 3) |
| 2629 | assert(!"Invalid grid description."); |
| 2630 | } else { |
| 2631 | xoff = yoff = 0; |
| 2632 | } |
| 2633 | |
| 2634 | xsz = width * tilesize; |
| 2635 | ysz = height * tilesize; |
| 2636 | |
| 2637 | sf_ctx.xmin = xoff - xsz/2; |
| 2638 | sf_ctx.xmax = xoff + xsz/2; |
| 2639 | sf_ctx.ymin = yoff - ysz/2; |
| 2640 | sf_ctx.ymax = yoff + ysz/2; |
| 2641 | |
| 2642 | debug(("penrose: centre (%f, %f) xsz %f ysz %f", |
| 2643 | 0.0, 0.0, xsz, ysz)); |
| 2644 | debug(("penrose: x range (%f --> %f), y range (%f --> %f)", |
| 2645 | sf_ctx.xmin, sf_ctx.xmax, sf_ctx.ymin, sf_ctx.ymax)); |
| 2646 | |
| 2647 | penrose(&ps, which); |
| 2648 | |
| 2649 | freetree234(points); |
| 2650 | assert(g->num_faces <= max_faces); |
| 2651 | assert(g->num_dots <= max_dots); |
| 2652 | |
| 2653 | debug(("penrose: %d faces total (equivalent to %d wide by %d high)", |
| 2654 | g->num_faces, g->num_faces/height, g->num_faces/width)); |
| 2655 | |
| 2656 | grid_trim_vigorously(g); |
| 2657 | grid_make_consistent(g); |
| 2658 | |
| 2659 | /* |
| 2660 | * Centre the grid in its originally promised rectangle. |
| 2661 | */ |
| 2662 | g->lowest_x -= ((sf_ctx.xmax - sf_ctx.xmin) - |
| 2663 | (g->highest_x - g->lowest_x)) / 2; |
| 2664 | g->highest_x = g->lowest_x + (sf_ctx.xmax - sf_ctx.xmin); |
| 2665 | g->lowest_y -= ((sf_ctx.ymax - sf_ctx.ymin) - |
| 2666 | (g->highest_y - g->lowest_y)) / 2; |
| 2667 | g->highest_y = g->lowest_y + (sf_ctx.ymax - sf_ctx.ymin); |
| 2668 | |
| 2669 | return g; |
| 2670 | } |
| 2671 | |
| 2672 | void grid_size_penrose_p2_kite(int width, int height, |
| 2673 | int *tilesize, int *xextent, int *yextent) |
| 2674 | { |
| 2675 | grid_size_penrose(width, height, tilesize, xextent, yextent); |
| 2676 | } |
| 2677 | |
| 2678 | void grid_size_penrose_p3_thick(int width, int height, |
| 2679 | int *tilesize, int *xextent, int *yextent) |
| 2680 | { |
| 2681 | grid_size_penrose(width, height, tilesize, xextent, yextent); |
| 2682 | } |
| 2683 | |
| 2684 | grid *grid_new_penrose_p2_kite(int width, int height, char *desc) |
| 2685 | { |
| 2686 | return grid_new_penrose(width, height, PENROSE_P2, desc); |
| 2687 | } |
| 2688 | |
| 2689 | grid *grid_new_penrose_p3_thick(int width, int height, char *desc) |
| 2690 | { |
| 2691 | return grid_new_penrose(width, height, PENROSE_P3, desc); |
| 2692 | } |
| 2693 | |
| 7c95608a |
2694 | /* ----------- End of grid generators ------------- */ |
| cebf0b0d |
2695 | |
| 2696 | #define FNNEW(upper,lower) &grid_new_ ## lower, |
| 2697 | #define FNSZ(upper,lower) &grid_size_ ## lower, |
| 2698 | |
| 2699 | static grid *(*(grid_news[]))(int, int, char*) = { GRIDGEN_LIST(FNNEW) }; |
| 2700 | static void(*(grid_sizes[]))(int, int, int*, int*, int*) = { GRIDGEN_LIST(FNSZ) }; |
| 2701 | |
| 2702 | char *grid_new_desc(grid_type type, int width, int height, random_state *rs) |
| 2703 | { |
| 2704 | if (type != GRID_PENROSE_P2 && type != GRID_PENROSE_P3) |
| 2705 | return NULL; |
| 2706 | |
| 2707 | return grid_new_desc_penrose(type, width, height, rs); |
| 2708 | } |
| 2709 | |
| 2710 | char *grid_validate_desc(grid_type type, int width, int height, char *desc) |
| 2711 | { |
| 2712 | if (type != GRID_PENROSE_P2 && type != GRID_PENROSE_P3) { |
| 2713 | if (desc != NULL) |
| 2714 | return "Grid description strings not used with this grid type"; |
| 2715 | return NULL; |
| 2716 | } |
| 2717 | |
| 2718 | return grid_validate_desc_penrose(type, width, height, desc); |
| 2719 | } |
| 2720 | |
| 2721 | grid *grid_new(grid_type type, int width, int height, char *desc) |
| 2722 | { |
| 2723 | char *err = grid_validate_desc(type, width, height, desc); |
| 2724 | if (err) assert(!"Invalid grid description."); |
| 2725 | |
| 2726 | return grid_news[type](width, height, desc); |
| 2727 | } |
| 2728 | |
| 2729 | void grid_compute_size(grid_type type, int width, int height, |
| 2730 | int *tilesize, int *xextent, int *yextent) |
| 2731 | { |
| 2732 | grid_sizes[type](width, height, tilesize, xextent, yextent); |
| 2733 | } |
| 2734 | |
| 2735 | /* ----------- End of grid helpers ------------- */ |
| 2736 | |
| 2737 | /* vim: set shiftwidth=4 tabstop=8: */ |
~mdw / sgt / puzzles / blame