2 * (c) Lambros Lambrou 2008
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.
22 /* Debugging options */
28 /* ----------------------------------------------------------------------
29 * Deallocate or dereference a grid
31 void grid_free(grid
*g
)
36 if (g
->refcount
== 0) {
38 for (i
= 0; i
< g
->num_faces
; i
++) {
39 sfree(g
->faces
[i
].dots
);
40 sfree(g
->faces
[i
].edges
);
42 for (i
= 0; i
< g
->num_dots
; i
++) {
43 sfree(g
->dots
[i
].faces
);
44 sfree(g
->dots
[i
].edges
);
53 /* Used by the other grid generators. Create a brand new grid with nothing
54 * initialised (all lists are NULL) */
55 static grid
*grid_empty(void)
61 g
->num_faces
= g
->num_edges
= g
->num_dots
= 0;
63 g
->lowest_x
= g
->lowest_y
= g
->highest_x
= g
->highest_y
= 0;
67 /* Helper function to calculate perpendicular distance from
68 * a point P to a line AB. A and B mustn't be equal here.
70 * Well-known formula for area A of a triangle:
72 * 2A = determinant of matrix | px ax bx |
75 * Also well-known: 2A = base * height
76 * = perpendicular distance * line-length.
78 * Combining gives: distance = determinant / line-length(a,b)
80 static double point_line_distance(long px
, long py
,
84 long det
= ax
*by
- bx
*ay
+ bx
*py
- px
*by
+ px
*ay
- ax
*py
;
87 len
= sqrt(SQ(ax
- bx
) + SQ(ay
- by
));
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
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.
105 * | edge2 is OK, but edge1 is not, even though
106 * | edge1 is perpendicularly closer to (x,y)
110 grid_edge
*grid_nearest_edge(grid
*g
, int x
, int y
)
112 grid_edge
*best_edge
;
113 double best_distance
= 0;
118 for (i
= 0; i
< g
->num_edges
; i
++) {
119 grid_edge
*e
= &g
->edges
[i
];
120 long e2
; /* squared length of edge */
121 long a2
, b2
; /* squared lengths of other sides */
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 */
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
);
131 if (a2
>= e2
+ b2
) continue;
132 if (b2
>= e2
+ a2
) continue;
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
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
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
);
147 /* Is dist more than half edge length ? */
148 if (4 * SQ(dist
) > e2
)
151 if (best_edge
== NULL
|| dist
< best_distance
) {
153 best_distance
= dist
;
159 /* ----------------------------------------------------------------------
169 #define FACE_COLOUR "red"
170 #define EDGE_COLOUR "blue"
171 #define DOT_COLOUR "black"
173 static void grid_output_svg(FILE *fp
, grid
*g
, int which
)
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\
182 <svg xmlns=\"http://www.w3.org/2000/svg\"\n\
183 xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n\n");
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) ? "" : " ",
195 fprintf(fp
, "\" style=\"fill: %s; fill-opacity: 0.2; stroke: %s\" />\n",
196 FACE_COLOUR
, FACE_COLOUR
);
198 fprintf(fp
, "</g>\n");
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
;
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
);
210 fprintf(fp
, "</g>\n");
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
);
220 fprintf(fp
, "</g>\n");
223 fprintf(fp
, "</svg>\n");
230 static void grid_try_svg(grid
*g
, int which
)
232 char *svg
= getenv("PUZZLES_SVG_GRID");
234 FILE *svgf
= fopen(svg
, "w");
236 grid_output_svg(svgf
, g
, which
);
239 fprintf(stderr
, "Unable to open file `%s': %s", svg
, strerror(errno
));
245 /* Show the basic grid information, before doing grid_make_consistent */
246 static void grid_debug_basic(grid
*g
)
248 /* TODO: Maybe we should generate an SVG image of the dots and lines
249 * of the grid here, before grid_make_consistent.
250 * Would help with debugging grid generation. */
253 printf("--- Basic Grid Data ---\n");
254 for (i
= 0; i
< g
->num_faces
; i
++) {
255 grid_face
*f
= g
->faces
+ i
;
256 printf("Face %d: dots[", i
);
258 for (j
= 0; j
< f
->order
; j
++) {
259 grid_dot
*d
= f
->dots
[j
];
260 printf("%s%d", j
? "," : "", (int)(d
- g
->dots
));
266 grid_try_svg(g
, SVG_FACES
);
270 /* Show the derived grid information, computed by grid_make_consistent */
271 static void grid_debug_derived(grid
*g
)
276 printf("--- Derived Grid Data ---\n");
277 for (i
= 0; i
< g
->num_edges
; i
++) {
278 grid_edge
*e
= g
->edges
+ i
;
279 printf("Edge %d: dots[%d,%d] faces[%d,%d]\n",
280 i
, (int)(e
->dot1
- g
->dots
), (int)(e
->dot2
- g
->dots
),
281 e
->face1
? (int)(e
->face1
- g
->faces
) : -1,
282 e
->face2
? (int)(e
->face2
- g
->faces
) : -1);
285 for (i
= 0; i
< g
->num_faces
; i
++) {
286 grid_face
*f
= g
->faces
+ i
;
288 printf("Face %d: faces[", i
);
289 for (j
= 0; j
< f
->order
; j
++) {
290 grid_edge
*e
= f
->edges
[j
];
291 grid_face
*f2
= (e
->face1
== f
) ? e
->face2
: e
->face1
;
292 printf("%s%d", j
? "," : "", f2
? (int)(f2
- g
->faces
) : -1);
297 for (i
= 0; i
< g
->num_dots
; i
++) {
298 grid_dot
*d
= g
->dots
+ i
;
300 printf("Dot %d: dots[", i
);
301 for (j
= 0; j
< d
->order
; j
++) {
302 grid_edge
*e
= d
->edges
[j
];
303 grid_dot
*d2
= (e
->dot1
== d
) ? e
->dot2
: e
->dot1
;
304 printf("%s%d", j
? "," : "", (int)(d2
- g
->dots
));
307 for (j
= 0; j
< d
->order
; j
++) {
308 grid_face
*f
= d
->faces
[j
];
309 printf("%s%d", j
? "," : "", f
? (int)(f
- g
->faces
) : -1);
315 grid_try_svg(g
, SVG_DOTS
| SVG_EDGES
| SVG_FACES
);
319 /* Helper function for building incomplete-edges list in
320 * grid_make_consistent() */
321 static int grid_edge_bydots_cmpfn(void *v1
, void *v2
)
327 /* Pointer subtraction is valid here, because all dots point into the
328 * same dot-list (g->dots).
329 * Edges are not "normalised" - the 2 dots could be stored in any order,
330 * so we need to take this into account when comparing edges. */
332 /* Compare first dots */
333 da
= (a
->dot1
< a
->dot2
) ? a
->dot1
: a
->dot2
;
334 db
= (b
->dot1
< b
->dot2
) ? b
->dot1
: b
->dot2
;
337 /* Compare last dots */
338 da
= (a
->dot1
< a
->dot2
) ? a
->dot2
: a
->dot1
;
339 db
= (b
->dot1
< b
->dot2
) ? b
->dot2
: b
->dot1
;
347 * 'Vigorously trim' a grid, by which I mean deleting any isolated or
348 * uninteresting faces. By which, in turn, I mean: ensure that the
349 * grid is composed solely of faces adjacent to at least one
350 * 'landlocked' dot (i.e. one not in contact with the infinite
351 * exterior face), and that all those dots are in a single connected
354 * This function operates on, and returns, a grid satisfying the
355 * preconditions to grid_make_consistent() rather than the
356 * postconditions. (So call it first.)
358 static void grid_trim_vigorously(grid
*g
)
360 int *dotpairs
, *faces
, *dots
;
362 int i
, j
, k
, size
, newfaces
, newdots
;
365 * First construct a matrix in which each ordered pair of dots is
366 * mapped to the index of the face in which those dots occur in
369 dotpairs
= snewn(g
->num_dots
* g
->num_dots
, int);
370 for (i
= 0; i
< g
->num_dots
; i
++)
371 for (j
= 0; j
< g
->num_dots
; j
++)
372 dotpairs
[i
*g
->num_dots
+j
] = -1;
373 for (i
= 0; i
< g
->num_faces
; i
++) {
374 grid_face
*f
= g
->faces
+ i
;
375 int dot0
= f
->dots
[f
->order
-1] - g
->dots
;
376 for (j
= 0; j
< f
->order
; j
++) {
377 int dot1
= f
->dots
[j
] - g
->dots
;
378 dotpairs
[dot0
* g
->num_dots
+ dot1
] = i
;
384 * Now we can identify landlocked dots: they're the ones all of
385 * whose edges have a mirror-image counterpart in this matrix.
387 dots
= snewn(g
->num_dots
, int);
388 for (i
= 0; i
< g
->num_dots
; i
++) {
390 for (j
= 0; j
< g
->num_dots
; j
++) {
391 if ((dotpairs
[i
*g
->num_dots
+j
] >= 0) ^
392 (dotpairs
[j
*g
->num_dots
+i
] >= 0))
393 dots
[i
] = FALSE
; /* non-duplicated edge: coastal dot */
398 * Now identify connected pairs of landlocked dots, and form a dsf
401 dsf
= snew_dsf(g
->num_dots
);
402 for (i
= 0; i
< g
->num_dots
; i
++)
403 for (j
= 0; j
< i
; j
++)
404 if (dots
[i
] && dots
[j
] &&
405 dotpairs
[i
*g
->num_dots
+j
] >= 0 &&
406 dotpairs
[j
*g
->num_dots
+i
] >= 0)
407 dsf_merge(dsf
, i
, j
);
410 * Now look for the largest component.
414 for (i
= 0; i
< g
->num_dots
; i
++) {
416 if (dots
[i
] && dsf_canonify(dsf
, i
) == i
&&
417 (newsize
= dsf_size(dsf
, i
)) > size
) {
424 * Work out which faces we're going to keep (precisely those with
425 * at least one dot in the same connected component as j) and
426 * which dots (those required by any face we're keeping).
428 * At this point we reuse the 'dots' array to indicate the dots
429 * we're keeping, rather than the ones that are landlocked.
431 faces
= snewn(g
->num_faces
, int);
432 for (i
= 0; i
< g
->num_faces
; i
++)
434 for (i
= 0; i
< g
->num_dots
; i
++)
436 for (i
= 0; i
< g
->num_faces
; i
++) {
437 grid_face
*f
= g
->faces
+ i
;
439 for (k
= 0; k
< f
->order
; k
++)
440 if (dsf_canonify(dsf
, f
->dots
[k
] - g
->dots
) == j
)
444 for (k
= 0; k
< f
->order
; k
++)
445 dots
[f
->dots
[k
]-g
->dots
] = TRUE
;
450 * Work out the new indices of those faces and dots, when we
451 * compact the arrays containing them.
453 for (i
= newfaces
= 0; i
< g
->num_faces
; i
++)
454 faces
[i
] = (faces
[i
] ? newfaces
++ : -1);
455 for (i
= newdots
= 0; i
< g
->num_dots
; i
++)
456 dots
[i
] = (dots
[i
] ? newdots
++ : -1);
459 * Free the dynamically allocated 'dots' pointer lists in faces
460 * we're going to discard.
462 for (i
= 0; i
< g
->num_faces
; i
++)
464 sfree(g
->faces
[i
].dots
);
467 * Go through and compact the arrays.
469 for (i
= 0; i
< g
->num_dots
; i
++)
471 grid_dot
*dnew
= g
->dots
+ dots
[i
], *dold
= g
->dots
+ i
;
472 *dnew
= *dold
; /* structure copy */
474 for (i
= 0; i
< g
->num_faces
; i
++)
476 grid_face
*fnew
= g
->faces
+ faces
[i
], *fold
= g
->faces
+ i
;
477 *fnew
= *fold
; /* structure copy */
478 for (j
= 0; j
< fnew
->order
; j
++) {
480 * Reindex the dots in this face.
482 k
= fnew
->dots
[j
] - g
->dots
;
483 fnew
->dots
[j
] = g
->dots
+ dots
[k
];
486 g
->num_faces
= newfaces
;
487 g
->num_dots
= newdots
;
495 /* Input: grid has its dots and faces initialised:
496 * - dots have (optionally) x and y coordinates, but no edges or faces
497 * (pointers are NULL).
498 * - edges not initialised at all
499 * - faces initialised and know which dots they have (but no edges yet). The
500 * dots around each face are assumed to be clockwise.
502 * Output: grid is complete and valid with all relationships defined.
504 static void grid_make_consistent(grid
*g
)
507 tree234
*incomplete_edges
;
508 grid_edge
*next_new_edge
; /* Where new edge will go into g->edges */
512 /* ====== Stage 1 ======
516 /* We know how many dots and faces there are, so we can find the exact
517 * number of edges from Euler's polyhedral formula: F + V = E + 2 .
518 * We use "-1", not "-2" here, because Euler's formula includes the
519 * infinite face, which we don't count. */
520 g
->num_edges
= g
->num_faces
+ g
->num_dots
- 1;
521 g
->edges
= snewn(g
->num_edges
, grid_edge
);
522 next_new_edge
= g
->edges
;
524 /* Iterate over faces, and over each face's dots, generating edges as we
525 * go. As we find each new edge, we can immediately fill in the edge's
526 * dots, but only one of the edge's faces. Later on in the iteration, we
527 * will find the same edge again (unless it's on the border), but we will
528 * know the other face.
529 * For efficiency, maintain a list of the incomplete edges, sorted by
531 incomplete_edges
= newtree234(grid_edge_bydots_cmpfn
);
532 for (i
= 0; i
< g
->num_faces
; i
++) {
533 grid_face
*f
= g
->faces
+ i
;
535 for (j
= 0; j
< f
->order
; j
++) {
536 grid_edge e
; /* fake edge for searching */
537 grid_edge
*edge_found
;
542 e
.dot2
= f
->dots
[j2
];
543 /* Use del234 instead of find234, because we always want to
544 * remove the edge if found */
545 edge_found
= del234(incomplete_edges
, &e
);
547 /* This edge already added, so fill out missing face.
548 * Edge is already removed from incomplete_edges. */
549 edge_found
->face2
= f
;
551 assert(next_new_edge
- g
->edges
< g
->num_edges
);
552 next_new_edge
->dot1
= e
.dot1
;
553 next_new_edge
->dot2
= e
.dot2
;
554 next_new_edge
->face1
= f
;
555 next_new_edge
->face2
= NULL
; /* potentially infinite face */
556 add234(incomplete_edges
, next_new_edge
);
561 freetree234(incomplete_edges
);
563 /* ====== Stage 2 ======
564 * For each face, build its edge list.
567 /* Allocate space for each edge list. Can do this, because each face's
568 * edge-list is the same size as its dot-list. */
569 for (i
= 0; i
< g
->num_faces
; i
++) {
570 grid_face
*f
= g
->faces
+ i
;
572 f
->edges
= snewn(f
->order
, grid_edge
*);
573 /* Preload with NULLs, to help detect potential bugs. */
574 for (j
= 0; j
< f
->order
; j
++)
578 /* Iterate over each edge, and over both its faces. Add this edge to
579 * the face's edge-list, after finding where it should go in the
581 for (i
= 0; i
< g
->num_edges
; i
++) {
582 grid_edge
*e
= g
->edges
+ i
;
584 for (j
= 0; j
< 2; j
++) {
585 grid_face
*f
= j
? e
->face2
: e
->face1
;
587 if (f
== NULL
) continue;
588 /* Find one of the dots around the face */
589 for (k
= 0; k
< f
->order
; k
++) {
590 if (f
->dots
[k
] == e
->dot1
)
591 break; /* found dot1 */
593 assert(k
!= f
->order
); /* Must find the dot around this face */
595 /* Labelling scheme: as we walk clockwise around the face,
596 * starting at dot0 (f->dots[0]), we hit:
597 * (dot0), edge0, dot1, edge1, dot2,...
607 * Therefore, edgeK joins dotK and dot{K+1}
610 /* Around this face, either the next dot or the previous dot
611 * must be e->dot2. Otherwise the edge is wrong. */
615 if (f
->dots
[k2
] == e
->dot2
) {
616 /* dot1(k) and dot2(k2) go clockwise around this face, so add
617 * this edge at position k (see diagram). */
618 assert(f
->edges
[k
] == NULL
);
622 /* Try previous dot */
626 if (f
->dots
[k2
] == e
->dot2
) {
627 /* dot1(k) and dot2(k2) go anticlockwise around this face. */
628 assert(f
->edges
[k2
] == NULL
);
632 assert(!"Grid broken: bad edge-face relationship");
636 /* ====== Stage 3 ======
637 * For each dot, build its edge-list and face-list.
640 /* We don't know how many edges/faces go around each dot, so we can't
641 * allocate the right space for these lists. Pre-compute the sizes by
642 * iterating over each edge and recording a tally against each dot. */
643 for (i
= 0; i
< g
->num_dots
; i
++) {
644 g
->dots
[i
].order
= 0;
646 for (i
= 0; i
< g
->num_edges
; i
++) {
647 grid_edge
*e
= g
->edges
+ i
;
651 /* Now we have the sizes, pre-allocate the edge and face lists. */
652 for (i
= 0; i
< g
->num_dots
; i
++) {
653 grid_dot
*d
= g
->dots
+ i
;
655 assert(d
->order
>= 2); /* sanity check */
656 d
->edges
= snewn(d
->order
, grid_edge
*);
657 d
->faces
= snewn(d
->order
, grid_face
*);
658 for (j
= 0; j
< d
->order
; j
++) {
663 /* For each dot, need to find a face that touches it, so we can seed
664 * the edge-face-edge-face process around each dot. */
665 for (i
= 0; i
< g
->num_faces
; i
++) {
666 grid_face
*f
= g
->faces
+ i
;
668 for (j
= 0; j
< f
->order
; j
++) {
669 grid_dot
*d
= f
->dots
[j
];
673 /* Each dot now has a face in its first slot. Generate the remaining
674 * faces and edges around the dot, by searching both clockwise and
675 * anticlockwise from the first face. Need to do both directions,
676 * because of the possibility of hitting the infinite face, which
677 * blocks progress. But there's only one such face, so we will
678 * succeed in finding every edge and face this way. */
679 for (i
= 0; i
< g
->num_dots
; i
++) {
680 grid_dot
*d
= g
->dots
+ i
;
681 int current_face1
= 0; /* ascends clockwise */
682 int current_face2
= 0; /* descends anticlockwise */
684 /* Labelling scheme: as we walk clockwise around the dot, starting
685 * at face0 (d->faces[0]), we hit:
686 * (face0), edge0, face1, edge1, face2,...
698 * So, for example, face1 should be joined to edge0 and edge1,
699 * and those edges should appear in an anticlockwise sense around
700 * that face (see diagram). */
702 /* clockwise search */
704 grid_face
*f
= d
->faces
[current_face1
];
708 /* find dot around this face */
709 for (j
= 0; j
< f
->order
; j
++) {
713 assert(j
!= f
->order
); /* must find dot */
715 /* Around f, required edge is anticlockwise from the dot. See
716 * the other labelling scheme higher up, for why we subtract 1
722 d
->edges
[current_face1
] = e
; /* set edge */
724 if (current_face1
== d
->order
)
728 d
->faces
[current_face1
] =
729 (e
->face1
== f
) ? e
->face2
: e
->face1
;
730 if (d
->faces
[current_face1
] == NULL
)
731 break; /* cannot progress beyond infinite face */
734 /* If the clockwise search made it all the way round, don't need to
735 * bother with the anticlockwise search. */
736 if (current_face1
== d
->order
)
737 continue; /* this dot is complete, move on to next dot */
739 /* anticlockwise search */
741 grid_face
*f
= d
->faces
[current_face2
];
745 /* find dot around this face */
746 for (j
= 0; j
< f
->order
; j
++) {
750 assert(j
!= f
->order
); /* must find dot */
752 /* Around f, required edge is clockwise from the dot. */
756 if (current_face2
== -1)
757 current_face2
= d
->order
- 1;
758 d
->edges
[current_face2
] = e
; /* set edge */
761 if (current_face2
== current_face1
)
763 d
->faces
[current_face2
] =
764 (e
->face1
== f
) ? e
->face2
: e
->face1
;
765 /* There's only 1 infinite face, so we must get all the way
766 * to current_face1 before we hit it. */
767 assert(d
->faces
[current_face2
]);
771 /* ====== Stage 4 ======
772 * Compute other grid settings
775 /* Bounding rectangle */
776 for (i
= 0; i
< g
->num_dots
; i
++) {
777 grid_dot
*d
= g
->dots
+ i
;
779 g
->lowest_x
= g
->highest_x
= d
->x
;
780 g
->lowest_y
= g
->highest_y
= d
->y
;
782 g
->lowest_x
= min(g
->lowest_x
, d
->x
);
783 g
->highest_x
= max(g
->highest_x
, d
->x
);
784 g
->lowest_y
= min(g
->lowest_y
, d
->y
);
785 g
->highest_y
= max(g
->highest_y
, d
->y
);
789 grid_debug_derived(g
);
792 /* Helpers for making grid-generation easier. These functions are only
793 * intended for use during grid generation. */
795 /* Comparison function for the (tree234) sorted dot list */
796 static int grid_point_cmp_fn(void *v1
, void *v2
)
801 return p2
->y
- p1
->y
;
803 return p2
->x
- p1
->x
;
805 /* Add a new face to the grid, with its dot list allocated.
806 * Assumes there's enough space allocated for the new face in grid->faces */
807 static void grid_face_add_new(grid
*g
, int face_size
)
810 grid_face
*new_face
= g
->faces
+ g
->num_faces
;
811 new_face
->order
= face_size
;
812 new_face
->dots
= snewn(face_size
, grid_dot
*);
813 for (i
= 0; i
< face_size
; i
++)
814 new_face
->dots
[i
] = NULL
;
815 new_face
->edges
= NULL
;
816 new_face
->has_incentre
= FALSE
;
819 /* Assumes dot list has enough space */
820 static grid_dot
*grid_dot_add_new(grid
*g
, int x
, int y
)
822 grid_dot
*new_dot
= g
->dots
+ g
->num_dots
;
824 new_dot
->edges
= NULL
;
825 new_dot
->faces
= NULL
;
831 /* Retrieve a dot with these (x,y) coordinates. Either return an existing dot
832 * in the dot_list, or add a new dot to the grid (and the dot_list) and
834 * Assumes g->dots has enough capacity allocated */
835 static grid_dot
*grid_get_dot(grid
*g
, tree234
*dot_list
, int x
, int y
)
844 ret
= find234(dot_list
, &test
, NULL
);
848 ret
= grid_dot_add_new(g
, x
, y
);
849 add234(dot_list
, ret
);
853 /* Sets the last face of the grid to include this dot, at this position
854 * around the face. Assumes num_faces is at least 1 (a new face has
855 * previously been added, with the required number of dots allocated) */
856 static void grid_face_set_dot(grid
*g
, grid_dot
*d
, int position
)
858 grid_face
*last_face
= g
->faces
+ g
->num_faces
- 1;
859 last_face
->dots
[position
] = d
;
863 * Helper routines for grid_find_incentre.
865 static int solve_2x2_matrix(double mx
[4], double vin
[2], double vout
[2])
869 det
= (mx
[0]*mx
[3] - mx
[1]*mx
[2]);
873 inv
[0] = mx
[3] / det
;
874 inv
[1] = -mx
[1] / det
;
875 inv
[2] = -mx
[2] / det
;
876 inv
[3] = mx
[0] / det
;
878 vout
[0] = inv
[0]*vin
[0] + inv
[1]*vin
[1];
879 vout
[1] = inv
[2]*vin
[0] + inv
[3]*vin
[1];
883 static int solve_3x3_matrix(double mx
[9], double vin
[3], double vout
[3])
888 det
= (mx
[0]*mx
[4]*mx
[8] + mx
[1]*mx
[5]*mx
[6] + mx
[2]*mx
[3]*mx
[7] -
889 mx
[0]*mx
[5]*mx
[7] - mx
[1]*mx
[3]*mx
[8] - mx
[2]*mx
[4]*mx
[6]);
893 inv
[0] = (mx
[4]*mx
[8] - mx
[5]*mx
[7]) / det
;
894 inv
[1] = (mx
[2]*mx
[7] - mx
[1]*mx
[8]) / det
;
895 inv
[2] = (mx
[1]*mx
[5] - mx
[2]*mx
[4]) / det
;
896 inv
[3] = (mx
[5]*mx
[6] - mx
[3]*mx
[8]) / det
;
897 inv
[4] = (mx
[0]*mx
[8] - mx
[2]*mx
[6]) / det
;
898 inv
[5] = (mx
[2]*mx
[3] - mx
[0]*mx
[5]) / det
;
899 inv
[6] = (mx
[3]*mx
[7] - mx
[4]*mx
[6]) / det
;
900 inv
[7] = (mx
[1]*mx
[6] - mx
[0]*mx
[7]) / det
;
901 inv
[8] = (mx
[0]*mx
[4] - mx
[1]*mx
[3]) / det
;
903 vout
[0] = inv
[0]*vin
[0] + inv
[1]*vin
[1] + inv
[2]*vin
[2];
904 vout
[1] = inv
[3]*vin
[0] + inv
[4]*vin
[1] + inv
[5]*vin
[2];
905 vout
[2] = inv
[6]*vin
[0] + inv
[7]*vin
[1] + inv
[8]*vin
[2];
910 void grid_find_incentre(grid_face
*f
)
912 double xbest
, ybest
, bestdist
;
914 grid_dot
*edgedot1
[3], *edgedot2
[3];
922 * Find the point in the polygon with the maximum distance to any
925 * Such a point must exist which is in contact with at least three
926 * edges and/or vertices. (Proof: if it's only in contact with two
927 * edges and/or vertices, it can't even be at a _local_ maximum -
928 * any such circle can always be expanded in some direction.) So
929 * we iterate through all 3-subsets of the combined set of edges
930 * and vertices; for each subset we generate one or two candidate
931 * points that might be the incentre, and then we vet each one to
932 * see if it's inside the polygon and what its maximum radius is.
934 * (There's one case which this algorithm will get noticeably
935 * wrong, and that's when a continuum of equally good answers
936 * exists due to parallel edges. Consider a long thin rectangle,
937 * for instance, or a parallelogram. This algorithm will pick a
938 * point near one end, and choose the end arbitrarily; obviously a
939 * nicer point to choose would be in the centre. To fix this I
940 * would have to introduce a special-case system which detected
941 * parallel edges in advance, set aside all candidate points
942 * generated using both edges in a parallel pair, and generated
943 * some additional candidate points half way between them. Also,
944 * of course, I'd have to cope with rounding error making such a
945 * point look worse than one of its endpoints. So I haven't done
946 * this for the moment, and will cross it if necessary when I come
949 * We don't actually iterate literally over _edges_, in the sense
950 * of grid_edge structures. Instead, we fill in edgedot1[] and
951 * edgedot2[] with a pair of dots adjacent in the face's list of
952 * vertices. This ensures that we get the edges in consistent
953 * orientation, which we could not do from the grid structure
954 * alone. (A moment's consideration of an order-3 vertex should
955 * make it clear that if a notional arrow was written on each
956 * edge, _at least one_ of the three faces bordering that vertex
957 * would have to have the two arrows tip-to-tip or tail-to-tail
958 * rather than tip-to-tail.)
964 for (i
= 0; i
+2 < 2*f
->order
; i
++) {
966 edgedot1
[nedges
] = f
->dots
[i
];
967 edgedot2
[nedges
++] = f
->dots
[(i
+1)%f
->order
];
969 dots
[ndots
++] = f
->dots
[i
- f
->order
];
971 for (j
= i
+1; j
+1 < 2*f
->order
; j
++) {
973 edgedot1
[nedges
] = f
->dots
[j
];
974 edgedot2
[nedges
++] = f
->dots
[(j
+1)%f
->order
];
976 dots
[ndots
++] = f
->dots
[j
- f
->order
];
978 for (k
= j
+1; k
< 2*f
->order
; k
++) {
979 double cx
[2], cy
[2]; /* candidate positions */
980 int cn
= 0; /* number of candidates */
983 edgedot1
[nedges
] = f
->dots
[k
];
984 edgedot2
[nedges
++] = f
->dots
[(k
+1)%f
->order
];
986 dots
[ndots
++] = f
->dots
[k
- f
->order
];
989 * Find a point, or pair of points, equidistant from
990 * all the specified edges and/or vertices.
994 * Three edges. This is a linear matrix equation:
995 * each row of the matrix represents the fact that
996 * the point (x,y) we seek is at distance r from
997 * that edge, and we solve three of those
998 * simultaneously to obtain x,y,r. (We ignore r.)
1000 double matrix
[9], vector
[3], vector2
[3];
1003 for (m
= 0; m
< 3; m
++) {
1004 int x1
= edgedot1
[m
]->x
, x2
= edgedot2
[m
]->x
;
1005 int y1
= edgedot1
[m
]->y
, y2
= edgedot2
[m
]->y
;
1006 int dx
= x2
-x1
, dy
= y2
-y1
;
1009 * ((x,y) - (x1,y1)) . (dy,-dx) = r |(dx,dy)|
1011 * => x dy - y dx - r |(dx,dy)| = (x1 dy - y1 dx)
1014 matrix
[3*m
+1] = -dx
;
1015 matrix
[3*m
+2] = -sqrt((double)dx
*dx
+(double)dy
*dy
);
1016 vector
[m
] = (double)x1
*dy
- (double)y1
*dx
;
1019 if (solve_3x3_matrix(matrix
, vector
, vector2
)) {
1020 cx
[cn
] = vector2
[0];
1021 cy
[cn
] = vector2
[1];
1024 } else if (nedges
== 2) {
1026 * Two edges and a dot. This will end up in a
1027 * quadratic equation.
1029 * First, look at the two edges. Having our point
1030 * be some distance r from both of them gives rise
1031 * to a pair of linear equations in x,y,r of the
1034 * (x-x1) dy - (y-y1) dx = r sqrt(dx^2+dy^2)
1036 * We eliminate r between those equations to give
1037 * us a single linear equation in x,y describing
1038 * the locus of points equidistant from both lines
1039 * - i.e. the angle bisector.
1041 * We then choose one of x,y to be a parameter t,
1042 * and derive linear formulae for x,y,r in terms
1043 * of t. This enables us to write down the
1044 * circular equation (x-xd)^2+(y-yd)^2=r^2 as a
1045 * quadratic in t; solving that and substituting
1046 * in for x,y gives us two candidate points.
1048 double eqs
[2][4]; /* a,b,c,d : ax+by+cr=d */
1049 double eq
[3]; /* a,b,c: ax+by=c */
1050 double xt
[2], yt
[2], rt
[2]; /* a,b: {x,y,r}=at+b */
1051 double q
[3]; /* a,b,c: at^2+bt+c=0 */
1054 /* Find equations of the two input lines. */
1055 for (m
= 0; m
< 2; m
++) {
1056 int x1
= edgedot1
[m
]->x
, x2
= edgedot2
[m
]->x
;
1057 int y1
= edgedot1
[m
]->y
, y2
= edgedot2
[m
]->y
;
1058 int dx
= x2
-x1
, dy
= y2
-y1
;
1062 eqs
[m
][2] = -sqrt(dx
*dx
+dy
*dy
);
1063 eqs
[m
][3] = x1
*dy
- y1
*dx
;
1066 /* Derive the angle bisector by eliminating r. */
1067 eq
[0] = eqs
[0][0]*eqs
[1][2] - eqs
[1][0]*eqs
[0][2];
1068 eq
[1] = eqs
[0][1]*eqs
[1][2] - eqs
[1][1]*eqs
[0][2];
1069 eq
[2] = eqs
[0][3]*eqs
[1][2] - eqs
[1][3]*eqs
[0][2];
1071 /* Parametrise x and y in terms of some t. */
1072 if (fabs(eq
[0]) < fabs(eq
[1])) {
1073 /* Parameter is x. */
1074 xt
[0] = 1; xt
[1] = 0;
1075 yt
[0] = -eq
[0]/eq
[1]; yt
[1] = eq
[2]/eq
[1];
1077 /* Parameter is y. */
1078 yt
[0] = 1; yt
[1] = 0;
1079 xt
[0] = -eq
[1]/eq
[0]; xt
[1] = eq
[2]/eq
[0];
1082 /* Find a linear representation of r using eqs[0]. */
1083 rt
[0] = -(eqs
[0][0]*xt
[0] + eqs
[0][1]*yt
[0])/eqs
[0][2];
1084 rt
[1] = (eqs
[0][3] - eqs
[0][0]*xt
[1] -
1085 eqs
[0][1]*yt
[1])/eqs
[0][2];
1087 /* Construct the quadratic equation. */
1088 q
[0] = -rt
[0]*rt
[0];
1089 q
[1] = -2*rt
[0]*rt
[1];
1090 q
[2] = -rt
[1]*rt
[1];
1091 q
[0] += xt
[0]*xt
[0];
1092 q
[1] += 2*xt
[0]*(xt
[1]-dots
[0]->x
);
1093 q
[2] += (xt
[1]-dots
[0]->x
)*(xt
[1]-dots
[0]->x
);
1094 q
[0] += yt
[0]*yt
[0];
1095 q
[1] += 2*yt
[0]*(yt
[1]-dots
[0]->y
);
1096 q
[2] += (yt
[1]-dots
[0]->y
)*(yt
[1]-dots
[0]->y
);
1099 disc
= q
[1]*q
[1] - 4*q
[0]*q
[2];
1105 t
= (-q
[1] + disc
) / (2*q
[0]);
1106 cx
[cn
] = xt
[0]*t
+ xt
[1];
1107 cy
[cn
] = yt
[0]*t
+ yt
[1];
1110 t
= (-q
[1] - disc
) / (2*q
[0]);
1111 cx
[cn
] = xt
[0]*t
+ xt
[1];
1112 cy
[cn
] = yt
[0]*t
+ yt
[1];
1115 } else if (nedges
== 1) {
1117 * Two dots and an edge. This one's another
1118 * quadratic equation.
1120 * The point we want must lie on the perpendicular
1121 * bisector of the two dots; that much is obvious.
1122 * So we can construct a parametrisation of that
1123 * bisecting line, giving linear formulae for x,y
1124 * in terms of t. We can also express the distance
1125 * from the edge as such a linear formula.
1127 * Then we set that equal to the radius of the
1128 * circle passing through the two points, which is
1129 * a Pythagoras exercise; that gives rise to a
1130 * quadratic in t, which we solve.
1132 double xt
[2], yt
[2], rt
[2]; /* a,b: {x,y,r}=at+b */
1133 double q
[3]; /* a,b,c: at^2+bt+c=0 */
1137 /* Find parametric formulae for x,y. */
1139 int x1
= dots
[0]->x
, x2
= dots
[1]->x
;
1140 int y1
= dots
[0]->y
, y2
= dots
[1]->y
;
1141 int dx
= x2
-x1
, dy
= y2
-y1
;
1142 double d
= sqrt((double)dx
*dx
+ (double)dy
*dy
);
1144 xt
[1] = (x1
+x2
)/2.0;
1145 yt
[1] = (y1
+y2
)/2.0;
1146 /* It's convenient if we have t at standard scale. */
1150 /* Also note down half the separation between
1151 * the dots, for use in computing the circle radius. */
1155 /* Find a parametric formula for r. */
1157 int x1
= edgedot1
[0]->x
, x2
= edgedot2
[0]->x
;
1158 int y1
= edgedot1
[0]->y
, y2
= edgedot2
[0]->y
;
1159 int dx
= x2
-x1
, dy
= y2
-y1
;
1160 double d
= sqrt((double)dx
*dx
+ (double)dy
*dy
);
1161 rt
[0] = (xt
[0]*dy
- yt
[0]*dx
) / d
;
1162 rt
[1] = ((xt
[1]-x1
)*dy
- (yt
[1]-y1
)*dx
) / d
;
1165 /* Construct the quadratic equation. */
1167 q
[1] = 2*rt
[0]*rt
[1];
1170 q
[2] -= halfsep
*halfsep
;
1173 disc
= q
[1]*q
[1] - 4*q
[0]*q
[2];
1179 t
= (-q
[1] + disc
) / (2*q
[0]);
1180 cx
[cn
] = xt
[0]*t
+ xt
[1];
1181 cy
[cn
] = yt
[0]*t
+ yt
[1];
1184 t
= (-q
[1] - disc
) / (2*q
[0]);
1185 cx
[cn
] = xt
[0]*t
+ xt
[1];
1186 cy
[cn
] = yt
[0]*t
+ yt
[1];
1189 } else if (nedges
== 0) {
1191 * Three dots. This is another linear matrix
1192 * equation, this time with each row of the matrix
1193 * representing the perpendicular bisector between
1194 * two of the points. Of course we only need two
1195 * such lines to find their intersection, so we
1196 * need only solve a 2x2 matrix equation.
1199 double matrix
[4], vector
[2], vector2
[2];
1202 for (m
= 0; m
< 2; m
++) {
1203 int x1
= dots
[m
]->x
, x2
= dots
[m
+1]->x
;
1204 int y1
= dots
[m
]->y
, y2
= dots
[m
+1]->y
;
1205 int dx
= x2
-x1
, dy
= y2
-y1
;
1208 * ((x,y) - (x1,y1)) . (dx,dy) = 1/2 |(dx,dy)|^2
1210 * => 2x dx + 2y dy = dx^2+dy^2 + (2 x1 dx + 2 y1 dy)
1212 matrix
[2*m
+0] = 2*dx
;
1213 matrix
[2*m
+1] = 2*dy
;
1214 vector
[m
] = ((double)dx
*dx
+ (double)dy
*dy
+
1215 2.0*x1
*dx
+ 2.0*y1
*dy
);
1218 if (solve_2x2_matrix(matrix
, vector
, vector2
)) {
1219 cx
[cn
] = vector2
[0];
1220 cy
[cn
] = vector2
[1];
1226 * Now go through our candidate points and see if any
1227 * of them are better than what we've got so far.
1229 for (m
= 0; m
< cn
; m
++) {
1230 double x
= cx
[m
], y
= cy
[m
];
1233 * First, disqualify the point if it's not inside
1234 * the polygon, which we work out by counting the
1235 * edges to the right of the point. (For
1236 * tiebreaking purposes when edges start or end on
1237 * our y-coordinate or go right through it, we
1238 * consider our point to be offset by a small
1239 * _positive_ epsilon in both the x- and
1243 for (e
= 0; e
< f
->order
; e
++) {
1244 int xs
= f
->edges
[e
]->dot1
->x
;
1245 int xe
= f
->edges
[e
]->dot2
->x
;
1246 int ys
= f
->edges
[e
]->dot1
->y
;
1247 int ye
= f
->edges
[e
]->dot2
->y
;
1248 if ((y
>= ys
&& y
< ye
) || (y
>= ye
&& y
< ys
)) {
1250 * The line goes past our y-position. Now we need
1251 * to know if its x-coordinate when it does so is
1254 * The x-coordinate in question is mathematically
1255 * (y - ys) * (xe - xs) / (ye - ys), and we want
1256 * to know whether (x - xs) >= that. Of course we
1257 * avoid the division, so we can work in integers;
1258 * to do this we must multiply both sides of the
1259 * inequality by ye - ys, which means we must
1260 * first check that's not negative.
1262 int num
= xe
- xs
, denom
= ye
- ys
;
1267 if ((x
- xs
) * denom
>= (y
- ys
) * num
)
1274 double mindist
= HUGE_VAL
;
1277 double mindist
= DBL_MAX
;
1279 #error No way to get maximum floating-point number.
1285 * This point is inside the polygon, so now we check
1286 * its minimum distance to every edge and corner.
1287 * First the corners ...
1289 for (d
= 0; d
< f
->order
; d
++) {
1290 int xp
= f
->dots
[d
]->x
;
1291 int yp
= f
->dots
[d
]->y
;
1292 double dx
= x
- xp
, dy
= y
- yp
;
1293 double dist
= dx
*dx
+ dy
*dy
;
1299 * ... and now also check the perpendicular distance
1300 * to every edge, if the perpendicular lies between
1301 * the edge's endpoints.
1303 for (e
= 0; e
< f
->order
; e
++) {
1304 int xs
= f
->edges
[e
]->dot1
->x
;
1305 int xe
= f
->edges
[e
]->dot2
->x
;
1306 int ys
= f
->edges
[e
]->dot1
->y
;
1307 int ye
= f
->edges
[e
]->dot2
->y
;
1310 * If s and e are our endpoints, and p our
1311 * candidate circle centre, the foot of a
1312 * perpendicular from p to the line se lies
1313 * between s and e if and only if (p-s).(e-s) lies
1314 * strictly between 0 and (e-s).(e-s).
1316 int edx
= xe
- xs
, edy
= ye
- ys
;
1317 double pdx
= x
- xs
, pdy
= y
- ys
;
1318 double pde
= pdx
* edx
+ pdy
* edy
;
1319 long ede
= (long)edx
* edx
+ (long)edy
* edy
;
1320 if (0 < pde
&& pde
< ede
) {
1322 * Yes, the nearest point on this edge is
1323 * closer than either endpoint, so we must
1324 * take it into account by measuring the
1325 * perpendicular distance to the edge and
1326 * checking its square against mindist.
1329 double pdre
= pdx
* edy
- pdy
* edx
;
1330 double sqlen
= pdre
* pdre
/ ede
;
1332 if (mindist
> sqlen
)
1338 * Right. Now we know the biggest circle around this
1339 * point, so we can check it against bestdist.
1341 if (bestdist
< mindist
) {
1365 assert(bestdist
> 0);
1367 f
->has_incentre
= TRUE
;
1368 f
->ix
= xbest
+ 0.5; /* round to nearest */
1369 f
->iy
= ybest
+ 0.5;
1372 /* ------ Generate various types of grid ------ */
1374 /* General method is to generate faces, by calculating their dot coordinates.
1375 * As new faces are added, we keep track of all the dots so we can tell when
1376 * a new face reuses an existing dot. For example, two squares touching at an
1377 * edge would generate six unique dots: four dots from the first face, then
1378 * two additional dots for the second face, because we detect the other two
1379 * dots have already been taken up. This list is stored in a tree234
1380 * called "points". No extra memory-allocation needed here - we store the
1381 * actual grid_dot* pointers, which all point into the g->dots list.
1382 * For this reason, we have to calculate coordinates in such a way as to
1383 * eliminate any rounding errors, so we can detect when a dot on one
1384 * face precisely lands on a dot of a different face. No floating-point
1388 #define SQUARE_TILESIZE 20
1390 static void grid_size_square(int width
, int height
,
1391 int *tilesize
, int *xextent
, int *yextent
)
1393 int a
= SQUARE_TILESIZE
;
1396 *xextent
= width
* a
;
1397 *yextent
= height
* a
;
1400 static grid
*grid_new_square(int width
, int height
, const char *desc
)
1404 int a
= SQUARE_TILESIZE
;
1406 /* Upper bounds - don't have to be exact */
1407 int max_faces
= width
* height
;
1408 int max_dots
= (width
+ 1) * (height
+ 1);
1412 grid
*g
= grid_empty();
1414 g
->faces
= snewn(max_faces
, grid_face
);
1415 g
->dots
= snewn(max_dots
, grid_dot
);
1417 points
= newtree234(grid_point_cmp_fn
);
1419 /* generate square faces */
1420 for (y
= 0; y
< height
; y
++) {
1421 for (x
= 0; x
< width
; x
++) {
1427 grid_face_add_new(g
, 4);
1428 d
= grid_get_dot(g
, points
, px
, py
);
1429 grid_face_set_dot(g
, d
, 0);
1430 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1431 grid_face_set_dot(g
, d
, 1);
1432 d
= grid_get_dot(g
, points
, px
+ a
, py
+ a
);
1433 grid_face_set_dot(g
, d
, 2);
1434 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1435 grid_face_set_dot(g
, d
, 3);
1439 freetree234(points
);
1440 assert(g
->num_faces
<= max_faces
);
1441 assert(g
->num_dots
<= max_dots
);
1443 grid_make_consistent(g
);
1447 #define HONEY_TILESIZE 45
1448 /* Vector for side of hexagon - ratio is close to sqrt(3) */
1452 static void grid_size_honeycomb(int width
, int height
,
1453 int *tilesize
, int *xextent
, int *yextent
)
1458 *tilesize
= HONEY_TILESIZE
;
1459 *xextent
= (3 * a
* (width
-1)) + 4*a
;
1460 *yextent
= (2 * b
* (height
-1)) + 3*b
;
1463 static grid
*grid_new_honeycomb(int width
, int height
, const char *desc
)
1469 /* Upper bounds - don't have to be exact */
1470 int max_faces
= width
* height
;
1471 int max_dots
= 2 * (width
+ 1) * (height
+ 1);
1475 grid
*g
= grid_empty();
1476 g
->tilesize
= HONEY_TILESIZE
;
1477 g
->faces
= snewn(max_faces
, grid_face
);
1478 g
->dots
= snewn(max_dots
, grid_dot
);
1480 points
= newtree234(grid_point_cmp_fn
);
1482 /* generate hexagonal faces */
1483 for (y
= 0; y
< height
; y
++) {
1484 for (x
= 0; x
< width
; x
++) {
1491 grid_face_add_new(g
, 6);
1493 d
= grid_get_dot(g
, points
, cx
- a
, cy
- b
);
1494 grid_face_set_dot(g
, d
, 0);
1495 d
= grid_get_dot(g
, points
, cx
+ a
, cy
- b
);
1496 grid_face_set_dot(g
, d
, 1);
1497 d
= grid_get_dot(g
, points
, cx
+ 2*a
, cy
);
1498 grid_face_set_dot(g
, d
, 2);
1499 d
= grid_get_dot(g
, points
, cx
+ a
, cy
+ b
);
1500 grid_face_set_dot(g
, d
, 3);
1501 d
= grid_get_dot(g
, points
, cx
- a
, cy
+ b
);
1502 grid_face_set_dot(g
, d
, 4);
1503 d
= grid_get_dot(g
, points
, cx
- 2*a
, cy
);
1504 grid_face_set_dot(g
, d
, 5);
1508 freetree234(points
);
1509 assert(g
->num_faces
<= max_faces
);
1510 assert(g
->num_dots
<= max_dots
);
1512 grid_make_consistent(g
);
1516 #define TRIANGLE_TILESIZE 18
1517 /* Vector for side of triangle - ratio is close to sqrt(3) */
1518 #define TRIANGLE_VEC_X 15
1519 #define TRIANGLE_VEC_Y 26
1521 static void grid_size_triangular(int width
, int height
,
1522 int *tilesize
, int *xextent
, int *yextent
)
1524 int vec_x
= TRIANGLE_VEC_X
;
1525 int vec_y
= TRIANGLE_VEC_Y
;
1527 *tilesize
= TRIANGLE_TILESIZE
;
1528 *xextent
= (width
+1) * 2 * vec_x
;
1529 *yextent
= height
* vec_y
;
1532 static char *grid_validate_desc_triangular(grid_type type
, int width
,
1533 int height
, const char *desc
)
1536 * Triangular grids: an absent description is valid (indicating
1537 * the old-style approach which had 'ears', i.e. triangles
1538 * connected to only one other face, at some grid corners), and so
1539 * is a description reading just "0" (indicating the new-style
1540 * approach in which those ears are trimmed off). Anything else is
1544 if (!desc
|| !strcmp(desc
, "0"))
1547 return "Unrecognised grid description.";
1550 /* Doesn't use the previous method of generation, it pre-dates it!
1551 * A triangular grid is just about simple enough to do by "brute force" */
1552 static grid
*grid_new_triangular(int width
, int height
, const char *desc
)
1555 int version
= (desc
== NULL
? -1 : atoi(desc
));
1557 /* Vector for side of triangle - ratio is close to sqrt(3) */
1558 int vec_x
= TRIANGLE_VEC_X
;
1559 int vec_y
= TRIANGLE_VEC_Y
;
1563 /* convenient alias */
1566 grid
*g
= grid_empty();
1567 g
->tilesize
= TRIANGLE_TILESIZE
;
1569 if (version
== -1) {
1571 * Old-style triangular grid generation, preserved as-is for
1572 * backwards compatibility with old game ids, in which it's
1573 * just a little asymmetric and there are 'ears' (faces linked
1574 * to only one other face) at two grid corners.
1576 * Example old-style game ids, which should still work, and in
1577 * which you should see the ears in the TL/BR corners on the
1578 * first one and in the TL/BL corners on the second:
1580 * 5x5t1:2c2a1a2a201a1a1a1112a1a2b1211f0b21a2a2a0a
1581 * 5x6t1:a022a212h1a1d1a12c2b11a012b1a20d1a0a12e
1584 g
->num_faces
= width
* height
* 2;
1585 g
->num_dots
= (width
+ 1) * (height
+ 1);
1586 g
->faces
= snewn(g
->num_faces
, grid_face
);
1587 g
->dots
= snewn(g
->num_dots
, grid_dot
);
1591 for (y
= 0; y
<= height
; y
++) {
1592 for (x
= 0; x
<= width
; x
++) {
1593 grid_dot
*d
= g
->dots
+ index
;
1594 /* odd rows are offset to the right */
1598 d
->x
= x
* 2 * vec_x
+ ((y
% 2) ? vec_x
: 0);
1604 /* generate faces */
1606 for (y
= 0; y
< height
; y
++) {
1607 for (x
= 0; x
< width
; x
++) {
1608 /* initialise two faces for this (x,y) */
1609 grid_face
*f1
= g
->faces
+ index
;
1610 grid_face
*f2
= f1
+ 1;
1613 f1
->dots
= snewn(f1
->order
, grid_dot
*);
1614 f1
->has_incentre
= FALSE
;
1617 f2
->dots
= snewn(f2
->order
, grid_dot
*);
1618 f2
->has_incentre
= FALSE
;
1620 /* face descriptions depend on whether the row-number is
1623 f1
->dots
[0] = g
->dots
+ y
* w
+ x
;
1624 f1
->dots
[1] = g
->dots
+ (y
+ 1) * w
+ x
+ 1;
1625 f1
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
;
1626 f2
->dots
[0] = g
->dots
+ y
* w
+ x
;
1627 f2
->dots
[1] = g
->dots
+ y
* w
+ x
+ 1;
1628 f2
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
+ 1;
1630 f1
->dots
[0] = g
->dots
+ y
* w
+ x
;
1631 f1
->dots
[1] = g
->dots
+ y
* w
+ x
+ 1;
1632 f1
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
;
1633 f2
->dots
[0] = g
->dots
+ y
* w
+ x
+ 1;
1634 f2
->dots
[1] = g
->dots
+ (y
+ 1) * w
+ x
+ 1;
1635 f2
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
;
1642 * New-style approach, in which there are never any 'ears',
1643 * and if height is even then the grid is nicely 4-way
1646 * Example new-style grids:
1648 * 5x5t1:0_21120b11a1a01a1a00c1a0b211021c1h1a2a1a0a
1649 * 5x6t1:0_a1212c22c2a02a2f22a0c12a110d0e1c0c0a101121a1
1651 tree234
*points
= newtree234(grid_point_cmp_fn
);
1652 /* Upper bounds - don't have to be exact */
1653 int max_faces
= height
* (2*width
+1);
1654 int max_dots
= (height
+1) * (width
+1) * 4;
1656 g
->faces
= snewn(max_faces
, grid_face
);
1657 g
->dots
= snewn(max_dots
, grid_dot
);
1659 for (y
= 0; y
< height
; y
++) {
1661 * Each row contains (width+1) triangles one way up, and
1662 * (width) triangles the other way up. Which way up is
1663 * which varies with parity of y. Also, the dots around
1664 * each face will flip direction with parity of y, so we
1665 * set up n1 and n2 to cope with that easily.
1668 y0
= y1
= y
* vec_y
;
1677 for (x
= 0; x
<= width
; x
++) {
1678 int x0
= 2*x
* vec_x
, x1
= x0
+ vec_x
, x2
= x1
+ vec_x
;
1681 * If the grid has odd height, then we skip the first
1682 * and last triangles on this row, otherwise they'll
1685 if (height
% 2 == 1 && y
== height
-1 && (x
== 0 || x
== width
))
1688 grid_face_add_new(g
, 3);
1689 grid_face_set_dot(g
, grid_get_dot(g
, points
, x0
, y0
), 0);
1690 grid_face_set_dot(g
, grid_get_dot(g
, points
, x1
, y1
), n1
);
1691 grid_face_set_dot(g
, grid_get_dot(g
, points
, x2
, y0
), n2
);
1694 for (x
= 0; x
< width
; x
++) {
1695 int x0
= (2*x
+1) * vec_x
, x1
= x0
+ vec_x
, x2
= x1
+ vec_x
;
1697 grid_face_add_new(g
, 3);
1698 grid_face_set_dot(g
, grid_get_dot(g
, points
, x0
, y1
), 0);
1699 grid_face_set_dot(g
, grid_get_dot(g
, points
, x1
, y0
), n2
);
1700 grid_face_set_dot(g
, grid_get_dot(g
, points
, x2
, y1
), n1
);
1704 freetree234(points
);
1705 assert(g
->num_faces
<= max_faces
);
1706 assert(g
->num_dots
<= max_dots
);
1709 grid_make_consistent(g
);
1713 #define SNUBSQUARE_TILESIZE 18
1714 /* Vector for side of triangle - ratio is close to sqrt(3) */
1715 #define SNUBSQUARE_A 15
1716 #define SNUBSQUARE_B 26
1718 static void grid_size_snubsquare(int width
, int height
,
1719 int *tilesize
, int *xextent
, int *yextent
)
1721 int a
= SNUBSQUARE_A
;
1722 int b
= SNUBSQUARE_B
;
1724 *tilesize
= SNUBSQUARE_TILESIZE
;
1725 *xextent
= (a
+b
) * (width
-1) + a
+ b
;
1726 *yextent
= (a
+b
) * (height
-1) + a
+ b
;
1729 static grid
*grid_new_snubsquare(int width
, int height
, const char *desc
)
1732 int a
= SNUBSQUARE_A
;
1733 int b
= SNUBSQUARE_B
;
1735 /* Upper bounds - don't have to be exact */
1736 int max_faces
= 3 * width
* height
;
1737 int max_dots
= 2 * (width
+ 1) * (height
+ 1);
1741 grid
*g
= grid_empty();
1742 g
->tilesize
= SNUBSQUARE_TILESIZE
;
1743 g
->faces
= snewn(max_faces
, grid_face
);
1744 g
->dots
= snewn(max_dots
, grid_dot
);
1746 points
= newtree234(grid_point_cmp_fn
);
1748 for (y
= 0; y
< height
; y
++) {
1749 for (x
= 0; x
< width
; x
++) {
1752 int px
= (a
+ b
) * x
;
1753 int py
= (a
+ b
) * y
;
1755 /* generate square faces */
1756 grid_face_add_new(g
, 4);
1758 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1759 grid_face_set_dot(g
, d
, 0);
1760 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
);
1761 grid_face_set_dot(g
, d
, 1);
1762 d
= grid_get_dot(g
, points
, px
+ b
, py
+ a
+ b
);
1763 grid_face_set_dot(g
, d
, 2);
1764 d
= grid_get_dot(g
, points
, px
, py
+ b
);
1765 grid_face_set_dot(g
, d
, 3);
1767 d
= grid_get_dot(g
, points
, px
+ b
, py
);
1768 grid_face_set_dot(g
, d
, 0);
1769 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ b
);
1770 grid_face_set_dot(g
, d
, 1);
1771 d
= grid_get_dot(g
, points
, px
+ a
, py
+ a
+ b
);
1772 grid_face_set_dot(g
, d
, 2);
1773 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1774 grid_face_set_dot(g
, d
, 3);
1777 /* generate up/down triangles */
1779 grid_face_add_new(g
, 3);
1781 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1782 grid_face_set_dot(g
, d
, 0);
1783 d
= grid_get_dot(g
, points
, px
, py
+ b
);
1784 grid_face_set_dot(g
, d
, 1);
1785 d
= grid_get_dot(g
, points
, px
- a
, py
);
1786 grid_face_set_dot(g
, d
, 2);
1788 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1789 grid_face_set_dot(g
, d
, 0);
1790 d
= grid_get_dot(g
, points
, px
+ a
, py
+ a
+ b
);
1791 grid_face_set_dot(g
, d
, 1);
1792 d
= grid_get_dot(g
, points
, px
- a
, py
+ a
+ b
);
1793 grid_face_set_dot(g
, d
, 2);
1797 /* generate left/right triangles */
1799 grid_face_add_new(g
, 3);
1801 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1802 grid_face_set_dot(g
, d
, 0);
1803 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
- a
);
1804 grid_face_set_dot(g
, d
, 1);
1805 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
);
1806 grid_face_set_dot(g
, d
, 2);
1808 d
= grid_get_dot(g
, points
, px
, py
- a
);
1809 grid_face_set_dot(g
, d
, 0);
1810 d
= grid_get_dot(g
, points
, px
+ b
, py
);
1811 grid_face_set_dot(g
, d
, 1);
1812 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1813 grid_face_set_dot(g
, d
, 2);
1819 freetree234(points
);
1820 assert(g
->num_faces
<= max_faces
);
1821 assert(g
->num_dots
<= max_dots
);
1823 grid_make_consistent(g
);
1827 #define CAIRO_TILESIZE 40
1828 /* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */
1832 static void grid_size_cairo(int width
, int height
,
1833 int *tilesize
, int *xextent
, int *yextent
)
1835 int b
= CAIRO_B
; /* a unused in determining grid size. */
1837 *tilesize
= CAIRO_TILESIZE
;
1838 *xextent
= 2*b
*(width
-1) + 2*b
;
1839 *yextent
= 2*b
*(height
-1) + 2*b
;
1842 static grid
*grid_new_cairo(int width
, int height
, const char *desc
)
1848 /* Upper bounds - don't have to be exact */
1849 int max_faces
= 2 * width
* height
;
1850 int max_dots
= 3 * (width
+ 1) * (height
+ 1);
1854 grid
*g
= grid_empty();
1855 g
->tilesize
= CAIRO_TILESIZE
;
1856 g
->faces
= snewn(max_faces
, grid_face
);
1857 g
->dots
= snewn(max_dots
, grid_dot
);
1859 points
= newtree234(grid_point_cmp_fn
);
1861 for (y
= 0; y
< height
; y
++) {
1862 for (x
= 0; x
< width
; x
++) {
1868 /* horizontal pentagons */
1870 grid_face_add_new(g
, 5);
1872 d
= grid_get_dot(g
, points
, px
+ a
, py
- b
);
1873 grid_face_set_dot(g
, d
, 0);
1874 d
= grid_get_dot(g
, points
, px
+ 2*b
- a
, py
- b
);
1875 grid_face_set_dot(g
, d
, 1);
1876 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
1877 grid_face_set_dot(g
, d
, 2);
1878 d
= grid_get_dot(g
, points
, px
+ b
, py
+ a
);
1879 grid_face_set_dot(g
, d
, 3);
1880 d
= grid_get_dot(g
, points
, px
, py
);
1881 grid_face_set_dot(g
, d
, 4);
1883 d
= grid_get_dot(g
, points
, px
, py
);
1884 grid_face_set_dot(g
, d
, 0);
1885 d
= grid_get_dot(g
, points
, px
+ b
, py
- a
);
1886 grid_face_set_dot(g
, d
, 1);
1887 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
1888 grid_face_set_dot(g
, d
, 2);
1889 d
= grid_get_dot(g
, points
, px
+ 2*b
- a
, py
+ b
);
1890 grid_face_set_dot(g
, d
, 3);
1891 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1892 grid_face_set_dot(g
, d
, 4);
1895 /* vertical pentagons */
1897 grid_face_add_new(g
, 5);
1899 d
= grid_get_dot(g
, points
, px
, py
);
1900 grid_face_set_dot(g
, d
, 0);
1901 d
= grid_get_dot(g
, points
, px
+ b
, py
+ a
);
1902 grid_face_set_dot(g
, d
, 1);
1903 d
= grid_get_dot(g
, points
, px
+ b
, py
+ 2*b
- a
);
1904 grid_face_set_dot(g
, d
, 2);
1905 d
= grid_get_dot(g
, points
, px
, py
+ 2*b
);
1906 grid_face_set_dot(g
, d
, 3);
1907 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1908 grid_face_set_dot(g
, d
, 4);
1910 d
= grid_get_dot(g
, points
, px
, py
);
1911 grid_face_set_dot(g
, d
, 0);
1912 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1913 grid_face_set_dot(g
, d
, 1);
1914 d
= grid_get_dot(g
, points
, px
, py
+ 2*b
);
1915 grid_face_set_dot(g
, d
, 2);
1916 d
= grid_get_dot(g
, points
, px
- b
, py
+ 2*b
- a
);
1917 grid_face_set_dot(g
, d
, 3);
1918 d
= grid_get_dot(g
, points
, px
- b
, py
+ a
);
1919 grid_face_set_dot(g
, d
, 4);
1925 freetree234(points
);
1926 assert(g
->num_faces
<= max_faces
);
1927 assert(g
->num_dots
<= max_dots
);
1929 grid_make_consistent(g
);
1933 #define GREATHEX_TILESIZE 18
1934 /* Vector for side of triangle - ratio is close to sqrt(3) */
1935 #define GREATHEX_A 15
1936 #define GREATHEX_B 26
1938 static void grid_size_greathexagonal(int width
, int height
,
1939 int *tilesize
, int *xextent
, int *yextent
)
1944 *tilesize
= GREATHEX_TILESIZE
;
1945 *xextent
= (3*a
+ b
) * (width
-1) + 4*a
;
1946 *yextent
= (2*a
+ 2*b
) * (height
-1) + 3*b
+ a
;
1949 static grid
*grid_new_greathexagonal(int width
, int height
, const char *desc
)
1955 /* Upper bounds - don't have to be exact */
1956 int max_faces
= 6 * (width
+ 1) * (height
+ 1);
1957 int max_dots
= 6 * width
* height
;
1961 grid
*g
= grid_empty();
1962 g
->tilesize
= GREATHEX_TILESIZE
;
1963 g
->faces
= snewn(max_faces
, grid_face
);
1964 g
->dots
= snewn(max_dots
, grid_dot
);
1966 points
= newtree234(grid_point_cmp_fn
);
1968 for (y
= 0; y
< height
; y
++) {
1969 for (x
= 0; x
< width
; x
++) {
1971 /* centre of hexagon */
1972 int px
= (3*a
+ b
) * x
;
1973 int py
= (2*a
+ 2*b
) * y
;
1978 grid_face_add_new(g
, 6);
1979 d
= grid_get_dot(g
, points
, px
- a
, py
- b
);
1980 grid_face_set_dot(g
, d
, 0);
1981 d
= grid_get_dot(g
, points
, px
+ a
, py
- b
);
1982 grid_face_set_dot(g
, d
, 1);
1983 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
);
1984 grid_face_set_dot(g
, d
, 2);
1985 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1986 grid_face_set_dot(g
, d
, 3);
1987 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1988 grid_face_set_dot(g
, d
, 4);
1989 d
= grid_get_dot(g
, points
, px
- 2*a
, py
);
1990 grid_face_set_dot(g
, d
, 5);
1992 /* square below hexagon */
1993 if (y
< height
- 1) {
1994 grid_face_add_new(g
, 4);
1995 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1996 grid_face_set_dot(g
, d
, 0);
1997 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1998 grid_face_set_dot(g
, d
, 1);
1999 d
= grid_get_dot(g
, points
, px
+ a
, py
+ 2*a
+ b
);
2000 grid_face_set_dot(g
, d
, 2);
2001 d
= grid_get_dot(g
, points
, px
- a
, py
+ 2*a
+ b
);
2002 grid_face_set_dot(g
, d
, 3);
2005 /* square below right */
2006 if ((x
< width
- 1) && (((x
% 2) == 0) || (y
< height
- 1))) {
2007 grid_face_add_new(g
, 4);
2008 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
);
2009 grid_face_set_dot(g
, d
, 0);
2010 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
);
2011 grid_face_set_dot(g
, d
, 1);
2012 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
+ b
);
2013 grid_face_set_dot(g
, d
, 2);
2014 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
2015 grid_face_set_dot(g
, d
, 3);
2018 /* square below left */
2019 if ((x
> 0) && (((x
% 2) == 0) || (y
< height
- 1))) {
2020 grid_face_add_new(g
, 4);
2021 d
= grid_get_dot(g
, points
, px
- 2*a
, py
);
2022 grid_face_set_dot(g
, d
, 0);
2023 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
2024 grid_face_set_dot(g
, d
, 1);
2025 d
= grid_get_dot(g
, points
, px
- a
- b
, py
+ a
+ b
);
2026 grid_face_set_dot(g
, d
, 2);
2027 d
= grid_get_dot(g
, points
, px
- 2*a
- b
, py
+ a
);
2028 grid_face_set_dot(g
, d
, 3);
2031 /* Triangle below right */
2032 if ((x
< width
- 1) && (y
< height
- 1)) {
2033 grid_face_add_new(g
, 3);
2034 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
2035 grid_face_set_dot(g
, d
, 0);
2036 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
+ b
);
2037 grid_face_set_dot(g
, d
, 1);
2038 d
= grid_get_dot(g
, points
, px
+ a
, py
+ 2*a
+ b
);
2039 grid_face_set_dot(g
, d
, 2);
2042 /* Triangle below left */
2043 if ((x
> 0) && (y
< height
- 1)) {
2044 grid_face_add_new(g
, 3);
2045 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
2046 grid_face_set_dot(g
, d
, 0);
2047 d
= grid_get_dot(g
, points
, px
- a
, py
+ 2*a
+ b
);
2048 grid_face_set_dot(g
, d
, 1);
2049 d
= grid_get_dot(g
, points
, px
- a
- b
, py
+ a
+ b
);
2050 grid_face_set_dot(g
, d
, 2);
2055 freetree234(points
);
2056 assert(g
->num_faces
<= max_faces
);
2057 assert(g
->num_dots
<= max_dots
);
2059 grid_make_consistent(g
);
2063 #define OCTAGONAL_TILESIZE 40
2064 /* b/a approx sqrt(2) */
2065 #define OCTAGONAL_A 29
2066 #define OCTAGONAL_B 41
2068 static void grid_size_octagonal(int width
, int height
,
2069 int *tilesize
, int *xextent
, int *yextent
)
2071 int a
= OCTAGONAL_A
;
2072 int b
= OCTAGONAL_B
;
2074 *tilesize
= OCTAGONAL_TILESIZE
;
2075 *xextent
= (2*a
+ b
) * width
;
2076 *yextent
= (2*a
+ b
) * height
;
2079 static grid
*grid_new_octagonal(int width
, int height
, const char *desc
)
2082 int a
= OCTAGONAL_A
;
2083 int b
= OCTAGONAL_B
;
2085 /* Upper bounds - don't have to be exact */
2086 int max_faces
= 2 * width
* height
;
2087 int max_dots
= 4 * (width
+ 1) * (height
+ 1);
2091 grid
*g
= grid_empty();
2092 g
->tilesize
= OCTAGONAL_TILESIZE
;
2093 g
->faces
= snewn(max_faces
, grid_face
);
2094 g
->dots
= snewn(max_dots
, grid_dot
);
2096 points
= newtree234(grid_point_cmp_fn
);
2098 for (y
= 0; y
< height
; y
++) {
2099 for (x
= 0; x
< width
; x
++) {
2102 int px
= (2*a
+ b
) * x
;
2103 int py
= (2*a
+ b
) * y
;
2105 grid_face_add_new(g
, 8);
2106 d
= grid_get_dot(g
, points
, px
+ a
, py
);
2107 grid_face_set_dot(g
, d
, 0);
2108 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
);
2109 grid_face_set_dot(g
, d
, 1);
2110 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
);
2111 grid_face_set_dot(g
, d
, 2);
2112 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
+ b
);
2113 grid_face_set_dot(g
, d
, 3);
2114 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ 2*a
+ b
);
2115 grid_face_set_dot(g
, d
, 4);
2116 d
= grid_get_dot(g
, points
, px
+ a
, py
+ 2*a
+ b
);
2117 grid_face_set_dot(g
, d
, 5);
2118 d
= grid_get_dot(g
, points
, px
, py
+ a
+ b
);
2119 grid_face_set_dot(g
, d
, 6);
2120 d
= grid_get_dot(g
, points
, px
, py
+ a
);
2121 grid_face_set_dot(g
, d
, 7);
2124 if ((x
> 0) && (y
> 0)) {
2125 grid_face_add_new(g
, 4);
2126 d
= grid_get_dot(g
, points
, px
, py
- a
);
2127 grid_face_set_dot(g
, d
, 0);
2128 d
= grid_get_dot(g
, points
, px
+ a
, py
);
2129 grid_face_set_dot(g
, d
, 1);
2130 d
= grid_get_dot(g
, points
, px
, py
+ a
);
2131 grid_face_set_dot(g
, d
, 2);
2132 d
= grid_get_dot(g
, points
, px
- a
, py
);
2133 grid_face_set_dot(g
, d
, 3);
2138 freetree234(points
);
2139 assert(g
->num_faces
<= max_faces
);
2140 assert(g
->num_dots
<= max_dots
);
2142 grid_make_consistent(g
);
2146 #define KITE_TILESIZE 40
2147 /* b/a approx sqrt(3) */
2151 static void grid_size_kites(int width
, int height
,
2152 int *tilesize
, int *xextent
, int *yextent
)
2157 *tilesize
= KITE_TILESIZE
;
2158 *xextent
= 4*b
* width
+ 2*b
;
2159 *yextent
= 6*a
* (height
-1) + 8*a
;
2162 static grid
*grid_new_kites(int width
, int height
, const char *desc
)
2168 /* Upper bounds - don't have to be exact */
2169 int max_faces
= 6 * width
* height
;
2170 int max_dots
= 6 * (width
+ 1) * (height
+ 1);
2174 grid
*g
= grid_empty();
2175 g
->tilesize
= KITE_TILESIZE
;
2176 g
->faces
= snewn(max_faces
, grid_face
);
2177 g
->dots
= snewn(max_dots
, grid_dot
);
2179 points
= newtree234(grid_point_cmp_fn
);
2181 for (y
= 0; y
< height
; y
++) {
2182 for (x
= 0; x
< width
; x
++) {
2184 /* position of order-6 dot */
2190 /* kite pointing up-left */
2191 grid_face_add_new(g
, 4);
2192 d
= grid_get_dot(g
, points
, px
, py
);
2193 grid_face_set_dot(g
, d
, 0);
2194 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
2195 grid_face_set_dot(g
, d
, 1);
2196 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
+ 2*a
);
2197 grid_face_set_dot(g
, d
, 2);
2198 d
= grid_get_dot(g
, points
, px
+ b
, py
+ 3*a
);
2199 grid_face_set_dot(g
, d
, 3);
2201 /* kite pointing up */
2202 grid_face_add_new(g
, 4);
2203 d
= grid_get_dot(g
, points
, px
, py
);
2204 grid_face_set_dot(g
, d
, 0);
2205 d
= grid_get_dot(g
, points
, px
+ b
, py
+ 3*a
);
2206 grid_face_set_dot(g
, d
, 1);
2207 d
= grid_get_dot(g
, points
, px
, py
+ 4*a
);
2208 grid_face_set_dot(g
, d
, 2);
2209 d
= grid_get_dot(g
, points
, px
- b
, py
+ 3*a
);
2210 grid_face_set_dot(g
, d
, 3);
2212 /* kite pointing up-right */
2213 grid_face_add_new(g
, 4);
2214 d
= grid_get_dot(g
, points
, px
, py
);
2215 grid_face_set_dot(g
, d
, 0);
2216 d
= grid_get_dot(g
, points
, px
- b
, py
+ 3*a
);
2217 grid_face_set_dot(g
, d
, 1);
2218 d
= grid_get_dot(g
, points
, px
- 2*b
, py
+ 2*a
);
2219 grid_face_set_dot(g
, d
, 2);
2220 d
= grid_get_dot(g
, points
, px
- 2*b
, py
);
2221 grid_face_set_dot(g
, d
, 3);
2223 /* kite pointing down-right */
2224 grid_face_add_new(g
, 4);
2225 d
= grid_get_dot(g
, points
, px
, py
);
2226 grid_face_set_dot(g
, d
, 0);
2227 d
= grid_get_dot(g
, points
, px
- 2*b
, py
);
2228 grid_face_set_dot(g
, d
, 1);
2229 d
= grid_get_dot(g
, points
, px
- 2*b
, py
- 2*a
);
2230 grid_face_set_dot(g
, d
, 2);
2231 d
= grid_get_dot(g
, points
, px
- b
, py
- 3*a
);
2232 grid_face_set_dot(g
, d
, 3);
2234 /* kite pointing down */
2235 grid_face_add_new(g
, 4);
2236 d
= grid_get_dot(g
, points
, px
, py
);
2237 grid_face_set_dot(g
, d
, 0);
2238 d
= grid_get_dot(g
, points
, px
- b
, py
- 3*a
);
2239 grid_face_set_dot(g
, d
, 1);
2240 d
= grid_get_dot(g
, points
, px
, py
- 4*a
);
2241 grid_face_set_dot(g
, d
, 2);
2242 d
= grid_get_dot(g
, points
, px
+ b
, py
- 3*a
);
2243 grid_face_set_dot(g
, d
, 3);
2245 /* kite pointing down-left */
2246 grid_face_add_new(g
, 4);
2247 d
= grid_get_dot(g
, points
, px
, py
);
2248 grid_face_set_dot(g
, d
, 0);
2249 d
= grid_get_dot(g
, points
, px
+ b
, py
- 3*a
);
2250 grid_face_set_dot(g
, d
, 1);
2251 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
- 2*a
);
2252 grid_face_set_dot(g
, d
, 2);
2253 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
2254 grid_face_set_dot(g
, d
, 3);
2258 freetree234(points
);
2259 assert(g
->num_faces
<= max_faces
);
2260 assert(g
->num_dots
<= max_dots
);
2262 grid_make_consistent(g
);
2266 #define FLORET_TILESIZE 150
2267 /* -py/px is close to tan(30 - atan(sqrt(3)/9))
2268 * using py=26 makes everything lean to the left, rather than right
2270 #define FLORET_PX 75
2271 #define FLORET_PY -26
2273 static void grid_size_floret(int width
, int height
,
2274 int *tilesize
, int *xextent
, int *yextent
)
2276 int px
= FLORET_PX
, py
= FLORET_PY
; /* |( 75, -26)| = 79.43 */
2277 int qx
= 4*px
/5, qy
= -py
*2; /* |( 60, 52)| = 79.40 */
2279 /* rx unused in determining grid size. */
2281 *tilesize
= FLORET_TILESIZE
;
2282 *xextent
= (6*px
+3*qx
)/2 * (width
-1) + 4*qx
+ 2*px
;
2283 *yextent
= (5*qy
-4*py
) * (height
-1) + 4*qy
+ 2*ry
;
2286 static grid
*grid_new_floret(int width
, int height
, const char *desc
)
2289 /* Vectors for sides; weird numbers needed to keep puzzle aligned with window
2290 * -py/px is close to tan(30 - atan(sqrt(3)/9))
2291 * using py=26 makes everything lean to the left, rather than right
2293 int px
= FLORET_PX
, py
= FLORET_PY
; /* |( 75, -26)| = 79.43 */
2294 int qx
= 4*px
/5, qy
= -py
*2; /* |( 60, 52)| = 79.40 */
2295 int rx
= qx
-px
, ry
= qy
-py
; /* |(-15, 78)| = 79.38 */
2297 /* Upper bounds - don't have to be exact */
2298 int max_faces
= 6 * width
* height
;
2299 int max_dots
= 9 * (width
+ 1) * (height
+ 1);
2303 grid
*g
= grid_empty();
2304 g
->tilesize
= FLORET_TILESIZE
;
2305 g
->faces
= snewn(max_faces
, grid_face
);
2306 g
->dots
= snewn(max_dots
, grid_dot
);
2308 points
= newtree234(grid_point_cmp_fn
);
2310 /* generate pentagonal faces */
2311 for (y
= 0; y
< height
; y
++) {
2312 for (x
= 0; x
< width
; x
++) {
2315 int cx
= (6*px
+3*qx
)/2 * x
;
2316 int cy
= (4*py
-5*qy
) * y
;
2318 cy
-= (4*py
-5*qy
)/2;
2319 else if (y
&& y
== height
-1)
2320 continue; /* make better looking grids? try 3x3 for instance */
2322 grid_face_add_new(g
, 5);
2323 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2324 d
= grid_get_dot(g
, points
, cx
+2*rx
, cy
+2*ry
); grid_face_set_dot(g
, d
, 1);
2325 d
= grid_get_dot(g
, points
, cx
+2*rx
+qx
, cy
+2*ry
+qy
); grid_face_set_dot(g
, d
, 2);
2326 d
= grid_get_dot(g
, points
, cx
+2*qx
+rx
, cy
+2*qy
+ry
); grid_face_set_dot(g
, d
, 3);
2327 d
= grid_get_dot(g
, points
, cx
+2*qx
, cy
+2*qy
); grid_face_set_dot(g
, d
, 4);
2329 grid_face_add_new(g
, 5);
2330 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2331 d
= grid_get_dot(g
, points
, cx
+2*qx
, cy
+2*qy
); grid_face_set_dot(g
, d
, 1);
2332 d
= grid_get_dot(g
, points
, cx
+2*qx
+px
, cy
+2*qy
+py
); grid_face_set_dot(g
, d
, 2);
2333 d
= grid_get_dot(g
, points
, cx
+2*px
+qx
, cy
+2*py
+qy
); grid_face_set_dot(g
, d
, 3);
2334 d
= grid_get_dot(g
, points
, cx
+2*px
, cy
+2*py
); grid_face_set_dot(g
, d
, 4);
2336 grid_face_add_new(g
, 5);
2337 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2338 d
= grid_get_dot(g
, points
, cx
+2*px
, cy
+2*py
); grid_face_set_dot(g
, d
, 1);
2339 d
= grid_get_dot(g
, points
, cx
+2*px
-rx
, cy
+2*py
-ry
); grid_face_set_dot(g
, d
, 2);
2340 d
= grid_get_dot(g
, points
, cx
-2*rx
+px
, cy
-2*ry
+py
); grid_face_set_dot(g
, d
, 3);
2341 d
= grid_get_dot(g
, points
, cx
-2*rx
, cy
-2*ry
); grid_face_set_dot(g
, d
, 4);
2343 grid_face_add_new(g
, 5);
2344 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2345 d
= grid_get_dot(g
, points
, cx
-2*rx
, cy
-2*ry
); grid_face_set_dot(g
, d
, 1);
2346 d
= grid_get_dot(g
, points
, cx
-2*rx
-qx
, cy
-2*ry
-qy
); grid_face_set_dot(g
, d
, 2);
2347 d
= grid_get_dot(g
, points
, cx
-2*qx
-rx
, cy
-2*qy
-ry
); grid_face_set_dot(g
, d
, 3);
2348 d
= grid_get_dot(g
, points
, cx
-2*qx
, cy
-2*qy
); grid_face_set_dot(g
, d
, 4);
2350 grid_face_add_new(g
, 5);
2351 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2352 d
= grid_get_dot(g
, points
, cx
-2*qx
, cy
-2*qy
); grid_face_set_dot(g
, d
, 1);
2353 d
= grid_get_dot(g
, points
, cx
-2*qx
-px
, cy
-2*qy
-py
); grid_face_set_dot(g
, d
, 2);
2354 d
= grid_get_dot(g
, points
, cx
-2*px
-qx
, cy
-2*py
-qy
); grid_face_set_dot(g
, d
, 3);
2355 d
= grid_get_dot(g
, points
, cx
-2*px
, cy
-2*py
); grid_face_set_dot(g
, d
, 4);
2357 grid_face_add_new(g
, 5);
2358 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2359 d
= grid_get_dot(g
, points
, cx
-2*px
, cy
-2*py
); grid_face_set_dot(g
, d
, 1);
2360 d
= grid_get_dot(g
, points
, cx
-2*px
+rx
, cy
-2*py
+ry
); grid_face_set_dot(g
, d
, 2);
2361 d
= grid_get_dot(g
, points
, cx
+2*rx
-px
, cy
+2*ry
-py
); grid_face_set_dot(g
, d
, 3);
2362 d
= grid_get_dot(g
, points
, cx
+2*rx
, cy
+2*ry
); grid_face_set_dot(g
, d
, 4);
2366 freetree234(points
);
2367 assert(g
->num_faces
<= max_faces
);
2368 assert(g
->num_dots
<= max_dots
);
2370 grid_make_consistent(g
);
2374 /* DODEC_* are used for dodecagonal and great-dodecagonal grids. */
2375 #define DODEC_TILESIZE 26
2376 /* Vector for side of triangle - ratio is close to sqrt(3) */
2380 static void grid_size_dodecagonal(int width
, int height
,
2381 int *tilesize
, int *xextent
, int *yextent
)
2386 *tilesize
= DODEC_TILESIZE
;
2387 *xextent
= (4*a
+ 2*b
) * (width
-1) + 3*(2*a
+ b
);
2388 *yextent
= (3*a
+ 2*b
) * (height
-1) + 2*(2*a
+ b
);
2391 static grid
*grid_new_dodecagonal(int width
, int height
, const char *desc
)
2397 /* Upper bounds - don't have to be exact */
2398 int max_faces
= 3 * width
* height
;
2399 int max_dots
= 14 * width
* height
;
2403 grid
*g
= grid_empty();
2404 g
->tilesize
= DODEC_TILESIZE
;
2405 g
->faces
= snewn(max_faces
, grid_face
);
2406 g
->dots
= snewn(max_dots
, grid_dot
);
2408 points
= newtree234(grid_point_cmp_fn
);
2410 for (y
= 0; y
< height
; y
++) {
2411 for (x
= 0; x
< width
; x
++) {
2413 /* centre of dodecagon */
2414 int px
= (4*a
+ 2*b
) * x
;
2415 int py
= (3*a
+ 2*b
) * y
;
2420 grid_face_add_new(g
, 12);
2421 d
= grid_get_dot(g
, points
, px
+ ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2422 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 1);
2423 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 2);
2424 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 3);
2425 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 4);
2426 d
= grid_get_dot(g
, points
, px
+ ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2427 d
= grid_get_dot(g
, points
, px
- ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 6);
2428 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 7);
2429 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 8);
2430 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 9);
2431 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 10);
2432 d
= grid_get_dot(g
, points
, px
- ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 11);
2434 /* triangle below dodecagon */
2435 if ((y
< height
- 1 && (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2)))) {
2436 grid_face_add_new(g
, 3);
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
, py
+ (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2439 d
= grid_get_dot(g
, points
, px
- a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 2);
2442 /* triangle above dodecagon */
2443 if ((y
&& (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2)))) {
2444 grid_face_add_new(g
, 3);
2445 d
= grid_get_dot(g
, points
, px
- a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2446 d
= grid_get_dot(g
, points
, px
, py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2447 d
= grid_get_dot(g
, points
, px
+ a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 2);
2452 freetree234(points
);
2453 assert(g
->num_faces
<= max_faces
);
2454 assert(g
->num_dots
<= max_dots
);
2456 grid_make_consistent(g
);
2460 static void grid_size_greatdodecagonal(int width
, int height
,
2461 int *tilesize
, int *xextent
, int *yextent
)
2466 *tilesize
= DODEC_TILESIZE
;
2467 *xextent
= (6*a
+ 2*b
) * (width
-1) + 2*(2*a
+ b
) + 3*a
+ b
;
2468 *yextent
= (3*a
+ 3*b
) * (height
-1) + 2*(2*a
+ b
);
2471 static grid
*grid_new_greatdodecagonal(int width
, int height
, const char *desc
)
2474 /* Vector for side of triangle - ratio is close to sqrt(3) */
2478 /* Upper bounds - don't have to be exact */
2479 int max_faces
= 30 * width
* height
;
2480 int max_dots
= 200 * width
* height
;
2484 grid
*g
= grid_empty();
2485 g
->tilesize
= DODEC_TILESIZE
;
2486 g
->faces
= snewn(max_faces
, grid_face
);
2487 g
->dots
= snewn(max_dots
, grid_dot
);
2489 points
= newtree234(grid_point_cmp_fn
);
2491 for (y
= 0; y
< height
; y
++) {
2492 for (x
= 0; x
< width
; x
++) {
2494 /* centre of dodecagon */
2495 int px
= (6*a
+ 2*b
) * x
;
2496 int py
= (3*a
+ 3*b
) * y
;
2501 grid_face_add_new(g
, 12);
2502 d
= grid_get_dot(g
, points
, px
+ ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2503 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 1);
2504 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 2);
2505 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 3);
2506 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 4);
2507 d
= grid_get_dot(g
, points
, px
+ ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2508 d
= grid_get_dot(g
, points
, px
- ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 6);
2509 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 7);
2510 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 8);
2511 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 9);
2512 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 10);
2513 d
= grid_get_dot(g
, points
, px
- ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 11);
2515 /* hexagon below dodecagon */
2516 if (y
< height
- 1 && (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2))) {
2517 grid_face_add_new(g
, 6);
2518 d
= grid_get_dot(g
, points
, px
+ a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2519 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
+ (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2520 d
= grid_get_dot(g
, points
, px
+ a
, py
+ (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 2);
2521 d
= grid_get_dot(g
, points
, px
- a
, py
+ (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 3);
2522 d
= grid_get_dot(g
, points
, px
- 2*a
, py
+ (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 4);
2523 d
= grid_get_dot(g
, points
, px
- a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2526 /* hexagon above dodecagon */
2527 if (y
&& (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2))) {
2528 grid_face_add_new(g
, 6);
2529 d
= grid_get_dot(g
, points
, px
- a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2530 d
= grid_get_dot(g
, points
, px
- 2*a
, py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2531 d
= grid_get_dot(g
, points
, px
- a
, py
- (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 2);
2532 d
= grid_get_dot(g
, points
, px
+ a
, py
- (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 3);
2533 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 4);
2534 d
= grid_get_dot(g
, points
, px
+ a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2537 /* square on right of dodecagon */
2538 if (x
< width
- 1) {
2539 grid_face_add_new(g
, 4);
2540 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
- a
); grid_face_set_dot(g
, d
, 0);
2541 d
= grid_get_dot(g
, points
, px
+ 4*a
+ b
, py
- a
); grid_face_set_dot(g
, d
, 1);
2542 d
= grid_get_dot(g
, points
, px
+ 4*a
+ b
, py
+ a
); grid_face_set_dot(g
, d
, 2);
2543 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
); grid_face_set_dot(g
, d
, 3);
2546 /* square on top right of dodecagon */
2547 if (y
&& (x
< width
- 1 || !(y
% 2))) {
2548 grid_face_add_new(g
, 4);
2549 d
= grid_get_dot(g
, points
, px
+ ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2550 d
= grid_get_dot(g
, points
, px
+ (2*a
), py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2551 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- ( a
+ 2*b
)); grid_face_set_dot(g
, d
, 2);
2552 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 3);
2555 /* square on top left of dodecagon */
2556 if (y
&& (x
|| (y
% 2))) {
2557 grid_face_add_new(g
, 4);
2558 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 0);
2559 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
- ( a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2560 d
= grid_get_dot(g
, points
, px
- (2*a
), py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 2);
2561 d
= grid_get_dot(g
, points
, px
- ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 3);
2566 freetree234(points
);
2567 assert(g
->num_faces
<= max_faces
);
2568 assert(g
->num_dots
<= max_dots
);
2570 grid_make_consistent(g
);
2574 static void grid_size_greatgreatdodecagonal(int width
, int height
,
2575 int *tilesize
, int *xextent
, int *yextent
)
2580 *tilesize
= DODEC_TILESIZE
;
2581 *xextent
= (4*a
+ 4*b
) * (width
-1) + 2*(2*a
+ b
) + 2*a
+ 2*b
;
2582 *yextent
= (6*a
+ 2*b
) * (height
-1) + 2*(2*a
+ b
);
2585 static grid
*grid_new_greatgreatdodecagonal(int width
, int height
, const char *desc
)
2588 /* Vector for side of triangle - ratio is close to sqrt(3) */
2592 /* Upper bounds - don't have to be exact */
2593 int max_faces
= 50 * width
* height
;
2594 int max_dots
= 300 * width
* height
;
2598 grid
*g
= grid_empty();
2599 g
->tilesize
= DODEC_TILESIZE
;
2600 g
->faces
= snewn(max_faces
, grid_face
);
2601 g
->dots
= snewn(max_dots
, grid_dot
);
2603 points
= newtree234(grid_point_cmp_fn
);
2605 for (y
= 0; y
< height
; y
++) {
2606 for (x
= 0; x
< width
; x
++) {
2608 /* centre of dodecagon */
2609 int px
= (4*a
+ 4*b
) * x
;
2610 int py
= (6*a
+ 2*b
) * y
;
2615 grid_face_add_new(g
, 12);
2616 d
= grid_get_dot(g
, points
, px
+ ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2617 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 1);
2618 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 2);
2619 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 3);
2620 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 4);
2621 d
= grid_get_dot(g
, points
, px
+ ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2622 d
= grid_get_dot(g
, points
, px
- ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 6);
2623 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 7);
2624 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 8);
2625 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 9);
2626 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 10);
2627 d
= grid_get_dot(g
, points
, px
- ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 11);
2629 /* hexagon on top right of dodecagon */
2630 if (y
&& (x
< width
- 1 || !(y
% 2))) {
2631 grid_face_add_new(g
, 6);
2632 d
= grid_get_dot(g
, points
, px
+ (a
+ 2*b
), py
- (4*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2633 d
= grid_get_dot(g
, points
, px
+ (a
+ 2*b
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 1);
2634 d
= grid_get_dot(g
, points
, px
+ (a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 2);
2635 d
= grid_get_dot(g
, points
, px
+ (a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 3);
2636 d
= grid_get_dot(g
, points
, px
+ (a
), py
- (4*a
+ b
)); grid_face_set_dot(g
, d
, 4);
2637 d
= grid_get_dot(g
, points
, px
+ (a
+ b
), py
- (5*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2640 /* hexagon on right of dodecagon*/
2641 if (x
< width
- 1) {
2642 grid_face_add_new(g
, 6);
2643 d
= grid_get_dot(g
, points
, px
+ (2*a
+ 3*b
), py
- a
); grid_face_set_dot(g
, d
, 0);
2644 d
= grid_get_dot(g
, points
, px
+ (2*a
+ 3*b
), py
+ a
); grid_face_set_dot(g
, d
, 1);
2645 d
= grid_get_dot(g
, points
, px
+ (2*a
+ 2*b
), py
+ 2*a
); grid_face_set_dot(g
, d
, 2);
2646 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
+ a
); grid_face_set_dot(g
, d
, 3);
2647 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- a
); grid_face_set_dot(g
, d
, 4);
2648 d
= grid_get_dot(g
, points
, px
+ (2*a
+ 2*b
), py
- 2*a
); grid_face_set_dot(g
, d
, 5);
2651 /* hexagon on bottom right of dodecagon */
2652 if ((y
< height
- 1) && (x
< width
- 1 || !(y
% 2))) {
2653 grid_face_add_new(g
, 6);
2654 d
= grid_get_dot(g
, points
, px
+ (a
+ 2*b
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2655 d
= grid_get_dot(g
, points
, px
+ (a
+ 2*b
), py
+ (4*a
+ b
)); grid_face_set_dot(g
, d
, 1);
2656 d
= grid_get_dot(g
, points
, px
+ (a
+ b
), py
+ (5*a
+ b
)); grid_face_set_dot(g
, d
, 2);
2657 d
= grid_get_dot(g
, points
, px
+ (a
), py
+ (4*a
+ b
)); grid_face_set_dot(g
, d
, 3);
2658 d
= grid_get_dot(g
, points
, px
+ (a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 4);
2659 d
= grid_get_dot(g
, points
, px
+ (a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 5);
2662 /* square on top right of dodecagon */
2663 if (y
&& (x
< width
- 1 )) {
2664 grid_face_add_new(g
, 4);
2665 d
= grid_get_dot(g
, points
, px
+ ( a
+ 2*b
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2666 d
= grid_get_dot(g
, points
, px
+ (2*a
+ 2*b
), py
- (2*a
)); grid_face_set_dot(g
, d
, 1);
2667 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 2);
2668 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 3);
2671 /* square on bottom right of dodecagon */
2672 if ((y
< height
- 1) && (x
< width
- 1 )) {
2673 grid_face_add_new(g
, 4);
2674 d
= grid_get_dot(g
, points
, px
+ (2*a
+ 2*b
), py
+ (2*a
)); grid_face_set_dot(g
, d
, 0);
2675 d
= grid_get_dot(g
, points
, px
+ ( a
+ 2*b
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 1);
2676 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 2);
2677 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 3);
2680 /* square below dodecagon */
2681 if ((y
< height
- 1) && (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2))) {
2682 grid_face_add_new(g
, 4);
2683 d
= grid_get_dot(g
, points
, px
+ a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2684 d
= grid_get_dot(g
, points
, px
+ a
, py
+ (4*a
+ b
)); grid_face_set_dot(g
, d
, 1);
2685 d
= grid_get_dot(g
, points
, px
- a
, py
+ (4*a
+ b
)); grid_face_set_dot(g
, d
, 2);
2686 d
= grid_get_dot(g
, points
, px
- a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 3);
2689 /* square on bottom left of dodecagon */
2690 if (x
&& (y
< height
- 1)) {
2691 grid_face_add_new(g
, 4);
2692 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 0);
2693 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 1);
2694 d
= grid_get_dot(g
, points
, px
- ( a
+ 2*b
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 2);
2695 d
= grid_get_dot(g
, points
, px
- (2*a
+ 2*b
), py
+ (2*a
)); grid_face_set_dot(g
, d
, 3);
2698 /* square on top left of dodecagon */
2700 grid_face_add_new(g
, 4);
2701 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 0);
2702 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 1);
2703 d
= grid_get_dot(g
, points
, px
- (2*a
+ 2*b
), py
- (2*a
)); grid_face_set_dot(g
, d
, 2);
2704 d
= grid_get_dot(g
, points
, px
- ( a
+ 2*b
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 3);
2708 /* square above dodecagon */
2709 if (y
&& (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2))) {
2710 grid_face_add_new(g
, 4);
2711 d
= grid_get_dot(g
, points
, px
+ a
, py
- (4*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2712 d
= grid_get_dot(g
, points
, px
+ a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 1);
2713 d
= grid_get_dot(g
, points
, px
- a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 2);
2714 d
= grid_get_dot(g
, points
, px
- a
, py
- (4*a
+ b
)); grid_face_set_dot(g
, d
, 3);
2717 /* upper triangle (v) */
2718 if (y
&& (x
< width
- 1)) {
2719 grid_face_add_new(g
, 3);
2720 d
= grid_get_dot(g
, points
, px
+ (3*a
+ 2*b
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2721 d
= grid_get_dot(g
, points
, px
+ (2*a
+ 2*b
), py
- (2*a
)); grid_face_set_dot(g
, d
, 1);
2722 d
= grid_get_dot(g
, points
, px
+ ( a
+ 2*b
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 2);
2725 /* lower triangle (^) */
2726 if ((y
< height
- 1) && (x
< width
- 1)) {
2727 grid_face_add_new(g
, 3);
2728 d
= grid_get_dot(g
, points
, px
+ (3*a
+ 2*b
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2729 d
= grid_get_dot(g
, points
, px
+ ( a
+ 2*b
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 1);
2730 d
= grid_get_dot(g
, points
, px
+ (2*a
+ 2*b
), py
+ (2*a
)); grid_face_set_dot(g
, d
, 2);
2735 freetree234(points
);
2736 assert(g
->num_faces
<= max_faces
);
2737 assert(g
->num_dots
<= max_dots
);
2739 grid_make_consistent(g
);
2743 typedef struct setface_ctx
2745 int xmin
, xmax
, ymin
, ymax
;
2751 static double round_int_nearest_away(double r
)
2753 return (r
> 0.0) ? floor(r
+ 0.5) : ceil(r
- 0.5);
2756 static int set_faces(penrose_state
*state
, vector
*vs
, int n
, int depth
)
2758 setface_ctx
*sf_ctx
= (setface_ctx
*)state
->ctx
;
2762 if (depth
< state
->max_depth
) return 0;
2763 #ifdef DEBUG_PENROSE
2764 if (n
!= 4) return 0; /* triangles are sent as debugging. */
2767 for (i
= 0; i
< n
; i
++) {
2768 double tx
= v_x(vs
, i
), ty
= v_y(vs
, i
);
2770 xs
[i
] = (int)round_int_nearest_away(tx
);
2771 ys
[i
] = (int)round_int_nearest_away(ty
);
2773 if (xs
[i
] < sf_ctx
->xmin
|| xs
[i
] > sf_ctx
->xmax
) return 0;
2774 if (ys
[i
] < sf_ctx
->ymin
|| ys
[i
] > sf_ctx
->ymax
) return 0;
2777 grid_face_add_new(sf_ctx
->g
, n
);
2778 debug(("penrose: new face l=%f gen=%d...",
2779 penrose_side_length(state
->start_size
, depth
), depth
));
2780 for (i
= 0; i
< n
; i
++) {
2781 grid_dot
*d
= grid_get_dot(sf_ctx
->g
, sf_ctx
->points
,
2783 grid_face_set_dot(sf_ctx
->g
, d
, i
);
2784 debug((" ... dot 0x%x (%d,%d) (was %2.2f,%2.2f)",
2785 d
, d
->x
, d
->y
, v_x(vs
, i
), v_y(vs
, i
)));
2791 #define PENROSE_TILESIZE 100
2793 static void grid_size_penrose(int width
, int height
,
2794 int *tilesize
, int *xextent
, int *yextent
)
2796 int l
= PENROSE_TILESIZE
;
2799 *xextent
= l
* width
;
2800 *yextent
= l
* height
;
2803 static grid
*grid_new_penrose(int width
, int height
, int which
, const char *desc
); /* forward reference */
2805 static char *grid_new_desc_penrose(grid_type type
, int width
, int height
, random_state
*rs
)
2807 int tilesize
= PENROSE_TILESIZE
, startsz
, depth
, xoff
, yoff
, aoff
;
2808 double outer_radius
;
2811 int which
= (type
== GRID_PENROSE_P2
? PENROSE_P2
: PENROSE_P3
);
2815 /* We want to produce a random bit of penrose tiling, so we
2816 * calculate a random offset (within the patch that penrose.c
2817 * calculates for us) and an angle (multiple of 36) to rotate
2820 penrose_calculate_size(which
, tilesize
, width
, height
,
2821 &outer_radius
, &startsz
, &depth
);
2823 /* Calculate radius of (circumcircle of) patch, subtract from
2824 * radius calculated. */
2825 inner_radius
= (int)(outer_radius
- sqrt(width
*width
+ height
*height
));
2827 /* Pick a random offset (the easy way: choose within outer
2828 * square, discarding while it's outside the circle) */
2830 xoff
= random_upto(rs
, 2*inner_radius
) - inner_radius
;
2831 yoff
= random_upto(rs
, 2*inner_radius
) - inner_radius
;
2832 } while (sqrt(xoff
*xoff
+yoff
*yoff
) > inner_radius
);
2834 aoff
= random_upto(rs
, 360/36) * 36;
2836 debug(("grid_desc: ts %d, %dx%d patch, orad %2.2f irad %d",
2837 tilesize
, width
, height
, outer_radius
, inner_radius
));
2838 debug((" -> xoff %d yoff %d aoff %d", xoff
, yoff
, aoff
));
2840 sprintf(gd
, "G%d,%d,%d", xoff
, yoff
, aoff
);
2843 * Now test-generate our grid, to make sure it actually
2844 * produces something.
2846 g
= grid_new_penrose(width
, height
, which
, gd
);
2851 /* If not, go back to the top of this while loop and try again
2852 * with a different random offset. */
2858 static char *grid_validate_desc_penrose(grid_type type
, int width
, int height
,
2861 int tilesize
= PENROSE_TILESIZE
, startsz
, depth
, xoff
, yoff
, aoff
, inner_radius
;
2862 double outer_radius
;
2863 int which
= (type
== GRID_PENROSE_P2
? PENROSE_P2
: PENROSE_P3
);
2867 return "Missing grid description string.";
2869 penrose_calculate_size(which
, tilesize
, width
, height
,
2870 &outer_radius
, &startsz
, &depth
);
2871 inner_radius
= (int)(outer_radius
- sqrt(width
*width
+ height
*height
));
2873 if (sscanf(desc
, "G%d,%d,%d", &xoff
, &yoff
, &aoff
) != 3)
2874 return "Invalid format grid description string.";
2876 if (sqrt(xoff
*xoff
+ yoff
*yoff
) > inner_radius
)
2877 return "Patch offset out of bounds.";
2878 if ((aoff
% 36) != 0 || aoff
< 0 || aoff
>= 360)
2879 return "Angle offset out of bounds.";
2882 * Test-generate to ensure these parameters don't end us up with
2885 g
= grid_new_penrose(width
, height
, which
, desc
);
2887 return "Patch coordinates do not identify a usable grid fragment";
2894 * We're asked for a grid of a particular size, and we generate enough
2895 * of the tiling so we can be sure to have enough random grid from which
2899 static grid
*grid_new_penrose(int width
, int height
, int which
, const char *desc
)
2901 int max_faces
, max_dots
, tilesize
= PENROSE_TILESIZE
;
2902 int xsz
, ysz
, xoff
, yoff
, aoff
;
2911 penrose_calculate_size(which
, tilesize
, width
, height
,
2912 &rradius
, &ps
.start_size
, &ps
.max_depth
);
2914 debug(("penrose: w%d h%d, tile size %d, start size %d, depth %d",
2915 width
, height
, tilesize
, ps
.start_size
, ps
.max_depth
));
2917 ps
.new_tile
= set_faces
;
2920 max_faces
= (width
*3) * (height
*3); /* somewhat paranoid... */
2921 max_dots
= max_faces
* 4; /* ditto... */
2924 g
->tilesize
= tilesize
;
2925 g
->faces
= snewn(max_faces
, grid_face
);
2926 g
->dots
= snewn(max_dots
, grid_dot
);
2928 points
= newtree234(grid_point_cmp_fn
);
2930 memset(&sf_ctx
, 0, sizeof(sf_ctx
));
2932 sf_ctx
.points
= points
;
2935 if (sscanf(desc
, "G%d,%d,%d", &xoff
, &yoff
, &aoff
) != 3)
2936 assert(!"Invalid grid description.");
2938 xoff
= yoff
= aoff
= 0;
2941 xsz
= width
* tilesize
;
2942 ysz
= height
* tilesize
;
2944 sf_ctx
.xmin
= xoff
- xsz
/2;
2945 sf_ctx
.xmax
= xoff
+ xsz
/2;
2946 sf_ctx
.ymin
= yoff
- ysz
/2;
2947 sf_ctx
.ymax
= yoff
+ ysz
/2;
2949 debug(("penrose: centre (%f, %f) xsz %f ysz %f",
2950 0.0, 0.0, xsz
, ysz
));
2951 debug(("penrose: x range (%f --> %f), y range (%f --> %f)",
2952 sf_ctx
.xmin
, sf_ctx
.xmax
, sf_ctx
.ymin
, sf_ctx
.ymax
));
2954 penrose(&ps
, which
, aoff
);
2956 freetree234(points
);
2957 assert(g
->num_faces
<= max_faces
);
2958 assert(g
->num_dots
<= max_dots
);
2960 debug(("penrose: %d faces total (equivalent to %d wide by %d high)",
2961 g
->num_faces
, g
->num_faces
/height
, g
->num_faces
/width
));
2964 * Return NULL if we ended up with an empty grid, either because
2965 * the initial generation was over too small a rectangle to
2966 * encompass any face or because grid_trim_vigorously ended up
2967 * removing absolutely everything.
2969 if (g
->num_faces
== 0 || g
->num_dots
== 0) {
2973 grid_trim_vigorously(g
);
2974 if (g
->num_faces
== 0 || g
->num_dots
== 0) {
2979 grid_make_consistent(g
);
2982 * Centre the grid in its originally promised rectangle.
2984 g
->lowest_x
-= ((sf_ctx
.xmax
- sf_ctx
.xmin
) -
2985 (g
->highest_x
- g
->lowest_x
)) / 2;
2986 g
->highest_x
= g
->lowest_x
+ (sf_ctx
.xmax
- sf_ctx
.xmin
);
2987 g
->lowest_y
-= ((sf_ctx
.ymax
- sf_ctx
.ymin
) -
2988 (g
->highest_y
- g
->lowest_y
)) / 2;
2989 g
->highest_y
= g
->lowest_y
+ (sf_ctx
.ymax
- sf_ctx
.ymin
);
2994 static void grid_size_penrose_p2_kite(int width
, int height
,
2995 int *tilesize
, int *xextent
, int *yextent
)
2997 grid_size_penrose(width
, height
, tilesize
, xextent
, yextent
);
3000 static void grid_size_penrose_p3_thick(int width
, int height
,
3001 int *tilesize
, int *xextent
, int *yextent
)
3003 grid_size_penrose(width
, height
, tilesize
, xextent
, yextent
);
3006 static grid
*grid_new_penrose_p2_kite(int width
, int height
, const char *desc
)
3008 return grid_new_penrose(width
, height
, PENROSE_P2
, desc
);
3011 static grid
*grid_new_penrose_p3_thick(int width
, int height
, const char *desc
)
3013 return grid_new_penrose(width
, height
, PENROSE_P3
, desc
);
3016 /* ----------- End of grid generators ------------- */
3018 #define FNNEW(upper,lower) &grid_new_ ## lower,
3019 #define FNSZ(upper,lower) &grid_size_ ## lower,
3021 static grid
*(*(grid_news
[]))(int, int, const char*) = { GRIDGEN_LIST(FNNEW
) };
3022 static void(*(grid_sizes
[]))(int, int, int*, int*, int*) = { GRIDGEN_LIST(FNSZ
) };
3024 char *grid_new_desc(grid_type type
, int width
, int height
, random_state
*rs
)
3026 if (type
== GRID_PENROSE_P2
|| type
== GRID_PENROSE_P3
) {
3027 return grid_new_desc_penrose(type
, width
, height
, rs
);
3028 } else if (type
== GRID_TRIANGULAR
) {
3029 return dupstr("0"); /* up-to-date version of triangular grid */
3035 char *grid_validate_desc(grid_type type
, int width
, int height
,
3038 if (type
== GRID_PENROSE_P2
|| type
== GRID_PENROSE_P3
) {
3039 return grid_validate_desc_penrose(type
, width
, height
, desc
);
3040 } else if (type
== GRID_TRIANGULAR
) {
3041 return grid_validate_desc_triangular(type
, width
, height
, desc
);
3044 return "Grid description strings not used with this grid type";
3049 grid
*grid_new(grid_type type
, int width
, int height
, const char *desc
)
3051 char *err
= grid_validate_desc(type
, width
, height
, desc
);
3052 if (err
) assert(!"Invalid grid description.");
3054 return grid_news
[type
](width
, height
, desc
);
3057 void grid_compute_size(grid_type type
, int width
, int height
,
3058 int *tilesize
, int *xextent
, int *yextent
)
3060 grid_sizes
[type
](width
, height
, tilesize
, xextent
, yextent
);
3063 /* ----------- End of grid helpers ------------- */
3065 /* vim: set shiftwidth=4 tabstop=8: */