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()
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");
228 static void grid_try_svg(grid
*g
, int which
)
230 char *svg
= getenv("PUZZLES_SVG_GRID");
232 FILE *svgf
= fopen(svg
, "w");
234 grid_output_svg(svgf
, g
, which
);
237 fprintf(stderr
, "Unable to open file `%s': %s", svg
, strerror(errno
));
243 /* Show the basic grid information, before doing grid_make_consistent */
244 static void grid_debug_basic(grid
*g
)
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. */
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
);
256 for (j
= 0; j
< f
->order
; j
++) {
257 grid_dot
*d
= f
->dots
[j
];
258 printf("%s%d", j ?
"," : "", (int)(d
- g
->dots
));
264 grid_try_svg(g
, SVG_FACES
);
268 /* Show the derived grid information, computed by grid_make_consistent */
269 static void grid_debug_derived(grid
*g
)
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);
283 for (i
= 0; i
< g
->num_faces
; i
++) {
284 grid_face
*f
= g
->faces
+ i
;
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);
295 for (i
= 0; i
< g
->num_dots
; i
++) {
296 grid_dot
*d
= g
->dots
+ i
;
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
));
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);
313 grid_try_svg(g
, SVG_DOTS
| SVG_EDGES
| SVG_FACES
);
317 /* Helper function for building incomplete-edges list in
318 * grid_make_consistent() */
319 static int grid_edge_bydots_cmpfn(void *v1
, void *v2
)
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. */
330 /* Compare first dots */
331 da
= (a
->dot1
< a
->dot2
) ? a
->dot1
: a
->dot2
;
332 db
= (b
->dot1
< b
->dot2
) ? b
->dot1
: b
->dot2
;
335 /* Compare last dots */
336 da
= (a
->dot1
< a
->dot2
) ? a
->dot2
: a
->dot1
;
337 db
= (b
->dot1
< b
->dot2
) ? b
->dot2
: b
->dot1
;
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
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.)
356 static void grid_trim_vigorously(grid
*g
)
358 int *dotpairs
, *faces
, *dots
;
360 int i
, j
, k
, size
, newfaces
, newdots
;
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
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
;
382 * Now we can identify landlocked dots: they're the ones all of
383 * whose edges have a mirror-image counterpart in this matrix.
385 dots
= snewn(g
->num_dots
, int);
386 for (i
= 0; i
< g
->num_dots
; i
++) {
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 */
396 * Now identify connected pairs of landlocked dots, and form a dsf
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
);
408 * Now look for the largest component.
412 for (i
= 0; i
< g
->num_dots
; i
++) {
414 if (dots
[i
] && dsf_canonify(dsf
, i
) == i
&&
415 (newsize
= dsf_size(dsf
, i
)) > size
) {
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).
426 * At this point we reuse the 'dots' array to indicate the dots
427 * we're keeping, rather than the ones that are landlocked.
429 faces
= snewn(g
->num_faces
, int);
430 for (i
= 0; i
< g
->num_faces
; i
++)
432 for (i
= 0; i
< g
->num_dots
; i
++)
434 for (i
= 0; i
< g
->num_faces
; i
++) {
435 grid_face
*f
= g
->faces
+ i
;
437 for (k
= 0; k
< f
->order
; k
++)
438 if (dsf_canonify(dsf
, f
->dots
[k
] - g
->dots
) == j
)
442 for (k
= 0; k
< f
->order
; k
++)
443 dots
[f
->dots
[k
]-g
->dots
] = TRUE
;
448 * Work out the new indices of those faces and dots, when we
449 * compact the arrays containing them.
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);
457 * Go through and compact the arrays.
459 for (i
= 0; i
< g
->num_dots
; i
++)
461 grid_dot
*dnew
= g
->dots
+ dots
[i
], *dold
= g
->dots
+ i
;
462 *dnew
= *dold
; /* structure copy */
464 for (i
= 0; i
< g
->num_faces
; i
++)
466 grid_face
*fnew
= g
->faces
+ faces
[i
], *fold
= g
->faces
+ i
;
467 *fnew
= *fold
; /* structure copy */
468 for (j
= 0; j
< fnew
->order
; j
++) {
470 * Reindex the dots in this face.
472 k
= fnew
->dots
[j
] - g
->dots
;
473 fnew
->dots
[j
] = g
->dots
+ dots
[k
];
476 g
->num_faces
= newfaces
;
477 g
->num_dots
= newdots
;
485 /* Input: grid has its dots and faces initialised:
486 * - dots have (optionally) x and y coordinates, but no edges or faces
487 * (pointers are NULL).
488 * - edges not initialised at all
489 * - faces initialised and know which dots they have (but no edges yet). The
490 * dots around each face are assumed to be clockwise.
492 * Output: grid is complete and valid with all relationships defined.
494 static void grid_make_consistent(grid
*g
)
497 tree234
*incomplete_edges
;
498 grid_edge
*next_new_edge
; /* Where new edge will go into g->edges */
502 /* ====== Stage 1 ======
506 /* We know how many dots and faces there are, so we can find the exact
507 * number of edges from Euler's polyhedral formula: F + V = E + 2 .
508 * We use "-1", not "-2" here, because Euler's formula includes the
509 * infinite face, which we don't count. */
510 g
->num_edges
= g
->num_faces
+ g
->num_dots
- 1;
511 g
->edges
= snewn(g
->num_edges
, grid_edge
);
512 next_new_edge
= g
->edges
;
514 /* Iterate over faces, and over each face's dots, generating edges as we
515 * go. As we find each new edge, we can immediately fill in the edge's
516 * dots, but only one of the edge's faces. Later on in the iteration, we
517 * will find the same edge again (unless it's on the border), but we will
518 * know the other face.
519 * For efficiency, maintain a list of the incomplete edges, sorted by
521 incomplete_edges
= newtree234(grid_edge_bydots_cmpfn
);
522 for (i
= 0; i
< g
->num_faces
; i
++) {
523 grid_face
*f
= g
->faces
+ i
;
525 for (j
= 0; j
< f
->order
; j
++) {
526 grid_edge e
; /* fake edge for searching */
527 grid_edge
*edge_found
;
532 e
.dot2
= f
->dots
[j2
];
533 /* Use del234 instead of find234, because we always want to
534 * remove the edge if found */
535 edge_found
= del234(incomplete_edges
, &e
);
537 /* This edge already added, so fill out missing face.
538 * Edge is already removed from incomplete_edges. */
539 edge_found
->face2
= f
;
541 assert(next_new_edge
- g
->edges
< g
->num_edges
);
542 next_new_edge
->dot1
= e
.dot1
;
543 next_new_edge
->dot2
= e
.dot2
;
544 next_new_edge
->face1
= f
;
545 next_new_edge
->face2
= NULL
; /* potentially infinite face */
546 add234(incomplete_edges
, next_new_edge
);
551 freetree234(incomplete_edges
);
553 /* ====== Stage 2 ======
554 * For each face, build its edge list.
557 /* Allocate space for each edge list. Can do this, because each face's
558 * edge-list is the same size as its dot-list. */
559 for (i
= 0; i
< g
->num_faces
; i
++) {
560 grid_face
*f
= g
->faces
+ i
;
562 f
->edges
= snewn(f
->order
, grid_edge
*);
563 /* Preload with NULLs, to help detect potential bugs. */
564 for (j
= 0; j
< f
->order
; j
++)
568 /* Iterate over each edge, and over both its faces. Add this edge to
569 * the face's edge-list, after finding where it should go in the
571 for (i
= 0; i
< g
->num_edges
; i
++) {
572 grid_edge
*e
= g
->edges
+ i
;
574 for (j
= 0; j
< 2; j
++) {
575 grid_face
*f
= j ? e
->face2
: e
->face1
;
577 if (f
== NULL
) continue;
578 /* Find one of the dots around the face */
579 for (k
= 0; k
< f
->order
; k
++) {
580 if (f
->dots
[k
] == e
->dot1
)
581 break; /* found dot1 */
583 assert(k
!= f
->order
); /* Must find the dot around this face */
585 /* Labelling scheme: as we walk clockwise around the face,
586 * starting at dot0 (f->dots[0]), we hit:
587 * (dot0), edge0, dot1, edge1, dot2,...
597 * Therefore, edgeK joins dotK and dot{K+1}
600 /* Around this face, either the next dot or the previous dot
601 * must be e->dot2. Otherwise the edge is wrong. */
605 if (f
->dots
[k2
] == e
->dot2
) {
606 /* dot1(k) and dot2(k2) go clockwise around this face, so add
607 * this edge at position k (see diagram). */
608 assert(f
->edges
[k
] == NULL
);
612 /* Try previous dot */
616 if (f
->dots
[k2
] == e
->dot2
) {
617 /* dot1(k) and dot2(k2) go anticlockwise around this face. */
618 assert(f
->edges
[k2
] == NULL
);
622 assert(!"Grid broken: bad edge-face relationship");
626 /* ====== Stage 3 ======
627 * For each dot, build its edge-list and face-list.
630 /* We don't know how many edges/faces go around each dot, so we can't
631 * allocate the right space for these lists. Pre-compute the sizes by
632 * iterating over each edge and recording a tally against each dot. */
633 for (i
= 0; i
< g
->num_dots
; i
++) {
634 g
->dots
[i
].order
= 0;
636 for (i
= 0; i
< g
->num_edges
; i
++) {
637 grid_edge
*e
= g
->edges
+ i
;
641 /* Now we have the sizes, pre-allocate the edge and face lists. */
642 for (i
= 0; i
< g
->num_dots
; i
++) {
643 grid_dot
*d
= g
->dots
+ i
;
645 assert(d
->order
>= 2); /* sanity check */
646 d
->edges
= snewn(d
->order
, grid_edge
*);
647 d
->faces
= snewn(d
->order
, grid_face
*);
648 for (j
= 0; j
< d
->order
; j
++) {
653 /* For each dot, need to find a face that touches it, so we can seed
654 * the edge-face-edge-face process around each dot. */
655 for (i
= 0; i
< g
->num_faces
; i
++) {
656 grid_face
*f
= g
->faces
+ i
;
658 for (j
= 0; j
< f
->order
; j
++) {
659 grid_dot
*d
= f
->dots
[j
];
663 /* Each dot now has a face in its first slot. Generate the remaining
664 * faces and edges around the dot, by searching both clockwise and
665 * anticlockwise from the first face. Need to do both directions,
666 * because of the possibility of hitting the infinite face, which
667 * blocks progress. But there's only one such face, so we will
668 * succeed in finding every edge and face this way. */
669 for (i
= 0; i
< g
->num_dots
; i
++) {
670 grid_dot
*d
= g
->dots
+ i
;
671 int current_face1
= 0; /* ascends clockwise */
672 int current_face2
= 0; /* descends anticlockwise */
674 /* Labelling scheme: as we walk clockwise around the dot, starting
675 * at face0 (d->faces[0]), we hit:
676 * (face0), edge0, face1, edge1, face2,...
688 * So, for example, face1 should be joined to edge0 and edge1,
689 * and those edges should appear in an anticlockwise sense around
690 * that face (see diagram). */
692 /* clockwise search */
694 grid_face
*f
= d
->faces
[current_face1
];
698 /* find dot around this face */
699 for (j
= 0; j
< f
->order
; j
++) {
703 assert(j
!= f
->order
); /* must find dot */
705 /* Around f, required edge is anticlockwise from the dot. See
706 * the other labelling scheme higher up, for why we subtract 1
712 d
->edges
[current_face1
] = e
; /* set edge */
714 if (current_face1
== d
->order
)
718 d
->faces
[current_face1
] =
719 (e
->face1
== f
) ? e
->face2
: e
->face1
;
720 if (d
->faces
[current_face1
] == NULL
)
721 break; /* cannot progress beyond infinite face */
724 /* If the clockwise search made it all the way round, don't need to
725 * bother with the anticlockwise search. */
726 if (current_face1
== d
->order
)
727 continue; /* this dot is complete, move on to next dot */
729 /* anticlockwise search */
731 grid_face
*f
= d
->faces
[current_face2
];
735 /* find dot around this face */
736 for (j
= 0; j
< f
->order
; j
++) {
740 assert(j
!= f
->order
); /* must find dot */
742 /* Around f, required edge is clockwise from the dot. */
746 if (current_face2
== -1)
747 current_face2
= d
->order
- 1;
748 d
->edges
[current_face2
] = e
; /* set edge */
751 if (current_face2
== current_face1
)
753 d
->faces
[current_face2
] =
754 (e
->face1
== f
) ? e
->face2
: e
->face1
;
755 /* There's only 1 infinite face, so we must get all the way
756 * to current_face1 before we hit it. */
757 assert(d
->faces
[current_face2
]);
761 /* ====== Stage 4 ======
762 * Compute other grid settings
765 /* Bounding rectangle */
766 for (i
= 0; i
< g
->num_dots
; i
++) {
767 grid_dot
*d
= g
->dots
+ i
;
769 g
->lowest_x
= g
->highest_x
= d
->x
;
770 g
->lowest_y
= g
->highest_y
= d
->y
;
772 g
->lowest_x
= min(g
->lowest_x
, d
->x
);
773 g
->highest_x
= max(g
->highest_x
, d
->x
);
774 g
->lowest_y
= min(g
->lowest_y
, d
->y
);
775 g
->highest_y
= max(g
->highest_y
, d
->y
);
779 grid_debug_derived(g
);
782 /* Helpers for making grid-generation easier. These functions are only
783 * intended for use during grid generation. */
785 /* Comparison function for the (tree234) sorted dot list */
786 static int grid_point_cmp_fn(void *v1
, void *v2
)
791 return p2
->y
- p1
->y
;
793 return p2
->x
- p1
->x
;
795 /* Add a new face to the grid, with its dot list allocated.
796 * Assumes there's enough space allocated for the new face in grid->faces */
797 static void grid_face_add_new(grid
*g
, int face_size
)
800 grid_face
*new_face
= g
->faces
+ g
->num_faces
;
801 new_face
->order
= face_size
;
802 new_face
->dots
= snewn(face_size
, grid_dot
*);
803 for (i
= 0; i
< face_size
; i
++)
804 new_face
->dots
[i
] = NULL
;
805 new_face
->edges
= NULL
;
806 new_face
->has_incentre
= FALSE
;
809 /* Assumes dot list has enough space */
810 static grid_dot
*grid_dot_add_new(grid
*g
, int x
, int y
)
812 grid_dot
*new_dot
= g
->dots
+ g
->num_dots
;
814 new_dot
->edges
= NULL
;
815 new_dot
->faces
= NULL
;
821 /* Retrieve a dot with these (x,y) coordinates. Either return an existing dot
822 * in the dot_list, or add a new dot to the grid (and the dot_list) and
824 * Assumes g->dots has enough capacity allocated */
825 static grid_dot
*grid_get_dot(grid
*g
, tree234
*dot_list
, int x
, int y
)
834 ret
= find234(dot_list
, &test
, NULL
);
838 ret
= grid_dot_add_new(g
, x
, y
);
839 add234(dot_list
, ret
);
843 /* Sets the last face of the grid to include this dot, at this position
844 * around the face. Assumes num_faces is at least 1 (a new face has
845 * previously been added, with the required number of dots allocated) */
846 static void grid_face_set_dot(grid
*g
, grid_dot
*d
, int position
)
848 grid_face
*last_face
= g
->faces
+ g
->num_faces
- 1;
849 last_face
->dots
[position
] = d
;
853 * Helper routines for grid_find_incentre.
855 static int solve_2x2_matrix(double mx
[4], double vin
[2], double vout
[2])
859 det
= (mx
[0]*mx
[3] - mx
[1]*mx
[2]);
863 inv
[0] = mx
[3] / det
;
864 inv
[1] = -mx
[1] / det
;
865 inv
[2] = -mx
[2] / det
;
866 inv
[3] = mx
[0] / det
;
868 vout
[0] = inv
[0]*vin
[0] + inv
[1]*vin
[1];
869 vout
[1] = inv
[2]*vin
[0] + inv
[3]*vin
[1];
873 static int solve_3x3_matrix(double mx
[9], double vin
[3], double vout
[3])
878 det
= (mx
[0]*mx
[4]*mx
[8] + mx
[1]*mx
[5]*mx
[6] + mx
[2]*mx
[3]*mx
[7] -
879 mx
[0]*mx
[5]*mx
[7] - mx
[1]*mx
[3]*mx
[8] - mx
[2]*mx
[4]*mx
[6]);
883 inv
[0] = (mx
[4]*mx
[8] - mx
[5]*mx
[7]) / det
;
884 inv
[1] = (mx
[2]*mx
[7] - mx
[1]*mx
[8]) / det
;
885 inv
[2] = (mx
[1]*mx
[5] - mx
[2]*mx
[4]) / det
;
886 inv
[3] = (mx
[5]*mx
[6] - mx
[3]*mx
[8]) / det
;
887 inv
[4] = (mx
[0]*mx
[8] - mx
[2]*mx
[6]) / det
;
888 inv
[5] = (mx
[2]*mx
[3] - mx
[0]*mx
[5]) / det
;
889 inv
[6] = (mx
[3]*mx
[7] - mx
[4]*mx
[6]) / det
;
890 inv
[7] = (mx
[1]*mx
[6] - mx
[0]*mx
[7]) / det
;
891 inv
[8] = (mx
[0]*mx
[4] - mx
[1]*mx
[3]) / det
;
893 vout
[0] = inv
[0]*vin
[0] + inv
[1]*vin
[1] + inv
[2]*vin
[2];
894 vout
[1] = inv
[3]*vin
[0] + inv
[4]*vin
[1] + inv
[5]*vin
[2];
895 vout
[2] = inv
[6]*vin
[0] + inv
[7]*vin
[1] + inv
[8]*vin
[2];
900 void grid_find_incentre(grid_face
*f
)
902 double xbest
, ybest
, bestdist
;
904 grid_dot
*edgedot1
[3], *edgedot2
[3];
912 * Find the point in the polygon with the maximum distance to any
915 * Such a point must exist which is in contact with at least three
916 * edges and/or vertices. (Proof: if it's only in contact with two
917 * edges and/or vertices, it can't even be at a _local_ maximum -
918 * any such circle can always be expanded in some direction.) So
919 * we iterate through all 3-subsets of the combined set of edges
920 * and vertices; for each subset we generate one or two candidate
921 * points that might be the incentre, and then we vet each one to
922 * see if it's inside the polygon and what its maximum radius is.
924 * (There's one case which this algorithm will get noticeably
925 * wrong, and that's when a continuum of equally good answers
926 * exists due to parallel edges. Consider a long thin rectangle,
927 * for instance, or a parallelogram. This algorithm will pick a
928 * point near one end, and choose the end arbitrarily; obviously a
929 * nicer point to choose would be in the centre. To fix this I
930 * would have to introduce a special-case system which detected
931 * parallel edges in advance, set aside all candidate points
932 * generated using both edges in a parallel pair, and generated
933 * some additional candidate points half way between them. Also,
934 * of course, I'd have to cope with rounding error making such a
935 * point look worse than one of its endpoints. So I haven't done
936 * this for the moment, and will cross it if necessary when I come
939 * We don't actually iterate literally over _edges_, in the sense
940 * of grid_edge structures. Instead, we fill in edgedot1[] and
941 * edgedot2[] with a pair of dots adjacent in the face's list of
942 * vertices. This ensures that we get the edges in consistent
943 * orientation, which we could not do from the grid structure
944 * alone. (A moment's consideration of an order-3 vertex should
945 * make it clear that if a notional arrow was written on each
946 * edge, _at least one_ of the three faces bordering that vertex
947 * would have to have the two arrows tip-to-tip or tail-to-tail
948 * rather than tip-to-tail.)
954 for (i
= 0; i
+2 < 2*f
->order
; i
++) {
956 edgedot1
[nedges
] = f
->dots
[i
];
957 edgedot2
[nedges
++] = f
->dots
[(i
+1)%f
->order
];
959 dots
[ndots
++] = f
->dots
[i
- f
->order
];
961 for (j
= i
+1; j
+1 < 2*f
->order
; j
++) {
963 edgedot1
[nedges
] = f
->dots
[j
];
964 edgedot2
[nedges
++] = f
->dots
[(j
+1)%f
->order
];
966 dots
[ndots
++] = f
->dots
[j
- f
->order
];
968 for (k
= j
+1; k
< 2*f
->order
; k
++) {
969 double cx
[2], cy
[2]; /* candidate positions */
970 int cn
= 0; /* number of candidates */
973 edgedot1
[nedges
] = f
->dots
[k
];
974 edgedot2
[nedges
++] = f
->dots
[(k
+1)%f
->order
];
976 dots
[ndots
++] = f
->dots
[k
- f
->order
];
979 * Find a point, or pair of points, equidistant from
980 * all the specified edges and/or vertices.
984 * Three edges. This is a linear matrix equation:
985 * each row of the matrix represents the fact that
986 * the point (x,y) we seek is at distance r from
987 * that edge, and we solve three of those
988 * simultaneously to obtain x,y,r. (We ignore r.)
990 double matrix
[9], vector
[3], vector2
[3];
993 for (m
= 0; m
< 3; m
++) {
994 int x1
= edgedot1
[m
]->x
, x2
= edgedot2
[m
]->x
;
995 int y1
= edgedot1
[m
]->y
, y2
= edgedot2
[m
]->y
;
996 int dx
= x2
-x1
, dy
= y2
-y1
;
999 * ((x,y) - (x1,y1)) . (dy,-dx) = r |(dx,dy)|
1001 * => x dy - y dx - r |(dx,dy)| = (x1 dy - y1 dx)
1004 matrix
[3*m
+1] = -dx
;
1005 matrix
[3*m
+2] = -sqrt((double)dx
*dx
+(double)dy
*dy
);
1006 vector
[m
] = (double)x1
*dy
- (double)y1
*dx
;
1009 if (solve_3x3_matrix(matrix
, vector
, vector2
)) {
1010 cx
[cn
] = vector2
[0];
1011 cy
[cn
] = vector2
[1];
1014 } else if (nedges
== 2) {
1016 * Two edges and a dot. This will end up in a
1017 * quadratic equation.
1019 * First, look at the two edges. Having our point
1020 * be some distance r from both of them gives rise
1021 * to a pair of linear equations in x,y,r of the
1024 * (x-x1) dy - (y-y1) dx = r sqrt(dx^2+dy^2)
1026 * We eliminate r between those equations to give
1027 * us a single linear equation in x,y describing
1028 * the locus of points equidistant from both lines
1029 * - i.e. the angle bisector.
1031 * We then choose one of x,y to be a parameter t,
1032 * and derive linear formulae for x,y,r in terms
1033 * of t. This enables us to write down the
1034 * circular equation (x-xd)^2+(y-yd)^2=r^2 as a
1035 * quadratic in t; solving that and substituting
1036 * in for x,y gives us two candidate points.
1038 double eqs
[2][4]; /* a,b,c,d : ax+by+cr=d */
1039 double eq
[3]; /* a,b,c: ax+by=c */
1040 double xt
[2], yt
[2], rt
[2]; /* a,b: {x,y,r}=at+b */
1041 double q
[3]; /* a,b,c: at^2+bt+c=0 */
1044 /* Find equations of the two input lines. */
1045 for (m
= 0; m
< 2; m
++) {
1046 int x1
= edgedot1
[m
]->x
, x2
= edgedot2
[m
]->x
;
1047 int y1
= edgedot1
[m
]->y
, y2
= edgedot2
[m
]->y
;
1048 int dx
= x2
-x1
, dy
= y2
-y1
;
1052 eqs
[m
][2] = -sqrt(dx
*dx
+dy
*dy
);
1053 eqs
[m
][3] = x1
*dy
- y1
*dx
;
1056 /* Derive the angle bisector by eliminating r. */
1057 eq
[0] = eqs
[0][0]*eqs
[1][2] - eqs
[1][0]*eqs
[0][2];
1058 eq
[1] = eqs
[0][1]*eqs
[1][2] - eqs
[1][1]*eqs
[0][2];
1059 eq
[2] = eqs
[0][3]*eqs
[1][2] - eqs
[1][3]*eqs
[0][2];
1061 /* Parametrise x and y in terms of some t. */
1062 if (abs(eq
[0]) < abs(eq
[1])) {
1063 /* Parameter is x. */
1064 xt
[0] = 1; xt
[1] = 0;
1065 yt
[0] = -eq
[0]/eq
[1]; yt
[1] = eq
[2]/eq
[1];
1067 /* Parameter is y. */
1068 yt
[0] = 1; yt
[1] = 0;
1069 xt
[0] = -eq
[1]/eq
[0]; xt
[1] = eq
[2]/eq
[0];
1072 /* Find a linear representation of r using eqs[0]. */
1073 rt
[0] = -(eqs
[0][0]*xt
[0] + eqs
[0][1]*yt
[0])/eqs
[0][2];
1074 rt
[1] = (eqs
[0][3] - eqs
[0][0]*xt
[1] -
1075 eqs
[0][1]*yt
[1])/eqs
[0][2];
1077 /* Construct the quadratic equation. */
1078 q
[0] = -rt
[0]*rt
[0];
1079 q
[1] = -2*rt
[0]*rt
[1];
1080 q
[2] = -rt
[1]*rt
[1];
1081 q
[0] += xt
[0]*xt
[0];
1082 q
[1] += 2*xt
[0]*(xt
[1]-dots
[0]->x
);
1083 q
[2] += (xt
[1]-dots
[0]->x
)*(xt
[1]-dots
[0]->x
);
1084 q
[0] += yt
[0]*yt
[0];
1085 q
[1] += 2*yt
[0]*(yt
[1]-dots
[0]->y
);
1086 q
[2] += (yt
[1]-dots
[0]->y
)*(yt
[1]-dots
[0]->y
);
1089 disc
= q
[1]*q
[1] - 4*q
[0]*q
[2];
1095 t
= (-q
[1] + disc
) / (2*q
[0]);
1096 cx
[cn
] = xt
[0]*t
+ xt
[1];
1097 cy
[cn
] = yt
[0]*t
+ yt
[1];
1100 t
= (-q
[1] - disc
) / (2*q
[0]);
1101 cx
[cn
] = xt
[0]*t
+ xt
[1];
1102 cy
[cn
] = yt
[0]*t
+ yt
[1];
1105 } else if (nedges
== 1) {
1107 * Two dots and an edge. This one's another
1108 * quadratic equation.
1110 * The point we want must lie on the perpendicular
1111 * bisector of the two dots; that much is obvious.
1112 * So we can construct a parametrisation of that
1113 * bisecting line, giving linear formulae for x,y
1114 * in terms of t. We can also express the distance
1115 * from the edge as such a linear formula.
1117 * Then we set that equal to the radius of the
1118 * circle passing through the two points, which is
1119 * a Pythagoras exercise; that gives rise to a
1120 * quadratic in t, which we solve.
1122 double xt
[2], yt
[2], rt
[2]; /* a,b: {x,y,r}=at+b */
1123 double q
[3]; /* a,b,c: at^2+bt+c=0 */
1127 /* Find parametric formulae for x,y. */
1129 int x1
= dots
[0]->x
, x2
= dots
[1]->x
;
1130 int y1
= dots
[0]->y
, y2
= dots
[1]->y
;
1131 int dx
= x2
-x1
, dy
= y2
-y1
;
1132 double d
= sqrt((double)dx
*dx
+ (double)dy
*dy
);
1134 xt
[1] = (x1
+x2
)/2.0;
1135 yt
[1] = (y1
+y2
)/2.0;
1136 /* It's convenient if we have t at standard scale. */
1140 /* Also note down half the separation between
1141 * the dots, for use in computing the circle radius. */
1145 /* Find a parametric formula for r. */
1147 int x1
= edgedot1
[0]->x
, x2
= edgedot2
[0]->x
;
1148 int y1
= edgedot1
[0]->y
, y2
= edgedot2
[0]->y
;
1149 int dx
= x2
-x1
, dy
= y2
-y1
;
1150 double d
= sqrt((double)dx
*dx
+ (double)dy
*dy
);
1151 rt
[0] = (xt
[0]*dy
- yt
[0]*dx
) / d
;
1152 rt
[1] = ((xt
[1]-x1
)*dy
- (yt
[1]-y1
)*dx
) / d
;
1155 /* Construct the quadratic equation. */
1157 q
[1] = 2*rt
[0]*rt
[1];
1160 q
[2] -= halfsep
*halfsep
;
1163 disc
= q
[1]*q
[1] - 4*q
[0]*q
[2];
1169 t
= (-q
[1] + disc
) / (2*q
[0]);
1170 cx
[cn
] = xt
[0]*t
+ xt
[1];
1171 cy
[cn
] = yt
[0]*t
+ yt
[1];
1174 t
= (-q
[1] - disc
) / (2*q
[0]);
1175 cx
[cn
] = xt
[0]*t
+ xt
[1];
1176 cy
[cn
] = yt
[0]*t
+ yt
[1];
1179 } else if (nedges
== 0) {
1181 * Three dots. This is another linear matrix
1182 * equation, this time with each row of the matrix
1183 * representing the perpendicular bisector between
1184 * two of the points. Of course we only need two
1185 * such lines to find their intersection, so we
1186 * need only solve a 2x2 matrix equation.
1189 double matrix
[4], vector
[2], vector2
[2];
1192 for (m
= 0; m
< 2; m
++) {
1193 int x1
= dots
[m
]->x
, x2
= dots
[m
+1]->x
;
1194 int y1
= dots
[m
]->y
, y2
= dots
[m
+1]->y
;
1195 int dx
= x2
-x1
, dy
= y2
-y1
;
1198 * ((x,y) - (x1,y1)) . (dx,dy) = 1/2 |(dx,dy)|^2
1200 * => 2x dx + 2y dy = dx^2+dy^2 + (2 x1 dx + 2 y1 dy)
1202 matrix
[2*m
+0] = 2*dx
;
1203 matrix
[2*m
+1] = 2*dy
;
1204 vector
[m
] = ((double)dx
*dx
+ (double)dy
*dy
+
1205 2.0*x1
*dx
+ 2.0*y1
*dy
);
1208 if (solve_2x2_matrix(matrix
, vector
, vector2
)) {
1209 cx
[cn
] = vector2
[0];
1210 cy
[cn
] = vector2
[1];
1216 * Now go through our candidate points and see if any
1217 * of them are better than what we've got so far.
1219 for (m
= 0; m
< cn
; m
++) {
1220 double x
= cx
[m
], y
= cy
[m
];
1223 * First, disqualify the point if it's not inside
1224 * the polygon, which we work out by counting the
1225 * edges to the right of the point. (For
1226 * tiebreaking purposes when edges start or end on
1227 * our y-coordinate or go right through it, we
1228 * consider our point to be offset by a small
1229 * _positive_ epsilon in both the x- and
1233 for (e
= 0; e
< f
->order
; e
++) {
1234 int xs
= f
->edges
[e
]->dot1
->x
;
1235 int xe
= f
->edges
[e
]->dot2
->x
;
1236 int ys
= f
->edges
[e
]->dot1
->y
;
1237 int ye
= f
->edges
[e
]->dot2
->y
;
1238 if ((y
>= ys
&& y
< ye
) || (y
>= ye
&& y
< ys
)) {
1240 * The line goes past our y-position. Now we need
1241 * to know if its x-coordinate when it does so is
1244 * The x-coordinate in question is mathematically
1245 * (y - ys) * (xe - xs) / (ye - ys), and we want
1246 * to know whether (x - xs) >= that. Of course we
1247 * avoid the division, so we can work in integers;
1248 * to do this we must multiply both sides of the
1249 * inequality by ye - ys, which means we must
1250 * first check that's not negative.
1252 int num
= xe
- xs
, denom
= ye
- ys
;
1257 if ((x
- xs
) * denom
>= (y
- ys
) * num
)
1263 double mindist
= HUGE_VAL
;
1267 * This point is inside the polygon, so now we check
1268 * its minimum distance to every edge and corner.
1269 * First the corners ...
1271 for (d
= 0; d
< f
->order
; d
++) {
1272 int xp
= f
->dots
[d
]->x
;
1273 int yp
= f
->dots
[d
]->y
;
1274 double dx
= x
- xp
, dy
= y
- yp
;
1275 double dist
= dx
*dx
+ dy
*dy
;
1281 * ... and now also check the perpendicular distance
1282 * to every edge, if the perpendicular lies between
1283 * the edge's endpoints.
1285 for (e
= 0; e
< f
->order
; e
++) {
1286 int xs
= f
->edges
[e
]->dot1
->x
;
1287 int xe
= f
->edges
[e
]->dot2
->x
;
1288 int ys
= f
->edges
[e
]->dot1
->y
;
1289 int ye
= f
->edges
[e
]->dot2
->y
;
1292 * If s and e are our endpoints, and p our
1293 * candidate circle centre, the foot of a
1294 * perpendicular from p to the line se lies
1295 * between s and e if and only if (p-s).(e-s) lies
1296 * strictly between 0 and (e-s).(e-s).
1298 int edx
= xe
- xs
, edy
= ye
- ys
;
1299 double pdx
= x
- xs
, pdy
= y
- ys
;
1300 double pde
= pdx
* edx
+ pdy
* edy
;
1301 long ede
= (long)edx
* edx
+ (long)edy
* edy
;
1302 if (0 < pde
&& pde
< ede
) {
1304 * Yes, the nearest point on this edge is
1305 * closer than either endpoint, so we must
1306 * take it into account by measuring the
1307 * perpendicular distance to the edge and
1308 * checking its square against mindist.
1311 double pdre
= pdx
* edy
- pdy
* edx
;
1312 double sqlen
= pdre
* pdre
/ ede
;
1314 if (mindist
> sqlen
)
1320 * Right. Now we know the biggest circle around this
1321 * point, so we can check it against bestdist.
1323 if (bestdist
< mindist
) {
1347 assert(bestdist
> 0);
1349 f
->has_incentre
= TRUE
;
1350 f
->ix
= xbest
+ 0.5; /* round to nearest */
1351 f
->iy
= ybest
+ 0.5;
1354 /* ------ Generate various types of grid ------ */
1356 /* General method is to generate faces, by calculating their dot coordinates.
1357 * As new faces are added, we keep track of all the dots so we can tell when
1358 * a new face reuses an existing dot. For example, two squares touching at an
1359 * edge would generate six unique dots: four dots from the first face, then
1360 * two additional dots for the second face, because we detect the other two
1361 * dots have already been taken up. This list is stored in a tree234
1362 * called "points". No extra memory-allocation needed here - we store the
1363 * actual grid_dot* pointers, which all point into the g->dots list.
1364 * For this reason, we have to calculate coordinates in such a way as to
1365 * eliminate any rounding errors, so we can detect when a dot on one
1366 * face precisely lands on a dot of a different face. No floating-point
1370 #define SQUARE_TILESIZE 20
1372 void grid_size_square(int width
, int height
,
1373 int *tilesize
, int *xextent
, int *yextent
)
1375 int a
= SQUARE_TILESIZE
;
1378 *xextent
= width
* a
;
1379 *yextent
= height
* a
;
1382 grid
*grid_new_square(int width
, int height
, char *desc
)
1386 int a
= SQUARE_TILESIZE
;
1388 /* Upper bounds - don't have to be exact */
1389 int max_faces
= width
* height
;
1390 int max_dots
= (width
+ 1) * (height
+ 1);
1394 grid
*g
= grid_empty();
1396 g
->faces
= snewn(max_faces
, grid_face
);
1397 g
->dots
= snewn(max_dots
, grid_dot
);
1399 points
= newtree234(grid_point_cmp_fn
);
1401 /* generate square faces */
1402 for (y
= 0; y
< height
; y
++) {
1403 for (x
= 0; x
< width
; x
++) {
1409 grid_face_add_new(g
, 4);
1410 d
= grid_get_dot(g
, points
, px
, py
);
1411 grid_face_set_dot(g
, d
, 0);
1412 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1413 grid_face_set_dot(g
, d
, 1);
1414 d
= grid_get_dot(g
, points
, px
+ a
, py
+ a
);
1415 grid_face_set_dot(g
, d
, 2);
1416 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1417 grid_face_set_dot(g
, d
, 3);
1421 freetree234(points
);
1422 assert(g
->num_faces
<= max_faces
);
1423 assert(g
->num_dots
<= max_dots
);
1425 grid_make_consistent(g
);
1429 #define HONEY_TILESIZE 45
1430 /* Vector for side of hexagon - ratio is close to sqrt(3) */
1434 void grid_size_honeycomb(int width
, int height
,
1435 int *tilesize
, int *xextent
, int *yextent
)
1440 *tilesize
= HONEY_TILESIZE
;
1441 *xextent
= (3 * a
* (width
-1)) + 4*a
;
1442 *yextent
= (2 * b
* (height
-1)) + 3*b
;
1445 grid
*grid_new_honeycomb(int width
, int height
, char *desc
)
1451 /* Upper bounds - don't have to be exact */
1452 int max_faces
= width
* height
;
1453 int max_dots
= 2 * (width
+ 1) * (height
+ 1);
1457 grid
*g
= grid_empty();
1458 g
->tilesize
= HONEY_TILESIZE
;
1459 g
->faces
= snewn(max_faces
, grid_face
);
1460 g
->dots
= snewn(max_dots
, grid_dot
);
1462 points
= newtree234(grid_point_cmp_fn
);
1464 /* generate hexagonal faces */
1465 for (y
= 0; y
< height
; y
++) {
1466 for (x
= 0; x
< width
; x
++) {
1473 grid_face_add_new(g
, 6);
1475 d
= grid_get_dot(g
, points
, cx
- a
, cy
- b
);
1476 grid_face_set_dot(g
, d
, 0);
1477 d
= grid_get_dot(g
, points
, cx
+ a
, cy
- b
);
1478 grid_face_set_dot(g
, d
, 1);
1479 d
= grid_get_dot(g
, points
, cx
+ 2*a
, cy
);
1480 grid_face_set_dot(g
, d
, 2);
1481 d
= grid_get_dot(g
, points
, cx
+ a
, cy
+ b
);
1482 grid_face_set_dot(g
, d
, 3);
1483 d
= grid_get_dot(g
, points
, cx
- a
, cy
+ b
);
1484 grid_face_set_dot(g
, d
, 4);
1485 d
= grid_get_dot(g
, points
, cx
- 2*a
, cy
);
1486 grid_face_set_dot(g
, d
, 5);
1490 freetree234(points
);
1491 assert(g
->num_faces
<= max_faces
);
1492 assert(g
->num_dots
<= max_dots
);
1494 grid_make_consistent(g
);
1498 #define TRIANGLE_TILESIZE 18
1499 /* Vector for side of triangle - ratio is close to sqrt(3) */
1500 #define TRIANGLE_VEC_X 15
1501 #define TRIANGLE_VEC_Y 26
1503 void grid_size_triangular(int width
, int height
,
1504 int *tilesize
, int *xextent
, int *yextent
)
1506 int vec_x
= TRIANGLE_VEC_X
;
1507 int vec_y
= TRIANGLE_VEC_Y
;
1509 *tilesize
= TRIANGLE_TILESIZE
;
1510 *xextent
= width
* 2 * vec_x
+ vec_x
;
1511 *yextent
= height
* vec_y
;
1514 /* Doesn't use the previous method of generation, it pre-dates it!
1515 * A triangular grid is just about simple enough to do by "brute force" */
1516 grid
*grid_new_triangular(int width
, int height
, char *desc
)
1520 /* Vector for side of triangle - ratio is close to sqrt(3) */
1521 int vec_x
= TRIANGLE_VEC_X
;
1522 int vec_y
= TRIANGLE_VEC_Y
;
1526 /* convenient alias */
1529 grid
*g
= grid_empty();
1530 g
->tilesize
= TRIANGLE_TILESIZE
;
1532 g
->num_faces
= width
* height
* 2;
1533 g
->num_dots
= (width
+ 1) * (height
+ 1);
1534 g
->faces
= snewn(g
->num_faces
, grid_face
);
1535 g
->dots
= snewn(g
->num_dots
, grid_dot
);
1539 for (y
= 0; y
<= height
; y
++) {
1540 for (x
= 0; x
<= width
; x
++) {
1541 grid_dot
*d
= g
->dots
+ index
;
1542 /* odd rows are offset to the right */
1546 d
->x
= x
* 2 * vec_x
+ ((y
% 2) ? vec_x
: 0);
1552 /* generate faces */
1554 for (y
= 0; y
< height
; y
++) {
1555 for (x
= 0; x
< width
; x
++) {
1556 /* initialise two faces for this (x,y) */
1557 grid_face
*f1
= g
->faces
+ index
;
1558 grid_face
*f2
= f1
+ 1;
1561 f1
->dots
= snewn(f1
->order
, grid_dot
*);
1562 f1
->has_incentre
= FALSE
;
1565 f2
->dots
= snewn(f2
->order
, grid_dot
*);
1566 f2
->has_incentre
= FALSE
;
1568 /* face descriptions depend on whether the row-number is
1571 f1
->dots
[0] = g
->dots
+ y
* w
+ x
;
1572 f1
->dots
[1] = g
->dots
+ (y
+ 1) * w
+ x
+ 1;
1573 f1
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
;
1574 f2
->dots
[0] = g
->dots
+ y
* w
+ x
;
1575 f2
->dots
[1] = g
->dots
+ y
* w
+ x
+ 1;
1576 f2
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
+ 1;
1578 f1
->dots
[0] = g
->dots
+ y
* w
+ x
;
1579 f1
->dots
[1] = g
->dots
+ y
* w
+ x
+ 1;
1580 f1
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
;
1581 f2
->dots
[0] = g
->dots
+ y
* w
+ x
+ 1;
1582 f2
->dots
[1] = g
->dots
+ (y
+ 1) * w
+ x
+ 1;
1583 f2
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
;
1589 grid_make_consistent(g
);
1593 #define SNUBSQUARE_TILESIZE 18
1594 /* Vector for side of triangle - ratio is close to sqrt(3) */
1595 #define SNUBSQUARE_A 15
1596 #define SNUBSQUARE_B 26
1598 void grid_size_snubsquare(int width
, int height
,
1599 int *tilesize
, int *xextent
, int *yextent
)
1601 int a
= SNUBSQUARE_A
;
1602 int b
= SNUBSQUARE_B
;
1604 *tilesize
= SNUBSQUARE_TILESIZE
;
1605 *xextent
= (a
+b
) * (width
-1) + a
+ b
;
1606 *yextent
= (a
+b
) * (height
-1) + a
+ b
;
1609 grid
*grid_new_snubsquare(int width
, int height
, char *desc
)
1612 int a
= SNUBSQUARE_A
;
1613 int b
= SNUBSQUARE_B
;
1615 /* Upper bounds - don't have to be exact */
1616 int max_faces
= 3 * width
* height
;
1617 int max_dots
= 2 * (width
+ 1) * (height
+ 1);
1621 grid
*g
= grid_empty();
1622 g
->tilesize
= SNUBSQUARE_TILESIZE
;
1623 g
->faces
= snewn(max_faces
, grid_face
);
1624 g
->dots
= snewn(max_dots
, grid_dot
);
1626 points
= newtree234(grid_point_cmp_fn
);
1628 for (y
= 0; y
< height
; y
++) {
1629 for (x
= 0; x
< width
; x
++) {
1632 int px
= (a
+ b
) * x
;
1633 int py
= (a
+ b
) * y
;
1635 /* generate square faces */
1636 grid_face_add_new(g
, 4);
1638 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1639 grid_face_set_dot(g
, d
, 0);
1640 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
);
1641 grid_face_set_dot(g
, d
, 1);
1642 d
= grid_get_dot(g
, points
, px
+ b
, py
+ a
+ b
);
1643 grid_face_set_dot(g
, d
, 2);
1644 d
= grid_get_dot(g
, points
, px
, py
+ b
);
1645 grid_face_set_dot(g
, d
, 3);
1647 d
= grid_get_dot(g
, points
, px
+ b
, py
);
1648 grid_face_set_dot(g
, d
, 0);
1649 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ b
);
1650 grid_face_set_dot(g
, d
, 1);
1651 d
= grid_get_dot(g
, points
, px
+ a
, py
+ a
+ b
);
1652 grid_face_set_dot(g
, d
, 2);
1653 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1654 grid_face_set_dot(g
, d
, 3);
1657 /* generate up/down triangles */
1659 grid_face_add_new(g
, 3);
1661 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1662 grid_face_set_dot(g
, d
, 0);
1663 d
= grid_get_dot(g
, points
, px
, py
+ b
);
1664 grid_face_set_dot(g
, d
, 1);
1665 d
= grid_get_dot(g
, points
, px
- a
, py
);
1666 grid_face_set_dot(g
, d
, 2);
1668 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1669 grid_face_set_dot(g
, d
, 0);
1670 d
= grid_get_dot(g
, points
, px
+ a
, py
+ a
+ b
);
1671 grid_face_set_dot(g
, d
, 1);
1672 d
= grid_get_dot(g
, points
, px
- a
, py
+ a
+ b
);
1673 grid_face_set_dot(g
, d
, 2);
1677 /* generate left/right triangles */
1679 grid_face_add_new(g
, 3);
1681 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1682 grid_face_set_dot(g
, d
, 0);
1683 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
- a
);
1684 grid_face_set_dot(g
, d
, 1);
1685 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
);
1686 grid_face_set_dot(g
, d
, 2);
1688 d
= grid_get_dot(g
, points
, px
, py
- a
);
1689 grid_face_set_dot(g
, d
, 0);
1690 d
= grid_get_dot(g
, points
, px
+ b
, py
);
1691 grid_face_set_dot(g
, d
, 1);
1692 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1693 grid_face_set_dot(g
, d
, 2);
1699 freetree234(points
);
1700 assert(g
->num_faces
<= max_faces
);
1701 assert(g
->num_dots
<= max_dots
);
1703 grid_make_consistent(g
);
1707 #define CAIRO_TILESIZE 40
1708 /* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */
1712 void grid_size_cairo(int width
, int height
,
1713 int *tilesize
, int *xextent
, int *yextent
)
1715 int b
= CAIRO_B
; /* a unused in determining grid size. */
1717 *tilesize
= CAIRO_TILESIZE
;
1718 *xextent
= 2*b
*(width
-1) + 2*b
;
1719 *yextent
= 2*b
*(height
-1) + 2*b
;
1722 grid
*grid_new_cairo(int width
, int height
, char *desc
)
1728 /* Upper bounds - don't have to be exact */
1729 int max_faces
= 2 * width
* height
;
1730 int max_dots
= 3 * (width
+ 1) * (height
+ 1);
1734 grid
*g
= grid_empty();
1735 g
->tilesize
= CAIRO_TILESIZE
;
1736 g
->faces
= snewn(max_faces
, grid_face
);
1737 g
->dots
= snewn(max_dots
, grid_dot
);
1739 points
= newtree234(grid_point_cmp_fn
);
1741 for (y
= 0; y
< height
; y
++) {
1742 for (x
= 0; x
< width
; x
++) {
1748 /* horizontal pentagons */
1750 grid_face_add_new(g
, 5);
1752 d
= grid_get_dot(g
, points
, px
+ a
, py
- b
);
1753 grid_face_set_dot(g
, d
, 0);
1754 d
= grid_get_dot(g
, points
, px
+ 2*b
- a
, py
- b
);
1755 grid_face_set_dot(g
, d
, 1);
1756 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
1757 grid_face_set_dot(g
, d
, 2);
1758 d
= grid_get_dot(g
, points
, px
+ b
, py
+ a
);
1759 grid_face_set_dot(g
, d
, 3);
1760 d
= grid_get_dot(g
, points
, px
, py
);
1761 grid_face_set_dot(g
, d
, 4);
1763 d
= grid_get_dot(g
, points
, px
, py
);
1764 grid_face_set_dot(g
, d
, 0);
1765 d
= grid_get_dot(g
, points
, px
+ b
, py
- a
);
1766 grid_face_set_dot(g
, d
, 1);
1767 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
1768 grid_face_set_dot(g
, d
, 2);
1769 d
= grid_get_dot(g
, points
, px
+ 2*b
- a
, py
+ b
);
1770 grid_face_set_dot(g
, d
, 3);
1771 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1772 grid_face_set_dot(g
, d
, 4);
1775 /* vertical pentagons */
1777 grid_face_add_new(g
, 5);
1779 d
= grid_get_dot(g
, points
, px
, py
);
1780 grid_face_set_dot(g
, d
, 0);
1781 d
= grid_get_dot(g
, points
, px
+ b
, py
+ a
);
1782 grid_face_set_dot(g
, d
, 1);
1783 d
= grid_get_dot(g
, points
, px
+ b
, py
+ 2*b
- a
);
1784 grid_face_set_dot(g
, d
, 2);
1785 d
= grid_get_dot(g
, points
, px
, py
+ 2*b
);
1786 grid_face_set_dot(g
, d
, 3);
1787 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1788 grid_face_set_dot(g
, d
, 4);
1790 d
= grid_get_dot(g
, points
, px
, py
);
1791 grid_face_set_dot(g
, d
, 0);
1792 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1793 grid_face_set_dot(g
, d
, 1);
1794 d
= grid_get_dot(g
, points
, px
, py
+ 2*b
);
1795 grid_face_set_dot(g
, d
, 2);
1796 d
= grid_get_dot(g
, points
, px
- b
, py
+ 2*b
- a
);
1797 grid_face_set_dot(g
, d
, 3);
1798 d
= grid_get_dot(g
, points
, px
- b
, py
+ a
);
1799 grid_face_set_dot(g
, d
, 4);
1805 freetree234(points
);
1806 assert(g
->num_faces
<= max_faces
);
1807 assert(g
->num_dots
<= max_dots
);
1809 grid_make_consistent(g
);
1813 #define GREATHEX_TILESIZE 18
1814 /* Vector for side of triangle - ratio is close to sqrt(3) */
1815 #define GREATHEX_A 15
1816 #define GREATHEX_B 26
1818 void grid_size_greathexagonal(int width
, int height
,
1819 int *tilesize
, int *xextent
, int *yextent
)
1824 *tilesize
= GREATHEX_TILESIZE
;
1825 *xextent
= (3*a
+ b
) * (width
-1) + 4*a
;
1826 *yextent
= (2*a
+ 2*b
) * (height
-1) + 3*b
+ a
;
1829 grid
*grid_new_greathexagonal(int width
, int height
, char *desc
)
1835 /* Upper bounds - don't have to be exact */
1836 int max_faces
= 6 * (width
+ 1) * (height
+ 1);
1837 int max_dots
= 6 * width
* height
;
1841 grid
*g
= grid_empty();
1842 g
->tilesize
= GREATHEX_TILESIZE
;
1843 g
->faces
= snewn(max_faces
, grid_face
);
1844 g
->dots
= snewn(max_dots
, grid_dot
);
1846 points
= newtree234(grid_point_cmp_fn
);
1848 for (y
= 0; y
< height
; y
++) {
1849 for (x
= 0; x
< width
; x
++) {
1851 /* centre of hexagon */
1852 int px
= (3*a
+ b
) * x
;
1853 int py
= (2*a
+ 2*b
) * y
;
1858 grid_face_add_new(g
, 6);
1859 d
= grid_get_dot(g
, points
, px
- a
, py
- b
);
1860 grid_face_set_dot(g
, d
, 0);
1861 d
= grid_get_dot(g
, points
, px
+ a
, py
- b
);
1862 grid_face_set_dot(g
, d
, 1);
1863 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
);
1864 grid_face_set_dot(g
, d
, 2);
1865 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1866 grid_face_set_dot(g
, d
, 3);
1867 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1868 grid_face_set_dot(g
, d
, 4);
1869 d
= grid_get_dot(g
, points
, px
- 2*a
, py
);
1870 grid_face_set_dot(g
, d
, 5);
1872 /* square below hexagon */
1873 if (y
< height
- 1) {
1874 grid_face_add_new(g
, 4);
1875 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1876 grid_face_set_dot(g
, d
, 0);
1877 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1878 grid_face_set_dot(g
, d
, 1);
1879 d
= grid_get_dot(g
, points
, px
+ a
, py
+ 2*a
+ b
);
1880 grid_face_set_dot(g
, d
, 2);
1881 d
= grid_get_dot(g
, points
, px
- a
, py
+ 2*a
+ b
);
1882 grid_face_set_dot(g
, d
, 3);
1885 /* square below right */
1886 if ((x
< width
- 1) && (((x
% 2) == 0) || (y
< height
- 1))) {
1887 grid_face_add_new(g
, 4);
1888 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
);
1889 grid_face_set_dot(g
, d
, 0);
1890 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
);
1891 grid_face_set_dot(g
, d
, 1);
1892 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
+ b
);
1893 grid_face_set_dot(g
, d
, 2);
1894 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1895 grid_face_set_dot(g
, d
, 3);
1898 /* square below left */
1899 if ((x
> 0) && (((x
% 2) == 0) || (y
< height
- 1))) {
1900 grid_face_add_new(g
, 4);
1901 d
= grid_get_dot(g
, points
, px
- 2*a
, py
);
1902 grid_face_set_dot(g
, d
, 0);
1903 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1904 grid_face_set_dot(g
, d
, 1);
1905 d
= grid_get_dot(g
, points
, px
- a
- b
, py
+ a
+ b
);
1906 grid_face_set_dot(g
, d
, 2);
1907 d
= grid_get_dot(g
, points
, px
- 2*a
- b
, py
+ a
);
1908 grid_face_set_dot(g
, d
, 3);
1911 /* Triangle below right */
1912 if ((x
< width
- 1) && (y
< height
- 1)) {
1913 grid_face_add_new(g
, 3);
1914 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1915 grid_face_set_dot(g
, d
, 0);
1916 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
+ b
);
1917 grid_face_set_dot(g
, d
, 1);
1918 d
= grid_get_dot(g
, points
, px
+ a
, py
+ 2*a
+ b
);
1919 grid_face_set_dot(g
, d
, 2);
1922 /* Triangle below left */
1923 if ((x
> 0) && (y
< height
- 1)) {
1924 grid_face_add_new(g
, 3);
1925 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1926 grid_face_set_dot(g
, d
, 0);
1927 d
= grid_get_dot(g
, points
, px
- a
, py
+ 2*a
+ b
);
1928 grid_face_set_dot(g
, d
, 1);
1929 d
= grid_get_dot(g
, points
, px
- a
- b
, py
+ a
+ b
);
1930 grid_face_set_dot(g
, d
, 2);
1935 freetree234(points
);
1936 assert(g
->num_faces
<= max_faces
);
1937 assert(g
->num_dots
<= max_dots
);
1939 grid_make_consistent(g
);
1943 #define OCTAGONAL_TILESIZE 40
1944 /* b/a approx sqrt(2) */
1945 #define OCTAGONAL_A 29
1946 #define OCTAGONAL_B 41
1948 void grid_size_octagonal(int width
, int height
,
1949 int *tilesize
, int *xextent
, int *yextent
)
1951 int a
= OCTAGONAL_A
;
1952 int b
= OCTAGONAL_B
;
1954 *tilesize
= OCTAGONAL_TILESIZE
;
1955 *xextent
= (2*a
+ b
) * width
;
1956 *yextent
= (2*a
+ b
) * height
;
1959 grid
*grid_new_octagonal(int width
, int height
, char *desc
)
1962 int a
= OCTAGONAL_A
;
1963 int b
= OCTAGONAL_B
;
1965 /* Upper bounds - don't have to be exact */
1966 int max_faces
= 2 * width
* height
;
1967 int max_dots
= 4 * (width
+ 1) * (height
+ 1);
1971 grid
*g
= grid_empty();
1972 g
->tilesize
= OCTAGONAL_TILESIZE
;
1973 g
->faces
= snewn(max_faces
, grid_face
);
1974 g
->dots
= snewn(max_dots
, grid_dot
);
1976 points
= newtree234(grid_point_cmp_fn
);
1978 for (y
= 0; y
< height
; y
++) {
1979 for (x
= 0; x
< width
; x
++) {
1982 int px
= (2*a
+ b
) * x
;
1983 int py
= (2*a
+ b
) * y
;
1985 grid_face_add_new(g
, 8);
1986 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1987 grid_face_set_dot(g
, d
, 0);
1988 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
);
1989 grid_face_set_dot(g
, d
, 1);
1990 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
);
1991 grid_face_set_dot(g
, d
, 2);
1992 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
+ b
);
1993 grid_face_set_dot(g
, d
, 3);
1994 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ 2*a
+ b
);
1995 grid_face_set_dot(g
, d
, 4);
1996 d
= grid_get_dot(g
, points
, px
+ a
, py
+ 2*a
+ b
);
1997 grid_face_set_dot(g
, d
, 5);
1998 d
= grid_get_dot(g
, points
, px
, py
+ a
+ b
);
1999 grid_face_set_dot(g
, d
, 6);
2000 d
= grid_get_dot(g
, points
, px
, py
+ a
);
2001 grid_face_set_dot(g
, d
, 7);
2004 if ((x
> 0) && (y
> 0)) {
2005 grid_face_add_new(g
, 4);
2006 d
= grid_get_dot(g
, points
, px
, py
- a
);
2007 grid_face_set_dot(g
, d
, 0);
2008 d
= grid_get_dot(g
, points
, px
+ a
, py
);
2009 grid_face_set_dot(g
, d
, 1);
2010 d
= grid_get_dot(g
, points
, px
, py
+ a
);
2011 grid_face_set_dot(g
, d
, 2);
2012 d
= grid_get_dot(g
, points
, px
- a
, py
);
2013 grid_face_set_dot(g
, d
, 3);
2018 freetree234(points
);
2019 assert(g
->num_faces
<= max_faces
);
2020 assert(g
->num_dots
<= max_dots
);
2022 grid_make_consistent(g
);
2026 #define KITE_TILESIZE 40
2027 /* b/a approx sqrt(3) */
2031 void grid_size_kites(int width
, int height
,
2032 int *tilesize
, int *xextent
, int *yextent
)
2037 *tilesize
= KITE_TILESIZE
;
2038 *xextent
= 4*b
* width
+ 2*b
;
2039 *yextent
= 6*a
* (height
-1) + 8*a
;
2042 grid
*grid_new_kites(int width
, int height
, char *desc
)
2048 /* Upper bounds - don't have to be exact */
2049 int max_faces
= 6 * width
* height
;
2050 int max_dots
= 6 * (width
+ 1) * (height
+ 1);
2054 grid
*g
= grid_empty();
2055 g
->tilesize
= KITE_TILESIZE
;
2056 g
->faces
= snewn(max_faces
, grid_face
);
2057 g
->dots
= snewn(max_dots
, grid_dot
);
2059 points
= newtree234(grid_point_cmp_fn
);
2061 for (y
= 0; y
< height
; y
++) {
2062 for (x
= 0; x
< width
; x
++) {
2064 /* position of order-6 dot */
2070 /* kite pointing up-left */
2071 grid_face_add_new(g
, 4);
2072 d
= grid_get_dot(g
, points
, px
, py
);
2073 grid_face_set_dot(g
, d
, 0);
2074 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
2075 grid_face_set_dot(g
, d
, 1);
2076 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
+ 2*a
);
2077 grid_face_set_dot(g
, d
, 2);
2078 d
= grid_get_dot(g
, points
, px
+ b
, py
+ 3*a
);
2079 grid_face_set_dot(g
, d
, 3);
2081 /* kite pointing up */
2082 grid_face_add_new(g
, 4);
2083 d
= grid_get_dot(g
, points
, px
, py
);
2084 grid_face_set_dot(g
, d
, 0);
2085 d
= grid_get_dot(g
, points
, px
+ b
, py
+ 3*a
);
2086 grid_face_set_dot(g
, d
, 1);
2087 d
= grid_get_dot(g
, points
, px
, py
+ 4*a
);
2088 grid_face_set_dot(g
, d
, 2);
2089 d
= grid_get_dot(g
, points
, px
- b
, py
+ 3*a
);
2090 grid_face_set_dot(g
, d
, 3);
2092 /* kite pointing up-right */
2093 grid_face_add_new(g
, 4);
2094 d
= grid_get_dot(g
, points
, px
, py
);
2095 grid_face_set_dot(g
, d
, 0);
2096 d
= grid_get_dot(g
, points
, px
- b
, py
+ 3*a
);
2097 grid_face_set_dot(g
, d
, 1);
2098 d
= grid_get_dot(g
, points
, px
- 2*b
, py
+ 2*a
);
2099 grid_face_set_dot(g
, d
, 2);
2100 d
= grid_get_dot(g
, points
, px
- 2*b
, py
);
2101 grid_face_set_dot(g
, d
, 3);
2103 /* kite pointing down-right */
2104 grid_face_add_new(g
, 4);
2105 d
= grid_get_dot(g
, points
, px
, py
);
2106 grid_face_set_dot(g
, d
, 0);
2107 d
= grid_get_dot(g
, points
, px
- 2*b
, py
);
2108 grid_face_set_dot(g
, d
, 1);
2109 d
= grid_get_dot(g
, points
, px
- 2*b
, py
- 2*a
);
2110 grid_face_set_dot(g
, d
, 2);
2111 d
= grid_get_dot(g
, points
, px
- b
, py
- 3*a
);
2112 grid_face_set_dot(g
, d
, 3);
2114 /* kite pointing down */
2115 grid_face_add_new(g
, 4);
2116 d
= grid_get_dot(g
, points
, px
, py
);
2117 grid_face_set_dot(g
, d
, 0);
2118 d
= grid_get_dot(g
, points
, px
- b
, py
- 3*a
);
2119 grid_face_set_dot(g
, d
, 1);
2120 d
= grid_get_dot(g
, points
, px
, py
- 4*a
);
2121 grid_face_set_dot(g
, d
, 2);
2122 d
= grid_get_dot(g
, points
, px
+ b
, py
- 3*a
);
2123 grid_face_set_dot(g
, d
, 3);
2125 /* kite pointing down-left */
2126 grid_face_add_new(g
, 4);
2127 d
= grid_get_dot(g
, points
, px
, py
);
2128 grid_face_set_dot(g
, d
, 0);
2129 d
= grid_get_dot(g
, points
, px
+ b
, py
- 3*a
);
2130 grid_face_set_dot(g
, d
, 1);
2131 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
- 2*a
);
2132 grid_face_set_dot(g
, d
, 2);
2133 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
2134 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 FLORET_TILESIZE 150
2147 /* -py/px is close to tan(30 - atan(sqrt(3)/9))
2148 * using py=26 makes everything lean to the left, rather than right
2150 #define FLORET_PX 75
2151 #define FLORET_PY -26
2153 void grid_size_floret(int width
, int height
,
2154 int *tilesize
, int *xextent
, int *yextent
)
2156 int px
= FLORET_PX
, py
= FLORET_PY
; /* |( 75, -26)| = 79.43 */
2157 int qx
= 4*px
/5, qy
= -py
*2; /* |( 60, 52)| = 79.40 */
2159 /* rx unused in determining grid size. */
2161 *tilesize
= FLORET_TILESIZE
;
2162 *xextent
= (6*px
+3*qx
)/2 * (width
-1) + 4*qx
+ 2*px
;
2163 *yextent
= (5*qy
-4*py
) * (height
-1) + 4*qy
+ 2*ry
;
2166 grid
*grid_new_floret(int width
, int height
, char *desc
)
2169 /* Vectors for sides; weird numbers needed to keep puzzle aligned with window
2170 * -py/px is close to tan(30 - atan(sqrt(3)/9))
2171 * using py=26 makes everything lean to the left, rather than right
2173 int px
= FLORET_PX
, py
= FLORET_PY
; /* |( 75, -26)| = 79.43 */
2174 int qx
= 4*px
/5, qy
= -py
*2; /* |( 60, 52)| = 79.40 */
2175 int rx
= qx
-px
, ry
= qy
-py
; /* |(-15, 78)| = 79.38 */
2177 /* Upper bounds - don't have to be exact */
2178 int max_faces
= 6 * width
* height
;
2179 int max_dots
= 9 * (width
+ 1) * (height
+ 1);
2183 grid
*g
= grid_empty();
2184 g
->tilesize
= FLORET_TILESIZE
;
2185 g
->faces
= snewn(max_faces
, grid_face
);
2186 g
->dots
= snewn(max_dots
, grid_dot
);
2188 points
= newtree234(grid_point_cmp_fn
);
2190 /* generate pentagonal faces */
2191 for (y
= 0; y
< height
; y
++) {
2192 for (x
= 0; x
< width
; x
++) {
2195 int cx
= (6*px
+3*qx
)/2 * x
;
2196 int cy
= (4*py
-5*qy
) * y
;
2198 cy
-= (4*py
-5*qy
)/2;
2199 else if (y
&& y
== height
-1)
2200 continue; /* make better looking grids? try 3x3 for instance */
2202 grid_face_add_new(g
, 5);
2203 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2204 d
= grid_get_dot(g
, points
, cx
+2*rx
, cy
+2*ry
); grid_face_set_dot(g
, d
, 1);
2205 d
= grid_get_dot(g
, points
, cx
+2*rx
+qx
, cy
+2*ry
+qy
); grid_face_set_dot(g
, d
, 2);
2206 d
= grid_get_dot(g
, points
, cx
+2*qx
+rx
, cy
+2*qy
+ry
); grid_face_set_dot(g
, d
, 3);
2207 d
= grid_get_dot(g
, points
, cx
+2*qx
, cy
+2*qy
); grid_face_set_dot(g
, d
, 4);
2209 grid_face_add_new(g
, 5);
2210 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2211 d
= grid_get_dot(g
, points
, cx
+2*qx
, cy
+2*qy
); grid_face_set_dot(g
, d
, 1);
2212 d
= grid_get_dot(g
, points
, cx
+2*qx
+px
, cy
+2*qy
+py
); grid_face_set_dot(g
, d
, 2);
2213 d
= grid_get_dot(g
, points
, cx
+2*px
+qx
, cy
+2*py
+qy
); grid_face_set_dot(g
, d
, 3);
2214 d
= grid_get_dot(g
, points
, cx
+2*px
, cy
+2*py
); grid_face_set_dot(g
, d
, 4);
2216 grid_face_add_new(g
, 5);
2217 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2218 d
= grid_get_dot(g
, points
, cx
+2*px
, cy
+2*py
); grid_face_set_dot(g
, d
, 1);
2219 d
= grid_get_dot(g
, points
, cx
+2*px
-rx
, cy
+2*py
-ry
); grid_face_set_dot(g
, d
, 2);
2220 d
= grid_get_dot(g
, points
, cx
-2*rx
+px
, cy
-2*ry
+py
); grid_face_set_dot(g
, d
, 3);
2221 d
= grid_get_dot(g
, points
, cx
-2*rx
, cy
-2*ry
); grid_face_set_dot(g
, d
, 4);
2223 grid_face_add_new(g
, 5);
2224 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2225 d
= grid_get_dot(g
, points
, cx
-2*rx
, cy
-2*ry
); grid_face_set_dot(g
, d
, 1);
2226 d
= grid_get_dot(g
, points
, cx
-2*rx
-qx
, cy
-2*ry
-qy
); grid_face_set_dot(g
, d
, 2);
2227 d
= grid_get_dot(g
, points
, cx
-2*qx
-rx
, cy
-2*qy
-ry
); grid_face_set_dot(g
, d
, 3);
2228 d
= grid_get_dot(g
, points
, cx
-2*qx
, cy
-2*qy
); grid_face_set_dot(g
, d
, 4);
2230 grid_face_add_new(g
, 5);
2231 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2232 d
= grid_get_dot(g
, points
, cx
-2*qx
, cy
-2*qy
); grid_face_set_dot(g
, d
, 1);
2233 d
= grid_get_dot(g
, points
, cx
-2*qx
-px
, cy
-2*qy
-py
); grid_face_set_dot(g
, d
, 2);
2234 d
= grid_get_dot(g
, points
, cx
-2*px
-qx
, cy
-2*py
-qy
); grid_face_set_dot(g
, d
, 3);
2235 d
= grid_get_dot(g
, points
, cx
-2*px
, cy
-2*py
); grid_face_set_dot(g
, d
, 4);
2237 grid_face_add_new(g
, 5);
2238 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2239 d
= grid_get_dot(g
, points
, cx
-2*px
, cy
-2*py
); grid_face_set_dot(g
, d
, 1);
2240 d
= grid_get_dot(g
, points
, cx
-2*px
+rx
, cy
-2*py
+ry
); grid_face_set_dot(g
, d
, 2);
2241 d
= grid_get_dot(g
, points
, cx
+2*rx
-px
, cy
+2*ry
-py
); grid_face_set_dot(g
, d
, 3);
2242 d
= grid_get_dot(g
, points
, cx
+2*rx
, cy
+2*ry
); grid_face_set_dot(g
, d
, 4);
2246 freetree234(points
);
2247 assert(g
->num_faces
<= max_faces
);
2248 assert(g
->num_dots
<= max_dots
);
2250 grid_make_consistent(g
);
2254 /* DODEC_* are used for dodecagonal and great-dodecagonal grids. */
2255 #define DODEC_TILESIZE 26
2256 /* Vector for side of triangle - ratio is close to sqrt(3) */
2260 void grid_size_dodecagonal(int width
, int height
,
2261 int *tilesize
, int *xextent
, int *yextent
)
2266 *tilesize
= DODEC_TILESIZE
;
2267 *xextent
= (4*a
+ 2*b
) * (width
-1) + 3*(2*a
+ b
);
2268 *yextent
= (3*a
+ 2*b
) * (height
-1) + 2*(2*a
+ b
);
2271 grid
*grid_new_dodecagonal(int width
, int height
, char *desc
)
2277 /* Upper bounds - don't have to be exact */
2278 int max_faces
= 3 * width
* height
;
2279 int max_dots
= 14 * width
* height
;
2283 grid
*g
= grid_empty();
2284 g
->tilesize
= DODEC_TILESIZE
;
2285 g
->faces
= snewn(max_faces
, grid_face
);
2286 g
->dots
= snewn(max_dots
, grid_dot
);
2288 points
= newtree234(grid_point_cmp_fn
);
2290 for (y
= 0; y
< height
; y
++) {
2291 for (x
= 0; x
< width
; x
++) {
2293 /* centre of dodecagon */
2294 int px
= (4*a
+ 2*b
) * x
;
2295 int py
= (3*a
+ 2*b
) * y
;
2300 grid_face_add_new(g
, 12);
2301 d
= grid_get_dot(g
, points
, px
+ ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2302 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 1);
2303 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 2);
2304 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 3);
2305 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 4);
2306 d
= grid_get_dot(g
, points
, px
+ ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2307 d
= grid_get_dot(g
, points
, px
- ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 6);
2308 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 7);
2309 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 8);
2310 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 9);
2311 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 10);
2312 d
= grid_get_dot(g
, points
, px
- ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 11);
2314 /* triangle below dodecagon */
2315 if ((y
< height
- 1 && (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2)))) {
2316 grid_face_add_new(g
, 3);
2317 d
= grid_get_dot(g
, points
, px
+ a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2318 d
= grid_get_dot(g
, points
, px
, py
+ (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2319 d
= grid_get_dot(g
, points
, px
- a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 2);
2322 /* triangle above dodecagon */
2323 if ((y
&& (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);
2332 freetree234(points
);
2333 assert(g
->num_faces
<= max_faces
);
2334 assert(g
->num_dots
<= max_dots
);
2336 grid_make_consistent(g
);
2340 void grid_size_greatdodecagonal(int width
, int height
,
2341 int *tilesize
, int *xextent
, int *yextent
)
2346 *tilesize
= DODEC_TILESIZE
;
2347 *xextent
= (6*a
+ 2*b
) * (width
-1) + 2*(2*a
+ b
) + 3*a
+ b
;
2348 *yextent
= (3*a
+ 3*b
) * (height
-1) + 2*(2*a
+ b
);
2351 grid
*grid_new_greatdodecagonal(int width
, int height
, char *desc
)
2354 /* Vector for side of triangle - ratio is close to sqrt(3) */
2358 /* Upper bounds - don't have to be exact */
2359 int max_faces
= 30 * width
* height
;
2360 int max_dots
= 200 * width
* height
;
2364 grid
*g
= grid_empty();
2365 g
->tilesize
= DODEC_TILESIZE
;
2366 g
->faces
= snewn(max_faces
, grid_face
);
2367 g
->dots
= snewn(max_dots
, grid_dot
);
2369 points
= newtree234(grid_point_cmp_fn
);
2371 for (y
= 0; y
< height
; y
++) {
2372 for (x
= 0; x
< width
; x
++) {
2374 /* centre of dodecagon */
2375 int px
= (6*a
+ 2*b
) * x
;
2376 int py
= (3*a
+ 3*b
) * y
;
2381 grid_face_add_new(g
, 12);
2382 d
= grid_get_dot(g
, points
, px
+ ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2383 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 1);
2384 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 2);
2385 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 3);
2386 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 4);
2387 d
= grid_get_dot(g
, points
, px
+ ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2388 d
= grid_get_dot(g
, points
, px
- ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 6);
2389 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 7);
2390 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 8);
2391 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 9);
2392 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 10);
2393 d
= grid_get_dot(g
, points
, px
- ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 11);
2395 /* hexagon below dodecagon */
2396 if (y
< height
- 1 && (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2))) {
2397 grid_face_add_new(g
, 6);
2398 d
= grid_get_dot(g
, points
, px
+ a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2399 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
+ (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2400 d
= grid_get_dot(g
, points
, px
+ a
, py
+ (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 2);
2401 d
= grid_get_dot(g
, points
, px
- a
, py
+ (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 3);
2402 d
= grid_get_dot(g
, points
, px
- 2*a
, py
+ (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 4);
2403 d
= grid_get_dot(g
, points
, px
- a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2406 /* hexagon above dodecagon */
2407 if (y
&& (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2))) {
2408 grid_face_add_new(g
, 6);
2409 d
= grid_get_dot(g
, points
, px
- a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2410 d
= grid_get_dot(g
, points
, px
- 2*a
, py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2411 d
= grid_get_dot(g
, points
, px
- a
, py
- (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 2);
2412 d
= grid_get_dot(g
, points
, px
+ a
, py
- (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 3);
2413 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 4);
2414 d
= grid_get_dot(g
, points
, px
+ a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2417 /* square on right of dodecagon */
2418 if (x
< width
- 1) {
2419 grid_face_add_new(g
, 4);
2420 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
- a
); grid_face_set_dot(g
, d
, 0);
2421 d
= grid_get_dot(g
, points
, px
+ 4*a
+ b
, py
- a
); grid_face_set_dot(g
, d
, 1);
2422 d
= grid_get_dot(g
, points
, px
+ 4*a
+ b
, py
+ a
); grid_face_set_dot(g
, d
, 2);
2423 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
); grid_face_set_dot(g
, d
, 3);
2426 /* square on top right of dodecagon */
2427 if (y
&& (x
< width
- 1 || !(y
% 2))) {
2428 grid_face_add_new(g
, 4);
2429 d
= grid_get_dot(g
, points
, px
+ ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2430 d
= grid_get_dot(g
, points
, px
+ (2*a
), py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2431 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- ( a
+ 2*b
)); grid_face_set_dot(g
, d
, 2);
2432 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 3);
2435 /* square on top left of dodecagon */
2436 if (y
&& (x
|| (y
% 2))) {
2437 grid_face_add_new(g
, 4);
2438 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 0);
2439 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
- ( a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2440 d
= grid_get_dot(g
, points
, px
- (2*a
), py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 2);
2441 d
= grid_get_dot(g
, points
, px
- ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 3);
2446 freetree234(points
);
2447 assert(g
->num_faces
<= max_faces
);
2448 assert(g
->num_dots
<= max_dots
);
2450 grid_make_consistent(g
);
2454 typedef struct setface_ctx
2456 int xmin
, xmax
, ymin
, ymax
;
2463 double round(double r
)
2465 return (r
> 0.0) ?
floor(r
+ 0.5) : ceil(r
- 0.5);
2468 int set_faces(penrose_state
*state
, vector
*vs
, int n
, int depth
)
2470 setface_ctx
*sf_ctx
= (setface_ctx
*)state
->ctx
;
2473 double cosa
= cos(sf_ctx
->aoff
* PI
/ 180.0);
2474 double sina
= sin(sf_ctx
->aoff
* PI
/ 180.0);
2476 if (depth
< state
->max_depth
) return 0;
2477 #ifdef DEBUG_PENROSE
2478 if (n
!= 4) return 0; /* triangles are sent as debugging. */
2481 for (i
= 0; i
< n
; i
++) {
2482 double tx
= v_x(vs
, i
), ty
= v_y(vs
, i
);
2484 xs
[i
] = (int)round( tx
*cosa
+ ty
*sina
);
2485 ys
[i
] = (int)round(-tx
*sina
+ ty
*cosa
);
2487 if (xs
[i
] < sf_ctx
->xmin
|| xs
[i
] > sf_ctx
->xmax
) return 0;
2488 if (ys
[i
] < sf_ctx
->ymin
|| ys
[i
] > sf_ctx
->ymax
) return 0;
2491 grid_face_add_new(sf_ctx
->g
, n
);
2492 debug(("penrose: new face l=%f gen=%d...",
2493 penrose_side_length(state
->start_size
, depth
), depth
));
2494 for (i
= 0; i
< n
; i
++) {
2495 grid_dot
*d
= grid_get_dot(sf_ctx
->g
, sf_ctx
->points
,
2497 grid_face_set_dot(sf_ctx
->g
, d
, i
);
2498 debug((" ... dot 0x%x (%d,%d) (was %2.2f,%2.2f)",
2499 d
, d
->x
, d
->y
, v_x(vs
, i
), v_y(vs
, i
)));
2505 #define PENROSE_TILESIZE 100
2507 void grid_size_penrose(int width
, int height
,
2508 int *tilesize
, int *xextent
, int *yextent
)
2510 int l
= PENROSE_TILESIZE
;
2513 *xextent
= l
* width
;
2514 *yextent
= l
* height
;
2517 static char *grid_new_desc_penrose(grid_type type
, int width
, int height
, random_state
*rs
)
2519 int tilesize
= PENROSE_TILESIZE
, startsz
, depth
, xoff
, yoff
, aoff
;
2520 double outer_radius
;
2523 int which
= (type
== GRID_PENROSE_P2 ? PENROSE_P2
: PENROSE_P3
);
2525 /* We want to produce a random bit of penrose tiling, so we calculate
2526 * a random offset (within the patch that penrose.c calculates for us)
2527 * and an angle (multiple of 36) to rotate the patch. */
2529 penrose_calculate_size(which
, tilesize
, width
, height
,
2530 &outer_radius
, &startsz
, &depth
);
2532 /* Calculate radius of (circumcircle of) patch, subtract from
2533 * radius calculated. */
2534 inner_radius
= (int)(outer_radius
- sqrt(width
*width
+ height
*height
));
2536 /* Pick a random offset (the easy way: choose within outer square,
2537 * discarding while it's outside the circle) */
2539 xoff
= random_upto(rs
, 2*inner_radius
) - inner_radius
;
2540 yoff
= random_upto(rs
, 2*inner_radius
) - inner_radius
;
2541 } while (sqrt(xoff
*xoff
+yoff
*yoff
) > inner_radius
);
2543 aoff
= random_upto(rs
, 360/36) * 36;
2545 debug(("grid_desc: ts %d, %dx%d patch, orad %2.2f irad %d",
2546 tilesize
, width
, height
, outer_radius
, inner_radius
));
2547 debug((" -> xoff %d yoff %d aoff %d", xoff
, yoff
, aoff
));
2549 sprintf(gd
, "G%d,%d,%d", xoff
, yoff
, aoff
);
2554 static char *grid_validate_desc_penrose(grid_type type
, int width
, int height
, char *desc
)
2556 int tilesize
= PENROSE_TILESIZE
, startsz
, depth
, xoff
, yoff
, aoff
, inner_radius
;
2557 double outer_radius
;
2558 int which
= (type
== GRID_PENROSE_P2 ? PENROSE_P2
: PENROSE_P3
);
2561 return "Missing grid description string.";
2563 penrose_calculate_size(which
, tilesize
, width
, height
,
2564 &outer_radius
, &startsz
, &depth
);
2565 inner_radius
= (int)(outer_radius
- sqrt(width
*width
+ height
*height
));
2567 if (sscanf(desc
, "G%d,%d,%d", &xoff
, &yoff
, &aoff
) != 3)
2568 return "Invalid format grid description string.";
2570 if (sqrt(xoff
*xoff
+ yoff
*yoff
) > inner_radius
)
2571 return "Patch offset out of bounds.";
2572 if ((aoff
% 36) != 0 || aoff
< 0 || aoff
>= 360)
2573 return "Angle offset out of bounds.";
2579 * We're asked for a grid of a particular size, and we generate enough
2580 * of the tiling so we can be sure to have enough random grid from which
2584 static grid
*grid_new_penrose(int width
, int height
, int which
, char *desc
)
2586 int max_faces
, max_dots
, tilesize
= PENROSE_TILESIZE
;
2587 int xsz
, ysz
, xoff
, yoff
;
2596 penrose_calculate_size(which
, tilesize
, width
, height
,
2597 &rradius
, &ps
.start_size
, &ps
.max_depth
);
2599 debug(("penrose: w%d h%d, tile size %d, start size %d, depth %d",
2600 width
, height
, tilesize
, ps
.start_size
, ps
.max_depth
));
2602 ps
.new_tile
= set_faces
;
2605 max_faces
= (width
*3) * (height
*3); /* somewhat paranoid... */
2606 max_dots
= max_faces
* 4; /* ditto... */
2609 g
->tilesize
= tilesize
;
2610 g
->faces
= snewn(max_faces
, grid_face
);
2611 g
->dots
= snewn(max_dots
, grid_dot
);
2613 points
= newtree234(grid_point_cmp_fn
);
2615 memset(&sf_ctx
, 0, sizeof(sf_ctx
));
2617 sf_ctx
.points
= points
;
2620 if (sscanf(desc
, "G%d,%d,%d", &xoff
, &yoff
, &sf_ctx
.aoff
) != 3)
2621 assert(!"Invalid grid description.");
2626 xsz
= width
* tilesize
;
2627 ysz
= height
* tilesize
;
2629 sf_ctx
.xmin
= xoff
- xsz
/2;
2630 sf_ctx
.xmax
= xoff
+ xsz
/2;
2631 sf_ctx
.ymin
= yoff
- ysz
/2;
2632 sf_ctx
.ymax
= yoff
+ ysz
/2;
2634 debug(("penrose: centre (%f, %f) xsz %f ysz %f",
2635 0.0, 0.0, xsz
, ysz
));
2636 debug(("penrose: x range (%f --> %f), y range (%f --> %f)",
2637 sf_ctx
.xmin
, sf_ctx
.xmax
, sf_ctx
.ymin
, sf_ctx
.ymax
));
2639 penrose(&ps
, which
);
2641 freetree234(points
);
2642 assert(g
->num_faces
<= max_faces
);
2643 assert(g
->num_dots
<= max_dots
);
2645 debug(("penrose: %d faces total (equivalent to %d wide by %d high)",
2646 g
->num_faces
, g
->num_faces
/height
, g
->num_faces
/width
));
2648 grid_trim_vigorously(g
);
2649 grid_make_consistent(g
);
2652 * Centre the grid in its originally promised rectangle.
2654 g
->lowest_x
-= ((sf_ctx
.xmax
- sf_ctx
.xmin
) -
2655 (g
->highest_x
- g
->lowest_x
)) / 2;
2656 g
->highest_x
= g
->lowest_x
+ (sf_ctx
.xmax
- sf_ctx
.xmin
);
2657 g
->lowest_y
-= ((sf_ctx
.ymax
- sf_ctx
.ymin
) -
2658 (g
->highest_y
- g
->lowest_y
)) / 2;
2659 g
->highest_y
= g
->lowest_y
+ (sf_ctx
.ymax
- sf_ctx
.ymin
);
2664 void grid_size_penrose_p2_kite(int width
, int height
,
2665 int *tilesize
, int *xextent
, int *yextent
)
2667 grid_size_penrose(width
, height
, tilesize
, xextent
, yextent
);
2670 void grid_size_penrose_p3_thick(int width
, int height
,
2671 int *tilesize
, int *xextent
, int *yextent
)
2673 grid_size_penrose(width
, height
, tilesize
, xextent
, yextent
);
2676 grid
*grid_new_penrose_p2_kite(int width
, int height
, char *desc
)
2678 return grid_new_penrose(width
, height
, PENROSE_P2
, desc
);
2681 grid
*grid_new_penrose_p3_thick(int width
, int height
, char *desc
)
2683 return grid_new_penrose(width
, height
, PENROSE_P3
, desc
);
2686 /* ----------- End of grid generators ------------- */
2688 #define FNNEW(upper,lower) &grid_new_ ## lower,
2689 #define FNSZ(upper,lower) &grid_size_ ## lower,
2691 static grid
*(*(grid_news
[]))(int, int, char*) = { GRIDGEN_LIST(FNNEW
) };
2692 static void(*(grid_sizes
[]))(int, int, int*, int*, int*) = { GRIDGEN_LIST(FNSZ
) };
2694 char *grid_new_desc(grid_type type
, int width
, int height
, random_state
*rs
)
2696 if (type
!= GRID_PENROSE_P2
&& type
!= GRID_PENROSE_P3
)
2699 return grid_new_desc_penrose(type
, width
, height
, rs
);
2702 char *grid_validate_desc(grid_type type
, int width
, int height
, char *desc
)
2704 if (type
!= GRID_PENROSE_P2
&& type
!= GRID_PENROSE_P3
) {
2706 return "Grid description strings not used with this grid type";
2710 return grid_validate_desc_penrose(type
, width
, height
, desc
);
2713 grid
*grid_new(grid_type type
, int width
, int height
, char *desc
)
2715 char *err
= grid_validate_desc(type
, width
, height
, desc
);
2716 if (err
) assert(!"Invalid grid description.");
2718 return grid_news
[type
](width
, height
, desc
);
2721 void grid_compute_size(grid_type type
, int width
, int height
,
2722 int *tilesize
, int *xextent
, int *yextent
)
2724 grid_sizes
[type
](width
, height
, tilesize
, xextent
, yextent
);
2727 /* ----------- End of grid helpers ------------- */
2729 /* vim: set shiftwidth=4 tabstop=8: */