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 debug(("allocating room for %d edges\n", g
->num_edges
));
522 g
->edges
= snewn(g
->num_edges
, grid_edge
);
523 next_new_edge
= g
->edges
;
525 /* Iterate over faces, and over each face's dots, generating edges as we
526 * go. As we find each new edge, we can immediately fill in the edge's
527 * dots, but only one of the edge's faces. Later on in the iteration, we
528 * will find the same edge again (unless it's on the border), but we will
529 * know the other face.
530 * For efficiency, maintain a list of the incomplete edges, sorted by
532 incomplete_edges
= newtree234(grid_edge_bydots_cmpfn
);
533 for (i
= 0; i
< g
->num_faces
; i
++) {
534 grid_face
*f
= g
->faces
+ i
;
536 assert(f
->order
> 2);
537 for (j
= 0; j
< f
->order
; j
++) {
538 grid_edge e
; /* fake edge for searching */
539 grid_edge
*edge_found
;
544 e
.dot2
= f
->dots
[j2
];
545 /* Use del234 instead of find234, because we always want to
546 * remove the edge if found */
547 edge_found
= del234(incomplete_edges
, &e
);
549 /* This edge already added, so fill out missing face.
550 * Edge is already removed from incomplete_edges. */
551 edge_found
->face2
= f
;
553 assert(next_new_edge
- g
->edges
< g
->num_edges
);
554 next_new_edge
->dot1
= e
.dot1
;
555 next_new_edge
->dot2
= e
.dot2
;
556 next_new_edge
->face1
= f
;
557 next_new_edge
->face2
= NULL
; /* potentially infinite face */
558 add234(incomplete_edges
, next_new_edge
);
563 freetree234(incomplete_edges
);
565 /* ====== Stage 2 ======
566 * For each face, build its edge list.
569 /* Allocate space for each edge list. Can do this, because each face's
570 * edge-list is the same size as its dot-list. */
571 for (i
= 0; i
< g
->num_faces
; i
++) {
572 grid_face
*f
= g
->faces
+ i
;
574 f
->edges
= snewn(f
->order
, grid_edge
*);
575 /* Preload with NULLs, to help detect potential bugs. */
576 for (j
= 0; j
< f
->order
; j
++)
580 /* Iterate over each edge, and over both its faces. Add this edge to
581 * the face's edge-list, after finding where it should go in the
583 for (i
= 0; i
< g
->num_edges
; i
++) {
584 grid_edge
*e
= g
->edges
+ i
;
586 for (j
= 0; j
< 2; j
++) {
587 grid_face
*f
= j ? e
->face2
: e
->face1
;
589 if (f
== NULL
) continue;
590 /* Find one of the dots around the face */
591 for (k
= 0; k
< f
->order
; k
++) {
592 if (f
->dots
[k
] == e
->dot1
)
593 break; /* found dot1 */
595 assert(k
!= f
->order
); /* Must find the dot around this face */
597 /* Labelling scheme: as we walk clockwise around the face,
598 * starting at dot0 (f->dots[0]), we hit:
599 * (dot0), edge0, dot1, edge1, dot2,...
609 * Therefore, edgeK joins dotK and dot{K+1}
612 /* Around this face, either the next dot or the previous dot
613 * must be e->dot2. Otherwise the edge is wrong. */
617 if (f
->dots
[k2
] == e
->dot2
) {
618 /* dot1(k) and dot2(k2) go clockwise around this face, so add
619 * this edge at position k (see diagram). */
620 assert(f
->edges
[k
] == NULL
);
624 /* Try previous dot */
628 if (f
->dots
[k2
] == e
->dot2
) {
629 /* dot1(k) and dot2(k2) go anticlockwise around this face. */
630 assert(f
->edges
[k2
] == NULL
);
634 assert(!"Grid broken: bad edge-face relationship");
638 /* ====== Stage 3 ======
639 * For each dot, build its edge-list and face-list.
642 /* We don't know how many edges/faces go around each dot, so we can't
643 * allocate the right space for these lists. Pre-compute the sizes by
644 * iterating over each edge and recording a tally against each dot. */
645 for (i
= 0; i
< g
->num_dots
; i
++) {
646 g
->dots
[i
].order
= 0;
648 for (i
= 0; i
< g
->num_edges
; i
++) {
649 grid_edge
*e
= g
->edges
+ i
;
653 /* Now we have the sizes, pre-allocate the edge and face lists. */
654 for (i
= 0; i
< g
->num_dots
; i
++) {
655 grid_dot
*d
= g
->dots
+ i
;
657 assert(d
->order
>= 2); /* sanity check */
658 d
->edges
= snewn(d
->order
, grid_edge
*);
659 d
->faces
= snewn(d
->order
, grid_face
*);
660 for (j
= 0; j
< d
->order
; j
++) {
665 /* For each dot, need to find a face that touches it, so we can seed
666 * the edge-face-edge-face process around each dot. */
667 for (i
= 0; i
< g
->num_faces
; i
++) {
668 grid_face
*f
= g
->faces
+ i
;
670 for (j
= 0; j
< f
->order
; j
++) {
671 grid_dot
*d
= f
->dots
[j
];
675 /* Each dot now has a face in its first slot. Generate the remaining
676 * faces and edges around the dot, by searching both clockwise and
677 * anticlockwise from the first face. Need to do both directions,
678 * because of the possibility of hitting the infinite face, which
679 * blocks progress. But there's only one such face, so we will
680 * succeed in finding every edge and face this way. */
681 for (i
= 0; i
< g
->num_dots
; i
++) {
682 grid_dot
*d
= g
->dots
+ i
;
683 int current_face1
= 0; /* ascends clockwise */
684 int current_face2
= 0; /* descends anticlockwise */
686 /* Labelling scheme: as we walk clockwise around the dot, starting
687 * at face0 (d->faces[0]), we hit:
688 * (face0), edge0, face1, edge1, face2,...
700 * So, for example, face1 should be joined to edge0 and edge1,
701 * and those edges should appear in an anticlockwise sense around
702 * that face (see diagram). */
704 /* clockwise search */
706 grid_face
*f
= d
->faces
[current_face1
];
710 /* find dot around this face */
711 for (j
= 0; j
< f
->order
; j
++) {
715 assert(j
!= f
->order
); /* must find dot */
717 /* Around f, required edge is anticlockwise from the dot. See
718 * the other labelling scheme higher up, for why we subtract 1
724 d
->edges
[current_face1
] = e
; /* set edge */
726 if (current_face1
== d
->order
)
730 d
->faces
[current_face1
] =
731 (e
->face1
== f
) ? e
->face2
: e
->face1
;
732 if (d
->faces
[current_face1
] == NULL
)
733 break; /* cannot progress beyond infinite face */
736 /* If the clockwise search made it all the way round, don't need to
737 * bother with the anticlockwise search. */
738 if (current_face1
== d
->order
)
739 continue; /* this dot is complete, move on to next dot */
741 /* anticlockwise search */
743 grid_face
*f
= d
->faces
[current_face2
];
747 /* find dot around this face */
748 for (j
= 0; j
< f
->order
; j
++) {
752 assert(j
!= f
->order
); /* must find dot */
754 /* Around f, required edge is clockwise from the dot. */
758 if (current_face2
== -1)
759 current_face2
= d
->order
- 1;
760 d
->edges
[current_face2
] = e
; /* set edge */
763 if (current_face2
== current_face1
)
765 d
->faces
[current_face2
] =
766 (e
->face1
== f
) ? e
->face2
: e
->face1
;
767 /* There's only 1 infinite face, so we must get all the way
768 * to current_face1 before we hit it. */
769 assert(d
->faces
[current_face2
]);
773 /* ====== Stage 4 ======
774 * Compute other grid settings
777 /* Bounding rectangle */
778 for (i
= 0; i
< g
->num_dots
; i
++) {
779 grid_dot
*d
= g
->dots
+ i
;
781 g
->lowest_x
= g
->highest_x
= d
->x
;
782 g
->lowest_y
= g
->highest_y
= d
->y
;
784 g
->lowest_x
= min(g
->lowest_x
, d
->x
);
785 g
->highest_x
= max(g
->highest_x
, d
->x
);
786 g
->lowest_y
= min(g
->lowest_y
, d
->y
);
787 g
->highest_y
= max(g
->highest_y
, d
->y
);
791 grid_debug_derived(g
);
794 /* Helpers for making grid-generation easier. These functions are only
795 * intended for use during grid generation. */
797 /* Comparison function for the (tree234) sorted dot list */
798 static int grid_point_cmp_fn(void *v1
, void *v2
)
803 return p2
->y
- p1
->y
;
805 return p2
->x
- p1
->x
;
807 /* Add a new face to the grid, with its dot list allocated.
808 * Assumes there's enough space allocated for the new face in grid->faces */
809 static void grid_face_add_new(grid
*g
, int face_size
)
812 grid_face
*new_face
= g
->faces
+ g
->num_faces
;
813 new_face
->order
= face_size
;
814 new_face
->dots
= snewn(face_size
, grid_dot
*);
815 for (i
= 0; i
< face_size
; i
++)
816 new_face
->dots
[i
] = NULL
;
817 new_face
->edges
= NULL
;
818 new_face
->has_incentre
= FALSE
;
821 /* Assumes dot list has enough space */
822 static grid_dot
*grid_dot_add_new(grid
*g
, int x
, int y
)
824 grid_dot
*new_dot
= g
->dots
+ g
->num_dots
;
826 new_dot
->edges
= NULL
;
827 new_dot
->faces
= NULL
;
833 /* Retrieve a dot with these (x,y) coordinates. Either return an existing dot
834 * in the dot_list, or add a new dot to the grid (and the dot_list) and
836 * Assumes g->dots has enough capacity allocated */
837 static grid_dot
*grid_get_dot(grid
*g
, tree234
*dot_list
, int x
, int y
)
846 ret
= find234(dot_list
, &test
, NULL
);
850 ret
= grid_dot_add_new(g
, x
, y
);
851 add234(dot_list
, ret
);
855 /* Sets the last face of the grid to include this dot, at this position
856 * around the face. Assumes num_faces is at least 1 (a new face has
857 * previously been added, with the required number of dots allocated) */
858 static void grid_face_set_dot(grid
*g
, grid_dot
*d
, int position
)
860 grid_face
*last_face
= g
->faces
+ g
->num_faces
- 1;
861 last_face
->dots
[position
] = d
;
865 * Helper routines for grid_find_incentre.
867 static int solve_2x2_matrix(double mx
[4], double vin
[2], double vout
[2])
871 det
= (mx
[0]*mx
[3] - mx
[1]*mx
[2]);
875 inv
[0] = mx
[3] / det
;
876 inv
[1] = -mx
[1] / det
;
877 inv
[2] = -mx
[2] / det
;
878 inv
[3] = mx
[0] / det
;
880 vout
[0] = inv
[0]*vin
[0] + inv
[1]*vin
[1];
881 vout
[1] = inv
[2]*vin
[0] + inv
[3]*vin
[1];
885 static int solve_3x3_matrix(double mx
[9], double vin
[3], double vout
[3])
890 det
= (mx
[0]*mx
[4]*mx
[8] + mx
[1]*mx
[5]*mx
[6] + mx
[2]*mx
[3]*mx
[7] -
891 mx
[0]*mx
[5]*mx
[7] - mx
[1]*mx
[3]*mx
[8] - mx
[2]*mx
[4]*mx
[6]);
895 inv
[0] = (mx
[4]*mx
[8] - mx
[5]*mx
[7]) / det
;
896 inv
[1] = (mx
[2]*mx
[7] - mx
[1]*mx
[8]) / det
;
897 inv
[2] = (mx
[1]*mx
[5] - mx
[2]*mx
[4]) / det
;
898 inv
[3] = (mx
[5]*mx
[6] - mx
[3]*mx
[8]) / det
;
899 inv
[4] = (mx
[0]*mx
[8] - mx
[2]*mx
[6]) / det
;
900 inv
[5] = (mx
[2]*mx
[3] - mx
[0]*mx
[5]) / det
;
901 inv
[6] = (mx
[3]*mx
[7] - mx
[4]*mx
[6]) / det
;
902 inv
[7] = (mx
[1]*mx
[6] - mx
[0]*mx
[7]) / det
;
903 inv
[8] = (mx
[0]*mx
[4] - mx
[1]*mx
[3]) / det
;
905 vout
[0] = inv
[0]*vin
[0] + inv
[1]*vin
[1] + inv
[2]*vin
[2];
906 vout
[1] = inv
[3]*vin
[0] + inv
[4]*vin
[1] + inv
[5]*vin
[2];
907 vout
[2] = inv
[6]*vin
[0] + inv
[7]*vin
[1] + inv
[8]*vin
[2];
912 void grid_find_incentre(grid_face
*f
)
914 double xbest
, ybest
, bestdist
;
916 grid_dot
*edgedot1
[3], *edgedot2
[3];
924 * Find the point in the polygon with the maximum distance to any
927 * Such a point must exist which is in contact with at least three
928 * edges and/or vertices. (Proof: if it's only in contact with two
929 * edges and/or vertices, it can't even be at a _local_ maximum -
930 * any such circle can always be expanded in some direction.) So
931 * we iterate through all 3-subsets of the combined set of edges
932 * and vertices; for each subset we generate one or two candidate
933 * points that might be the incentre, and then we vet each one to
934 * see if it's inside the polygon and what its maximum radius is.
936 * (There's one case which this algorithm will get noticeably
937 * wrong, and that's when a continuum of equally good answers
938 * exists due to parallel edges. Consider a long thin rectangle,
939 * for instance, or a parallelogram. This algorithm will pick a
940 * point near one end, and choose the end arbitrarily; obviously a
941 * nicer point to choose would be in the centre. To fix this I
942 * would have to introduce a special-case system which detected
943 * parallel edges in advance, set aside all candidate points
944 * generated using both edges in a parallel pair, and generated
945 * some additional candidate points half way between them. Also,
946 * of course, I'd have to cope with rounding error making such a
947 * point look worse than one of its endpoints. So I haven't done
948 * this for the moment, and will cross it if necessary when I come
951 * We don't actually iterate literally over _edges_, in the sense
952 * of grid_edge structures. Instead, we fill in edgedot1[] and
953 * edgedot2[] with a pair of dots adjacent in the face's list of
954 * vertices. This ensures that we get the edges in consistent
955 * orientation, which we could not do from the grid structure
956 * alone. (A moment's consideration of an order-3 vertex should
957 * make it clear that if a notional arrow was written on each
958 * edge, _at least one_ of the three faces bordering that vertex
959 * would have to have the two arrows tip-to-tip or tail-to-tail
960 * rather than tip-to-tail.)
966 for (i
= 0; i
+2 < 2*f
->order
; i
++) {
968 edgedot1
[nedges
] = f
->dots
[i
];
969 edgedot2
[nedges
++] = f
->dots
[(i
+1)%f
->order
];
971 dots
[ndots
++] = f
->dots
[i
- f
->order
];
973 for (j
= i
+1; j
+1 < 2*f
->order
; j
++) {
975 edgedot1
[nedges
] = f
->dots
[j
];
976 edgedot2
[nedges
++] = f
->dots
[(j
+1)%f
->order
];
978 dots
[ndots
++] = f
->dots
[j
- f
->order
];
980 for (k
= j
+1; k
< 2*f
->order
; k
++) {
981 double cx
[2], cy
[2]; /* candidate positions */
982 int cn
= 0; /* number of candidates */
985 edgedot1
[nedges
] = f
->dots
[k
];
986 edgedot2
[nedges
++] = f
->dots
[(k
+1)%f
->order
];
988 dots
[ndots
++] = f
->dots
[k
- f
->order
];
991 * Find a point, or pair of points, equidistant from
992 * all the specified edges and/or vertices.
996 * Three edges. This is a linear matrix equation:
997 * each row of the matrix represents the fact that
998 * the point (x,y) we seek is at distance r from
999 * that edge, and we solve three of those
1000 * simultaneously to obtain x,y,r. (We ignore r.)
1002 double matrix
[9], vector
[3], vector2
[3];
1005 for (m
= 0; m
< 3; m
++) {
1006 int x1
= edgedot1
[m
]->x
, x2
= edgedot2
[m
]->x
;
1007 int y1
= edgedot1
[m
]->y
, y2
= edgedot2
[m
]->y
;
1008 int dx
= x2
-x1
, dy
= y2
-y1
;
1011 * ((x,y) - (x1,y1)) . (dy,-dx) = r |(dx,dy)|
1013 * => x dy - y dx - r |(dx,dy)| = (x1 dy - y1 dx)
1016 matrix
[3*m
+1] = -dx
;
1017 matrix
[3*m
+2] = -sqrt((double)dx
*dx
+(double)dy
*dy
);
1018 vector
[m
] = (double)x1
*dy
- (double)y1
*dx
;
1021 if (solve_3x3_matrix(matrix
, vector
, vector2
)) {
1022 cx
[cn
] = vector2
[0];
1023 cy
[cn
] = vector2
[1];
1026 } else if (nedges
== 2) {
1028 * Two edges and a dot. This will end up in a
1029 * quadratic equation.
1031 * First, look at the two edges. Having our point
1032 * be some distance r from both of them gives rise
1033 * to a pair of linear equations in x,y,r of the
1036 * (x-x1) dy - (y-y1) dx = r sqrt(dx^2+dy^2)
1038 * We eliminate r between those equations to give
1039 * us a single linear equation in x,y describing
1040 * the locus of points equidistant from both lines
1041 * - i.e. the angle bisector.
1043 * We then choose one of x,y to be a parameter t,
1044 * and derive linear formulae for x,y,r in terms
1045 * of t. This enables us to write down the
1046 * circular equation (x-xd)^2+(y-yd)^2=r^2 as a
1047 * quadratic in t; solving that and substituting
1048 * in for x,y gives us two candidate points.
1050 double eqs
[2][4]; /* a,b,c,d : ax+by+cr=d */
1051 double eq
[3]; /* a,b,c: ax+by=c */
1052 double xt
[2], yt
[2], rt
[2]; /* a,b: {x,y,r}=at+b */
1053 double q
[3]; /* a,b,c: at^2+bt+c=0 */
1056 /* Find equations of the two input lines. */
1057 for (m
= 0; m
< 2; m
++) {
1058 int x1
= edgedot1
[m
]->x
, x2
= edgedot2
[m
]->x
;
1059 int y1
= edgedot1
[m
]->y
, y2
= edgedot2
[m
]->y
;
1060 int dx
= x2
-x1
, dy
= y2
-y1
;
1064 eqs
[m
][2] = -sqrt(dx
*dx
+dy
*dy
);
1065 eqs
[m
][3] = x1
*dy
- y1
*dx
;
1068 /* Derive the angle bisector by eliminating r. */
1069 eq
[0] = eqs
[0][0]*eqs
[1][2] - eqs
[1][0]*eqs
[0][2];
1070 eq
[1] = eqs
[0][1]*eqs
[1][2] - eqs
[1][1]*eqs
[0][2];
1071 eq
[2] = eqs
[0][3]*eqs
[1][2] - eqs
[1][3]*eqs
[0][2];
1073 /* Parametrise x and y in terms of some t. */
1074 if (abs(eq
[0]) < abs(eq
[1])) {
1075 /* Parameter is x. */
1076 xt
[0] = 1; xt
[1] = 0;
1077 yt
[0] = -eq
[0]/eq
[1]; yt
[1] = eq
[2]/eq
[1];
1079 /* Parameter is y. */
1080 yt
[0] = 1; yt
[1] = 0;
1081 xt
[0] = -eq
[1]/eq
[0]; xt
[1] = eq
[2]/eq
[0];
1084 /* Find a linear representation of r using eqs[0]. */
1085 rt
[0] = -(eqs
[0][0]*xt
[0] + eqs
[0][1]*yt
[0])/eqs
[0][2];
1086 rt
[1] = (eqs
[0][3] - eqs
[0][0]*xt
[1] -
1087 eqs
[0][1]*yt
[1])/eqs
[0][2];
1089 /* Construct the quadratic equation. */
1090 q
[0] = -rt
[0]*rt
[0];
1091 q
[1] = -2*rt
[0]*rt
[1];
1092 q
[2] = -rt
[1]*rt
[1];
1093 q
[0] += xt
[0]*xt
[0];
1094 q
[1] += 2*xt
[0]*(xt
[1]-dots
[0]->x
);
1095 q
[2] += (xt
[1]-dots
[0]->x
)*(xt
[1]-dots
[0]->x
);
1096 q
[0] += yt
[0]*yt
[0];
1097 q
[1] += 2*yt
[0]*(yt
[1]-dots
[0]->y
);
1098 q
[2] += (yt
[1]-dots
[0]->y
)*(yt
[1]-dots
[0]->y
);
1101 disc
= q
[1]*q
[1] - 4*q
[0]*q
[2];
1107 t
= (-q
[1] + disc
) / (2*q
[0]);
1108 cx
[cn
] = xt
[0]*t
+ xt
[1];
1109 cy
[cn
] = yt
[0]*t
+ yt
[1];
1112 t
= (-q
[1] - disc
) / (2*q
[0]);
1113 cx
[cn
] = xt
[0]*t
+ xt
[1];
1114 cy
[cn
] = yt
[0]*t
+ yt
[1];
1117 } else if (nedges
== 1) {
1119 * Two dots and an edge. This one's another
1120 * quadratic equation.
1122 * The point we want must lie on the perpendicular
1123 * bisector of the two dots; that much is obvious.
1124 * So we can construct a parametrisation of that
1125 * bisecting line, giving linear formulae for x,y
1126 * in terms of t. We can also express the distance
1127 * from the edge as such a linear formula.
1129 * Then we set that equal to the radius of the
1130 * circle passing through the two points, which is
1131 * a Pythagoras exercise; that gives rise to a
1132 * quadratic in t, which we solve.
1134 double xt
[2], yt
[2], rt
[2]; /* a,b: {x,y,r}=at+b */
1135 double q
[3]; /* a,b,c: at^2+bt+c=0 */
1139 /* Find parametric formulae for x,y. */
1141 int x1
= dots
[0]->x
, x2
= dots
[1]->x
;
1142 int y1
= dots
[0]->y
, y2
= dots
[1]->y
;
1143 int dx
= x2
-x1
, dy
= y2
-y1
;
1144 double d
= sqrt((double)dx
*dx
+ (double)dy
*dy
);
1146 xt
[1] = (x1
+x2
)/2.0;
1147 yt
[1] = (y1
+y2
)/2.0;
1148 /* It's convenient if we have t at standard scale. */
1152 /* Also note down half the separation between
1153 * the dots, for use in computing the circle radius. */
1157 /* Find a parametric formula for r. */
1159 int x1
= edgedot1
[0]->x
, x2
= edgedot2
[0]->x
;
1160 int y1
= edgedot1
[0]->y
, y2
= edgedot2
[0]->y
;
1161 int dx
= x2
-x1
, dy
= y2
-y1
;
1162 double d
= sqrt((double)dx
*dx
+ (double)dy
*dy
);
1163 rt
[0] = (xt
[0]*dy
- yt
[0]*dx
) / d
;
1164 rt
[1] = ((xt
[1]-x1
)*dy
- (yt
[1]-y1
)*dx
) / d
;
1167 /* Construct the quadratic equation. */
1169 q
[1] = 2*rt
[0]*rt
[1];
1172 q
[2] -= halfsep
*halfsep
;
1175 disc
= q
[1]*q
[1] - 4*q
[0]*q
[2];
1181 t
= (-q
[1] + disc
) / (2*q
[0]);
1182 cx
[cn
] = xt
[0]*t
+ xt
[1];
1183 cy
[cn
] = yt
[0]*t
+ yt
[1];
1186 t
= (-q
[1] - disc
) / (2*q
[0]);
1187 cx
[cn
] = xt
[0]*t
+ xt
[1];
1188 cy
[cn
] = yt
[0]*t
+ yt
[1];
1191 } else if (nedges
== 0) {
1193 * Three dots. This is another linear matrix
1194 * equation, this time with each row of the matrix
1195 * representing the perpendicular bisector between
1196 * two of the points. Of course we only need two
1197 * such lines to find their intersection, so we
1198 * need only solve a 2x2 matrix equation.
1201 double matrix
[4], vector
[2], vector2
[2];
1204 for (m
= 0; m
< 2; m
++) {
1205 int x1
= dots
[m
]->x
, x2
= dots
[m
+1]->x
;
1206 int y1
= dots
[m
]->y
, y2
= dots
[m
+1]->y
;
1207 int dx
= x2
-x1
, dy
= y2
-y1
;
1210 * ((x,y) - (x1,y1)) . (dx,dy) = 1/2 |(dx,dy)|^2
1212 * => 2x dx + 2y dy = dx^2+dy^2 + (2 x1 dx + 2 y1 dy)
1214 matrix
[2*m
+0] = 2*dx
;
1215 matrix
[2*m
+1] = 2*dy
;
1216 vector
[m
] = ((double)dx
*dx
+ (double)dy
*dy
+
1217 2.0*x1
*dx
+ 2.0*y1
*dy
);
1220 if (solve_2x2_matrix(matrix
, vector
, vector2
)) {
1221 cx
[cn
] = vector2
[0];
1222 cy
[cn
] = vector2
[1];
1228 * Now go through our candidate points and see if any
1229 * of them are better than what we've got so far.
1231 for (m
= 0; m
< cn
; m
++) {
1232 double x
= cx
[m
], y
= cy
[m
];
1235 * First, disqualify the point if it's not inside
1236 * the polygon, which we work out by counting the
1237 * edges to the right of the point. (For
1238 * tiebreaking purposes when edges start or end on
1239 * our y-coordinate or go right through it, we
1240 * consider our point to be offset by a small
1241 * _positive_ epsilon in both the x- and
1245 for (e
= 0; e
< f
->order
; e
++) {
1246 int xs
= f
->edges
[e
]->dot1
->x
;
1247 int xe
= f
->edges
[e
]->dot2
->x
;
1248 int ys
= f
->edges
[e
]->dot1
->y
;
1249 int ye
= f
->edges
[e
]->dot2
->y
;
1250 if ((y
>= ys
&& y
< ye
) || (y
>= ye
&& y
< ys
)) {
1252 * The line goes past our y-position. Now we need
1253 * to know if its x-coordinate when it does so is
1256 * The x-coordinate in question is mathematically
1257 * (y - ys) * (xe - xs) / (ye - ys), and we want
1258 * to know whether (x - xs) >= that. Of course we
1259 * avoid the division, so we can work in integers;
1260 * to do this we must multiply both sides of the
1261 * inequality by ye - ys, which means we must
1262 * first check that's not negative.
1264 int num
= xe
- xs
, denom
= ye
- ys
;
1269 if ((x
- xs
) * denom
>= (y
- ys
) * num
)
1276 double mindist
= HUGE_VAL
;
1279 double mindist
= DBL_MAX
;
1281 #error No way to get maximum floating-point number.
1287 * This point is inside the polygon, so now we check
1288 * its minimum distance to every edge and corner.
1289 * First the corners ...
1291 for (d
= 0; d
< f
->order
; d
++) {
1292 int xp
= f
->dots
[d
]->x
;
1293 int yp
= f
->dots
[d
]->y
;
1294 double dx
= x
- xp
, dy
= y
- yp
;
1295 double dist
= dx
*dx
+ dy
*dy
;
1301 * ... and now also check the perpendicular distance
1302 * to every edge, if the perpendicular lies between
1303 * the edge's endpoints.
1305 for (e
= 0; e
< f
->order
; e
++) {
1306 int xs
= f
->edges
[e
]->dot1
->x
;
1307 int xe
= f
->edges
[e
]->dot2
->x
;
1308 int ys
= f
->edges
[e
]->dot1
->y
;
1309 int ye
= f
->edges
[e
]->dot2
->y
;
1312 * If s and e are our endpoints, and p our
1313 * candidate circle centre, the foot of a
1314 * perpendicular from p to the line se lies
1315 * between s and e if and only if (p-s).(e-s) lies
1316 * strictly between 0 and (e-s).(e-s).
1318 int edx
= xe
- xs
, edy
= ye
- ys
;
1319 double pdx
= x
- xs
, pdy
= y
- ys
;
1320 double pde
= pdx
* edx
+ pdy
* edy
;
1321 long ede
= (long)edx
* edx
+ (long)edy
* edy
;
1322 if (0 < pde
&& pde
< ede
) {
1324 * Yes, the nearest point on this edge is
1325 * closer than either endpoint, so we must
1326 * take it into account by measuring the
1327 * perpendicular distance to the edge and
1328 * checking its square against mindist.
1331 double pdre
= pdx
* edy
- pdy
* edx
;
1332 double sqlen
= pdre
* pdre
/ ede
;
1334 if (mindist
> sqlen
)
1340 * Right. Now we know the biggest circle around this
1341 * point, so we can check it against bestdist.
1343 if (bestdist
< mindist
) {
1367 assert(bestdist
> 0);
1369 f
->has_incentre
= TRUE
;
1370 f
->ix
= xbest
+ 0.5; /* round to nearest */
1371 f
->iy
= ybest
+ 0.5;
1374 /* Generate the dual to a grid
1375 * Returns a new dynamically-allocated grid whose dots are the
1376 * faces of the input, and whose faces are the dots of the input.
1377 * A few modifications are made: dots on input that have only two
1378 * edges are deleted, and the infinite exterior face is also removed
1379 * before conversion.
1381 static grid
*grid_dual(grid
*g
)
1387 new_g
= grid_empty();
1388 new_g
->tilesize
= g
->tilesize
;
1389 new_g
->faces
= snewn(g
->num_dots
, grid_face
);
1390 new_g
->dots
= snewn(g
->num_faces
, grid_dot
);
1391 debug(("taking the dual of a grid with %d faces and %d dots\n",
1392 g
->num_faces
,g
->num_dots
));
1394 points
= newtree234(grid_point_cmp_fn
);
1396 for (i
=0;i
<g
->num_faces
;i
++)
1398 grid_find_incentre(&(g
->faces
[i
]));
1400 for (i
=0;i
<g
->num_dots
;i
++)
1408 for (j
=0;j
<d
->order
;j
++)
1410 if (!d
->faces
[j
]) order
--;
1414 grid_face_add_new(new_g
, order
);
1415 for (j
=0,k
=0;j
<d
->order
;j
++)
1420 new_d
= grid_get_dot(new_g
, points
,
1421 d
->faces
[j
]->ix
, d
->faces
[j
]->iy
);
1422 grid_face_set_dot(new_g
, new_d
, k
++);
1429 freetree234(points
);
1430 assert(new_g
->num_faces
<= g
->num_dots
);
1431 assert(new_g
->num_dots
<= g
->num_faces
);
1433 debug(("dual has %d faces and %d dots\n",
1434 new_g
->num_faces
,new_g
->num_dots
));
1435 grid_make_consistent(new_g
);
1438 /* ------ Generate various types of grid ------ */
1440 /* General method is to generate faces, by calculating their dot coordinates.
1441 * As new faces are added, we keep track of all the dots so we can tell when
1442 * a new face reuses an existing dot. For example, two squares touching at an
1443 * edge would generate six unique dots: four dots from the first face, then
1444 * two additional dots for the second face, because we detect the other two
1445 * dots have already been taken up. This list is stored in a tree234
1446 * called "points". No extra memory-allocation needed here - we store the
1447 * actual grid_dot* pointers, which all point into the g->dots list.
1448 * For this reason, we have to calculate coordinates in such a way as to
1449 * eliminate any rounding errors, so we can detect when a dot on one
1450 * face precisely lands on a dot of a different face. No floating-point
1454 #define SQUARE_TILESIZE 20
1456 static void grid_size_square(int width
, int height
,
1457 int *tilesize
, int *xextent
, int *yextent
)
1459 int a
= SQUARE_TILESIZE
;
1462 *xextent
= width
* a
;
1463 *yextent
= height
* a
;
1466 static grid
*grid_new_square(int width
, int height
, char *desc
)
1470 int a
= SQUARE_TILESIZE
;
1472 /* Upper bounds - don't have to be exact */
1473 int max_faces
= width
* height
;
1474 int max_dots
= (width
+ 1) * (height
+ 1);
1478 grid
*g
= grid_empty();
1480 g
->faces
= snewn(max_faces
, grid_face
);
1481 g
->dots
= snewn(max_dots
, grid_dot
);
1483 points
= newtree234(grid_point_cmp_fn
);
1485 /* generate square faces */
1486 for (y
= 0; y
< height
; y
++) {
1487 for (x
= 0; x
< width
; x
++) {
1493 grid_face_add_new(g
, 4);
1494 d
= grid_get_dot(g
, points
, px
, py
);
1495 grid_face_set_dot(g
, d
, 0);
1496 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1497 grid_face_set_dot(g
, d
, 1);
1498 d
= grid_get_dot(g
, points
, px
+ a
, py
+ a
);
1499 grid_face_set_dot(g
, d
, 2);
1500 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1501 grid_face_set_dot(g
, d
, 3);
1505 freetree234(points
);
1506 assert(g
->num_faces
<= max_faces
);
1507 assert(g
->num_dots
<= max_dots
);
1509 grid_make_consistent(g
);
1513 #define HONEY_TILESIZE 45
1514 /* Vector for side of hexagon - ratio is close to sqrt(3) */
1518 static void grid_size_honeycomb(int width
, int height
,
1519 int *tilesize
, int *xextent
, int *yextent
)
1524 *tilesize
= HONEY_TILESIZE
;
1525 *xextent
= (3 * a
* (width
-1)) + 4*a
;
1526 *yextent
= (2 * b
* (height
-1)) + 3*b
;
1529 static grid
*grid_new_honeycomb(int width
, int height
, char *desc
)
1535 /* Upper bounds - don't have to be exact */
1536 int max_faces
= width
* height
;
1537 int max_dots
= 2 * (width
+ 1) * (height
+ 1);
1541 grid
*g
= grid_empty();
1542 g
->tilesize
= HONEY_TILESIZE
;
1543 g
->faces
= snewn(max_faces
, grid_face
);
1544 g
->dots
= snewn(max_dots
, grid_dot
);
1546 points
= newtree234(grid_point_cmp_fn
);
1548 /* generate hexagonal faces */
1549 for (y
= 0; y
< height
; y
++) {
1550 for (x
= 0; x
< width
; x
++) {
1557 grid_face_add_new(g
, 6);
1559 d
= grid_get_dot(g
, points
, cx
- a
, cy
- b
);
1560 grid_face_set_dot(g
, d
, 0);
1561 d
= grid_get_dot(g
, points
, cx
+ a
, cy
- b
);
1562 grid_face_set_dot(g
, d
, 1);
1563 d
= grid_get_dot(g
, points
, cx
+ 2*a
, cy
);
1564 grid_face_set_dot(g
, d
, 2);
1565 d
= grid_get_dot(g
, points
, cx
+ a
, cy
+ b
);
1566 grid_face_set_dot(g
, d
, 3);
1567 d
= grid_get_dot(g
, points
, cx
- a
, cy
+ b
);
1568 grid_face_set_dot(g
, d
, 4);
1569 d
= grid_get_dot(g
, points
, cx
- 2*a
, cy
);
1570 grid_face_set_dot(g
, d
, 5);
1574 freetree234(points
);
1575 assert(g
->num_faces
<= max_faces
);
1576 assert(g
->num_dots
<= max_dots
);
1578 grid_make_consistent(g
);
1582 #define TRIANGLE_TILESIZE 18
1583 /* Vector for side of triangle - ratio is close to sqrt(3) */
1584 #define TRIANGLE_VEC_X 15
1585 #define TRIANGLE_VEC_Y 26
1587 static void grid_size_triangular(int width
, int height
,
1588 int *tilesize
, int *xextent
, int *yextent
)
1590 int vec_x
= TRIANGLE_VEC_X
;
1591 int vec_y
= TRIANGLE_VEC_Y
;
1593 *tilesize
= TRIANGLE_TILESIZE
;
1594 *xextent
= width
* 2 * vec_x
+ vec_x
;
1595 *yextent
= height
* vec_y
;
1598 /* Doesn't use the previous method of generation, it pre-dates it!
1599 * A triangular grid is just about simple enough to do by "brute force" */
1600 static grid
*grid_new_triangular(int width
, int height
, char *desc
)
1604 /* Vector for side of triangle - ratio is close to sqrt(3) */
1605 int vec_x
= TRIANGLE_VEC_X
;
1606 int vec_y
= TRIANGLE_VEC_Y
;
1610 /* convenient alias */
1613 grid
*g
= grid_empty();
1614 g
->tilesize
= TRIANGLE_TILESIZE
;
1616 g
->num_faces
= width
* height
* 2;
1617 g
->num_dots
= (width
+ 1) * (height
+ 1);
1618 g
->faces
= snewn(g
->num_faces
, grid_face
);
1619 g
->dots
= snewn(g
->num_dots
, grid_dot
);
1623 for (y
= 0; y
<= height
; y
++) {
1624 for (x
= 0; x
<= width
; x
++) {
1625 grid_dot
*d
= g
->dots
+ index
;
1626 /* odd rows are offset to the right */
1630 d
->x
= x
* 2 * vec_x
+ ((y
% 2) ? vec_x
: 0);
1636 /* generate faces */
1638 for (y
= 0; y
< height
; y
++) {
1639 for (x
= 0; x
< width
; x
++) {
1640 /* initialise two faces for this (x,y) */
1641 grid_face
*f1
= g
->faces
+ index
;
1642 grid_face
*f2
= f1
+ 1;
1645 f1
->dots
= snewn(f1
->order
, grid_dot
*);
1646 f1
->has_incentre
= FALSE
;
1649 f2
->dots
= snewn(f2
->order
, grid_dot
*);
1650 f2
->has_incentre
= FALSE
;
1652 /* face descriptions depend on whether the row-number is
1655 f1
->dots
[0] = g
->dots
+ y
* w
+ x
;
1656 f1
->dots
[1] = g
->dots
+ (y
+ 1) * w
+ x
+ 1;
1657 f1
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
;
1658 f2
->dots
[0] = g
->dots
+ y
* w
+ x
;
1659 f2
->dots
[1] = g
->dots
+ y
* w
+ x
+ 1;
1660 f2
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
+ 1;
1662 f1
->dots
[0] = g
->dots
+ y
* w
+ x
;
1663 f1
->dots
[1] = g
->dots
+ y
* w
+ x
+ 1;
1664 f1
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
;
1665 f2
->dots
[0] = g
->dots
+ y
* w
+ x
+ 1;
1666 f2
->dots
[1] = g
->dots
+ (y
+ 1) * w
+ x
+ 1;
1667 f2
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
;
1673 grid_make_consistent(g
);
1677 #define SNUBSQUARE_TILESIZE 18
1678 /* Vector for side of triangle - ratio is close to sqrt(3) */
1679 #define SNUBSQUARE_A 15
1680 #define SNUBSQUARE_B 26
1682 static void grid_size_snubsquare(int width
, int height
,
1683 int *tilesize
, int *xextent
, int *yextent
)
1685 int a
= SNUBSQUARE_A
;
1686 int b
= SNUBSQUARE_B
;
1688 *tilesize
= SNUBSQUARE_TILESIZE
;
1689 *xextent
= (a
+b
) * (width
-1) + a
+ b
;
1690 *yextent
= (a
+b
) * (height
-1) + a
+ b
;
1693 static grid
*grid_new_snubsquare(int width
, int height
, char *desc
)
1696 int a
= SNUBSQUARE_A
;
1697 int b
= SNUBSQUARE_B
;
1699 /* Upper bounds - don't have to be exact */
1700 int max_faces
= 3 * width
* height
;
1701 int max_dots
= 2 * (width
+ 1) * (height
+ 1);
1705 grid
*g
= grid_empty();
1706 g
->tilesize
= SNUBSQUARE_TILESIZE
;
1707 g
->faces
= snewn(max_faces
, grid_face
);
1708 g
->dots
= snewn(max_dots
, grid_dot
);
1710 points
= newtree234(grid_point_cmp_fn
);
1712 for (y
= 0; y
< height
; y
++) {
1713 for (x
= 0; x
< width
; x
++) {
1716 int px
= (a
+ b
) * x
;
1717 int py
= (a
+ b
) * y
;
1719 /* generate square faces */
1720 grid_face_add_new(g
, 4);
1722 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1723 grid_face_set_dot(g
, d
, 0);
1724 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
);
1725 grid_face_set_dot(g
, d
, 1);
1726 d
= grid_get_dot(g
, points
, px
+ b
, py
+ a
+ b
);
1727 grid_face_set_dot(g
, d
, 2);
1728 d
= grid_get_dot(g
, points
, px
, py
+ b
);
1729 grid_face_set_dot(g
, d
, 3);
1731 d
= grid_get_dot(g
, points
, px
+ b
, py
);
1732 grid_face_set_dot(g
, d
, 0);
1733 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ b
);
1734 grid_face_set_dot(g
, d
, 1);
1735 d
= grid_get_dot(g
, points
, px
+ a
, py
+ a
+ b
);
1736 grid_face_set_dot(g
, d
, 2);
1737 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1738 grid_face_set_dot(g
, d
, 3);
1741 /* generate up/down triangles */
1743 grid_face_add_new(g
, 3);
1745 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1746 grid_face_set_dot(g
, d
, 0);
1747 d
= grid_get_dot(g
, points
, px
, py
+ b
);
1748 grid_face_set_dot(g
, d
, 1);
1749 d
= grid_get_dot(g
, points
, px
- a
, py
);
1750 grid_face_set_dot(g
, d
, 2);
1752 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1753 grid_face_set_dot(g
, d
, 0);
1754 d
= grid_get_dot(g
, points
, px
+ a
, py
+ a
+ b
);
1755 grid_face_set_dot(g
, d
, 1);
1756 d
= grid_get_dot(g
, points
, px
- a
, py
+ a
+ b
);
1757 grid_face_set_dot(g
, d
, 2);
1761 /* generate left/right triangles */
1763 grid_face_add_new(g
, 3);
1765 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1766 grid_face_set_dot(g
, d
, 0);
1767 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
- a
);
1768 grid_face_set_dot(g
, d
, 1);
1769 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
);
1770 grid_face_set_dot(g
, d
, 2);
1772 d
= grid_get_dot(g
, points
, px
, py
- a
);
1773 grid_face_set_dot(g
, d
, 0);
1774 d
= grid_get_dot(g
, points
, px
+ b
, py
);
1775 grid_face_set_dot(g
, d
, 1);
1776 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1777 grid_face_set_dot(g
, d
, 2);
1783 freetree234(points
);
1784 assert(g
->num_faces
<= max_faces
);
1785 assert(g
->num_dots
<= max_dots
);
1787 grid_make_consistent(g
);
1791 #define CAIRO_TILESIZE 40
1792 /* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */
1796 static void grid_size_cairo(int width
, int height
,
1797 int *tilesize
, int *xextent
, int *yextent
)
1799 int b
= CAIRO_B
; /* a unused in determining grid size. */
1801 *tilesize
= CAIRO_TILESIZE
;
1802 *xextent
= 2*b
*(width
-1) + 2*b
;
1803 *yextent
= 2*b
*(height
-1) + 2*b
;
1806 static grid
*grid_new_cairo(int width
, int height
, char *desc
)
1812 /* Upper bounds - don't have to be exact */
1813 int max_faces
= 2 * width
* height
;
1814 int max_dots
= 3 * (width
+ 1) * (height
+ 1);
1818 grid
*g
= grid_empty();
1819 g
->tilesize
= CAIRO_TILESIZE
;
1820 g
->faces
= snewn(max_faces
, grid_face
);
1821 g
->dots
= snewn(max_dots
, grid_dot
);
1823 points
= newtree234(grid_point_cmp_fn
);
1825 for (y
= 0; y
< height
; y
++) {
1826 for (x
= 0; x
< width
; x
++) {
1832 /* horizontal pentagons */
1834 grid_face_add_new(g
, 5);
1836 d
= grid_get_dot(g
, points
, px
+ a
, py
- b
);
1837 grid_face_set_dot(g
, d
, 0);
1838 d
= grid_get_dot(g
, points
, px
+ 2*b
- a
, py
- b
);
1839 grid_face_set_dot(g
, d
, 1);
1840 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
1841 grid_face_set_dot(g
, d
, 2);
1842 d
= grid_get_dot(g
, points
, px
+ b
, py
+ a
);
1843 grid_face_set_dot(g
, d
, 3);
1844 d
= grid_get_dot(g
, points
, px
, py
);
1845 grid_face_set_dot(g
, d
, 4);
1847 d
= grid_get_dot(g
, points
, px
, py
);
1848 grid_face_set_dot(g
, d
, 0);
1849 d
= grid_get_dot(g
, points
, px
+ b
, py
- a
);
1850 grid_face_set_dot(g
, d
, 1);
1851 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
1852 grid_face_set_dot(g
, d
, 2);
1853 d
= grid_get_dot(g
, points
, px
+ 2*b
- a
, py
+ b
);
1854 grid_face_set_dot(g
, d
, 3);
1855 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1856 grid_face_set_dot(g
, d
, 4);
1859 /* vertical pentagons */
1861 grid_face_add_new(g
, 5);
1863 d
= grid_get_dot(g
, points
, px
, py
);
1864 grid_face_set_dot(g
, d
, 0);
1865 d
= grid_get_dot(g
, points
, px
+ b
, py
+ a
);
1866 grid_face_set_dot(g
, d
, 1);
1867 d
= grid_get_dot(g
, points
, px
+ b
, py
+ 2*b
- a
);
1868 grid_face_set_dot(g
, d
, 2);
1869 d
= grid_get_dot(g
, points
, px
, py
+ 2*b
);
1870 grid_face_set_dot(g
, d
, 3);
1871 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1872 grid_face_set_dot(g
, d
, 4);
1874 d
= grid_get_dot(g
, points
, px
, py
);
1875 grid_face_set_dot(g
, d
, 0);
1876 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1877 grid_face_set_dot(g
, d
, 1);
1878 d
= grid_get_dot(g
, points
, px
, py
+ 2*b
);
1879 grid_face_set_dot(g
, d
, 2);
1880 d
= grid_get_dot(g
, points
, px
- b
, py
+ 2*b
- a
);
1881 grid_face_set_dot(g
, d
, 3);
1882 d
= grid_get_dot(g
, points
, px
- b
, py
+ a
);
1883 grid_face_set_dot(g
, d
, 4);
1889 freetree234(points
);
1890 assert(g
->num_faces
<= max_faces
);
1891 assert(g
->num_dots
<= max_dots
);
1893 grid_make_consistent(g
);
1897 #define GREATHEX_TILESIZE 18
1898 /* Vector for side of triangle - ratio is close to sqrt(3) */
1899 #define GREATHEX_A 15
1900 #define GREATHEX_B 26
1902 static void grid_size_greathexagonal(int width
, int height
,
1903 int *tilesize
, int *xextent
, int *yextent
)
1908 *tilesize
= GREATHEX_TILESIZE
;
1909 *xextent
= (3*a
+ b
) * (width
-1) + 4*a
;
1910 *yextent
= (2*a
+ 2*b
) * (height
-1) + 3*b
+ a
;
1913 static grid
*grid_new_greathexagonal(int width
, int height
, char *desc
)
1919 /* Upper bounds - don't have to be exact */
1920 int max_faces
= 6 * (width
+ 1) * (height
+ 1);
1921 int max_dots
= 6 * width
* height
;
1925 grid
*g
= grid_empty();
1926 g
->tilesize
= GREATHEX_TILESIZE
;
1927 g
->faces
= snewn(max_faces
, grid_face
);
1928 g
->dots
= snewn(max_dots
, grid_dot
);
1930 points
= newtree234(grid_point_cmp_fn
);
1932 for (y
= 0; y
< height
; y
++) {
1933 for (x
= 0; x
< width
; x
++) {
1935 /* centre of hexagon */
1936 int px
= (3*a
+ b
) * x
;
1937 int py
= (2*a
+ 2*b
) * y
;
1942 grid_face_add_new(g
, 6);
1943 d
= grid_get_dot(g
, points
, px
- a
, py
- b
);
1944 grid_face_set_dot(g
, d
, 0);
1945 d
= grid_get_dot(g
, points
, px
+ a
, py
- b
);
1946 grid_face_set_dot(g
, d
, 1);
1947 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
);
1948 grid_face_set_dot(g
, d
, 2);
1949 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1950 grid_face_set_dot(g
, d
, 3);
1951 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1952 grid_face_set_dot(g
, d
, 4);
1953 d
= grid_get_dot(g
, points
, px
- 2*a
, py
);
1954 grid_face_set_dot(g
, d
, 5);
1956 /* square below hexagon */
1957 if (y
< height
- 1) {
1958 grid_face_add_new(g
, 4);
1959 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1960 grid_face_set_dot(g
, d
, 0);
1961 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1962 grid_face_set_dot(g
, d
, 1);
1963 d
= grid_get_dot(g
, points
, px
+ a
, py
+ 2*a
+ b
);
1964 grid_face_set_dot(g
, d
, 2);
1965 d
= grid_get_dot(g
, points
, px
- a
, py
+ 2*a
+ b
);
1966 grid_face_set_dot(g
, d
, 3);
1969 /* square below right */
1970 if ((x
< width
- 1) && (((x
% 2) == 0) || (y
< height
- 1))) {
1971 grid_face_add_new(g
, 4);
1972 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
);
1973 grid_face_set_dot(g
, d
, 0);
1974 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
);
1975 grid_face_set_dot(g
, d
, 1);
1976 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
+ b
);
1977 grid_face_set_dot(g
, d
, 2);
1978 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1979 grid_face_set_dot(g
, d
, 3);
1982 /* square below left */
1983 if ((x
> 0) && (((x
% 2) == 0) || (y
< height
- 1))) {
1984 grid_face_add_new(g
, 4);
1985 d
= grid_get_dot(g
, points
, px
- 2*a
, py
);
1986 grid_face_set_dot(g
, d
, 0);
1987 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1988 grid_face_set_dot(g
, d
, 1);
1989 d
= grid_get_dot(g
, points
, px
- a
- b
, py
+ a
+ b
);
1990 grid_face_set_dot(g
, d
, 2);
1991 d
= grid_get_dot(g
, points
, px
- 2*a
- b
, py
+ a
);
1992 grid_face_set_dot(g
, d
, 3);
1995 /* Triangle below right */
1996 if ((x
< width
- 1) && (y
< height
- 1)) {
1997 grid_face_add_new(g
, 3);
1998 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1999 grid_face_set_dot(g
, d
, 0);
2000 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
+ b
);
2001 grid_face_set_dot(g
, d
, 1);
2002 d
= grid_get_dot(g
, points
, px
+ a
, py
+ 2*a
+ b
);
2003 grid_face_set_dot(g
, d
, 2);
2006 /* Triangle below left */
2007 if ((x
> 0) && (y
< height
- 1)) {
2008 grid_face_add_new(g
, 3);
2009 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
2010 grid_face_set_dot(g
, d
, 0);
2011 d
= grid_get_dot(g
, points
, px
- a
, py
+ 2*a
+ b
);
2012 grid_face_set_dot(g
, d
, 1);
2013 d
= grid_get_dot(g
, points
, px
- a
- b
, py
+ a
+ b
);
2014 grid_face_set_dot(g
, d
, 2);
2019 freetree234(points
);
2020 assert(g
->num_faces
<= max_faces
);
2021 assert(g
->num_dots
<= max_dots
);
2023 grid_make_consistent(g
);
2026 #define OCTAGONAL_TILESIZE 40
2027 /* b/a approx sqrt(2) */
2028 #define OCTAGONAL_A 29
2029 #define OCTAGONAL_B 41
2031 static void grid_size_octagonal(int width
, int height
,
2032 int *tilesize
, int *xextent
, int *yextent
)
2034 int a
= OCTAGONAL_A
;
2035 int b
= OCTAGONAL_B
;
2037 *tilesize
= OCTAGONAL_TILESIZE
;
2038 *xextent
= (2*a
+ b
) * width
;
2039 *yextent
= (2*a
+ b
) * height
;
2042 static grid
*grid_new_octagonal(int width
, int height
, char *desc
)
2045 int a
= OCTAGONAL_A
;
2046 int b
= OCTAGONAL_B
;
2048 /* Upper bounds - don't have to be exact */
2049 int max_faces
= 2 * width
* height
;
2050 int max_dots
= 4 * (width
+ 1) * (height
+ 1);
2054 grid
*g
= grid_empty();
2055 g
->tilesize
= OCTAGONAL_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
++) {
2065 int px
= (2*a
+ b
) * x
;
2066 int py
= (2*a
+ b
) * y
;
2068 grid_face_add_new(g
, 8);
2069 d
= grid_get_dot(g
, points
, px
+ a
, py
);
2070 grid_face_set_dot(g
, d
, 0);
2071 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
);
2072 grid_face_set_dot(g
, d
, 1);
2073 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
);
2074 grid_face_set_dot(g
, d
, 2);
2075 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
+ b
);
2076 grid_face_set_dot(g
, d
, 3);
2077 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ 2*a
+ b
);
2078 grid_face_set_dot(g
, d
, 4);
2079 d
= grid_get_dot(g
, points
, px
+ a
, py
+ 2*a
+ b
);
2080 grid_face_set_dot(g
, d
, 5);
2081 d
= grid_get_dot(g
, points
, px
, py
+ a
+ b
);
2082 grid_face_set_dot(g
, d
, 6);
2083 d
= grid_get_dot(g
, points
, px
, py
+ a
);
2084 grid_face_set_dot(g
, d
, 7);
2087 if ((x
> 0) && (y
> 0)) {
2088 grid_face_add_new(g
, 4);
2089 d
= grid_get_dot(g
, points
, px
, py
- a
);
2090 grid_face_set_dot(g
, d
, 0);
2091 d
= grid_get_dot(g
, points
, px
+ a
, py
);
2092 grid_face_set_dot(g
, d
, 1);
2093 d
= grid_get_dot(g
, points
, px
, py
+ a
);
2094 grid_face_set_dot(g
, d
, 2);
2095 d
= grid_get_dot(g
, points
, px
- a
, py
);
2096 grid_face_set_dot(g
, d
, 3);
2101 freetree234(points
);
2102 assert(g
->num_faces
<= max_faces
);
2103 assert(g
->num_dots
<= max_dots
);
2105 grid_make_consistent(g
);
2109 #define KITE_TILESIZE 40
2110 /* b/a approx sqrt(3) */
2114 static void grid_size_kites(int width
, int height
,
2115 int *tilesize
, int *xextent
, int *yextent
)
2120 *tilesize
= KITE_TILESIZE
;
2121 *xextent
= 4*b
* width
+ 2*b
;
2122 *yextent
= 6*a
* (height
-1) + 8*a
;
2125 static grid
*grid_new_kites(int width
, int height
, char *desc
)
2131 /* Upper bounds - don't have to be exact */
2132 int max_faces
= 6 * width
* height
;
2133 int max_dots
= 6 * (width
+ 1) * (height
+ 1);
2137 grid
*g
= grid_empty();
2138 g
->tilesize
= KITE_TILESIZE
;
2139 g
->faces
= snewn(max_faces
, grid_face
);
2140 g
->dots
= snewn(max_dots
, grid_dot
);
2142 points
= newtree234(grid_point_cmp_fn
);
2144 for (y
= 0; y
< height
; y
++) {
2145 for (x
= 0; x
< width
; x
++) {
2147 /* position of order-6 dot */
2153 /* kite pointing up-left */
2154 grid_face_add_new(g
, 4);
2155 d
= grid_get_dot(g
, points
, px
, py
);
2156 grid_face_set_dot(g
, d
, 0);
2157 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
2158 grid_face_set_dot(g
, d
, 1);
2159 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
+ 2*a
);
2160 grid_face_set_dot(g
, d
, 2);
2161 d
= grid_get_dot(g
, points
, px
+ b
, py
+ 3*a
);
2162 grid_face_set_dot(g
, d
, 3);
2164 /* kite pointing up */
2165 grid_face_add_new(g
, 4);
2166 d
= grid_get_dot(g
, points
, px
, py
);
2167 grid_face_set_dot(g
, d
, 0);
2168 d
= grid_get_dot(g
, points
, px
+ b
, py
+ 3*a
);
2169 grid_face_set_dot(g
, d
, 1);
2170 d
= grid_get_dot(g
, points
, px
, py
+ 4*a
);
2171 grid_face_set_dot(g
, d
, 2);
2172 d
= grid_get_dot(g
, points
, px
- b
, py
+ 3*a
);
2173 grid_face_set_dot(g
, d
, 3);
2175 /* kite pointing up-right */
2176 grid_face_add_new(g
, 4);
2177 d
= grid_get_dot(g
, points
, px
, py
);
2178 grid_face_set_dot(g
, d
, 0);
2179 d
= grid_get_dot(g
, points
, px
- b
, py
+ 3*a
);
2180 grid_face_set_dot(g
, d
, 1);
2181 d
= grid_get_dot(g
, points
, px
- 2*b
, py
+ 2*a
);
2182 grid_face_set_dot(g
, d
, 2);
2183 d
= grid_get_dot(g
, points
, px
- 2*b
, py
);
2184 grid_face_set_dot(g
, d
, 3);
2186 /* kite pointing down-right */
2187 grid_face_add_new(g
, 4);
2188 d
= grid_get_dot(g
, points
, px
, py
);
2189 grid_face_set_dot(g
, d
, 0);
2190 d
= grid_get_dot(g
, points
, px
- 2*b
, py
);
2191 grid_face_set_dot(g
, d
, 1);
2192 d
= grid_get_dot(g
, points
, px
- 2*b
, py
- 2*a
);
2193 grid_face_set_dot(g
, d
, 2);
2194 d
= grid_get_dot(g
, points
, px
- b
, py
- 3*a
);
2195 grid_face_set_dot(g
, d
, 3);
2197 /* kite pointing down */
2198 grid_face_add_new(g
, 4);
2199 d
= grid_get_dot(g
, points
, px
, py
);
2200 grid_face_set_dot(g
, d
, 0);
2201 d
= grid_get_dot(g
, points
, px
- b
, py
- 3*a
);
2202 grid_face_set_dot(g
, d
, 1);
2203 d
= grid_get_dot(g
, points
, px
, py
- 4*a
);
2204 grid_face_set_dot(g
, d
, 2);
2205 d
= grid_get_dot(g
, points
, px
+ b
, py
- 3*a
);
2206 grid_face_set_dot(g
, d
, 3);
2208 /* kite pointing down-left */
2209 grid_face_add_new(g
, 4);
2210 d
= grid_get_dot(g
, points
, px
, py
);
2211 grid_face_set_dot(g
, d
, 0);
2212 d
= grid_get_dot(g
, points
, px
+ b
, py
- 3*a
);
2213 grid_face_set_dot(g
, d
, 1);
2214 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
- 2*a
);
2215 grid_face_set_dot(g
, d
, 2);
2216 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
2217 grid_face_set_dot(g
, d
, 3);
2221 freetree234(points
);
2222 assert(g
->num_faces
<= max_faces
);
2223 assert(g
->num_dots
<= max_dots
);
2225 grid_make_consistent(g
);
2229 #define FLORET_TILESIZE 150
2230 /* -py/px is close to tan(30 - atan(sqrt(3)/9))
2231 * using py=26 makes everything lean to the left, rather than right
2233 #define FLORET_PX 75
2234 #define FLORET_PY -26
2236 static void grid_size_floret(int width
, int height
,
2237 int *tilesize
, int *xextent
, int *yextent
)
2239 int px
= FLORET_PX
, py
= FLORET_PY
; /* |( 75, -26)| = 79.43 */
2240 int qx
= 4*px
/5, qy
= -py
*2; /* |( 60, 52)| = 79.40 */
2242 /* rx unused in determining grid size. */
2244 *tilesize
= FLORET_TILESIZE
;
2245 *xextent
= (6*px
+3*qx
)/2 * (width
-1) + 4*qx
+ 2*px
;
2246 *yextent
= (5*qy
-4*py
) * (height
-1) + 4*qy
+ 2*ry
;
2249 static grid
*grid_new_floret(int width
, int height
, char *desc
)
2252 /* Vectors for sides; weird numbers needed to keep puzzle aligned with window
2253 * -py/px is close to tan(30 - atan(sqrt(3)/9))
2254 * using py=26 makes everything lean to the left, rather than right
2256 int px
= FLORET_PX
, py
= FLORET_PY
; /* |( 75, -26)| = 79.43 */
2257 int qx
= 4*px
/5, qy
= -py
*2; /* |( 60, 52)| = 79.40 */
2258 int rx
= qx
-px
, ry
= qy
-py
; /* |(-15, 78)| = 79.38 */
2260 /* Upper bounds - don't have to be exact */
2261 int max_faces
= 6 * width
* height
;
2262 int max_dots
= 9 * (width
+ 1) * (height
+ 1);
2266 grid
*g
= grid_empty();
2267 g
->tilesize
= FLORET_TILESIZE
;
2268 g
->faces
= snewn(max_faces
, grid_face
);
2269 g
->dots
= snewn(max_dots
, grid_dot
);
2271 points
= newtree234(grid_point_cmp_fn
);
2273 /* generate pentagonal faces */
2274 for (y
= 0; y
< height
; y
++) {
2275 for (x
= 0; x
< width
; x
++) {
2278 int cx
= (6*px
+3*qx
)/2 * x
;
2279 int cy
= (4*py
-5*qy
) * y
;
2281 cy
-= (4*py
-5*qy
)/2;
2282 else if (y
&& y
== height
-1)
2283 continue; /* make better looking grids? try 3x3 for instance */
2285 grid_face_add_new(g
, 5);
2286 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2287 d
= grid_get_dot(g
, points
, cx
+2*rx
, cy
+2*ry
); grid_face_set_dot(g
, d
, 1);
2288 d
= grid_get_dot(g
, points
, cx
+2*rx
+qx
, cy
+2*ry
+qy
); grid_face_set_dot(g
, d
, 2);
2289 d
= grid_get_dot(g
, points
, cx
+2*qx
+rx
, cy
+2*qy
+ry
); grid_face_set_dot(g
, d
, 3);
2290 d
= grid_get_dot(g
, points
, cx
+2*qx
, cy
+2*qy
); grid_face_set_dot(g
, d
, 4);
2292 grid_face_add_new(g
, 5);
2293 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2294 d
= grid_get_dot(g
, points
, cx
+2*qx
, cy
+2*qy
); grid_face_set_dot(g
, d
, 1);
2295 d
= grid_get_dot(g
, points
, cx
+2*qx
+px
, cy
+2*qy
+py
); grid_face_set_dot(g
, d
, 2);
2296 d
= grid_get_dot(g
, points
, cx
+2*px
+qx
, cy
+2*py
+qy
); grid_face_set_dot(g
, d
, 3);
2297 d
= grid_get_dot(g
, points
, cx
+2*px
, cy
+2*py
); grid_face_set_dot(g
, d
, 4);
2299 grid_face_add_new(g
, 5);
2300 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2301 d
= grid_get_dot(g
, points
, cx
+2*px
, cy
+2*py
); grid_face_set_dot(g
, d
, 1);
2302 d
= grid_get_dot(g
, points
, cx
+2*px
-rx
, cy
+2*py
-ry
); grid_face_set_dot(g
, d
, 2);
2303 d
= grid_get_dot(g
, points
, cx
-2*rx
+px
, cy
-2*ry
+py
); grid_face_set_dot(g
, d
, 3);
2304 d
= grid_get_dot(g
, points
, cx
-2*rx
, cy
-2*ry
); grid_face_set_dot(g
, d
, 4);
2306 grid_face_add_new(g
, 5);
2307 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2308 d
= grid_get_dot(g
, points
, cx
-2*rx
, cy
-2*ry
); grid_face_set_dot(g
, d
, 1);
2309 d
= grid_get_dot(g
, points
, cx
-2*rx
-qx
, cy
-2*ry
-qy
); grid_face_set_dot(g
, d
, 2);
2310 d
= grid_get_dot(g
, points
, cx
-2*qx
-rx
, cy
-2*qy
-ry
); grid_face_set_dot(g
, d
, 3);
2311 d
= grid_get_dot(g
, points
, cx
-2*qx
, cy
-2*qy
); grid_face_set_dot(g
, d
, 4);
2313 grid_face_add_new(g
, 5);
2314 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2315 d
= grid_get_dot(g
, points
, cx
-2*qx
, cy
-2*qy
); grid_face_set_dot(g
, d
, 1);
2316 d
= grid_get_dot(g
, points
, cx
-2*qx
-px
, cy
-2*qy
-py
); grid_face_set_dot(g
, d
, 2);
2317 d
= grid_get_dot(g
, points
, cx
-2*px
-qx
, cy
-2*py
-qy
); grid_face_set_dot(g
, d
, 3);
2318 d
= grid_get_dot(g
, points
, cx
-2*px
, cy
-2*py
); grid_face_set_dot(g
, d
, 4);
2320 grid_face_add_new(g
, 5);
2321 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2322 d
= grid_get_dot(g
, points
, cx
-2*px
, cy
-2*py
); grid_face_set_dot(g
, d
, 1);
2323 d
= grid_get_dot(g
, points
, cx
-2*px
+rx
, cy
-2*py
+ry
); grid_face_set_dot(g
, d
, 2);
2324 d
= grid_get_dot(g
, points
, cx
+2*rx
-px
, cy
+2*ry
-py
); grid_face_set_dot(g
, d
, 3);
2325 d
= grid_get_dot(g
, points
, cx
+2*rx
, cy
+2*ry
); grid_face_set_dot(g
, d
, 4);
2329 freetree234(points
);
2330 assert(g
->num_faces
<= max_faces
);
2331 assert(g
->num_dots
<= max_dots
);
2333 grid_make_consistent(g
);
2337 /* DODEC_* are used for dodecagonal and great-dodecagonal grids. */
2338 #define DODEC_TILESIZE 26
2339 /* Vector for side of triangle - ratio is close to sqrt(3) */
2343 static void grid_size_dodecagonal(int width
, int height
,
2344 int *tilesize
, int *xextent
, int *yextent
)
2349 *tilesize
= DODEC_TILESIZE
;
2350 *xextent
= (4*a
+ 2*b
) * (width
-1) + 3*(2*a
+ b
);
2351 *yextent
= (3*a
+ 2*b
) * (height
-1) + 2*(2*a
+ b
);
2354 static grid
*grid_new_dodecagonal(int width
, int height
, char *desc
)
2360 /* Upper bounds - don't have to be exact */
2361 int max_faces
= 3 * width
* height
;
2362 int max_dots
= 14 * width
* height
;
2366 grid
*g
= grid_empty();
2367 g
->tilesize
= DODEC_TILESIZE
;
2368 g
->faces
= snewn(max_faces
, grid_face
);
2369 g
->dots
= snewn(max_dots
, grid_dot
);
2371 points
= newtree234(grid_point_cmp_fn
);
2373 for (y
= 0; y
< height
; y
++) {
2374 for (x
= 0; x
< width
; x
++) {
2376 /* centre of dodecagon */
2377 int px
= (4*a
+ 2*b
) * x
;
2378 int py
= (3*a
+ 2*b
) * y
;
2383 grid_face_add_new(g
, 12);
2384 d
= grid_get_dot(g
, points
, px
+ ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2385 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 1);
2386 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 2);
2387 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 3);
2388 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 4);
2389 d
= grid_get_dot(g
, points
, px
+ ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2390 d
= grid_get_dot(g
, points
, px
- ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 6);
2391 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 7);
2392 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 8);
2393 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 9);
2394 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 10);
2395 d
= grid_get_dot(g
, points
, px
- ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 11);
2397 /* triangle below dodecagon */
2398 if ((y
< height
- 1 && (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2)))) {
2399 grid_face_add_new(g
, 3);
2400 d
= grid_get_dot(g
, points
, px
+ a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2401 d
= grid_get_dot(g
, points
, px
, py
+ (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2402 d
= grid_get_dot(g
, points
, px
- a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 2);
2405 /* triangle above dodecagon */
2406 if ((y
&& (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2)))) {
2407 grid_face_add_new(g
, 3);
2408 d
= grid_get_dot(g
, points
, px
- a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2409 d
= grid_get_dot(g
, points
, px
, py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2410 d
= grid_get_dot(g
, points
, px
+ a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 2);
2415 freetree234(points
);
2416 assert(g
->num_faces
<= max_faces
);
2417 assert(g
->num_dots
<= max_dots
);
2419 grid_make_consistent(g
);
2423 static void grid_size_greatdodecagonal(int width
, int height
,
2424 int *tilesize
, int *xextent
, int *yextent
)
2429 *tilesize
= DODEC_TILESIZE
;
2430 *xextent
= (6*a
+ 2*b
) * (width
-1) + 2*(2*a
+ b
) + 3*a
+ b
;
2431 *yextent
= (3*a
+ 3*b
) * (height
-1) + 2*(2*a
+ b
);
2434 static grid
*grid_new_greatdodecagonal(int width
, int height
, char *desc
)
2437 /* Vector for side of triangle - ratio is close to sqrt(3) */
2441 /* Upper bounds - don't have to be exact */
2442 int max_faces
= 30 * width
* height
;
2443 int max_dots
= 200 * width
* height
;
2447 grid
*g
= grid_empty();
2448 g
->tilesize
= DODEC_TILESIZE
;
2449 g
->faces
= snewn(max_faces
, grid_face
);
2450 g
->dots
= snewn(max_dots
, grid_dot
);
2452 points
= newtree234(grid_point_cmp_fn
);
2454 for (y
= 0; y
< height
; y
++) {
2455 for (x
= 0; x
< width
; x
++) {
2457 /* centre of dodecagon */
2458 int px
= (6*a
+ 2*b
) * x
;
2459 int py
= (3*a
+ 3*b
) * y
;
2464 grid_face_add_new(g
, 12);
2465 d
= grid_get_dot(g
, points
, px
+ ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2466 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 1);
2467 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 2);
2468 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 3);
2469 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 4);
2470 d
= grid_get_dot(g
, points
, px
+ ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2471 d
= grid_get_dot(g
, points
, px
- ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 6);
2472 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 7);
2473 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 8);
2474 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 9);
2475 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 10);
2476 d
= grid_get_dot(g
, points
, px
- ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 11);
2478 /* hexagon below dodecagon */
2479 if (y
< height
- 1 && (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2))) {
2480 grid_face_add_new(g
, 6);
2481 d
= grid_get_dot(g
, points
, px
+ a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2482 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
+ (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2483 d
= grid_get_dot(g
, points
, px
+ a
, py
+ (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 2);
2484 d
= grid_get_dot(g
, points
, px
- a
, py
+ (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 3);
2485 d
= grid_get_dot(g
, points
, px
- 2*a
, py
+ (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 4);
2486 d
= grid_get_dot(g
, points
, px
- a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2489 /* hexagon above dodecagon */
2490 if (y
&& (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2))) {
2491 grid_face_add_new(g
, 6);
2492 d
= grid_get_dot(g
, points
, px
- a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2493 d
= grid_get_dot(g
, points
, px
- 2*a
, py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2494 d
= grid_get_dot(g
, points
, px
- a
, py
- (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 2);
2495 d
= grid_get_dot(g
, points
, px
+ a
, py
- (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 3);
2496 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 4);
2497 d
= grid_get_dot(g
, points
, px
+ a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2500 /* square on right of dodecagon */
2501 if (x
< width
- 1) {
2502 grid_face_add_new(g
, 4);
2503 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
- a
); grid_face_set_dot(g
, d
, 0);
2504 d
= grid_get_dot(g
, points
, px
+ 4*a
+ b
, py
- a
); grid_face_set_dot(g
, d
, 1);
2505 d
= grid_get_dot(g
, points
, px
+ 4*a
+ b
, py
+ a
); grid_face_set_dot(g
, d
, 2);
2506 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
); grid_face_set_dot(g
, d
, 3);
2509 /* square on top right of dodecagon */
2510 if (y
&& (x
< width
- 1 || !(y
% 2))) {
2511 grid_face_add_new(g
, 4);
2512 d
= grid_get_dot(g
, points
, px
+ ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2513 d
= grid_get_dot(g
, points
, px
+ (2*a
), py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2514 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- ( a
+ 2*b
)); grid_face_set_dot(g
, d
, 2);
2515 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 3);
2518 /* square on top left of dodecagon */
2519 if (y
&& (x
|| (y
% 2))) {
2520 grid_face_add_new(g
, 4);
2521 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 0);
2522 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
- ( a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2523 d
= grid_get_dot(g
, points
, px
- (2*a
), py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 2);
2524 d
= grid_get_dot(g
, points
, px
- ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 3);
2529 freetree234(points
);
2530 assert(g
->num_faces
<= max_faces
);
2531 assert(g
->num_dots
<= max_dots
);
2533 grid_make_consistent(g
);
2537 typedef struct setface_ctx
2539 int xmin
, xmax
, ymin
, ymax
;
2545 static double round_int_nearest_away(double r
)
2547 return (r
> 0.0) ?
floor(r
+ 0.5) : ceil(r
- 0.5);
2550 static int set_faces(penrose_state
*state
, vector
*vs
, int n
, int depth
)
2552 setface_ctx
*sf_ctx
= (setface_ctx
*)state
->ctx
;
2556 if (depth
< state
->max_depth
) return 0;
2557 #ifdef DEBUG_PENROSE
2558 if (n
!= 4) return 0; /* triangles are sent as debugging. */
2561 for (i
= 0; i
< n
; i
++) {
2562 double tx
= v_x(vs
, i
), ty
= v_y(vs
, i
);
2564 xs
[i
] = (int)round_int_nearest_away(tx
);
2565 ys
[i
] = (int)round_int_nearest_away(ty
);
2567 if (xs
[i
] < sf_ctx
->xmin
|| xs
[i
] > sf_ctx
->xmax
) return 0;
2568 if (ys
[i
] < sf_ctx
->ymin
|| ys
[i
] > sf_ctx
->ymax
) return 0;
2571 grid_face_add_new(sf_ctx
->g
, n
);
2572 debug(("penrose: new face l=%f gen=%d...",
2573 penrose_side_length(state
->start_size
, depth
), depth
));
2574 for (i
= 0; i
< n
; i
++) {
2575 grid_dot
*d
= grid_get_dot(sf_ctx
->g
, sf_ctx
->points
,
2577 grid_face_set_dot(sf_ctx
->g
, d
, i
);
2578 debug((" ... dot 0x%x (%d,%d) (was %2.2f,%2.2f)",
2579 d
, d
->x
, d
->y
, v_x(vs
, i
), v_y(vs
, i
)));
2585 #define PENROSE_TILESIZE 100
2587 static void grid_size_penrose(int width
, int height
,
2588 int *tilesize
, int *xextent
, int *yextent
)
2590 int l
= PENROSE_TILESIZE
;
2593 *xextent
= l
* width
;
2594 *yextent
= l
* height
;
2597 static char *grid_new_desc_penrose(grid_type type
, int width
, int height
, random_state
*rs
)
2599 int tilesize
= PENROSE_TILESIZE
, startsz
, depth
, xoff
, yoff
, aoff
;
2600 double outer_radius
;
2603 int which
= (type
== GRID_PENROSE_P2 ? PENROSE_P2
: PENROSE_P3
);
2605 /* We want to produce a random bit of penrose tiling, so we calculate
2606 * a random offset (within the patch that penrose.c calculates for us)
2607 * and an angle (multiple of 36) to rotate the patch. */
2609 penrose_calculate_size(which
, tilesize
, width
, height
,
2610 &outer_radius
, &startsz
, &depth
);
2612 /* Calculate radius of (circumcircle of) patch, subtract from
2613 * radius calculated. */
2614 inner_radius
= (int)(outer_radius
- sqrt(width
*width
+ height
*height
));
2616 /* Pick a random offset (the easy way: choose within outer square,
2617 * discarding while it's outside the circle) */
2619 xoff
= random_upto(rs
, 2*inner_radius
) - inner_radius
;
2620 yoff
= random_upto(rs
, 2*inner_radius
) - inner_radius
;
2621 } while (sqrt(xoff
*xoff
+yoff
*yoff
) > inner_radius
);
2623 aoff
= random_upto(rs
, 360/36) * 36;
2625 debug(("grid_desc: ts %d, %dx%d patch, orad %2.2f irad %d",
2626 tilesize
, width
, height
, outer_radius
, inner_radius
));
2627 debug((" -> xoff %d yoff %d aoff %d", xoff
, yoff
, aoff
));
2629 sprintf(gd
, "G%d,%d,%d", xoff
, yoff
, aoff
);
2634 static char *grid_validate_desc_penrose(grid_type type
, int width
, int height
, char *desc
)
2636 int tilesize
= PENROSE_TILESIZE
, startsz
, depth
, xoff
, yoff
, aoff
, inner_radius
;
2637 double outer_radius
;
2638 int which
= (type
== GRID_PENROSE_P2 ? PENROSE_P2
: PENROSE_P3
);
2641 return "Missing grid description string.";
2643 penrose_calculate_size(which
, tilesize
, width
, height
,
2644 &outer_radius
, &startsz
, &depth
);
2645 inner_radius
= (int)(outer_radius
- sqrt(width
*width
+ height
*height
));
2647 if (sscanf(desc
, "G%d,%d,%d", &xoff
, &yoff
, &aoff
) != 3)
2648 return "Invalid format grid description string.";
2650 if (sqrt(xoff
*xoff
+ yoff
*yoff
) > inner_radius
)
2651 return "Patch offset out of bounds.";
2652 if ((aoff
% 36) != 0 || aoff
< 0 || aoff
>= 360)
2653 return "Angle offset out of bounds.";
2659 * We're asked for a grid of a particular size, and we generate enough
2660 * of the tiling so we can be sure to have enough random grid from which
2664 static grid
*grid_new_penrose(int width
, int height
, int which
, char *desc
)
2666 int max_faces
, max_dots
, tilesize
= PENROSE_TILESIZE
;
2667 int xsz
, ysz
, xoff
, yoff
, aoff
;
2676 penrose_calculate_size(which
, tilesize
, width
, height
,
2677 &rradius
, &ps
.start_size
, &ps
.max_depth
);
2679 debug(("penrose: w%d h%d, tile size %d, start size %d, depth %d",
2680 width
, height
, tilesize
, ps
.start_size
, ps
.max_depth
));
2682 ps
.new_tile
= set_faces
;
2685 max_faces
= (width
*3) * (height
*3); /* somewhat paranoid... */
2686 max_dots
= max_faces
* 4; /* ditto... */
2689 g
->tilesize
= tilesize
;
2690 g
->faces
= snewn(max_faces
, grid_face
);
2691 g
->dots
= snewn(max_dots
, grid_dot
);
2693 points
= newtree234(grid_point_cmp_fn
);
2695 memset(&sf_ctx
, 0, sizeof(sf_ctx
));
2697 sf_ctx
.points
= points
;
2700 if (sscanf(desc
, "G%d,%d,%d", &xoff
, &yoff
, &aoff
) != 3)
2701 assert(!"Invalid grid description.");
2706 xsz
= width
* tilesize
;
2707 ysz
= height
* tilesize
;
2709 sf_ctx
.xmin
= xoff
- xsz
/2;
2710 sf_ctx
.xmax
= xoff
+ xsz
/2;
2711 sf_ctx
.ymin
= yoff
- ysz
/2;
2712 sf_ctx
.ymax
= yoff
+ ysz
/2;
2714 debug(("penrose: centre (%f, %f) xsz %f ysz %f",
2715 0.0, 0.0, xsz
, ysz
));
2716 debug(("penrose: x range (%f --> %f), y range (%f --> %f)",
2717 sf_ctx
.xmin
, sf_ctx
.xmax
, sf_ctx
.ymin
, sf_ctx
.ymax
));
2719 penrose(&ps
, which
, aoff
);
2721 freetree234(points
);
2722 assert(g
->num_faces
<= max_faces
);
2723 assert(g
->num_dots
<= max_dots
);
2725 debug(("penrose: %d faces total (equivalent to %d wide by %d high)",
2726 g
->num_faces
, g
->num_faces
/height
, g
->num_faces
/width
));
2728 grid_trim_vigorously(g
);
2729 grid_make_consistent(g
);
2732 * Centre the grid in its originally promised rectangle.
2734 g
->lowest_x
-= ((sf_ctx
.xmax
- sf_ctx
.xmin
) -
2735 (g
->highest_x
- g
->lowest_x
)) / 2;
2736 g
->highest_x
= g
->lowest_x
+ (sf_ctx
.xmax
- sf_ctx
.xmin
);
2737 g
->lowest_y
-= ((sf_ctx
.ymax
- sf_ctx
.ymin
) -
2738 (g
->highest_y
- g
->lowest_y
)) / 2;
2739 g
->highest_y
= g
->lowest_y
+ (sf_ctx
.ymax
- sf_ctx
.ymin
);
2744 static void grid_size_penrose_p2_kite(int width
, int height
,
2745 int *tilesize
, int *xextent
, int *yextent
)
2747 grid_size_penrose(width
, height
, tilesize
, xextent
, yextent
);
2750 static void grid_size_penrose_p3_thick(int width
, int height
,
2751 int *tilesize
, int *xextent
, int *yextent
)
2753 grid_size_penrose(width
, height
, tilesize
, xextent
, yextent
);
2756 static grid
*grid_new_penrose_p2_kite(int width
, int height
, char *desc
)
2758 return grid_new_penrose(width
, height
, PENROSE_P2
, desc
);
2761 static grid
*grid_new_penrose_p3_thick(int width
, int height
, char *desc
)
2763 return grid_new_penrose(width
, height
, PENROSE_P3
, desc
);
2766 /* ----------- End of grid generators ------------- */
2768 #define FNNEW(upper,lower) &grid_new_ ## lower,
2769 #define FNSZ(upper,lower) &grid_size_ ## lower,
2771 static grid
*(*(grid_news
[]))(int, int, char*) = { GRIDGEN_LIST(FNNEW
) };
2772 static void(*(grid_sizes
[]))(int, int, int*, int*, int*) = { GRIDGEN_LIST(FNSZ
) };
2774 char *grid_new_desc(grid_type type
, int width
, int height
, int dual
, random_state
*rs
)
2776 if (type
!= GRID_PENROSE_P2
&& type
!= GRID_PENROSE_P3
)
2779 return grid_new_desc_penrose(type
, width
, height
, rs
);
2782 char *grid_validate_desc(grid_type type
, int width
, int height
, int dual
, char *desc
)
2784 if (type
!= GRID_PENROSE_P2
&& type
!= GRID_PENROSE_P3
) {
2786 return "Grid description strings not used with this grid type";
2790 return grid_validate_desc_penrose(type
, width
, height
, desc
);
2793 grid
*grid_new(grid_type type
, int width
, int height
, int dual
, char *desc
)
2795 char *err
= grid_validate_desc(type
, width
, height
, dual
, desc
);
2796 if (err
) assert(!"Invalid grid description.");
2800 return grid_news
[type
](width
, height
, desc
);
2807 temp
= grid_news
[type
](width
, height
, desc
);
2808 g
= grid_dual(temp
);
2814 void grid_compute_size(grid_type type
, int width
, int height
,
2815 int *tilesize
, int *xextent
, int *yextent
)
2817 grid_sizes
[type
](width
, height
, tilesize
, xextent
, yextent
);
2820 /* ----------- End of grid helpers ------------- */
2822 /* vim: set shiftwidth=4 tabstop=8: */