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 * Free the dynamically allocated 'dots' pointer lists in faces
458 * we're going to discard.
460 for (i
= 0; i
< g
->num_faces
; i
++)
462 sfree(g
->faces
[i
].dots
);
465 * Go through and compact the arrays.
467 for (i
= 0; i
< g
->num_dots
; i
++)
469 grid_dot
*dnew
= g
->dots
+ dots
[i
], *dold
= g
->dots
+ i
;
470 *dnew
= *dold
; /* structure copy */
472 for (i
= 0; i
< g
->num_faces
; i
++)
474 grid_face
*fnew
= g
->faces
+ faces
[i
], *fold
= g
->faces
+ i
;
475 *fnew
= *fold
; /* structure copy */
476 for (j
= 0; j
< fnew
->order
; j
++) {
478 * Reindex the dots in this face.
480 k
= fnew
->dots
[j
] - g
->dots
;
481 fnew
->dots
[j
] = g
->dots
+ dots
[k
];
484 g
->num_faces
= newfaces
;
485 g
->num_dots
= newdots
;
493 /* Input: grid has its dots and faces initialised:
494 * - dots have (optionally) x and y coordinates, but no edges or faces
495 * (pointers are NULL).
496 * - edges not initialised at all
497 * - faces initialised and know which dots they have (but no edges yet). The
498 * dots around each face are assumed to be clockwise.
500 * Output: grid is complete and valid with all relationships defined.
502 static void grid_make_consistent(grid
*g
)
505 tree234
*incomplete_edges
;
506 grid_edge
*next_new_edge
; /* Where new edge will go into g->edges */
510 /* ====== Stage 1 ======
514 /* We know how many dots and faces there are, so we can find the exact
515 * number of edges from Euler's polyhedral formula: F + V = E + 2 .
516 * We use "-1", not "-2" here, because Euler's formula includes the
517 * infinite face, which we don't count. */
518 g
->num_edges
= g
->num_faces
+ g
->num_dots
- 1;
519 g
->edges
= snewn(g
->num_edges
, grid_edge
);
520 next_new_edge
= g
->edges
;
522 /* Iterate over faces, and over each face's dots, generating edges as we
523 * go. As we find each new edge, we can immediately fill in the edge's
524 * dots, but only one of the edge's faces. Later on in the iteration, we
525 * will find the same edge again (unless it's on the border), but we will
526 * know the other face.
527 * For efficiency, maintain a list of the incomplete edges, sorted by
529 incomplete_edges
= newtree234(grid_edge_bydots_cmpfn
);
530 for (i
= 0; i
< g
->num_faces
; i
++) {
531 grid_face
*f
= g
->faces
+ i
;
533 for (j
= 0; j
< f
->order
; j
++) {
534 grid_edge e
; /* fake edge for searching */
535 grid_edge
*edge_found
;
540 e
.dot2
= f
->dots
[j2
];
541 /* Use del234 instead of find234, because we always want to
542 * remove the edge if found */
543 edge_found
= del234(incomplete_edges
, &e
);
545 /* This edge already added, so fill out missing face.
546 * Edge is already removed from incomplete_edges. */
547 edge_found
->face2
= f
;
549 assert(next_new_edge
- g
->edges
< g
->num_edges
);
550 next_new_edge
->dot1
= e
.dot1
;
551 next_new_edge
->dot2
= e
.dot2
;
552 next_new_edge
->face1
= f
;
553 next_new_edge
->face2
= NULL
; /* potentially infinite face */
554 add234(incomplete_edges
, next_new_edge
);
559 freetree234(incomplete_edges
);
561 /* ====== Stage 2 ======
562 * For each face, build its edge list.
565 /* Allocate space for each edge list. Can do this, because each face's
566 * edge-list is the same size as its dot-list. */
567 for (i
= 0; i
< g
->num_faces
; i
++) {
568 grid_face
*f
= g
->faces
+ i
;
570 f
->edges
= snewn(f
->order
, grid_edge
*);
571 /* Preload with NULLs, to help detect potential bugs. */
572 for (j
= 0; j
< f
->order
; j
++)
576 /* Iterate over each edge, and over both its faces. Add this edge to
577 * the face's edge-list, after finding where it should go in the
579 for (i
= 0; i
< g
->num_edges
; i
++) {
580 grid_edge
*e
= g
->edges
+ i
;
582 for (j
= 0; j
< 2; j
++) {
583 grid_face
*f
= j ? e
->face2
: e
->face1
;
585 if (f
== NULL
) continue;
586 /* Find one of the dots around the face */
587 for (k
= 0; k
< f
->order
; k
++) {
588 if (f
->dots
[k
] == e
->dot1
)
589 break; /* found dot1 */
591 assert(k
!= f
->order
); /* Must find the dot around this face */
593 /* Labelling scheme: as we walk clockwise around the face,
594 * starting at dot0 (f->dots[0]), we hit:
595 * (dot0), edge0, dot1, edge1, dot2,...
605 * Therefore, edgeK joins dotK and dot{K+1}
608 /* Around this face, either the next dot or the previous dot
609 * must be e->dot2. Otherwise the edge is wrong. */
613 if (f
->dots
[k2
] == e
->dot2
) {
614 /* dot1(k) and dot2(k2) go clockwise around this face, so add
615 * this edge at position k (see diagram). */
616 assert(f
->edges
[k
] == NULL
);
620 /* Try previous dot */
624 if (f
->dots
[k2
] == e
->dot2
) {
625 /* dot1(k) and dot2(k2) go anticlockwise around this face. */
626 assert(f
->edges
[k2
] == NULL
);
630 assert(!"Grid broken: bad edge-face relationship");
634 /* ====== Stage 3 ======
635 * For each dot, build its edge-list and face-list.
638 /* We don't know how many edges/faces go around each dot, so we can't
639 * allocate the right space for these lists. Pre-compute the sizes by
640 * iterating over each edge and recording a tally against each dot. */
641 for (i
= 0; i
< g
->num_dots
; i
++) {
642 g
->dots
[i
].order
= 0;
644 for (i
= 0; i
< g
->num_edges
; i
++) {
645 grid_edge
*e
= g
->edges
+ i
;
649 /* Now we have the sizes, pre-allocate the edge and face lists. */
650 for (i
= 0; i
< g
->num_dots
; i
++) {
651 grid_dot
*d
= g
->dots
+ i
;
653 assert(d
->order
>= 2); /* sanity check */
654 d
->edges
= snewn(d
->order
, grid_edge
*);
655 d
->faces
= snewn(d
->order
, grid_face
*);
656 for (j
= 0; j
< d
->order
; j
++) {
661 /* For each dot, need to find a face that touches it, so we can seed
662 * the edge-face-edge-face process around each dot. */
663 for (i
= 0; i
< g
->num_faces
; i
++) {
664 grid_face
*f
= g
->faces
+ i
;
666 for (j
= 0; j
< f
->order
; j
++) {
667 grid_dot
*d
= f
->dots
[j
];
671 /* Each dot now has a face in its first slot. Generate the remaining
672 * faces and edges around the dot, by searching both clockwise and
673 * anticlockwise from the first face. Need to do both directions,
674 * because of the possibility of hitting the infinite face, which
675 * blocks progress. But there's only one such face, so we will
676 * succeed in finding every edge and face this way. */
677 for (i
= 0; i
< g
->num_dots
; i
++) {
678 grid_dot
*d
= g
->dots
+ i
;
679 int current_face1
= 0; /* ascends clockwise */
680 int current_face2
= 0; /* descends anticlockwise */
682 /* Labelling scheme: as we walk clockwise around the dot, starting
683 * at face0 (d->faces[0]), we hit:
684 * (face0), edge0, face1, edge1, face2,...
696 * So, for example, face1 should be joined to edge0 and edge1,
697 * and those edges should appear in an anticlockwise sense around
698 * that face (see diagram). */
700 /* clockwise search */
702 grid_face
*f
= d
->faces
[current_face1
];
706 /* find dot around this face */
707 for (j
= 0; j
< f
->order
; j
++) {
711 assert(j
!= f
->order
); /* must find dot */
713 /* Around f, required edge is anticlockwise from the dot. See
714 * the other labelling scheme higher up, for why we subtract 1
720 d
->edges
[current_face1
] = e
; /* set edge */
722 if (current_face1
== d
->order
)
726 d
->faces
[current_face1
] =
727 (e
->face1
== f
) ? e
->face2
: e
->face1
;
728 if (d
->faces
[current_face1
] == NULL
)
729 break; /* cannot progress beyond infinite face */
732 /* If the clockwise search made it all the way round, don't need to
733 * bother with the anticlockwise search. */
734 if (current_face1
== d
->order
)
735 continue; /* this dot is complete, move on to next dot */
737 /* anticlockwise search */
739 grid_face
*f
= d
->faces
[current_face2
];
743 /* find dot around this face */
744 for (j
= 0; j
< f
->order
; j
++) {
748 assert(j
!= f
->order
); /* must find dot */
750 /* Around f, required edge is clockwise from the dot. */
754 if (current_face2
== -1)
755 current_face2
= d
->order
- 1;
756 d
->edges
[current_face2
] = e
; /* set edge */
759 if (current_face2
== current_face1
)
761 d
->faces
[current_face2
] =
762 (e
->face1
== f
) ? e
->face2
: e
->face1
;
763 /* There's only 1 infinite face, so we must get all the way
764 * to current_face1 before we hit it. */
765 assert(d
->faces
[current_face2
]);
769 /* ====== Stage 4 ======
770 * Compute other grid settings
773 /* Bounding rectangle */
774 for (i
= 0; i
< g
->num_dots
; i
++) {
775 grid_dot
*d
= g
->dots
+ i
;
777 g
->lowest_x
= g
->highest_x
= d
->x
;
778 g
->lowest_y
= g
->highest_y
= d
->y
;
780 g
->lowest_x
= min(g
->lowest_x
, d
->x
);
781 g
->highest_x
= max(g
->highest_x
, d
->x
);
782 g
->lowest_y
= min(g
->lowest_y
, d
->y
);
783 g
->highest_y
= max(g
->highest_y
, d
->y
);
787 grid_debug_derived(g
);
790 /* Helpers for making grid-generation easier. These functions are only
791 * intended for use during grid generation. */
793 /* Comparison function for the (tree234) sorted dot list */
794 static int grid_point_cmp_fn(void *v1
, void *v2
)
799 return p2
->y
- p1
->y
;
801 return p2
->x
- p1
->x
;
803 /* Add a new face to the grid, with its dot list allocated.
804 * Assumes there's enough space allocated for the new face in grid->faces */
805 static void grid_face_add_new(grid
*g
, int face_size
)
808 grid_face
*new_face
= g
->faces
+ g
->num_faces
;
809 new_face
->order
= face_size
;
810 new_face
->dots
= snewn(face_size
, grid_dot
*);
811 for (i
= 0; i
< face_size
; i
++)
812 new_face
->dots
[i
] = NULL
;
813 new_face
->edges
= NULL
;
814 new_face
->has_incentre
= FALSE
;
817 /* Assumes dot list has enough space */
818 static grid_dot
*grid_dot_add_new(grid
*g
, int x
, int y
)
820 grid_dot
*new_dot
= g
->dots
+ g
->num_dots
;
822 new_dot
->edges
= NULL
;
823 new_dot
->faces
= NULL
;
829 /* Retrieve a dot with these (x,y) coordinates. Either return an existing dot
830 * in the dot_list, or add a new dot to the grid (and the dot_list) and
832 * Assumes g->dots has enough capacity allocated */
833 static grid_dot
*grid_get_dot(grid
*g
, tree234
*dot_list
, int x
, int y
)
842 ret
= find234(dot_list
, &test
, NULL
);
846 ret
= grid_dot_add_new(g
, x
, y
);
847 add234(dot_list
, ret
);
851 /* Sets the last face of the grid to include this dot, at this position
852 * around the face. Assumes num_faces is at least 1 (a new face has
853 * previously been added, with the required number of dots allocated) */
854 static void grid_face_set_dot(grid
*g
, grid_dot
*d
, int position
)
856 grid_face
*last_face
= g
->faces
+ g
->num_faces
- 1;
857 last_face
->dots
[position
] = d
;
861 * Helper routines for grid_find_incentre.
863 static int solve_2x2_matrix(double mx
[4], double vin
[2], double vout
[2])
867 det
= (mx
[0]*mx
[3] - mx
[1]*mx
[2]);
871 inv
[0] = mx
[3] / det
;
872 inv
[1] = -mx
[1] / det
;
873 inv
[2] = -mx
[2] / det
;
874 inv
[3] = mx
[0] / det
;
876 vout
[0] = inv
[0]*vin
[0] + inv
[1]*vin
[1];
877 vout
[1] = inv
[2]*vin
[0] + inv
[3]*vin
[1];
881 static int solve_3x3_matrix(double mx
[9], double vin
[3], double vout
[3])
886 det
= (mx
[0]*mx
[4]*mx
[8] + mx
[1]*mx
[5]*mx
[6] + mx
[2]*mx
[3]*mx
[7] -
887 mx
[0]*mx
[5]*mx
[7] - mx
[1]*mx
[3]*mx
[8] - mx
[2]*mx
[4]*mx
[6]);
891 inv
[0] = (mx
[4]*mx
[8] - mx
[5]*mx
[7]) / det
;
892 inv
[1] = (mx
[2]*mx
[7] - mx
[1]*mx
[8]) / det
;
893 inv
[2] = (mx
[1]*mx
[5] - mx
[2]*mx
[4]) / det
;
894 inv
[3] = (mx
[5]*mx
[6] - mx
[3]*mx
[8]) / det
;
895 inv
[4] = (mx
[0]*mx
[8] - mx
[2]*mx
[6]) / det
;
896 inv
[5] = (mx
[2]*mx
[3] - mx
[0]*mx
[5]) / det
;
897 inv
[6] = (mx
[3]*mx
[7] - mx
[4]*mx
[6]) / det
;
898 inv
[7] = (mx
[1]*mx
[6] - mx
[0]*mx
[7]) / det
;
899 inv
[8] = (mx
[0]*mx
[4] - mx
[1]*mx
[3]) / det
;
901 vout
[0] = inv
[0]*vin
[0] + inv
[1]*vin
[1] + inv
[2]*vin
[2];
902 vout
[1] = inv
[3]*vin
[0] + inv
[4]*vin
[1] + inv
[5]*vin
[2];
903 vout
[2] = inv
[6]*vin
[0] + inv
[7]*vin
[1] + inv
[8]*vin
[2];
908 void grid_find_incentre(grid_face
*f
)
910 double xbest
, ybest
, bestdist
;
912 grid_dot
*edgedot1
[3], *edgedot2
[3];
920 * Find the point in the polygon with the maximum distance to any
923 * Such a point must exist which is in contact with at least three
924 * edges and/or vertices. (Proof: if it's only in contact with two
925 * edges and/or vertices, it can't even be at a _local_ maximum -
926 * any such circle can always be expanded in some direction.) So
927 * we iterate through all 3-subsets of the combined set of edges
928 * and vertices; for each subset we generate one or two candidate
929 * points that might be the incentre, and then we vet each one to
930 * see if it's inside the polygon and what its maximum radius is.
932 * (There's one case which this algorithm will get noticeably
933 * wrong, and that's when a continuum of equally good answers
934 * exists due to parallel edges. Consider a long thin rectangle,
935 * for instance, or a parallelogram. This algorithm will pick a
936 * point near one end, and choose the end arbitrarily; obviously a
937 * nicer point to choose would be in the centre. To fix this I
938 * would have to introduce a special-case system which detected
939 * parallel edges in advance, set aside all candidate points
940 * generated using both edges in a parallel pair, and generated
941 * some additional candidate points half way between them. Also,
942 * of course, I'd have to cope with rounding error making such a
943 * point look worse than one of its endpoints. So I haven't done
944 * this for the moment, and will cross it if necessary when I come
947 * We don't actually iterate literally over _edges_, in the sense
948 * of grid_edge structures. Instead, we fill in edgedot1[] and
949 * edgedot2[] with a pair of dots adjacent in the face's list of
950 * vertices. This ensures that we get the edges in consistent
951 * orientation, which we could not do from the grid structure
952 * alone. (A moment's consideration of an order-3 vertex should
953 * make it clear that if a notional arrow was written on each
954 * edge, _at least one_ of the three faces bordering that vertex
955 * would have to have the two arrows tip-to-tip or tail-to-tail
956 * rather than tip-to-tail.)
962 for (i
= 0; i
+2 < 2*f
->order
; i
++) {
964 edgedot1
[nedges
] = f
->dots
[i
];
965 edgedot2
[nedges
++] = f
->dots
[(i
+1)%f
->order
];
967 dots
[ndots
++] = f
->dots
[i
- f
->order
];
969 for (j
= i
+1; j
+1 < 2*f
->order
; j
++) {
971 edgedot1
[nedges
] = f
->dots
[j
];
972 edgedot2
[nedges
++] = f
->dots
[(j
+1)%f
->order
];
974 dots
[ndots
++] = f
->dots
[j
- f
->order
];
976 for (k
= j
+1; k
< 2*f
->order
; k
++) {
977 double cx
[2], cy
[2]; /* candidate positions */
978 int cn
= 0; /* number of candidates */
981 edgedot1
[nedges
] = f
->dots
[k
];
982 edgedot2
[nedges
++] = f
->dots
[(k
+1)%f
->order
];
984 dots
[ndots
++] = f
->dots
[k
- f
->order
];
987 * Find a point, or pair of points, equidistant from
988 * all the specified edges and/or vertices.
992 * Three edges. This is a linear matrix equation:
993 * each row of the matrix represents the fact that
994 * the point (x,y) we seek is at distance r from
995 * that edge, and we solve three of those
996 * simultaneously to obtain x,y,r. (We ignore r.)
998 double matrix
[9], vector
[3], vector2
[3];
1001 for (m
= 0; m
< 3; m
++) {
1002 int x1
= edgedot1
[m
]->x
, x2
= edgedot2
[m
]->x
;
1003 int y1
= edgedot1
[m
]->y
, y2
= edgedot2
[m
]->y
;
1004 int dx
= x2
-x1
, dy
= y2
-y1
;
1007 * ((x,y) - (x1,y1)) . (dy,-dx) = r |(dx,dy)|
1009 * => x dy - y dx - r |(dx,dy)| = (x1 dy - y1 dx)
1012 matrix
[3*m
+1] = -dx
;
1013 matrix
[3*m
+2] = -sqrt((double)dx
*dx
+(double)dy
*dy
);
1014 vector
[m
] = (double)x1
*dy
- (double)y1
*dx
;
1017 if (solve_3x3_matrix(matrix
, vector
, vector2
)) {
1018 cx
[cn
] = vector2
[0];
1019 cy
[cn
] = vector2
[1];
1022 } else if (nedges
== 2) {
1024 * Two edges and a dot. This will end up in a
1025 * quadratic equation.
1027 * First, look at the two edges. Having our point
1028 * be some distance r from both of them gives rise
1029 * to a pair of linear equations in x,y,r of the
1032 * (x-x1) dy - (y-y1) dx = r sqrt(dx^2+dy^2)
1034 * We eliminate r between those equations to give
1035 * us a single linear equation in x,y describing
1036 * the locus of points equidistant from both lines
1037 * - i.e. the angle bisector.
1039 * We then choose one of x,y to be a parameter t,
1040 * and derive linear formulae for x,y,r in terms
1041 * of t. This enables us to write down the
1042 * circular equation (x-xd)^2+(y-yd)^2=r^2 as a
1043 * quadratic in t; solving that and substituting
1044 * in for x,y gives us two candidate points.
1046 double eqs
[2][4]; /* a,b,c,d : ax+by+cr=d */
1047 double eq
[3]; /* a,b,c: ax+by=c */
1048 double xt
[2], yt
[2], rt
[2]; /* a,b: {x,y,r}=at+b */
1049 double q
[3]; /* a,b,c: at^2+bt+c=0 */
1052 /* Find equations of the two input lines. */
1053 for (m
= 0; m
< 2; m
++) {
1054 int x1
= edgedot1
[m
]->x
, x2
= edgedot2
[m
]->x
;
1055 int y1
= edgedot1
[m
]->y
, y2
= edgedot2
[m
]->y
;
1056 int dx
= x2
-x1
, dy
= y2
-y1
;
1060 eqs
[m
][2] = -sqrt(dx
*dx
+dy
*dy
);
1061 eqs
[m
][3] = x1
*dy
- y1
*dx
;
1064 /* Derive the angle bisector by eliminating r. */
1065 eq
[0] = eqs
[0][0]*eqs
[1][2] - eqs
[1][0]*eqs
[0][2];
1066 eq
[1] = eqs
[0][1]*eqs
[1][2] - eqs
[1][1]*eqs
[0][2];
1067 eq
[2] = eqs
[0][3]*eqs
[1][2] - eqs
[1][3]*eqs
[0][2];
1069 /* Parametrise x and y in terms of some t. */
1070 if (abs(eq
[0]) < abs(eq
[1])) {
1071 /* Parameter is x. */
1072 xt
[0] = 1; xt
[1] = 0;
1073 yt
[0] = -eq
[0]/eq
[1]; yt
[1] = eq
[2]/eq
[1];
1075 /* Parameter is y. */
1076 yt
[0] = 1; yt
[1] = 0;
1077 xt
[0] = -eq
[1]/eq
[0]; xt
[1] = eq
[2]/eq
[0];
1080 /* Find a linear representation of r using eqs[0]. */
1081 rt
[0] = -(eqs
[0][0]*xt
[0] + eqs
[0][1]*yt
[0])/eqs
[0][2];
1082 rt
[1] = (eqs
[0][3] - eqs
[0][0]*xt
[1] -
1083 eqs
[0][1]*yt
[1])/eqs
[0][2];
1085 /* Construct the quadratic equation. */
1086 q
[0] = -rt
[0]*rt
[0];
1087 q
[1] = -2*rt
[0]*rt
[1];
1088 q
[2] = -rt
[1]*rt
[1];
1089 q
[0] += xt
[0]*xt
[0];
1090 q
[1] += 2*xt
[0]*(xt
[1]-dots
[0]->x
);
1091 q
[2] += (xt
[1]-dots
[0]->x
)*(xt
[1]-dots
[0]->x
);
1092 q
[0] += yt
[0]*yt
[0];
1093 q
[1] += 2*yt
[0]*(yt
[1]-dots
[0]->y
);
1094 q
[2] += (yt
[1]-dots
[0]->y
)*(yt
[1]-dots
[0]->y
);
1097 disc
= q
[1]*q
[1] - 4*q
[0]*q
[2];
1103 t
= (-q
[1] + disc
) / (2*q
[0]);
1104 cx
[cn
] = xt
[0]*t
+ xt
[1];
1105 cy
[cn
] = yt
[0]*t
+ yt
[1];
1108 t
= (-q
[1] - disc
) / (2*q
[0]);
1109 cx
[cn
] = xt
[0]*t
+ xt
[1];
1110 cy
[cn
] = yt
[0]*t
+ yt
[1];
1113 } else if (nedges
== 1) {
1115 * Two dots and an edge. This one's another
1116 * quadratic equation.
1118 * The point we want must lie on the perpendicular
1119 * bisector of the two dots; that much is obvious.
1120 * So we can construct a parametrisation of that
1121 * bisecting line, giving linear formulae for x,y
1122 * in terms of t. We can also express the distance
1123 * from the edge as such a linear formula.
1125 * Then we set that equal to the radius of the
1126 * circle passing through the two points, which is
1127 * a Pythagoras exercise; that gives rise to a
1128 * quadratic in t, which we solve.
1130 double xt
[2], yt
[2], rt
[2]; /* a,b: {x,y,r}=at+b */
1131 double q
[3]; /* a,b,c: at^2+bt+c=0 */
1135 /* Find parametric formulae for x,y. */
1137 int x1
= dots
[0]->x
, x2
= dots
[1]->x
;
1138 int y1
= dots
[0]->y
, y2
= dots
[1]->y
;
1139 int dx
= x2
-x1
, dy
= y2
-y1
;
1140 double d
= sqrt((double)dx
*dx
+ (double)dy
*dy
);
1142 xt
[1] = (x1
+x2
)/2.0;
1143 yt
[1] = (y1
+y2
)/2.0;
1144 /* It's convenient if we have t at standard scale. */
1148 /* Also note down half the separation between
1149 * the dots, for use in computing the circle radius. */
1153 /* Find a parametric formula for r. */
1155 int x1
= edgedot1
[0]->x
, x2
= edgedot2
[0]->x
;
1156 int y1
= edgedot1
[0]->y
, y2
= edgedot2
[0]->y
;
1157 int dx
= x2
-x1
, dy
= y2
-y1
;
1158 double d
= sqrt((double)dx
*dx
+ (double)dy
*dy
);
1159 rt
[0] = (xt
[0]*dy
- yt
[0]*dx
) / d
;
1160 rt
[1] = ((xt
[1]-x1
)*dy
- (yt
[1]-y1
)*dx
) / d
;
1163 /* Construct the quadratic equation. */
1165 q
[1] = 2*rt
[0]*rt
[1];
1168 q
[2] -= halfsep
*halfsep
;
1171 disc
= q
[1]*q
[1] - 4*q
[0]*q
[2];
1177 t
= (-q
[1] + disc
) / (2*q
[0]);
1178 cx
[cn
] = xt
[0]*t
+ xt
[1];
1179 cy
[cn
] = yt
[0]*t
+ yt
[1];
1182 t
= (-q
[1] - disc
) / (2*q
[0]);
1183 cx
[cn
] = xt
[0]*t
+ xt
[1];
1184 cy
[cn
] = yt
[0]*t
+ yt
[1];
1187 } else if (nedges
== 0) {
1189 * Three dots. This is another linear matrix
1190 * equation, this time with each row of the matrix
1191 * representing the perpendicular bisector between
1192 * two of the points. Of course we only need two
1193 * such lines to find their intersection, so we
1194 * need only solve a 2x2 matrix equation.
1197 double matrix
[4], vector
[2], vector2
[2];
1200 for (m
= 0; m
< 2; m
++) {
1201 int x1
= dots
[m
]->x
, x2
= dots
[m
+1]->x
;
1202 int y1
= dots
[m
]->y
, y2
= dots
[m
+1]->y
;
1203 int dx
= x2
-x1
, dy
= y2
-y1
;
1206 * ((x,y) - (x1,y1)) . (dx,dy) = 1/2 |(dx,dy)|^2
1208 * => 2x dx + 2y dy = dx^2+dy^2 + (2 x1 dx + 2 y1 dy)
1210 matrix
[2*m
+0] = 2*dx
;
1211 matrix
[2*m
+1] = 2*dy
;
1212 vector
[m
] = ((double)dx
*dx
+ (double)dy
*dy
+
1213 2.0*x1
*dx
+ 2.0*y1
*dy
);
1216 if (solve_2x2_matrix(matrix
, vector
, vector2
)) {
1217 cx
[cn
] = vector2
[0];
1218 cy
[cn
] = vector2
[1];
1224 * Now go through our candidate points and see if any
1225 * of them are better than what we've got so far.
1227 for (m
= 0; m
< cn
; m
++) {
1228 double x
= cx
[m
], y
= cy
[m
];
1231 * First, disqualify the point if it's not inside
1232 * the polygon, which we work out by counting the
1233 * edges to the right of the point. (For
1234 * tiebreaking purposes when edges start or end on
1235 * our y-coordinate or go right through it, we
1236 * consider our point to be offset by a small
1237 * _positive_ epsilon in both the x- and
1241 for (e
= 0; e
< f
->order
; e
++) {
1242 int xs
= f
->edges
[e
]->dot1
->x
;
1243 int xe
= f
->edges
[e
]->dot2
->x
;
1244 int ys
= f
->edges
[e
]->dot1
->y
;
1245 int ye
= f
->edges
[e
]->dot2
->y
;
1246 if ((y
>= ys
&& y
< ye
) || (y
>= ye
&& y
< ys
)) {
1248 * The line goes past our y-position. Now we need
1249 * to know if its x-coordinate when it does so is
1252 * The x-coordinate in question is mathematically
1253 * (y - ys) * (xe - xs) / (ye - ys), and we want
1254 * to know whether (x - xs) >= that. Of course we
1255 * avoid the division, so we can work in integers;
1256 * to do this we must multiply both sides of the
1257 * inequality by ye - ys, which means we must
1258 * first check that's not negative.
1260 int num
= xe
- xs
, denom
= ye
- ys
;
1265 if ((x
- xs
) * denom
>= (y
- ys
) * num
)
1271 double mindist
= HUGE_VAL
;
1275 * This point is inside the polygon, so now we check
1276 * its minimum distance to every edge and corner.
1277 * First the corners ...
1279 for (d
= 0; d
< f
->order
; d
++) {
1280 int xp
= f
->dots
[d
]->x
;
1281 int yp
= f
->dots
[d
]->y
;
1282 double dx
= x
- xp
, dy
= y
- yp
;
1283 double dist
= dx
*dx
+ dy
*dy
;
1289 * ... and now also check the perpendicular distance
1290 * to every edge, if the perpendicular lies between
1291 * the edge's endpoints.
1293 for (e
= 0; e
< f
->order
; e
++) {
1294 int xs
= f
->edges
[e
]->dot1
->x
;
1295 int xe
= f
->edges
[e
]->dot2
->x
;
1296 int ys
= f
->edges
[e
]->dot1
->y
;
1297 int ye
= f
->edges
[e
]->dot2
->y
;
1300 * If s and e are our endpoints, and p our
1301 * candidate circle centre, the foot of a
1302 * perpendicular from p to the line se lies
1303 * between s and e if and only if (p-s).(e-s) lies
1304 * strictly between 0 and (e-s).(e-s).
1306 int edx
= xe
- xs
, edy
= ye
- ys
;
1307 double pdx
= x
- xs
, pdy
= y
- ys
;
1308 double pde
= pdx
* edx
+ pdy
* edy
;
1309 long ede
= (long)edx
* edx
+ (long)edy
* edy
;
1310 if (0 < pde
&& pde
< ede
) {
1312 * Yes, the nearest point on this edge is
1313 * closer than either endpoint, so we must
1314 * take it into account by measuring the
1315 * perpendicular distance to the edge and
1316 * checking its square against mindist.
1319 double pdre
= pdx
* edy
- pdy
* edx
;
1320 double sqlen
= pdre
* pdre
/ ede
;
1322 if (mindist
> sqlen
)
1328 * Right. Now we know the biggest circle around this
1329 * point, so we can check it against bestdist.
1331 if (bestdist
< mindist
) {
1355 assert(bestdist
> 0);
1357 f
->has_incentre
= TRUE
;
1358 f
->ix
= xbest
+ 0.5; /* round to nearest */
1359 f
->iy
= ybest
+ 0.5;
1362 /* ------ Generate various types of grid ------ */
1364 /* General method is to generate faces, by calculating their dot coordinates.
1365 * As new faces are added, we keep track of all the dots so we can tell when
1366 * a new face reuses an existing dot. For example, two squares touching at an
1367 * edge would generate six unique dots: four dots from the first face, then
1368 * two additional dots for the second face, because we detect the other two
1369 * dots have already been taken up. This list is stored in a tree234
1370 * called "points". No extra memory-allocation needed here - we store the
1371 * actual grid_dot* pointers, which all point into the g->dots list.
1372 * For this reason, we have to calculate coordinates in such a way as to
1373 * eliminate any rounding errors, so we can detect when a dot on one
1374 * face precisely lands on a dot of a different face. No floating-point
1378 #define SQUARE_TILESIZE 20
1380 void grid_size_square(int width
, int height
,
1381 int *tilesize
, int *xextent
, int *yextent
)
1383 int a
= SQUARE_TILESIZE
;
1386 *xextent
= width
* a
;
1387 *yextent
= height
* a
;
1390 grid
*grid_new_square(int width
, int height
, char *desc
)
1394 int a
= SQUARE_TILESIZE
;
1396 /* Upper bounds - don't have to be exact */
1397 int max_faces
= width
* height
;
1398 int max_dots
= (width
+ 1) * (height
+ 1);
1402 grid
*g
= grid_empty();
1404 g
->faces
= snewn(max_faces
, grid_face
);
1405 g
->dots
= snewn(max_dots
, grid_dot
);
1407 points
= newtree234(grid_point_cmp_fn
);
1409 /* generate square faces */
1410 for (y
= 0; y
< height
; y
++) {
1411 for (x
= 0; x
< width
; x
++) {
1417 grid_face_add_new(g
, 4);
1418 d
= grid_get_dot(g
, points
, px
, py
);
1419 grid_face_set_dot(g
, d
, 0);
1420 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1421 grid_face_set_dot(g
, d
, 1);
1422 d
= grid_get_dot(g
, points
, px
+ a
, py
+ a
);
1423 grid_face_set_dot(g
, d
, 2);
1424 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1425 grid_face_set_dot(g
, d
, 3);
1429 freetree234(points
);
1430 assert(g
->num_faces
<= max_faces
);
1431 assert(g
->num_dots
<= max_dots
);
1433 grid_make_consistent(g
);
1437 #define HONEY_TILESIZE 45
1438 /* Vector for side of hexagon - ratio is close to sqrt(3) */
1442 void grid_size_honeycomb(int width
, int height
,
1443 int *tilesize
, int *xextent
, int *yextent
)
1448 *tilesize
= HONEY_TILESIZE
;
1449 *xextent
= (3 * a
* (width
-1)) + 4*a
;
1450 *yextent
= (2 * b
* (height
-1)) + 3*b
;
1453 grid
*grid_new_honeycomb(int width
, int height
, char *desc
)
1459 /* Upper bounds - don't have to be exact */
1460 int max_faces
= width
* height
;
1461 int max_dots
= 2 * (width
+ 1) * (height
+ 1);
1465 grid
*g
= grid_empty();
1466 g
->tilesize
= HONEY_TILESIZE
;
1467 g
->faces
= snewn(max_faces
, grid_face
);
1468 g
->dots
= snewn(max_dots
, grid_dot
);
1470 points
= newtree234(grid_point_cmp_fn
);
1472 /* generate hexagonal faces */
1473 for (y
= 0; y
< height
; y
++) {
1474 for (x
= 0; x
< width
; x
++) {
1481 grid_face_add_new(g
, 6);
1483 d
= grid_get_dot(g
, points
, cx
- a
, cy
- b
);
1484 grid_face_set_dot(g
, d
, 0);
1485 d
= grid_get_dot(g
, points
, cx
+ a
, cy
- b
);
1486 grid_face_set_dot(g
, d
, 1);
1487 d
= grid_get_dot(g
, points
, cx
+ 2*a
, cy
);
1488 grid_face_set_dot(g
, d
, 2);
1489 d
= grid_get_dot(g
, points
, cx
+ a
, cy
+ b
);
1490 grid_face_set_dot(g
, d
, 3);
1491 d
= grid_get_dot(g
, points
, cx
- a
, cy
+ b
);
1492 grid_face_set_dot(g
, d
, 4);
1493 d
= grid_get_dot(g
, points
, cx
- 2*a
, cy
);
1494 grid_face_set_dot(g
, d
, 5);
1498 freetree234(points
);
1499 assert(g
->num_faces
<= max_faces
);
1500 assert(g
->num_dots
<= max_dots
);
1502 grid_make_consistent(g
);
1506 #define TRIANGLE_TILESIZE 18
1507 /* Vector for side of triangle - ratio is close to sqrt(3) */
1508 #define TRIANGLE_VEC_X 15
1509 #define TRIANGLE_VEC_Y 26
1511 void grid_size_triangular(int width
, int height
,
1512 int *tilesize
, int *xextent
, int *yextent
)
1514 int vec_x
= TRIANGLE_VEC_X
;
1515 int vec_y
= TRIANGLE_VEC_Y
;
1517 *tilesize
= TRIANGLE_TILESIZE
;
1518 *xextent
= width
* 2 * vec_x
+ vec_x
;
1519 *yextent
= height
* vec_y
;
1522 /* Doesn't use the previous method of generation, it pre-dates it!
1523 * A triangular grid is just about simple enough to do by "brute force" */
1524 grid
*grid_new_triangular(int width
, int height
, char *desc
)
1528 /* Vector for side of triangle - ratio is close to sqrt(3) */
1529 int vec_x
= TRIANGLE_VEC_X
;
1530 int vec_y
= TRIANGLE_VEC_Y
;
1534 /* convenient alias */
1537 grid
*g
= grid_empty();
1538 g
->tilesize
= TRIANGLE_TILESIZE
;
1540 g
->num_faces
= width
* height
* 2;
1541 g
->num_dots
= (width
+ 1) * (height
+ 1);
1542 g
->faces
= snewn(g
->num_faces
, grid_face
);
1543 g
->dots
= snewn(g
->num_dots
, grid_dot
);
1547 for (y
= 0; y
<= height
; y
++) {
1548 for (x
= 0; x
<= width
; x
++) {
1549 grid_dot
*d
= g
->dots
+ index
;
1550 /* odd rows are offset to the right */
1554 d
->x
= x
* 2 * vec_x
+ ((y
% 2) ? vec_x
: 0);
1560 /* generate faces */
1562 for (y
= 0; y
< height
; y
++) {
1563 for (x
= 0; x
< width
; x
++) {
1564 /* initialise two faces for this (x,y) */
1565 grid_face
*f1
= g
->faces
+ index
;
1566 grid_face
*f2
= f1
+ 1;
1569 f1
->dots
= snewn(f1
->order
, grid_dot
*);
1570 f1
->has_incentre
= FALSE
;
1573 f2
->dots
= snewn(f2
->order
, grid_dot
*);
1574 f2
->has_incentre
= FALSE
;
1576 /* face descriptions depend on whether the row-number is
1579 f1
->dots
[0] = g
->dots
+ y
* w
+ x
;
1580 f1
->dots
[1] = g
->dots
+ (y
+ 1) * w
+ x
+ 1;
1581 f1
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
;
1582 f2
->dots
[0] = g
->dots
+ y
* w
+ x
;
1583 f2
->dots
[1] = g
->dots
+ y
* w
+ x
+ 1;
1584 f2
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
+ 1;
1586 f1
->dots
[0] = g
->dots
+ y
* w
+ x
;
1587 f1
->dots
[1] = g
->dots
+ y
* w
+ x
+ 1;
1588 f1
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
;
1589 f2
->dots
[0] = g
->dots
+ y
* w
+ x
+ 1;
1590 f2
->dots
[1] = g
->dots
+ (y
+ 1) * w
+ x
+ 1;
1591 f2
->dots
[2] = g
->dots
+ (y
+ 1) * w
+ x
;
1597 grid_make_consistent(g
);
1601 #define SNUBSQUARE_TILESIZE 18
1602 /* Vector for side of triangle - ratio is close to sqrt(3) */
1603 #define SNUBSQUARE_A 15
1604 #define SNUBSQUARE_B 26
1606 void grid_size_snubsquare(int width
, int height
,
1607 int *tilesize
, int *xextent
, int *yextent
)
1609 int a
= SNUBSQUARE_A
;
1610 int b
= SNUBSQUARE_B
;
1612 *tilesize
= SNUBSQUARE_TILESIZE
;
1613 *xextent
= (a
+b
) * (width
-1) + a
+ b
;
1614 *yextent
= (a
+b
) * (height
-1) + a
+ b
;
1617 grid
*grid_new_snubsquare(int width
, int height
, char *desc
)
1620 int a
= SNUBSQUARE_A
;
1621 int b
= SNUBSQUARE_B
;
1623 /* Upper bounds - don't have to be exact */
1624 int max_faces
= 3 * width
* height
;
1625 int max_dots
= 2 * (width
+ 1) * (height
+ 1);
1629 grid
*g
= grid_empty();
1630 g
->tilesize
= SNUBSQUARE_TILESIZE
;
1631 g
->faces
= snewn(max_faces
, grid_face
);
1632 g
->dots
= snewn(max_dots
, grid_dot
);
1634 points
= newtree234(grid_point_cmp_fn
);
1636 for (y
= 0; y
< height
; y
++) {
1637 for (x
= 0; x
< width
; x
++) {
1640 int px
= (a
+ b
) * x
;
1641 int py
= (a
+ b
) * y
;
1643 /* generate square faces */
1644 grid_face_add_new(g
, 4);
1646 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1647 grid_face_set_dot(g
, d
, 0);
1648 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
);
1649 grid_face_set_dot(g
, d
, 1);
1650 d
= grid_get_dot(g
, points
, px
+ b
, py
+ a
+ b
);
1651 grid_face_set_dot(g
, d
, 2);
1652 d
= grid_get_dot(g
, points
, px
, py
+ b
);
1653 grid_face_set_dot(g
, d
, 3);
1655 d
= grid_get_dot(g
, points
, px
+ b
, py
);
1656 grid_face_set_dot(g
, d
, 0);
1657 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ b
);
1658 grid_face_set_dot(g
, d
, 1);
1659 d
= grid_get_dot(g
, points
, px
+ a
, py
+ a
+ b
);
1660 grid_face_set_dot(g
, d
, 2);
1661 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1662 grid_face_set_dot(g
, d
, 3);
1665 /* generate up/down triangles */
1667 grid_face_add_new(g
, 3);
1669 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1670 grid_face_set_dot(g
, d
, 0);
1671 d
= grid_get_dot(g
, points
, px
, py
+ b
);
1672 grid_face_set_dot(g
, d
, 1);
1673 d
= grid_get_dot(g
, points
, px
- a
, py
);
1674 grid_face_set_dot(g
, d
, 2);
1676 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1677 grid_face_set_dot(g
, d
, 0);
1678 d
= grid_get_dot(g
, points
, px
+ a
, py
+ a
+ b
);
1679 grid_face_set_dot(g
, d
, 1);
1680 d
= grid_get_dot(g
, points
, px
- a
, py
+ a
+ b
);
1681 grid_face_set_dot(g
, d
, 2);
1685 /* generate left/right triangles */
1687 grid_face_add_new(g
, 3);
1689 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1690 grid_face_set_dot(g
, d
, 0);
1691 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
- a
);
1692 grid_face_set_dot(g
, d
, 1);
1693 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
);
1694 grid_face_set_dot(g
, d
, 2);
1696 d
= grid_get_dot(g
, points
, px
, py
- a
);
1697 grid_face_set_dot(g
, d
, 0);
1698 d
= grid_get_dot(g
, points
, px
+ b
, py
);
1699 grid_face_set_dot(g
, d
, 1);
1700 d
= grid_get_dot(g
, points
, px
, py
+ a
);
1701 grid_face_set_dot(g
, d
, 2);
1707 freetree234(points
);
1708 assert(g
->num_faces
<= max_faces
);
1709 assert(g
->num_dots
<= max_dots
);
1711 grid_make_consistent(g
);
1715 #define CAIRO_TILESIZE 40
1716 /* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */
1720 void grid_size_cairo(int width
, int height
,
1721 int *tilesize
, int *xextent
, int *yextent
)
1723 int b
= CAIRO_B
; /* a unused in determining grid size. */
1725 *tilesize
= CAIRO_TILESIZE
;
1726 *xextent
= 2*b
*(width
-1) + 2*b
;
1727 *yextent
= 2*b
*(height
-1) + 2*b
;
1730 grid
*grid_new_cairo(int width
, int height
, char *desc
)
1736 /* Upper bounds - don't have to be exact */
1737 int max_faces
= 2 * width
* height
;
1738 int max_dots
= 3 * (width
+ 1) * (height
+ 1);
1742 grid
*g
= grid_empty();
1743 g
->tilesize
= CAIRO_TILESIZE
;
1744 g
->faces
= snewn(max_faces
, grid_face
);
1745 g
->dots
= snewn(max_dots
, grid_dot
);
1747 points
= newtree234(grid_point_cmp_fn
);
1749 for (y
= 0; y
< height
; y
++) {
1750 for (x
= 0; x
< width
; x
++) {
1756 /* horizontal pentagons */
1758 grid_face_add_new(g
, 5);
1760 d
= grid_get_dot(g
, points
, px
+ a
, py
- b
);
1761 grid_face_set_dot(g
, d
, 0);
1762 d
= grid_get_dot(g
, points
, px
+ 2*b
- a
, py
- b
);
1763 grid_face_set_dot(g
, d
, 1);
1764 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
1765 grid_face_set_dot(g
, d
, 2);
1766 d
= grid_get_dot(g
, points
, px
+ b
, py
+ a
);
1767 grid_face_set_dot(g
, d
, 3);
1768 d
= grid_get_dot(g
, points
, px
, py
);
1769 grid_face_set_dot(g
, d
, 4);
1771 d
= grid_get_dot(g
, points
, px
, py
);
1772 grid_face_set_dot(g
, d
, 0);
1773 d
= grid_get_dot(g
, points
, px
+ b
, py
- a
);
1774 grid_face_set_dot(g
, d
, 1);
1775 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
1776 grid_face_set_dot(g
, d
, 2);
1777 d
= grid_get_dot(g
, points
, px
+ 2*b
- a
, py
+ b
);
1778 grid_face_set_dot(g
, d
, 3);
1779 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1780 grid_face_set_dot(g
, d
, 4);
1783 /* vertical pentagons */
1785 grid_face_add_new(g
, 5);
1787 d
= grid_get_dot(g
, points
, px
, py
);
1788 grid_face_set_dot(g
, d
, 0);
1789 d
= grid_get_dot(g
, points
, px
+ b
, py
+ a
);
1790 grid_face_set_dot(g
, d
, 1);
1791 d
= grid_get_dot(g
, points
, px
+ b
, py
+ 2*b
- a
);
1792 grid_face_set_dot(g
, d
, 2);
1793 d
= grid_get_dot(g
, points
, px
, py
+ 2*b
);
1794 grid_face_set_dot(g
, d
, 3);
1795 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1796 grid_face_set_dot(g
, d
, 4);
1798 d
= grid_get_dot(g
, points
, px
, py
);
1799 grid_face_set_dot(g
, d
, 0);
1800 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1801 grid_face_set_dot(g
, d
, 1);
1802 d
= grid_get_dot(g
, points
, px
, py
+ 2*b
);
1803 grid_face_set_dot(g
, d
, 2);
1804 d
= grid_get_dot(g
, points
, px
- b
, py
+ 2*b
- a
);
1805 grid_face_set_dot(g
, d
, 3);
1806 d
= grid_get_dot(g
, points
, px
- b
, py
+ a
);
1807 grid_face_set_dot(g
, d
, 4);
1813 freetree234(points
);
1814 assert(g
->num_faces
<= max_faces
);
1815 assert(g
->num_dots
<= max_dots
);
1817 grid_make_consistent(g
);
1821 #define GREATHEX_TILESIZE 18
1822 /* Vector for side of triangle - ratio is close to sqrt(3) */
1823 #define GREATHEX_A 15
1824 #define GREATHEX_B 26
1826 void grid_size_greathexagonal(int width
, int height
,
1827 int *tilesize
, int *xextent
, int *yextent
)
1832 *tilesize
= GREATHEX_TILESIZE
;
1833 *xextent
= (3*a
+ b
) * (width
-1) + 4*a
;
1834 *yextent
= (2*a
+ 2*b
) * (height
-1) + 3*b
+ a
;
1837 grid
*grid_new_greathexagonal(int width
, int height
, char *desc
)
1843 /* Upper bounds - don't have to be exact */
1844 int max_faces
= 6 * (width
+ 1) * (height
+ 1);
1845 int max_dots
= 6 * width
* height
;
1849 grid
*g
= grid_empty();
1850 g
->tilesize
= GREATHEX_TILESIZE
;
1851 g
->faces
= snewn(max_faces
, grid_face
);
1852 g
->dots
= snewn(max_dots
, grid_dot
);
1854 points
= newtree234(grid_point_cmp_fn
);
1856 for (y
= 0; y
< height
; y
++) {
1857 for (x
= 0; x
< width
; x
++) {
1859 /* centre of hexagon */
1860 int px
= (3*a
+ b
) * x
;
1861 int py
= (2*a
+ 2*b
) * y
;
1866 grid_face_add_new(g
, 6);
1867 d
= grid_get_dot(g
, points
, px
- a
, py
- b
);
1868 grid_face_set_dot(g
, d
, 0);
1869 d
= grid_get_dot(g
, points
, px
+ a
, py
- b
);
1870 grid_face_set_dot(g
, d
, 1);
1871 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
);
1872 grid_face_set_dot(g
, d
, 2);
1873 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1874 grid_face_set_dot(g
, d
, 3);
1875 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1876 grid_face_set_dot(g
, d
, 4);
1877 d
= grid_get_dot(g
, points
, px
- 2*a
, py
);
1878 grid_face_set_dot(g
, d
, 5);
1880 /* square below hexagon */
1881 if (y
< height
- 1) {
1882 grid_face_add_new(g
, 4);
1883 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1884 grid_face_set_dot(g
, d
, 0);
1885 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1886 grid_face_set_dot(g
, d
, 1);
1887 d
= grid_get_dot(g
, points
, px
+ a
, py
+ 2*a
+ b
);
1888 grid_face_set_dot(g
, d
, 2);
1889 d
= grid_get_dot(g
, points
, px
- a
, py
+ 2*a
+ b
);
1890 grid_face_set_dot(g
, d
, 3);
1893 /* square below right */
1894 if ((x
< width
- 1) && (((x
% 2) == 0) || (y
< height
- 1))) {
1895 grid_face_add_new(g
, 4);
1896 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
);
1897 grid_face_set_dot(g
, d
, 0);
1898 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
);
1899 grid_face_set_dot(g
, d
, 1);
1900 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
+ b
);
1901 grid_face_set_dot(g
, d
, 2);
1902 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1903 grid_face_set_dot(g
, d
, 3);
1906 /* square below left */
1907 if ((x
> 0) && (((x
% 2) == 0) || (y
< height
- 1))) {
1908 grid_face_add_new(g
, 4);
1909 d
= grid_get_dot(g
, points
, px
- 2*a
, py
);
1910 grid_face_set_dot(g
, d
, 0);
1911 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1912 grid_face_set_dot(g
, d
, 1);
1913 d
= grid_get_dot(g
, points
, px
- a
- b
, py
+ a
+ b
);
1914 grid_face_set_dot(g
, d
, 2);
1915 d
= grid_get_dot(g
, points
, px
- 2*a
- b
, py
+ a
);
1916 grid_face_set_dot(g
, d
, 3);
1919 /* Triangle below right */
1920 if ((x
< width
- 1) && (y
< height
- 1)) {
1921 grid_face_add_new(g
, 3);
1922 d
= grid_get_dot(g
, points
, px
+ a
, py
+ b
);
1923 grid_face_set_dot(g
, d
, 0);
1924 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ a
+ b
);
1925 grid_face_set_dot(g
, d
, 1);
1926 d
= grid_get_dot(g
, points
, px
+ a
, py
+ 2*a
+ b
);
1927 grid_face_set_dot(g
, d
, 2);
1930 /* Triangle below left */
1931 if ((x
> 0) && (y
< height
- 1)) {
1932 grid_face_add_new(g
, 3);
1933 d
= grid_get_dot(g
, points
, px
- a
, py
+ b
);
1934 grid_face_set_dot(g
, d
, 0);
1935 d
= grid_get_dot(g
, points
, px
- a
, py
+ 2*a
+ b
);
1936 grid_face_set_dot(g
, d
, 1);
1937 d
= grid_get_dot(g
, points
, px
- a
- b
, py
+ a
+ b
);
1938 grid_face_set_dot(g
, d
, 2);
1943 freetree234(points
);
1944 assert(g
->num_faces
<= max_faces
);
1945 assert(g
->num_dots
<= max_dots
);
1947 grid_make_consistent(g
);
1951 #define OCTAGONAL_TILESIZE 40
1952 /* b/a approx sqrt(2) */
1953 #define OCTAGONAL_A 29
1954 #define OCTAGONAL_B 41
1956 void grid_size_octagonal(int width
, int height
,
1957 int *tilesize
, int *xextent
, int *yextent
)
1959 int a
= OCTAGONAL_A
;
1960 int b
= OCTAGONAL_B
;
1962 *tilesize
= OCTAGONAL_TILESIZE
;
1963 *xextent
= (2*a
+ b
) * width
;
1964 *yextent
= (2*a
+ b
) * height
;
1967 grid
*grid_new_octagonal(int width
, int height
, char *desc
)
1970 int a
= OCTAGONAL_A
;
1971 int b
= OCTAGONAL_B
;
1973 /* Upper bounds - don't have to be exact */
1974 int max_faces
= 2 * width
* height
;
1975 int max_dots
= 4 * (width
+ 1) * (height
+ 1);
1979 grid
*g
= grid_empty();
1980 g
->tilesize
= OCTAGONAL_TILESIZE
;
1981 g
->faces
= snewn(max_faces
, grid_face
);
1982 g
->dots
= snewn(max_dots
, grid_dot
);
1984 points
= newtree234(grid_point_cmp_fn
);
1986 for (y
= 0; y
< height
; y
++) {
1987 for (x
= 0; x
< width
; x
++) {
1990 int px
= (2*a
+ b
) * x
;
1991 int py
= (2*a
+ b
) * y
;
1993 grid_face_add_new(g
, 8);
1994 d
= grid_get_dot(g
, points
, px
+ a
, py
);
1995 grid_face_set_dot(g
, d
, 0);
1996 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
);
1997 grid_face_set_dot(g
, d
, 1);
1998 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
);
1999 grid_face_set_dot(g
, d
, 2);
2000 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
+ b
);
2001 grid_face_set_dot(g
, d
, 3);
2002 d
= grid_get_dot(g
, points
, px
+ a
+ b
, py
+ 2*a
+ b
);
2003 grid_face_set_dot(g
, d
, 4);
2004 d
= grid_get_dot(g
, points
, px
+ a
, py
+ 2*a
+ b
);
2005 grid_face_set_dot(g
, d
, 5);
2006 d
= grid_get_dot(g
, points
, px
, py
+ a
+ b
);
2007 grid_face_set_dot(g
, d
, 6);
2008 d
= grid_get_dot(g
, points
, px
, py
+ a
);
2009 grid_face_set_dot(g
, d
, 7);
2012 if ((x
> 0) && (y
> 0)) {
2013 grid_face_add_new(g
, 4);
2014 d
= grid_get_dot(g
, points
, px
, py
- a
);
2015 grid_face_set_dot(g
, d
, 0);
2016 d
= grid_get_dot(g
, points
, px
+ a
, py
);
2017 grid_face_set_dot(g
, d
, 1);
2018 d
= grid_get_dot(g
, points
, px
, py
+ a
);
2019 grid_face_set_dot(g
, d
, 2);
2020 d
= grid_get_dot(g
, points
, px
- a
, py
);
2021 grid_face_set_dot(g
, d
, 3);
2026 freetree234(points
);
2027 assert(g
->num_faces
<= max_faces
);
2028 assert(g
->num_dots
<= max_dots
);
2030 grid_make_consistent(g
);
2034 #define KITE_TILESIZE 40
2035 /* b/a approx sqrt(3) */
2039 void grid_size_kites(int width
, int height
,
2040 int *tilesize
, int *xextent
, int *yextent
)
2045 *tilesize
= KITE_TILESIZE
;
2046 *xextent
= 4*b
* width
+ 2*b
;
2047 *yextent
= 6*a
* (height
-1) + 8*a
;
2050 grid
*grid_new_kites(int width
, int height
, char *desc
)
2056 /* Upper bounds - don't have to be exact */
2057 int max_faces
= 6 * width
* height
;
2058 int max_dots
= 6 * (width
+ 1) * (height
+ 1);
2062 grid
*g
= grid_empty();
2063 g
->tilesize
= KITE_TILESIZE
;
2064 g
->faces
= snewn(max_faces
, grid_face
);
2065 g
->dots
= snewn(max_dots
, grid_dot
);
2067 points
= newtree234(grid_point_cmp_fn
);
2069 for (y
= 0; y
< height
; y
++) {
2070 for (x
= 0; x
< width
; x
++) {
2072 /* position of order-6 dot */
2078 /* kite pointing up-left */
2079 grid_face_add_new(g
, 4);
2080 d
= grid_get_dot(g
, points
, px
, py
);
2081 grid_face_set_dot(g
, d
, 0);
2082 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
2083 grid_face_set_dot(g
, d
, 1);
2084 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
+ 2*a
);
2085 grid_face_set_dot(g
, d
, 2);
2086 d
= grid_get_dot(g
, points
, px
+ b
, py
+ 3*a
);
2087 grid_face_set_dot(g
, d
, 3);
2089 /* kite pointing up */
2090 grid_face_add_new(g
, 4);
2091 d
= grid_get_dot(g
, points
, px
, py
);
2092 grid_face_set_dot(g
, d
, 0);
2093 d
= grid_get_dot(g
, points
, px
+ b
, py
+ 3*a
);
2094 grid_face_set_dot(g
, d
, 1);
2095 d
= grid_get_dot(g
, points
, px
, py
+ 4*a
);
2096 grid_face_set_dot(g
, d
, 2);
2097 d
= grid_get_dot(g
, points
, px
- b
, py
+ 3*a
);
2098 grid_face_set_dot(g
, d
, 3);
2100 /* kite pointing up-right */
2101 grid_face_add_new(g
, 4);
2102 d
= grid_get_dot(g
, points
, px
, py
);
2103 grid_face_set_dot(g
, d
, 0);
2104 d
= grid_get_dot(g
, points
, px
- b
, py
+ 3*a
);
2105 grid_face_set_dot(g
, d
, 1);
2106 d
= grid_get_dot(g
, points
, px
- 2*b
, py
+ 2*a
);
2107 grid_face_set_dot(g
, d
, 2);
2108 d
= grid_get_dot(g
, points
, px
- 2*b
, py
);
2109 grid_face_set_dot(g
, d
, 3);
2111 /* kite pointing down-right */
2112 grid_face_add_new(g
, 4);
2113 d
= grid_get_dot(g
, points
, px
, py
);
2114 grid_face_set_dot(g
, d
, 0);
2115 d
= grid_get_dot(g
, points
, px
- 2*b
, py
);
2116 grid_face_set_dot(g
, d
, 1);
2117 d
= grid_get_dot(g
, points
, px
- 2*b
, py
- 2*a
);
2118 grid_face_set_dot(g
, d
, 2);
2119 d
= grid_get_dot(g
, points
, px
- b
, py
- 3*a
);
2120 grid_face_set_dot(g
, d
, 3);
2122 /* kite pointing down */
2123 grid_face_add_new(g
, 4);
2124 d
= grid_get_dot(g
, points
, px
, py
);
2125 grid_face_set_dot(g
, d
, 0);
2126 d
= grid_get_dot(g
, points
, px
- b
, py
- 3*a
);
2127 grid_face_set_dot(g
, d
, 1);
2128 d
= grid_get_dot(g
, points
, px
, py
- 4*a
);
2129 grid_face_set_dot(g
, d
, 2);
2130 d
= grid_get_dot(g
, points
, px
+ b
, py
- 3*a
);
2131 grid_face_set_dot(g
, d
, 3);
2133 /* kite pointing down-left */
2134 grid_face_add_new(g
, 4);
2135 d
= grid_get_dot(g
, points
, px
, py
);
2136 grid_face_set_dot(g
, d
, 0);
2137 d
= grid_get_dot(g
, points
, px
+ b
, py
- 3*a
);
2138 grid_face_set_dot(g
, d
, 1);
2139 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
- 2*a
);
2140 grid_face_set_dot(g
, d
, 2);
2141 d
= grid_get_dot(g
, points
, px
+ 2*b
, py
);
2142 grid_face_set_dot(g
, d
, 3);
2146 freetree234(points
);
2147 assert(g
->num_faces
<= max_faces
);
2148 assert(g
->num_dots
<= max_dots
);
2150 grid_make_consistent(g
);
2154 #define FLORET_TILESIZE 150
2155 /* -py/px is close to tan(30 - atan(sqrt(3)/9))
2156 * using py=26 makes everything lean to the left, rather than right
2158 #define FLORET_PX 75
2159 #define FLORET_PY -26
2161 void grid_size_floret(int width
, int height
,
2162 int *tilesize
, int *xextent
, int *yextent
)
2164 int px
= FLORET_PX
, py
= FLORET_PY
; /* |( 75, -26)| = 79.43 */
2165 int qx
= 4*px
/5, qy
= -py
*2; /* |( 60, 52)| = 79.40 */
2167 /* rx unused in determining grid size. */
2169 *tilesize
= FLORET_TILESIZE
;
2170 *xextent
= (6*px
+3*qx
)/2 * (width
-1) + 4*qx
+ 2*px
;
2171 *yextent
= (5*qy
-4*py
) * (height
-1) + 4*qy
+ 2*ry
;
2174 grid
*grid_new_floret(int width
, int height
, char *desc
)
2177 /* Vectors for sides; weird numbers needed to keep puzzle aligned with window
2178 * -py/px is close to tan(30 - atan(sqrt(3)/9))
2179 * using py=26 makes everything lean to the left, rather than right
2181 int px
= FLORET_PX
, py
= FLORET_PY
; /* |( 75, -26)| = 79.43 */
2182 int qx
= 4*px
/5, qy
= -py
*2; /* |( 60, 52)| = 79.40 */
2183 int rx
= qx
-px
, ry
= qy
-py
; /* |(-15, 78)| = 79.38 */
2185 /* Upper bounds - don't have to be exact */
2186 int max_faces
= 6 * width
* height
;
2187 int max_dots
= 9 * (width
+ 1) * (height
+ 1);
2191 grid
*g
= grid_empty();
2192 g
->tilesize
= FLORET_TILESIZE
;
2193 g
->faces
= snewn(max_faces
, grid_face
);
2194 g
->dots
= snewn(max_dots
, grid_dot
);
2196 points
= newtree234(grid_point_cmp_fn
);
2198 /* generate pentagonal faces */
2199 for (y
= 0; y
< height
; y
++) {
2200 for (x
= 0; x
< width
; x
++) {
2203 int cx
= (6*px
+3*qx
)/2 * x
;
2204 int cy
= (4*py
-5*qy
) * y
;
2206 cy
-= (4*py
-5*qy
)/2;
2207 else if (y
&& y
== height
-1)
2208 continue; /* make better looking grids? try 3x3 for instance */
2210 grid_face_add_new(g
, 5);
2211 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2212 d
= grid_get_dot(g
, points
, cx
+2*rx
, cy
+2*ry
); grid_face_set_dot(g
, d
, 1);
2213 d
= grid_get_dot(g
, points
, cx
+2*rx
+qx
, cy
+2*ry
+qy
); grid_face_set_dot(g
, d
, 2);
2214 d
= grid_get_dot(g
, points
, cx
+2*qx
+rx
, cy
+2*qy
+ry
); grid_face_set_dot(g
, d
, 3);
2215 d
= grid_get_dot(g
, points
, cx
+2*qx
, cy
+2*qy
); grid_face_set_dot(g
, d
, 4);
2217 grid_face_add_new(g
, 5);
2218 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2219 d
= grid_get_dot(g
, points
, cx
+2*qx
, cy
+2*qy
); grid_face_set_dot(g
, d
, 1);
2220 d
= grid_get_dot(g
, points
, cx
+2*qx
+px
, cy
+2*qy
+py
); grid_face_set_dot(g
, d
, 2);
2221 d
= grid_get_dot(g
, points
, cx
+2*px
+qx
, cy
+2*py
+qy
); grid_face_set_dot(g
, d
, 3);
2222 d
= grid_get_dot(g
, points
, cx
+2*px
, cy
+2*py
); grid_face_set_dot(g
, d
, 4);
2224 grid_face_add_new(g
, 5);
2225 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2226 d
= grid_get_dot(g
, points
, cx
+2*px
, cy
+2*py
); grid_face_set_dot(g
, d
, 1);
2227 d
= grid_get_dot(g
, points
, cx
+2*px
-rx
, cy
+2*py
-ry
); grid_face_set_dot(g
, d
, 2);
2228 d
= grid_get_dot(g
, points
, cx
-2*rx
+px
, cy
-2*ry
+py
); grid_face_set_dot(g
, d
, 3);
2229 d
= grid_get_dot(g
, points
, cx
-2*rx
, cy
-2*ry
); grid_face_set_dot(g
, d
, 4);
2231 grid_face_add_new(g
, 5);
2232 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2233 d
= grid_get_dot(g
, points
, cx
-2*rx
, cy
-2*ry
); grid_face_set_dot(g
, d
, 1);
2234 d
= grid_get_dot(g
, points
, cx
-2*rx
-qx
, cy
-2*ry
-qy
); grid_face_set_dot(g
, d
, 2);
2235 d
= grid_get_dot(g
, points
, cx
-2*qx
-rx
, cy
-2*qy
-ry
); grid_face_set_dot(g
, d
, 3);
2236 d
= grid_get_dot(g
, points
, cx
-2*qx
, cy
-2*qy
); grid_face_set_dot(g
, d
, 4);
2238 grid_face_add_new(g
, 5);
2239 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2240 d
= grid_get_dot(g
, points
, cx
-2*qx
, cy
-2*qy
); grid_face_set_dot(g
, d
, 1);
2241 d
= grid_get_dot(g
, points
, cx
-2*qx
-px
, cy
-2*qy
-py
); grid_face_set_dot(g
, d
, 2);
2242 d
= grid_get_dot(g
, points
, cx
-2*px
-qx
, cy
-2*py
-qy
); grid_face_set_dot(g
, d
, 3);
2243 d
= grid_get_dot(g
, points
, cx
-2*px
, cy
-2*py
); grid_face_set_dot(g
, d
, 4);
2245 grid_face_add_new(g
, 5);
2246 d
= grid_get_dot(g
, points
, cx
, cy
); grid_face_set_dot(g
, d
, 0);
2247 d
= grid_get_dot(g
, points
, cx
-2*px
, cy
-2*py
); grid_face_set_dot(g
, d
, 1);
2248 d
= grid_get_dot(g
, points
, cx
-2*px
+rx
, cy
-2*py
+ry
); grid_face_set_dot(g
, d
, 2);
2249 d
= grid_get_dot(g
, points
, cx
+2*rx
-px
, cy
+2*ry
-py
); grid_face_set_dot(g
, d
, 3);
2250 d
= grid_get_dot(g
, points
, cx
+2*rx
, cy
+2*ry
); grid_face_set_dot(g
, d
, 4);
2254 freetree234(points
);
2255 assert(g
->num_faces
<= max_faces
);
2256 assert(g
->num_dots
<= max_dots
);
2258 grid_make_consistent(g
);
2262 /* DODEC_* are used for dodecagonal and great-dodecagonal grids. */
2263 #define DODEC_TILESIZE 26
2264 /* Vector for side of triangle - ratio is close to sqrt(3) */
2268 void grid_size_dodecagonal(int width
, int height
,
2269 int *tilesize
, int *xextent
, int *yextent
)
2274 *tilesize
= DODEC_TILESIZE
;
2275 *xextent
= (4*a
+ 2*b
) * (width
-1) + 3*(2*a
+ b
);
2276 *yextent
= (3*a
+ 2*b
) * (height
-1) + 2*(2*a
+ b
);
2279 grid
*grid_new_dodecagonal(int width
, int height
, char *desc
)
2285 /* Upper bounds - don't have to be exact */
2286 int max_faces
= 3 * width
* height
;
2287 int max_dots
= 14 * width
* height
;
2291 grid
*g
= grid_empty();
2292 g
->tilesize
= DODEC_TILESIZE
;
2293 g
->faces
= snewn(max_faces
, grid_face
);
2294 g
->dots
= snewn(max_dots
, grid_dot
);
2296 points
= newtree234(grid_point_cmp_fn
);
2298 for (y
= 0; y
< height
; y
++) {
2299 for (x
= 0; x
< width
; x
++) {
2301 /* centre of dodecagon */
2302 int px
= (4*a
+ 2*b
) * x
;
2303 int py
= (3*a
+ 2*b
) * y
;
2308 grid_face_add_new(g
, 12);
2309 d
= grid_get_dot(g
, points
, px
+ ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2310 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 1);
2311 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 2);
2312 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 3);
2313 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 4);
2314 d
= grid_get_dot(g
, points
, px
+ ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2315 d
= grid_get_dot(g
, points
, px
- ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 6);
2316 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 7);
2317 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 8);
2318 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 9);
2319 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 10);
2320 d
= grid_get_dot(g
, points
, px
- ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 11);
2322 /* triangle below dodecagon */
2323 if ((y
< height
- 1 && (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2)))) {
2324 grid_face_add_new(g
, 3);
2325 d
= grid_get_dot(g
, points
, px
+ a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2326 d
= grid_get_dot(g
, points
, px
, py
+ (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2327 d
= grid_get_dot(g
, points
, px
- a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 2);
2330 /* triangle above dodecagon */
2331 if ((y
&& (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2)))) {
2332 grid_face_add_new(g
, 3);
2333 d
= grid_get_dot(g
, points
, px
- a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2334 d
= grid_get_dot(g
, points
, px
, py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2335 d
= grid_get_dot(g
, points
, px
+ a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 2);
2340 freetree234(points
);
2341 assert(g
->num_faces
<= max_faces
);
2342 assert(g
->num_dots
<= max_dots
);
2344 grid_make_consistent(g
);
2348 void grid_size_greatdodecagonal(int width
, int height
,
2349 int *tilesize
, int *xextent
, int *yextent
)
2354 *tilesize
= DODEC_TILESIZE
;
2355 *xextent
= (6*a
+ 2*b
) * (width
-1) + 2*(2*a
+ b
) + 3*a
+ b
;
2356 *yextent
= (3*a
+ 3*b
) * (height
-1) + 2*(2*a
+ b
);
2359 grid
*grid_new_greatdodecagonal(int width
, int height
, char *desc
)
2362 /* Vector for side of triangle - ratio is close to sqrt(3) */
2366 /* Upper bounds - don't have to be exact */
2367 int max_faces
= 30 * width
* height
;
2368 int max_dots
= 200 * width
* height
;
2372 grid
*g
= grid_empty();
2373 g
->tilesize
= DODEC_TILESIZE
;
2374 g
->faces
= snewn(max_faces
, grid_face
);
2375 g
->dots
= snewn(max_dots
, grid_dot
);
2377 points
= newtree234(grid_point_cmp_fn
);
2379 for (y
= 0; y
< height
; y
++) {
2380 for (x
= 0; x
< width
; x
++) {
2382 /* centre of dodecagon */
2383 int px
= (6*a
+ 2*b
) * x
;
2384 int py
= (3*a
+ 3*b
) * y
;
2389 grid_face_add_new(g
, 12);
2390 d
= grid_get_dot(g
, points
, px
+ ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2391 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 1);
2392 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 2);
2393 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 3);
2394 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 4);
2395 d
= grid_get_dot(g
, points
, px
+ ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2396 d
= grid_get_dot(g
, points
, px
- ( a
), py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 6);
2397 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
+ ( a
+ b
)); grid_face_set_dot(g
, d
, 7);
2398 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
+ ( a
)); grid_face_set_dot(g
, d
, 8);
2399 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
- ( a
)); grid_face_set_dot(g
, d
, 9);
2400 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 10);
2401 d
= grid_get_dot(g
, points
, px
- ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 11);
2403 /* hexagon below dodecagon */
2404 if (y
< height
- 1 && (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2))) {
2405 grid_face_add_new(g
, 6);
2406 d
= grid_get_dot(g
, points
, px
+ a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2407 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
+ (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2408 d
= grid_get_dot(g
, points
, px
+ a
, py
+ (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 2);
2409 d
= grid_get_dot(g
, points
, px
- a
, py
+ (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 3);
2410 d
= grid_get_dot(g
, points
, px
- 2*a
, py
+ (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 4);
2411 d
= grid_get_dot(g
, points
, px
- a
, py
+ (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2414 /* hexagon above dodecagon */
2415 if (y
&& (x
< width
- 1 || !(y
% 2)) && (x
> 0 || (y
% 2))) {
2416 grid_face_add_new(g
, 6);
2417 d
= grid_get_dot(g
, points
, px
- a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2418 d
= grid_get_dot(g
, points
, px
- 2*a
, py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2419 d
= grid_get_dot(g
, points
, px
- a
, py
- (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 2);
2420 d
= grid_get_dot(g
, points
, px
+ a
, py
- (2*a
+ 3*b
)); grid_face_set_dot(g
, d
, 3);
2421 d
= grid_get_dot(g
, points
, px
+ 2*a
, py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 4);
2422 d
= grid_get_dot(g
, points
, px
+ a
, py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 5);
2425 /* square on right of dodecagon */
2426 if (x
< width
- 1) {
2427 grid_face_add_new(g
, 4);
2428 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
- a
); grid_face_set_dot(g
, d
, 0);
2429 d
= grid_get_dot(g
, points
, px
+ 4*a
+ b
, py
- a
); grid_face_set_dot(g
, d
, 1);
2430 d
= grid_get_dot(g
, points
, px
+ 4*a
+ b
, py
+ a
); grid_face_set_dot(g
, d
, 2);
2431 d
= grid_get_dot(g
, points
, px
+ 2*a
+ b
, py
+ a
); grid_face_set_dot(g
, d
, 3);
2434 /* square on top right of dodecagon */
2435 if (y
&& (x
< width
- 1 || !(y
% 2))) {
2436 grid_face_add_new(g
, 4);
2437 d
= grid_get_dot(g
, points
, px
+ ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 0);
2438 d
= grid_get_dot(g
, points
, px
+ (2*a
), py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2439 d
= grid_get_dot(g
, points
, px
+ (2*a
+ b
), py
- ( a
+ 2*b
)); grid_face_set_dot(g
, d
, 2);
2440 d
= grid_get_dot(g
, points
, px
+ ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 3);
2443 /* square on top left of dodecagon */
2444 if (y
&& (x
|| (y
% 2))) {
2445 grid_face_add_new(g
, 4);
2446 d
= grid_get_dot(g
, points
, px
- ( a
+ b
), py
- ( a
+ b
)); grid_face_set_dot(g
, d
, 0);
2447 d
= grid_get_dot(g
, points
, px
- (2*a
+ b
), py
- ( a
+ 2*b
)); grid_face_set_dot(g
, d
, 1);
2448 d
= grid_get_dot(g
, points
, px
- (2*a
), py
- (2*a
+ 2*b
)); grid_face_set_dot(g
, d
, 2);
2449 d
= grid_get_dot(g
, points
, px
- ( a
), py
- (2*a
+ b
)); grid_face_set_dot(g
, d
, 3);
2454 freetree234(points
);
2455 assert(g
->num_faces
<= max_faces
);
2456 assert(g
->num_dots
<= max_dots
);
2458 grid_make_consistent(g
);
2462 typedef struct setface_ctx
2464 int xmin
, xmax
, ymin
, ymax
;
2471 double round(double r
)
2473 return (r
> 0.0) ?
floor(r
+ 0.5) : ceil(r
- 0.5);
2476 int set_faces(penrose_state
*state
, vector
*vs
, int n
, int depth
)
2478 setface_ctx
*sf_ctx
= (setface_ctx
*)state
->ctx
;
2481 double cosa
= cos(sf_ctx
->aoff
* PI
/ 180.0);
2482 double sina
= sin(sf_ctx
->aoff
* PI
/ 180.0);
2484 if (depth
< state
->max_depth
) return 0;
2485 #ifdef DEBUG_PENROSE
2486 if (n
!= 4) return 0; /* triangles are sent as debugging. */
2489 for (i
= 0; i
< n
; i
++) {
2490 double tx
= v_x(vs
, i
), ty
= v_y(vs
, i
);
2492 xs
[i
] = (int)round( tx
*cosa
+ ty
*sina
);
2493 ys
[i
] = (int)round(-tx
*sina
+ ty
*cosa
);
2495 if (xs
[i
] < sf_ctx
->xmin
|| xs
[i
] > sf_ctx
->xmax
) return 0;
2496 if (ys
[i
] < sf_ctx
->ymin
|| ys
[i
] > sf_ctx
->ymax
) return 0;
2499 grid_face_add_new(sf_ctx
->g
, n
);
2500 debug(("penrose: new face l=%f gen=%d...",
2501 penrose_side_length(state
->start_size
, depth
), depth
));
2502 for (i
= 0; i
< n
; i
++) {
2503 grid_dot
*d
= grid_get_dot(sf_ctx
->g
, sf_ctx
->points
,
2505 grid_face_set_dot(sf_ctx
->g
, d
, i
);
2506 debug((" ... dot 0x%x (%d,%d) (was %2.2f,%2.2f)",
2507 d
, d
->x
, d
->y
, v_x(vs
, i
), v_y(vs
, i
)));
2513 #define PENROSE_TILESIZE 100
2515 void grid_size_penrose(int width
, int height
,
2516 int *tilesize
, int *xextent
, int *yextent
)
2518 int l
= PENROSE_TILESIZE
;
2521 *xextent
= l
* width
;
2522 *yextent
= l
* height
;
2525 static char *grid_new_desc_penrose(grid_type type
, int width
, int height
, random_state
*rs
)
2527 int tilesize
= PENROSE_TILESIZE
, startsz
, depth
, xoff
, yoff
, aoff
;
2528 double outer_radius
;
2531 int which
= (type
== GRID_PENROSE_P2 ? PENROSE_P2
: PENROSE_P3
);
2533 /* We want to produce a random bit of penrose tiling, so we calculate
2534 * a random offset (within the patch that penrose.c calculates for us)
2535 * and an angle (multiple of 36) to rotate the patch. */
2537 penrose_calculate_size(which
, tilesize
, width
, height
,
2538 &outer_radius
, &startsz
, &depth
);
2540 /* Calculate radius of (circumcircle of) patch, subtract from
2541 * radius calculated. */
2542 inner_radius
= (int)(outer_radius
- sqrt(width
*width
+ height
*height
));
2544 /* Pick a random offset (the easy way: choose within outer square,
2545 * discarding while it's outside the circle) */
2547 xoff
= random_upto(rs
, 2*inner_radius
) - inner_radius
;
2548 yoff
= random_upto(rs
, 2*inner_radius
) - inner_radius
;
2549 } while (sqrt(xoff
*xoff
+yoff
*yoff
) > inner_radius
);
2551 aoff
= random_upto(rs
, 360/36) * 36;
2553 debug(("grid_desc: ts %d, %dx%d patch, orad %2.2f irad %d",
2554 tilesize
, width
, height
, outer_radius
, inner_radius
));
2555 debug((" -> xoff %d yoff %d aoff %d", xoff
, yoff
, aoff
));
2557 sprintf(gd
, "G%d,%d,%d", xoff
, yoff
, aoff
);
2562 static char *grid_validate_desc_penrose(grid_type type
, int width
, int height
, char *desc
)
2564 int tilesize
= PENROSE_TILESIZE
, startsz
, depth
, xoff
, yoff
, aoff
, inner_radius
;
2565 double outer_radius
;
2566 int which
= (type
== GRID_PENROSE_P2 ? PENROSE_P2
: PENROSE_P3
);
2569 return "Missing grid description string.";
2571 penrose_calculate_size(which
, tilesize
, width
, height
,
2572 &outer_radius
, &startsz
, &depth
);
2573 inner_radius
= (int)(outer_radius
- sqrt(width
*width
+ height
*height
));
2575 if (sscanf(desc
, "G%d,%d,%d", &xoff
, &yoff
, &aoff
) != 3)
2576 return "Invalid format grid description string.";
2578 if (sqrt(xoff
*xoff
+ yoff
*yoff
) > inner_radius
)
2579 return "Patch offset out of bounds.";
2580 if ((aoff
% 36) != 0 || aoff
< 0 || aoff
>= 360)
2581 return "Angle offset out of bounds.";
2587 * We're asked for a grid of a particular size, and we generate enough
2588 * of the tiling so we can be sure to have enough random grid from which
2592 static grid
*grid_new_penrose(int width
, int height
, int which
, char *desc
)
2594 int max_faces
, max_dots
, tilesize
= PENROSE_TILESIZE
;
2595 int xsz
, ysz
, xoff
, yoff
;
2604 penrose_calculate_size(which
, tilesize
, width
, height
,
2605 &rradius
, &ps
.start_size
, &ps
.max_depth
);
2607 debug(("penrose: w%d h%d, tile size %d, start size %d, depth %d",
2608 width
, height
, tilesize
, ps
.start_size
, ps
.max_depth
));
2610 ps
.new_tile
= set_faces
;
2613 max_faces
= (width
*3) * (height
*3); /* somewhat paranoid... */
2614 max_dots
= max_faces
* 4; /* ditto... */
2617 g
->tilesize
= tilesize
;
2618 g
->faces
= snewn(max_faces
, grid_face
);
2619 g
->dots
= snewn(max_dots
, grid_dot
);
2621 points
= newtree234(grid_point_cmp_fn
);
2623 memset(&sf_ctx
, 0, sizeof(sf_ctx
));
2625 sf_ctx
.points
= points
;
2628 if (sscanf(desc
, "G%d,%d,%d", &xoff
, &yoff
, &sf_ctx
.aoff
) != 3)
2629 assert(!"Invalid grid description.");
2634 xsz
= width
* tilesize
;
2635 ysz
= height
* tilesize
;
2637 sf_ctx
.xmin
= xoff
- xsz
/2;
2638 sf_ctx
.xmax
= xoff
+ xsz
/2;
2639 sf_ctx
.ymin
= yoff
- ysz
/2;
2640 sf_ctx
.ymax
= yoff
+ ysz
/2;
2642 debug(("penrose: centre (%f, %f) xsz %f ysz %f",
2643 0.0, 0.0, xsz
, ysz
));
2644 debug(("penrose: x range (%f --> %f), y range (%f --> %f)",
2645 sf_ctx
.xmin
, sf_ctx
.xmax
, sf_ctx
.ymin
, sf_ctx
.ymax
));
2647 penrose(&ps
, which
);
2649 freetree234(points
);
2650 assert(g
->num_faces
<= max_faces
);
2651 assert(g
->num_dots
<= max_dots
);
2653 debug(("penrose: %d faces total (equivalent to %d wide by %d high)",
2654 g
->num_faces
, g
->num_faces
/height
, g
->num_faces
/width
));
2656 grid_trim_vigorously(g
);
2657 grid_make_consistent(g
);
2660 * Centre the grid in its originally promised rectangle.
2662 g
->lowest_x
-= ((sf_ctx
.xmax
- sf_ctx
.xmin
) -
2663 (g
->highest_x
- g
->lowest_x
)) / 2;
2664 g
->highest_x
= g
->lowest_x
+ (sf_ctx
.xmax
- sf_ctx
.xmin
);
2665 g
->lowest_y
-= ((sf_ctx
.ymax
- sf_ctx
.ymin
) -
2666 (g
->highest_y
- g
->lowest_y
)) / 2;
2667 g
->highest_y
= g
->lowest_y
+ (sf_ctx
.ymax
- sf_ctx
.ymin
);
2672 void grid_size_penrose_p2_kite(int width
, int height
,
2673 int *tilesize
, int *xextent
, int *yextent
)
2675 grid_size_penrose(width
, height
, tilesize
, xextent
, yextent
);
2678 void grid_size_penrose_p3_thick(int width
, int height
,
2679 int *tilesize
, int *xextent
, int *yextent
)
2681 grid_size_penrose(width
, height
, tilesize
, xextent
, yextent
);
2684 grid
*grid_new_penrose_p2_kite(int width
, int height
, char *desc
)
2686 return grid_new_penrose(width
, height
, PENROSE_P2
, desc
);
2689 grid
*grid_new_penrose_p3_thick(int width
, int height
, char *desc
)
2691 return grid_new_penrose(width
, height
, PENROSE_P3
, desc
);
2694 /* ----------- End of grid generators ------------- */
2696 #define FNNEW(upper,lower) &grid_new_ ## lower,
2697 #define FNSZ(upper,lower) &grid_size_ ## lower,
2699 static grid
*(*(grid_news
[]))(int, int, char*) = { GRIDGEN_LIST(FNNEW
) };
2700 static void(*(grid_sizes
[]))(int, int, int*, int*, int*) = { GRIDGEN_LIST(FNSZ
) };
2702 char *grid_new_desc(grid_type type
, int width
, int height
, random_state
*rs
)
2704 if (type
!= GRID_PENROSE_P2
&& type
!= GRID_PENROSE_P3
)
2707 return grid_new_desc_penrose(type
, width
, height
, rs
);
2710 char *grid_validate_desc(grid_type type
, int width
, int height
, char *desc
)
2712 if (type
!= GRID_PENROSE_P2
&& type
!= GRID_PENROSE_P3
) {
2714 return "Grid description strings not used with this grid type";
2718 return grid_validate_desc_penrose(type
, width
, height
, desc
);
2721 grid
*grid_new(grid_type type
, int width
, int height
, char *desc
)
2723 char *err
= grid_validate_desc(type
, width
, height
, desc
);
2724 if (err
) assert(!"Invalid grid description.");
2726 return grid_news
[type
](width
, height
, desc
);
2729 void grid_compute_size(grid_type type
, int width
, int height
,
2730 int *tilesize
, int *xextent
, int *yextent
)
2732 grid_sizes
[type
](width
, height
, tilesize
, xextent
, yextent
);
2735 /* ----------- End of grid helpers ------------- */
2737 /* vim: set shiftwidth=4 tabstop=8: */