1 /*
2 * Copyright © 2004 Carl Worth
3 * Copyright © 2006 Red Hat, Inc.
4 * Copyright © 2008 Chris Wilson
5 *
6 * This library is free software; you can redistribute it and/or
7 * modify it either under the terms of the GNU Lesser General Public
8 * License version 2.1 as published by the Free Software Foundation
9 * (the "LGPL") or, at your option, under the terms of the Mozilla
10 * Public License Version 1.1 (the "MPL"). If you do not alter this
11 * notice, a recipient may use your version of this file under either
12 * the MPL or the LGPL.
13 *
14 * You should have received a copy of the LGPL along with this library
15 * in the file COPYING-LGPL-2.1; if not, write to the Free Software
16 * Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA
17 * You should have received a copy of the MPL along with this library
18 * in the file COPYING-MPL-1.1
19 *
20 * The contents of this file are subject to the Mozilla Public License
21 * Version 1.1 (the "License"); you may not use this file except in
22 * compliance with the License. You may obtain a copy of the License at
23 * http://www.mozilla.org/MPL/
24 *
25 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
26 * OF ANY KIND, either express or implied. See the LGPL or the MPL for
27 * the specific language governing rights and limitations.
28 *
29 * The Original Code is the cairo graphics library.
30 *
31 * The Initial Developer of the Original Code is Carl Worth
32 *
33 * Contributor(s):
34 * Carl D. Worth <cworth@cworth.org>
35 * Chris Wilson <chris@chris-wilson.co.uk>
36 */
37
38 /* Provide definitions for standalone compilation */
39 #include "cairoint.h"
40
41 #include "cairo-combsort-inline.h"
42 #include "cairo-error-private.h"
43 #include "cairo-freelist-private.h"
44 #include "cairo-line-inline.h"
45 #include "cairo-traps-private.h"
46
47 #define DEBUG_PRINT_STATE 0
48 #define DEBUG_EVENTS 0
49 #define DEBUG_TRAPS 0
50
51 typedef cairo_point_t cairo_bo_point32_t;
52
53 typedef struct _cairo_bo_intersect_ordinate {
54 int32_t ordinate;
55 enum { EXACT, INEXACT } exactness;
56 } cairo_bo_intersect_ordinate_t;
57
58 typedef struct _cairo_bo_intersect_point {
59 cairo_bo_intersect_ordinate_t x;
60 cairo_bo_intersect_ordinate_t y;
61 } cairo_bo_intersect_point_t;
62
63 typedef struct _cairo_bo_edge cairo_bo_edge_t;
64 typedef struct _cairo_bo_trap cairo_bo_trap_t;
65
66 /* A deferred trapezoid of an edge */
67 struct _cairo_bo_trap {
68 cairo_bo_edge_t *right;
69 int32_t top;
70 };
71
72 struct _cairo_bo_edge {
73 cairo_edge_t edge;
74 cairo_bo_edge_t *prev;
75 cairo_bo_edge_t *next;
76 cairo_bo_edge_t *colinear;
77 cairo_bo_trap_t deferred_trap;
78 };
79
80 /* the parent is always given by index/2 */
81 #define PQ_PARENT_INDEX(i) ((i) >> 1)
82 #define PQ_FIRST_ENTRY 1
83
84 /* left and right children are index * 2 and (index * 2) +1 respectively */
85 #define PQ_LEFT_CHILD_INDEX(i) ((i) << 1)
86
87 typedef enum {
88 CAIRO_BO_EVENT_TYPE_STOP,
89 CAIRO_BO_EVENT_TYPE_INTERSECTION,
90 CAIRO_BO_EVENT_TYPE_START
91 } cairo_bo_event_type_t;
92
93 typedef struct _cairo_bo_event {
94 cairo_bo_event_type_t type;
95 cairo_point_t point;
96 } cairo_bo_event_t;
97
98 typedef struct _cairo_bo_start_event {
99 cairo_bo_event_type_t type;
100 cairo_point_t point;
101 cairo_bo_edge_t edge;
102 } cairo_bo_start_event_t;
103
104 typedef struct _cairo_bo_queue_event {
105 cairo_bo_event_type_t type;
106 cairo_point_t point;
107 cairo_bo_edge_t *e1;
108 cairo_bo_edge_t *e2;
109 } cairo_bo_queue_event_t;
110
111 typedef struct _pqueue {
112 int size, max_size;
113
114 cairo_bo_event_t **elements;
115 cairo_bo_event_t *elements_embedded[1024];
116 } pqueue_t;
117
118 typedef struct _cairo_bo_event_queue {
119 cairo_freepool_t pool;
120 pqueue_t pqueue;
121 cairo_bo_event_t **start_events;
122 } cairo_bo_event_queue_t;
123
124 typedef struct _cairo_bo_sweep_line {
125 cairo_bo_edge_t *head;
126 cairo_bo_edge_t *stopped;
127 int32_t current_y;
128 cairo_bo_edge_t *current_edge;
129 } cairo_bo_sweep_line_t;
130
131 #if DEBUG_TRAPS
132 static void
dump_traps(cairo_traps_t * traps,const char * filename)133 dump_traps (cairo_traps_t *traps, const char *filename)
134 {
135 FILE *file;
136 cairo_box_t extents;
137 int n;
138
139 if (getenv ("CAIRO_DEBUG_TRAPS") == NULL)
140 return;
141
142 #if 0
143 if (traps->has_limits) {
144 printf ("%s: limits=(%d, %d, %d, %d)\n",
145 filename,
146 traps->limits.p1.x, traps->limits.p1.y,
147 traps->limits.p2.x, traps->limits.p2.y);
148 }
149 #endif
150 _cairo_traps_extents (traps, &extents);
151 printf ("%s: extents=(%d, %d, %d, %d)\n",
152 filename,
153 extents.p1.x, extents.p1.y,
154 extents.p2.x, extents.p2.y);
155
156 file = fopen (filename, "a");
157 if (file != NULL) {
158 for (n = 0; n < traps->num_traps; n++) {
159 fprintf (file, "%d %d L:(%d, %d), (%d, %d) R:(%d, %d), (%d, %d)\n",
160 traps->traps[n].top,
161 traps->traps[n].bottom,
162 traps->traps[n].left.p1.x,
163 traps->traps[n].left.p1.y,
164 traps->traps[n].left.p2.x,
165 traps->traps[n].left.p2.y,
166 traps->traps[n].right.p1.x,
167 traps->traps[n].right.p1.y,
168 traps->traps[n].right.p2.x,
169 traps->traps[n].right.p2.y);
170 }
171 fprintf (file, "\n");
172 fclose (file);
173 }
174 }
175
176 static void
dump_edges(cairo_bo_start_event_t * events,int num_edges,const char * filename)177 dump_edges (cairo_bo_start_event_t *events,
178 int num_edges,
179 const char *filename)
180 {
181 FILE *file;
182 int n;
183
184 if (getenv ("CAIRO_DEBUG_TRAPS") == NULL)
185 return;
186
187 file = fopen (filename, "a");
188 if (file != NULL) {
189 for (n = 0; n < num_edges; n++) {
190 fprintf (file, "(%d, %d), (%d, %d) %d %d %d\n",
191 events[n].edge.edge.line.p1.x,
192 events[n].edge.edge.line.p1.y,
193 events[n].edge.edge.line.p2.x,
194 events[n].edge.edge.line.p2.y,
195 events[n].edge.edge.top,
196 events[n].edge.edge.bottom,
197 events[n].edge.edge.dir);
198 }
199 fprintf (file, "\n");
200 fclose (file);
201 }
202 }
203 #endif
204
205 static cairo_fixed_t
_line_compute_intersection_x_for_y(const cairo_line_t * line,cairo_fixed_t y)206 _line_compute_intersection_x_for_y (const cairo_line_t *line,
207 cairo_fixed_t y)
208 {
209 cairo_fixed_t x, dy;
210
211 if (y == line->p1.y)
212 return line->p1.x;
213 if (y == line->p2.y)
214 return line->p2.x;
215
216 x = line->p1.x;
217 dy = line->p2.y - line->p1.y;
218 if (dy != 0) {
219 x += _cairo_fixed_mul_div_floor (y - line->p1.y,
220 line->p2.x - line->p1.x,
221 dy);
222 }
223
224 return x;
225 }
226
227 static inline int
_cairo_bo_point32_compare(cairo_bo_point32_t const * a,cairo_bo_point32_t const * b)228 _cairo_bo_point32_compare (cairo_bo_point32_t const *a,
229 cairo_bo_point32_t const *b)
230 {
231 int cmp;
232
233 cmp = a->y - b->y;
234 if (cmp)
235 return cmp;
236
237 return a->x - b->x;
238 }
239
240 /* Compare the slope of a to the slope of b, returning 1, 0, -1 if the
241 * slope a is respectively greater than, equal to, or less than the
242 * slope of b.
243 *
244 * For each edge, consider the direction vector formed from:
245 *
246 * top -> bottom
247 *
248 * which is:
249 *
250 * (dx, dy) = (line.p2.x - line.p1.x, line.p2.y - line.p1.y)
251 *
252 * We then define the slope of each edge as dx/dy, (which is the
253 * inverse of the slope typically used in math instruction). We never
254 * compute a slope directly as the value approaches infinity, but we
255 * can derive a slope comparison without division as follows, (where
256 * the ? represents our compare operator).
257 *
258 * 1. slope(a) ? slope(b)
259 * 2. adx/ady ? bdx/bdy
260 * 3. (adx * bdy) ? (bdx * ady)
261 *
262 * Note that from step 2 to step 3 there is no change needed in the
263 * sign of the result since both ady and bdy are guaranteed to be
264 * greater than or equal to 0.
265 *
266 * When using this slope comparison to sort edges, some care is needed
267 * when interpreting the results. Since the slope compare operates on
268 * distance vectors from top to bottom it gives a correct left to
269 * right sort for edges that have a common top point, (such as two
270 * edges with start events at the same location). On the other hand,
271 * the sense of the result will be exactly reversed for two edges that
272 * have a common stop point.
273 */
274 static inline int
_slope_compare(const cairo_bo_edge_t * a,const cairo_bo_edge_t * b)275 _slope_compare (const cairo_bo_edge_t *a,
276 const cairo_bo_edge_t *b)
277 {
278 /* XXX: We're assuming here that dx and dy will still fit in 32
279 * bits. That's not true in general as there could be overflow. We
280 * should prevent that before the tessellation algorithm
281 * begins.
282 */
283 int32_t adx = a->edge.line.p2.x - a->edge.line.p1.x;
284 int32_t bdx = b->edge.line.p2.x - b->edge.line.p1.x;
285
286 /* Since the dy's are all positive by construction we can fast
287 * path several common cases.
288 */
289
290 /* First check for vertical lines. */
291 if (adx == 0)
292 return -bdx;
293 if (bdx == 0)
294 return adx;
295
296 /* Then where the two edges point in different directions wrt x. */
297 if ((adx ^ bdx) < 0)
298 return adx;
299
300 /* Finally we actually need to do the general comparison. */
301 {
302 int32_t ady = a->edge.line.p2.y - a->edge.line.p1.y;
303 int32_t bdy = b->edge.line.p2.y - b->edge.line.p1.y;
304 cairo_int64_t adx_bdy = _cairo_int32x32_64_mul (adx, bdy);
305 cairo_int64_t bdx_ady = _cairo_int32x32_64_mul (bdx, ady);
306
307 return _cairo_int64_cmp (adx_bdy, bdx_ady);
308 }
309 }
310
311
312 /*
313 * We need to compare the x-coordinate of a line for a particular y wrt to a
314 * given x, without loss of precision.
315 *
316 * The x-coordinate along an edge for a given y is:
317 * X = A_x + (Y - A_y) * A_dx / A_dy
318 *
319 * So the inequality we wish to test is:
320 * A_x + (Y - A_y) * A_dx / A_dy ∘ X
321 * where ∘ is our inequality operator.
322 *
323 * By construction, we know that A_dy (and (Y - A_y)) are
324 * all positive, so we can rearrange it thus without causing a sign change:
325 * (Y - A_y) * A_dx ∘ (X - A_x) * A_dy
326 *
327 * Given the assumption that all the deltas fit within 32 bits, we can compute
328 * this comparison directly using 64 bit arithmetic.
329 *
330 * See the similar discussion for _slope_compare() and
331 * edges_compare_x_for_y_general().
332 */
333 static int
edge_compare_for_y_against_x(const cairo_bo_edge_t * a,int32_t y,int32_t x)334 edge_compare_for_y_against_x (const cairo_bo_edge_t *a,
335 int32_t y,
336 int32_t x)
337 {
338 int32_t adx, ady;
339 int32_t dx, dy;
340 cairo_int64_t L, R;
341
342 if (x < a->edge.line.p1.x && x < a->edge.line.p2.x)
343 return 1;
344 if (x > a->edge.line.p1.x && x > a->edge.line.p2.x)
345 return -1;
346
347 adx = a->edge.line.p2.x - a->edge.line.p1.x;
348 dx = x - a->edge.line.p1.x;
349
350 if (adx == 0)
351 return -dx;
352 if (dx == 0 || (adx ^ dx) < 0)
353 return adx;
354
355 dy = y - a->edge.line.p1.y;
356 ady = a->edge.line.p2.y - a->edge.line.p1.y;
357
358 L = _cairo_int32x32_64_mul (dy, adx);
359 R = _cairo_int32x32_64_mul (dx, ady);
360
361 return _cairo_int64_cmp (L, R);
362 }
363
364 static inline int
_cairo_bo_sweep_line_compare_edges(const cairo_bo_sweep_line_t * sweep_line,const cairo_bo_edge_t * a,const cairo_bo_edge_t * b)365 _cairo_bo_sweep_line_compare_edges (const cairo_bo_sweep_line_t *sweep_line,
366 const cairo_bo_edge_t *a,
367 const cairo_bo_edge_t *b)
368 {
369 int cmp;
370
371 cmp = _cairo_lines_compare_at_y (&a->edge.line,
372 &b->edge.line,
373 sweep_line->current_y);
374 if (cmp)
375 return cmp;
376
377 /* We've got two collinear edges now. */
378 return b->edge.bottom - a->edge.bottom;
379 }
380
381 static inline cairo_int64_t
det32_64(int32_t a,int32_t b,int32_t c,int32_t d)382 det32_64 (int32_t a, int32_t b,
383 int32_t c, int32_t d)
384 {
385 /* det = a * d - b * c */
386 return _cairo_int64_sub (_cairo_int32x32_64_mul (a, d),
387 _cairo_int32x32_64_mul (b, c));
388 }
389
390 static inline cairo_int128_t
det64x32_128(cairo_int64_t a,int32_t b,cairo_int64_t c,int32_t d)391 det64x32_128 (cairo_int64_t a, int32_t b,
392 cairo_int64_t c, int32_t d)
393 {
394 /* det = a * d - b * c */
395 return _cairo_int128_sub (_cairo_int64x32_128_mul (a, d),
396 _cairo_int64x32_128_mul (c, b));
397 }
398
399 /* Compute the intersection of two lines as defined by two edges. The
400 * result is provided as a coordinate pair of 128-bit integers.
401 *
402 * Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection or
403 * %CAIRO_BO_STATUS_PARALLEL if the two lines are exactly parallel.
404 */
405 static cairo_bool_t
intersect_lines(cairo_bo_edge_t * a,cairo_bo_edge_t * b,cairo_bo_intersect_point_t * intersection)406 intersect_lines (cairo_bo_edge_t *a,
407 cairo_bo_edge_t *b,
408 cairo_bo_intersect_point_t *intersection)
409 {
410 cairo_int64_t a_det, b_det;
411
412 /* XXX: We're assuming here that dx and dy will still fit in 32
413 * bits. That's not true in general as there could be overflow. We
414 * should prevent that before the tessellation algorithm begins.
415 * What we're doing to mitigate this is to perform clamping in
416 * cairo_bo_tessellate_polygon().
417 */
418 int32_t dx1 = a->edge.line.p1.x - a->edge.line.p2.x;
419 int32_t dy1 = a->edge.line.p1.y - a->edge.line.p2.y;
420
421 int32_t dx2 = b->edge.line.p1.x - b->edge.line.p2.x;
422 int32_t dy2 = b->edge.line.p1.y - b->edge.line.p2.y;
423
424 cairo_int64_t den_det;
425 cairo_int64_t R;
426 cairo_quorem64_t qr;
427
428 den_det = det32_64 (dx1, dy1, dx2, dy2);
429
430 /* Q: Can we determine that the lines do not intersect (within range)
431 * much more cheaply than computing the intersection point i.e. by
432 * avoiding the division?
433 *
434 * X = ax + t * adx = bx + s * bdx;
435 * Y = ay + t * ady = by + s * bdy;
436 * ∴ t * (ady*bdx - bdy*adx) = bdx * (by - ay) + bdy * (ax - bx)
437 * => t * L = R
438 *
439 * Therefore we can reject any intersection (under the criteria for
440 * valid intersection events) if:
441 * L^R < 0 => t < 0, or
442 * L<R => t > 1
443 *
444 * (where top/bottom must at least extend to the line endpoints).
445 *
446 * A similar substitution can be performed for s, yielding:
447 * s * (ady*bdx - bdy*adx) = ady * (ax - bx) - adx * (ay - by)
448 */
449 R = det32_64 (dx2, dy2,
450 b->edge.line.p1.x - a->edge.line.p1.x,
451 b->edge.line.p1.y - a->edge.line.p1.y);
452 if (_cairo_int64_negative (den_det)) {
453 if (_cairo_int64_ge (den_det, R))
454 return FALSE;
455 } else {
456 if (_cairo_int64_le (den_det, R))
457 return FALSE;
458 }
459
460 R = det32_64 (dy1, dx1,
461 a->edge.line.p1.y - b->edge.line.p1.y,
462 a->edge.line.p1.x - b->edge.line.p1.x);
463 if (_cairo_int64_negative (den_det)) {
464 if (_cairo_int64_ge (den_det, R))
465 return FALSE;
466 } else {
467 if (_cairo_int64_le (den_det, R))
468 return FALSE;
469 }
470
471 /* We now know that the two lines should intersect within range. */
472
473 a_det = det32_64 (a->edge.line.p1.x, a->edge.line.p1.y,
474 a->edge.line.p2.x, a->edge.line.p2.y);
475 b_det = det32_64 (b->edge.line.p1.x, b->edge.line.p1.y,
476 b->edge.line.p2.x, b->edge.line.p2.y);
477
478 /* x = det (a_det, dx1, b_det, dx2) / den_det */
479 qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dx1,
480 b_det, dx2),
481 den_det);
482 if (_cairo_int64_eq (qr.rem, den_det))
483 return FALSE;
484 #if 0
485 intersection->x.exactness = _cairo_int64_is_zero (qr.rem) ? EXACT : INEXACT;
486 #else
487 intersection->x.exactness = EXACT;
488 if (! _cairo_int64_is_zero (qr.rem)) {
489 if (_cairo_int64_negative (den_det) ^ _cairo_int64_negative (qr.rem))
490 qr.rem = _cairo_int64_negate (qr.rem);
491 qr.rem = _cairo_int64_mul (qr.rem, _cairo_int32_to_int64 (2));
492 if (_cairo_int64_ge (qr.rem, den_det)) {
493 qr.quo = _cairo_int64_add (qr.quo,
494 _cairo_int32_to_int64 (_cairo_int64_negative (qr.quo) ? -1 : 1));
495 } else
496 intersection->x.exactness = INEXACT;
497 }
498 #endif
499 intersection->x.ordinate = _cairo_int64_to_int32 (qr.quo);
500
501 /* y = det (a_det, dy1, b_det, dy2) / den_det */
502 qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dy1,
503 b_det, dy2),
504 den_det);
505 if (_cairo_int64_eq (qr.rem, den_det))
506 return FALSE;
507 #if 0
508 intersection->y.exactness = _cairo_int64_is_zero (qr.rem) ? EXACT : INEXACT;
509 #else
510 intersection->y.exactness = EXACT;
511 if (! _cairo_int64_is_zero (qr.rem)) {
512 if (_cairo_int64_negative (den_det) ^ _cairo_int64_negative (qr.rem))
513 qr.rem = _cairo_int64_negate (qr.rem);
514 qr.rem = _cairo_int64_mul (qr.rem, _cairo_int32_to_int64 (2));
515 if (_cairo_int64_ge (qr.rem, den_det)) {
516 qr.quo = _cairo_int64_add (qr.quo,
517 _cairo_int32_to_int64 (_cairo_int64_negative (qr.quo) ? -1 : 1));
518 } else
519 intersection->y.exactness = INEXACT;
520 }
521 #endif
522 intersection->y.ordinate = _cairo_int64_to_int32 (qr.quo);
523
524 return TRUE;
525 }
526
527 static int
_cairo_bo_intersect_ordinate_32_compare(cairo_bo_intersect_ordinate_t a,int32_t b)528 _cairo_bo_intersect_ordinate_32_compare (cairo_bo_intersect_ordinate_t a,
529 int32_t b)
530 {
531 /* First compare the quotient */
532 if (a.ordinate > b)
533 return +1;
534 if (a.ordinate < b)
535 return -1;
536 /* With quotient identical, if remainder is 0 then compare equal */
537 /* Otherwise, the non-zero remainder makes a > b */
538 return INEXACT == a.exactness;
539 }
540
541 /* Does the given edge contain the given point. The point must already
542 * be known to be contained within the line determined by the edge,
543 * (most likely the point results from an intersection of this edge
544 * with another).
545 *
546 * If we had exact arithmetic, then this function would simply be a
547 * matter of examining whether the y value of the point lies within
548 * the range of y values of the edge. But since intersection points
549 * are not exact due to being rounded to the nearest integer within
550 * the available precision, we must also examine the x value of the
551 * point.
552 *
553 * The definition of "contains" here is that the given intersection
554 * point will be seen by the sweep line after the start event for the
555 * given edge and before the stop event for the edge. See the comments
556 * in the implementation for more details.
557 */
558 static cairo_bool_t
_cairo_bo_edge_contains_intersect_point(cairo_bo_edge_t * edge,cairo_bo_intersect_point_t * point)559 _cairo_bo_edge_contains_intersect_point (cairo_bo_edge_t *edge,
560 cairo_bo_intersect_point_t *point)
561 {
562 int cmp_top, cmp_bottom;
563
564 /* XXX: When running the actual algorithm, we don't actually need to
565 * compare against edge->top at all here, since any intersection above
566 * top is eliminated early via a slope comparison. We're leaving these
567 * here for now only for the sake of the quadratic-time intersection
568 * finder which needs them.
569 */
570
571 cmp_top = _cairo_bo_intersect_ordinate_32_compare (point->y,
572 edge->edge.top);
573 cmp_bottom = _cairo_bo_intersect_ordinate_32_compare (point->y,
574 edge->edge.bottom);
575
576 if (cmp_top < 0 || cmp_bottom > 0)
577 {
578 return FALSE;
579 }
580
581 if (cmp_top > 0 && cmp_bottom < 0)
582 {
583 return TRUE;
584 }
585
586 /* At this stage, the point lies on the same y value as either
587 * edge->top or edge->bottom, so we have to examine the x value in
588 * order to properly determine containment. */
589
590 /* If the y value of the point is the same as the y value of the
591 * top of the edge, then the x value of the point must be greater
592 * to be considered as inside the edge. Similarly, if the y value
593 * of the point is the same as the y value of the bottom of the
594 * edge, then the x value of the point must be less to be
595 * considered as inside. */
596
597 if (cmp_top == 0) {
598 cairo_fixed_t top_x;
599
600 top_x = _line_compute_intersection_x_for_y (&edge->edge.line,
601 edge->edge.top);
602 return _cairo_bo_intersect_ordinate_32_compare (point->x, top_x) > 0;
603 } else { /* cmp_bottom == 0 */
604 cairo_fixed_t bot_x;
605
606 bot_x = _line_compute_intersection_x_for_y (&edge->edge.line,
607 edge->edge.bottom);
608 return _cairo_bo_intersect_ordinate_32_compare (point->x, bot_x) < 0;
609 }
610 }
611
612 /* Compute the intersection of two edges. The result is provided as a
613 * coordinate pair of 128-bit integers.
614 *
615 * Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection
616 * that is within both edges, %CAIRO_BO_STATUS_NO_INTERSECTION if the
617 * intersection of the lines defined by the edges occurs outside of
618 * one or both edges, and %CAIRO_BO_STATUS_PARALLEL if the two edges
619 * are exactly parallel.
620 *
621 * Note that when determining if a candidate intersection is "inside"
622 * an edge, we consider both the infinitesimal shortening and the
623 * infinitesimal tilt rules described by John Hobby. Specifically, if
624 * the intersection is exactly the same as an edge point, it is
625 * effectively outside (no intersection is returned). Also, if the
626 * intersection point has the same
627 */
628 static cairo_bool_t
_cairo_bo_edge_intersect(cairo_bo_edge_t * a,cairo_bo_edge_t * b,cairo_bo_point32_t * intersection)629 _cairo_bo_edge_intersect (cairo_bo_edge_t *a,
630 cairo_bo_edge_t *b,
631 cairo_bo_point32_t *intersection)
632 {
633 cairo_bo_intersect_point_t quorem;
634
635 if (! intersect_lines (a, b, &quorem))
636 return FALSE;
637
638 if (! _cairo_bo_edge_contains_intersect_point (a, &quorem))
639 return FALSE;
640
641 if (! _cairo_bo_edge_contains_intersect_point (b, &quorem))
642 return FALSE;
643
644 /* Now that we've correctly compared the intersection point and
645 * determined that it lies within the edge, then we know that we
646 * no longer need any more bits of storage for the intersection
647 * than we do for our edge coordinates. We also no longer need the
648 * remainder from the division. */
649 intersection->x = quorem.x.ordinate;
650 intersection->y = quorem.y.ordinate;
651
652 return TRUE;
653 }
654
655 static inline int
cairo_bo_event_compare(const cairo_bo_event_t * a,const cairo_bo_event_t * b)656 cairo_bo_event_compare (const cairo_bo_event_t *a,
657 const cairo_bo_event_t *b)
658 {
659 int cmp;
660
661 cmp = _cairo_bo_point32_compare (&a->point, &b->point);
662 if (cmp)
663 return cmp;
664
665 cmp = a->type - b->type;
666 if (cmp)
667 return cmp;
668
669 return a - b;
670 }
671
672 static inline void
_pqueue_init(pqueue_t * pq)673 _pqueue_init (pqueue_t *pq)
674 {
675 pq->max_size = ARRAY_LENGTH (pq->elements_embedded);
676 pq->size = 0;
677
678 pq->elements = pq->elements_embedded;
679 }
680
681 static inline void
_pqueue_fini(pqueue_t * pq)682 _pqueue_fini (pqueue_t *pq)
683 {
684 if (pq->elements != pq->elements_embedded)
685 free (pq->elements);
686 }
687
688 static cairo_status_t
_pqueue_grow(pqueue_t * pq)689 _pqueue_grow (pqueue_t *pq)
690 {
691 cairo_bo_event_t **new_elements;
692 pq->max_size *= 2;
693
694 if (pq->elements == pq->elements_embedded) {
695 new_elements = _cairo_malloc_ab (pq->max_size,
696 sizeof (cairo_bo_event_t *));
697 if (unlikely (new_elements == NULL))
698 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
699
700 memcpy (new_elements, pq->elements_embedded,
701 sizeof (pq->elements_embedded));
702 } else {
703 new_elements = _cairo_realloc_ab (pq->elements,
704 pq->max_size,
705 sizeof (cairo_bo_event_t *));
706 if (unlikely (new_elements == NULL))
707 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
708 }
709
710 pq->elements = new_elements;
711 return CAIRO_STATUS_SUCCESS;
712 }
713
714 static inline cairo_status_t
_pqueue_push(pqueue_t * pq,cairo_bo_event_t * event)715 _pqueue_push (pqueue_t *pq, cairo_bo_event_t *event)
716 {
717 cairo_bo_event_t **elements;
718 int i, parent;
719
720 if (unlikely (pq->size + 1 == pq->max_size)) {
721 cairo_status_t status;
722
723 status = _pqueue_grow (pq);
724 if (unlikely (status))
725 return status;
726 }
727
728 elements = pq->elements;
729
730 for (i = ++pq->size;
731 i != PQ_FIRST_ENTRY &&
732 cairo_bo_event_compare (event,
733 elements[parent = PQ_PARENT_INDEX (i)]) < 0;
734 i = parent)
735 {
736 elements[i] = elements[parent];
737 }
738
739 elements[i] = event;
740
741 return CAIRO_STATUS_SUCCESS;
742 }
743
744 static inline void
_pqueue_pop(pqueue_t * pq)745 _pqueue_pop (pqueue_t *pq)
746 {
747 cairo_bo_event_t **elements = pq->elements;
748 cairo_bo_event_t *tail;
749 int child, i;
750
751 tail = elements[pq->size--];
752 if (pq->size == 0) {
753 elements[PQ_FIRST_ENTRY] = NULL;
754 return;
755 }
756
757 for (i = PQ_FIRST_ENTRY;
758 (child = PQ_LEFT_CHILD_INDEX (i)) <= pq->size;
759 i = child)
760 {
761 if (child != pq->size &&
762 cairo_bo_event_compare (elements[child+1],
763 elements[child]) < 0)
764 {
765 child++;
766 }
767
768 if (cairo_bo_event_compare (elements[child], tail) >= 0)
769 break;
770
771 elements[i] = elements[child];
772 }
773 elements[i] = tail;
774 }
775
776 static inline cairo_status_t
_cairo_bo_event_queue_insert(cairo_bo_event_queue_t * queue,cairo_bo_event_type_t type,cairo_bo_edge_t * e1,cairo_bo_edge_t * e2,const cairo_point_t * point)777 _cairo_bo_event_queue_insert (cairo_bo_event_queue_t *queue,
778 cairo_bo_event_type_t type,
779 cairo_bo_edge_t *e1,
780 cairo_bo_edge_t *e2,
781 const cairo_point_t *point)
782 {
783 cairo_bo_queue_event_t *event;
784
785 event = _cairo_freepool_alloc (&queue->pool);
786 if (unlikely (event == NULL))
787 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
788
789 event->type = type;
790 event->e1 = e1;
791 event->e2 = e2;
792 event->point = *point;
793
794 return _pqueue_push (&queue->pqueue, (cairo_bo_event_t *) event);
795 }
796
797 static void
_cairo_bo_event_queue_delete(cairo_bo_event_queue_t * queue,cairo_bo_event_t * event)798 _cairo_bo_event_queue_delete (cairo_bo_event_queue_t *queue,
799 cairo_bo_event_t *event)
800 {
801 _cairo_freepool_free (&queue->pool, event);
802 }
803
804 static cairo_bo_event_t *
_cairo_bo_event_dequeue(cairo_bo_event_queue_t * event_queue)805 _cairo_bo_event_dequeue (cairo_bo_event_queue_t *event_queue)
806 {
807 cairo_bo_event_t *event, *cmp;
808
809 event = event_queue->pqueue.elements[PQ_FIRST_ENTRY];
810 cmp = *event_queue->start_events;
811 if (event == NULL ||
812 (cmp != NULL && cairo_bo_event_compare (cmp, event) < 0))
813 {
814 event = cmp;
815 event_queue->start_events++;
816 }
817 else
818 {
819 _pqueue_pop (&event_queue->pqueue);
820 }
821
822 return event;
823 }
824
CAIRO_COMBSORT_DECLARE(_cairo_bo_event_queue_sort,cairo_bo_event_t *,cairo_bo_event_compare)825 CAIRO_COMBSORT_DECLARE (_cairo_bo_event_queue_sort,
826 cairo_bo_event_t *,
827 cairo_bo_event_compare)
828
829 static void
830 _cairo_bo_event_queue_init (cairo_bo_event_queue_t *event_queue,
831 cairo_bo_event_t **start_events,
832 int num_events)
833 {
834 event_queue->start_events = start_events;
835
836 _cairo_freepool_init (&event_queue->pool,
837 sizeof (cairo_bo_queue_event_t));
838 _pqueue_init (&event_queue->pqueue);
839 event_queue->pqueue.elements[PQ_FIRST_ENTRY] = NULL;
840 }
841
842 static cairo_status_t
_cairo_bo_event_queue_insert_stop(cairo_bo_event_queue_t * event_queue,cairo_bo_edge_t * edge)843 _cairo_bo_event_queue_insert_stop (cairo_bo_event_queue_t *event_queue,
844 cairo_bo_edge_t *edge)
845 {
846 cairo_bo_point32_t point;
847
848 point.y = edge->edge.bottom;
849 point.x = _line_compute_intersection_x_for_y (&edge->edge.line,
850 point.y);
851 return _cairo_bo_event_queue_insert (event_queue,
852 CAIRO_BO_EVENT_TYPE_STOP,
853 edge, NULL,
854 &point);
855 }
856
857 static void
_cairo_bo_event_queue_fini(cairo_bo_event_queue_t * event_queue)858 _cairo_bo_event_queue_fini (cairo_bo_event_queue_t *event_queue)
859 {
860 _pqueue_fini (&event_queue->pqueue);
861 _cairo_freepool_fini (&event_queue->pool);
862 }
863
864 static inline cairo_status_t
_cairo_bo_event_queue_insert_if_intersect_below_current_y(cairo_bo_event_queue_t * event_queue,cairo_bo_edge_t * left,cairo_bo_edge_t * right)865 _cairo_bo_event_queue_insert_if_intersect_below_current_y (cairo_bo_event_queue_t *event_queue,
866 cairo_bo_edge_t *left,
867 cairo_bo_edge_t *right)
868 {
869 cairo_bo_point32_t intersection;
870
871 if (MAX (left->edge.line.p1.x, left->edge.line.p2.x) <=
872 MIN (right->edge.line.p1.x, right->edge.line.p2.x))
873 return CAIRO_STATUS_SUCCESS;
874
875 if (cairo_lines_equal (&left->edge.line, &right->edge.line))
876 return CAIRO_STATUS_SUCCESS;
877
878 /* The names "left" and "right" here are correct descriptions of
879 * the order of the two edges within the active edge list. So if a
880 * slope comparison also puts left less than right, then we know
881 * that the intersection of these two segments has already
882 * occurred before the current sweep line position. */
883 if (_slope_compare (left, right) <= 0)
884 return CAIRO_STATUS_SUCCESS;
885
886 if (! _cairo_bo_edge_intersect (left, right, &intersection))
887 return CAIRO_STATUS_SUCCESS;
888
889 return _cairo_bo_event_queue_insert (event_queue,
890 CAIRO_BO_EVENT_TYPE_INTERSECTION,
891 left, right,
892 &intersection);
893 }
894
895 static void
_cairo_bo_sweep_line_init(cairo_bo_sweep_line_t * sweep_line)896 _cairo_bo_sweep_line_init (cairo_bo_sweep_line_t *sweep_line)
897 {
898 sweep_line->head = NULL;
899 sweep_line->stopped = NULL;
900 sweep_line->current_y = INT32_MIN;
901 sweep_line->current_edge = NULL;
902 }
903
904 static void
_cairo_bo_sweep_line_insert(cairo_bo_sweep_line_t * sweep_line,cairo_bo_edge_t * edge)905 _cairo_bo_sweep_line_insert (cairo_bo_sweep_line_t *sweep_line,
906 cairo_bo_edge_t *edge)
907 {
908 if (sweep_line->current_edge != NULL) {
909 cairo_bo_edge_t *prev, *next;
910 int cmp;
911
912 cmp = _cairo_bo_sweep_line_compare_edges (sweep_line,
913 sweep_line->current_edge,
914 edge);
915 if (cmp < 0) {
916 prev = sweep_line->current_edge;
917 next = prev->next;
918 while (next != NULL &&
919 _cairo_bo_sweep_line_compare_edges (sweep_line,
920 next, edge) < 0)
921 {
922 prev = next, next = prev->next;
923 }
924
925 prev->next = edge;
926 edge->prev = prev;
927 edge->next = next;
928 if (next != NULL)
929 next->prev = edge;
930 } else if (cmp > 0) {
931 next = sweep_line->current_edge;
932 prev = next->prev;
933 while (prev != NULL &&
934 _cairo_bo_sweep_line_compare_edges (sweep_line,
935 prev, edge) > 0)
936 {
937 next = prev, prev = next->prev;
938 }
939
940 next->prev = edge;
941 edge->next = next;
942 edge->prev = prev;
943 if (prev != NULL)
944 prev->next = edge;
945 else
946 sweep_line->head = edge;
947 } else {
948 prev = sweep_line->current_edge;
949 edge->prev = prev;
950 edge->next = prev->next;
951 if (prev->next != NULL)
952 prev->next->prev = edge;
953 prev->next = edge;
954 }
955 } else {
956 sweep_line->head = edge;
957 edge->next = NULL;
958 }
959
960 sweep_line->current_edge = edge;
961 }
962
963 static void
_cairo_bo_sweep_line_delete(cairo_bo_sweep_line_t * sweep_line,cairo_bo_edge_t * edge)964 _cairo_bo_sweep_line_delete (cairo_bo_sweep_line_t *sweep_line,
965 cairo_bo_edge_t *edge)
966 {
967 if (edge->prev != NULL)
968 edge->prev->next = edge->next;
969 else
970 sweep_line->head = edge->next;
971
972 if (edge->next != NULL)
973 edge->next->prev = edge->prev;
974
975 if (sweep_line->current_edge == edge)
976 sweep_line->current_edge = edge->prev ? edge->prev : edge->next;
977 }
978
979 static void
_cairo_bo_sweep_line_swap(cairo_bo_sweep_line_t * sweep_line,cairo_bo_edge_t * left,cairo_bo_edge_t * right)980 _cairo_bo_sweep_line_swap (cairo_bo_sweep_line_t *sweep_line,
981 cairo_bo_edge_t *left,
982 cairo_bo_edge_t *right)
983 {
984 if (left->prev != NULL)
985 left->prev->next = right;
986 else
987 sweep_line->head = right;
988
989 if (right->next != NULL)
990 right->next->prev = left;
991
992 left->next = right->next;
993 right->next = left;
994
995 right->prev = left->prev;
996 left->prev = right;
997 }
998
999 #if DEBUG_PRINT_STATE
1000 static void
_cairo_bo_edge_print(cairo_bo_edge_t * edge)1001 _cairo_bo_edge_print (cairo_bo_edge_t *edge)
1002 {
1003 printf ("(0x%x, 0x%x)-(0x%x, 0x%x)",
1004 edge->edge.line.p1.x, edge->edge.line.p1.y,
1005 edge->edge.line.p2.x, edge->edge.line.p2.y);
1006 }
1007
1008 static void
_cairo_bo_event_print(cairo_bo_event_t * event)1009 _cairo_bo_event_print (cairo_bo_event_t *event)
1010 {
1011 switch (event->type) {
1012 case CAIRO_BO_EVENT_TYPE_START:
1013 printf ("Start: ");
1014 break;
1015 case CAIRO_BO_EVENT_TYPE_STOP:
1016 printf ("Stop: ");
1017 break;
1018 case CAIRO_BO_EVENT_TYPE_INTERSECTION:
1019 printf ("Intersection: ");
1020 break;
1021 }
1022 printf ("(%d, %d)\t", event->point.x, event->point.y);
1023 _cairo_bo_edge_print (event->e1);
1024 if (event->type == CAIRO_BO_EVENT_TYPE_INTERSECTION) {
1025 printf (" X ");
1026 _cairo_bo_edge_print (event->e2);
1027 }
1028 printf ("\n");
1029 }
1030
1031 static void
_cairo_bo_event_queue_print(cairo_bo_event_queue_t * event_queue)1032 _cairo_bo_event_queue_print (cairo_bo_event_queue_t *event_queue)
1033 {
1034 /* XXX: fixme to print the start/stop array too. */
1035 printf ("Event queue:\n");
1036 }
1037
1038 static void
_cairo_bo_sweep_line_print(cairo_bo_sweep_line_t * sweep_line)1039 _cairo_bo_sweep_line_print (cairo_bo_sweep_line_t *sweep_line)
1040 {
1041 cairo_bool_t first = TRUE;
1042 cairo_bo_edge_t *edge;
1043
1044 printf ("Sweep line from edge list: ");
1045 first = TRUE;
1046 for (edge = sweep_line->head;
1047 edge;
1048 edge = edge->next)
1049 {
1050 if (!first)
1051 printf (", ");
1052 _cairo_bo_edge_print (edge);
1053 first = FALSE;
1054 }
1055 printf ("\n");
1056 }
1057
1058 static void
print_state(const char * msg,cairo_bo_event_t * event,cairo_bo_event_queue_t * event_queue,cairo_bo_sweep_line_t * sweep_line)1059 print_state (const char *msg,
1060 cairo_bo_event_t *event,
1061 cairo_bo_event_queue_t *event_queue,
1062 cairo_bo_sweep_line_t *sweep_line)
1063 {
1064 printf ("%s ", msg);
1065 _cairo_bo_event_print (event);
1066 _cairo_bo_event_queue_print (event_queue);
1067 _cairo_bo_sweep_line_print (sweep_line);
1068 printf ("\n");
1069 }
1070 #endif
1071
1072 #if DEBUG_EVENTS
1073 static void CAIRO_PRINTF_FORMAT (1, 2)
event_log(const char * fmt,...)1074 event_log (const char *fmt, ...)
1075 {
1076 FILE *file;
1077
1078 if (getenv ("CAIRO_DEBUG_EVENTS") == NULL)
1079 return;
1080
1081 file = fopen ("bo-events.txt", "a");
1082 if (file != NULL) {
1083 va_list ap;
1084
1085 va_start (ap, fmt);
1086 vfprintf (file, fmt, ap);
1087 va_end (ap);
1088
1089 fclose (file);
1090 }
1091 }
1092 #endif
1093
1094 #define HAS_COLINEAR(a, b) ((cairo_bo_edge_t *)(((uintptr_t)(a))&~1) == (b))
1095 #define IS_COLINEAR(e) (((uintptr_t)(e))&1)
1096 #define MARK_COLINEAR(e, v) ((cairo_bo_edge_t *)(((uintptr_t)(e))|(v)))
1097
1098 static inline cairo_bool_t
edges_colinear(cairo_bo_edge_t * a,const cairo_bo_edge_t * b)1099 edges_colinear (cairo_bo_edge_t *a, const cairo_bo_edge_t *b)
1100 {
1101 unsigned p;
1102
1103 if (HAS_COLINEAR(a->colinear, b))
1104 return IS_COLINEAR(a->colinear);
1105
1106 if (HAS_COLINEAR(b->colinear, a)) {
1107 p = IS_COLINEAR(b->colinear);
1108 a->colinear = MARK_COLINEAR(b, p);
1109 return p;
1110 }
1111
1112 p = 0;
1113 p |= (a->edge.line.p1.x == b->edge.line.p1.x) << 0;
1114 p |= (a->edge.line.p1.y == b->edge.line.p1.y) << 1;
1115 p |= (a->edge.line.p2.x == b->edge.line.p2.x) << 3;
1116 p |= (a->edge.line.p2.y == b->edge.line.p2.y) << 4;
1117 if (p == ((1 << 0) | (1 << 1) | (1 << 3) | (1 << 4))) {
1118 a->colinear = MARK_COLINEAR(b, 1);
1119 return TRUE;
1120 }
1121
1122 if (_slope_compare (a, b)) {
1123 a->colinear = MARK_COLINEAR(b, 0);
1124 return FALSE;
1125 }
1126
1127 /* The choice of y is not truly arbitrary since we must guarantee that it
1128 * is greater than the start of either line.
1129 */
1130 if (p != 0) {
1131 /* colinear if either end-point are coincident */
1132 p = (((p >> 1) & p) & 5) != 0;
1133 } else if (a->edge.line.p1.y < b->edge.line.p1.y) {
1134 p = edge_compare_for_y_against_x (b,
1135 a->edge.line.p1.y,
1136 a->edge.line.p1.x) == 0;
1137 } else {
1138 p = edge_compare_for_y_against_x (a,
1139 b->edge.line.p1.y,
1140 b->edge.line.p1.x) == 0;
1141 }
1142
1143 a->colinear = MARK_COLINEAR(b, p);
1144 return p;
1145 }
1146
1147 /* Adds the trapezoid, if any, of the left edge to the #cairo_traps_t */
1148 static void
_cairo_bo_edge_end_trap(cairo_bo_edge_t * left,int32_t bot,cairo_traps_t * traps)1149 _cairo_bo_edge_end_trap (cairo_bo_edge_t *left,
1150 int32_t bot,
1151 cairo_traps_t *traps)
1152 {
1153 cairo_bo_trap_t *trap = &left->deferred_trap;
1154
1155 /* Only emit (trivial) non-degenerate trapezoids with positive height. */
1156 if (likely (trap->top < bot)) {
1157 _cairo_traps_add_trap (traps,
1158 trap->top, bot,
1159 &left->edge.line, &trap->right->edge.line);
1160
1161 #if DEBUG_PRINT_STATE
1162 printf ("Deferred trap: left=(%x, %x)-(%x,%x) "
1163 "right=(%x,%x)-(%x,%x) top=%x, bot=%x\n",
1164 left->edge.line.p1.x, left->edge.line.p1.y,
1165 left->edge.line.p2.x, left->edge.line.p2.y,
1166 trap->right->edge.line.p1.x, trap->right->edge.line.p1.y,
1167 trap->right->edge.line.p2.x, trap->right->edge.line.p2.y,
1168 trap->top, bot);
1169 #endif
1170 #if DEBUG_EVENTS
1171 event_log ("end trap: %lu %lu %d %d\n",
1172 (long) left,
1173 (long) trap->right,
1174 trap->top,
1175 bot);
1176 #endif
1177 }
1178
1179 trap->right = NULL;
1180 }
1181
1182
1183 /* Start a new trapezoid at the given top y coordinate, whose edges
1184 * are `edge' and `edge->next'. If `edge' already has a trapezoid,
1185 * then either add it to the traps in `traps', if the trapezoid's
1186 * right edge differs from `edge->next', or do nothing if the new
1187 * trapezoid would be a continuation of the existing one. */
1188 static inline void
_cairo_bo_edge_start_or_continue_trap(cairo_bo_edge_t * left,cairo_bo_edge_t * right,int top,cairo_traps_t * traps)1189 _cairo_bo_edge_start_or_continue_trap (cairo_bo_edge_t *left,
1190 cairo_bo_edge_t *right,
1191 int top,
1192 cairo_traps_t *traps)
1193 {
1194 if (left->deferred_trap.right == right)
1195 return;
1196
1197 assert (right);
1198 if (left->deferred_trap.right != NULL) {
1199 if (edges_colinear (left->deferred_trap.right, right))
1200 {
1201 /* continuation on right, so just swap edges */
1202 left->deferred_trap.right = right;
1203 return;
1204 }
1205
1206 _cairo_bo_edge_end_trap (left, top, traps);
1207 }
1208
1209 if (! edges_colinear (left, right)) {
1210 left->deferred_trap.top = top;
1211 left->deferred_trap.right = right;
1212
1213 #if DEBUG_EVENTS
1214 event_log ("begin trap: %lu %lu %d\n",
1215 (long) left,
1216 (long) right,
1217 top);
1218 #endif
1219 }
1220 }
1221
1222 static inline void
_active_edges_to_traps(cairo_bo_edge_t * pos,int32_t top,unsigned mask,cairo_traps_t * traps)1223 _active_edges_to_traps (cairo_bo_edge_t *pos,
1224 int32_t top,
1225 unsigned mask,
1226 cairo_traps_t *traps)
1227 {
1228 cairo_bo_edge_t *left;
1229 int in_out;
1230
1231
1232 #if DEBUG_PRINT_STATE
1233 printf ("Processing active edges for %x\n", top);
1234 #endif
1235
1236 in_out = 0;
1237 left = pos;
1238 while (pos != NULL) {
1239 if (pos != left && pos->deferred_trap.right) {
1240 /* XXX It shouldn't be possible to here with 2 deferred traps
1241 * on colinear edges... See bug-bo-rictoz.
1242 */
1243 if (left->deferred_trap.right == NULL &&
1244 edges_colinear (left, pos))
1245 {
1246 /* continuation on left */
1247 left->deferred_trap = pos->deferred_trap;
1248 pos->deferred_trap.right = NULL;
1249 }
1250 else
1251 {
1252 _cairo_bo_edge_end_trap (pos, top, traps);
1253 }
1254 }
1255
1256 in_out += pos->edge.dir;
1257 if ((in_out & mask) == 0) {
1258 /* skip co-linear edges */
1259 if (pos->next == NULL || ! edges_colinear (pos, pos->next)) {
1260 _cairo_bo_edge_start_or_continue_trap (left, pos, top, traps);
1261 left = pos->next;
1262 }
1263 }
1264
1265 pos = pos->next;
1266 }
1267 }
1268
1269 /* Execute a single pass of the Bentley-Ottmann algorithm on edges,
1270 * generating trapezoids according to the fill_rule and appending them
1271 * to traps. */
1272 static cairo_status_t
_cairo_bentley_ottmann_tessellate_bo_edges(cairo_bo_event_t ** start_events,int num_events,unsigned fill_rule,cairo_traps_t * traps,int * num_intersections)1273 _cairo_bentley_ottmann_tessellate_bo_edges (cairo_bo_event_t **start_events,
1274 int num_events,
1275 unsigned fill_rule,
1276 cairo_traps_t *traps,
1277 int *num_intersections)
1278 {
1279 cairo_status_t status;
1280 int intersection_count = 0;
1281 cairo_bo_event_queue_t event_queue;
1282 cairo_bo_sweep_line_t sweep_line;
1283 cairo_bo_event_t *event;
1284 cairo_bo_edge_t *left, *right;
1285 cairo_bo_edge_t *e1, *e2;
1286
1287 /* convert the fill_rule into a winding mask */
1288 if (fill_rule == CAIRO_FILL_RULE_WINDING)
1289 fill_rule = (unsigned) -1;
1290 else
1291 fill_rule = 1;
1292
1293 #if DEBUG_EVENTS
1294 {
1295 int i;
1296
1297 for (i = 0; i < num_events; i++) {
1298 cairo_bo_start_event_t *event =
1299 ((cairo_bo_start_event_t **) start_events)[i];
1300 event_log ("edge: %lu (%d, %d) (%d, %d) (%d, %d) %d\n",
1301 (long) &events[i].edge,
1302 event->edge.edge.line.p1.x,
1303 event->edge.edge.line.p1.y,
1304 event->edge.edge.line.p2.x,
1305 event->edge.edge.line.p2.y,
1306 event->edge.top,
1307 event->edge.bottom,
1308 event->edge.edge.dir);
1309 }
1310 }
1311 #endif
1312
1313 _cairo_bo_event_queue_init (&event_queue, start_events, num_events);
1314 _cairo_bo_sweep_line_init (&sweep_line);
1315
1316 while ((event = _cairo_bo_event_dequeue (&event_queue))) {
1317 if (event->point.y != sweep_line.current_y) {
1318 for (e1 = sweep_line.stopped; e1; e1 = e1->next) {
1319 if (e1->deferred_trap.right != NULL) {
1320 _cairo_bo_edge_end_trap (e1,
1321 e1->edge.bottom,
1322 traps);
1323 }
1324 }
1325 sweep_line.stopped = NULL;
1326
1327 _active_edges_to_traps (sweep_line.head,
1328 sweep_line.current_y,
1329 fill_rule, traps);
1330
1331 sweep_line.current_y = event->point.y;
1332 }
1333
1334 #if DEBUG_EVENTS
1335 event_log ("event: %d (%ld, %ld) %lu, %lu\n",
1336 event->type,
1337 (long) event->point.x,
1338 (long) event->point.y,
1339 (long) event->e1,
1340 (long) event->e2);
1341 #endif
1342
1343 switch (event->type) {
1344 case CAIRO_BO_EVENT_TYPE_START:
1345 e1 = &((cairo_bo_start_event_t *) event)->edge;
1346
1347 _cairo_bo_sweep_line_insert (&sweep_line, e1);
1348
1349 status = _cairo_bo_event_queue_insert_stop (&event_queue, e1);
1350 if (unlikely (status))
1351 goto unwind;
1352
1353 /* check to see if this is a continuation of a stopped edge */
1354 /* XXX change to an infinitesimal lengthening rule */
1355 for (left = sweep_line.stopped; left; left = left->next) {
1356 if (e1->edge.top <= left->edge.bottom &&
1357 edges_colinear (e1, left))
1358 {
1359 e1->deferred_trap = left->deferred_trap;
1360 if (left->prev != NULL)
1361 left->prev = left->next;
1362 else
1363 sweep_line.stopped = left->next;
1364 if (left->next != NULL)
1365 left->next->prev = left->prev;
1366 break;
1367 }
1368 }
1369
1370 left = e1->prev;
1371 right = e1->next;
1372
1373 if (left != NULL) {
1374 status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, e1);
1375 if (unlikely (status))
1376 goto unwind;
1377 }
1378
1379 if (right != NULL) {
1380 status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right);
1381 if (unlikely (status))
1382 goto unwind;
1383 }
1384
1385 break;
1386
1387 case CAIRO_BO_EVENT_TYPE_STOP:
1388 e1 = ((cairo_bo_queue_event_t *) event)->e1;
1389 _cairo_bo_event_queue_delete (&event_queue, event);
1390
1391 left = e1->prev;
1392 right = e1->next;
1393
1394 _cairo_bo_sweep_line_delete (&sweep_line, e1);
1395
1396 /* first, check to see if we have a continuation via a fresh edge */
1397 if (e1->deferred_trap.right != NULL) {
1398 e1->next = sweep_line.stopped;
1399 if (sweep_line.stopped != NULL)
1400 sweep_line.stopped->prev = e1;
1401 sweep_line.stopped = e1;
1402 e1->prev = NULL;
1403 }
1404
1405 if (left != NULL && right != NULL) {
1406 status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, right);
1407 if (unlikely (status))
1408 goto unwind;
1409 }
1410
1411 break;
1412
1413 case CAIRO_BO_EVENT_TYPE_INTERSECTION:
1414 e1 = ((cairo_bo_queue_event_t *) event)->e1;
1415 e2 = ((cairo_bo_queue_event_t *) event)->e2;
1416 _cairo_bo_event_queue_delete (&event_queue, event);
1417
1418 /* skip this intersection if its edges are not adjacent */
1419 if (e2 != e1->next)
1420 break;
1421
1422 intersection_count++;
1423
1424 left = e1->prev;
1425 right = e2->next;
1426
1427 _cairo_bo_sweep_line_swap (&sweep_line, e1, e2);
1428
1429 /* after the swap e2 is left of e1 */
1430
1431 if (left != NULL) {
1432 status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, e2);
1433 if (unlikely (status))
1434 goto unwind;
1435 }
1436
1437 if (right != NULL) {
1438 status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right);
1439 if (unlikely (status))
1440 goto unwind;
1441 }
1442
1443 break;
1444 }
1445 }
1446
1447 *num_intersections = intersection_count;
1448 for (e1 = sweep_line.stopped; e1; e1 = e1->next) {
1449 if (e1->deferred_trap.right != NULL) {
1450 _cairo_bo_edge_end_trap (e1, e1->edge.bottom, traps);
1451 }
1452 }
1453 status = traps->status;
1454 unwind:
1455 _cairo_bo_event_queue_fini (&event_queue);
1456
1457 #if DEBUG_EVENTS
1458 event_log ("\n");
1459 #endif
1460
1461 return status;
1462 }
1463
1464 cairo_status_t
_cairo_bentley_ottmann_tessellate_polygon(cairo_traps_t * traps,const cairo_polygon_t * polygon,cairo_fill_rule_t fill_rule)1465 _cairo_bentley_ottmann_tessellate_polygon (cairo_traps_t *traps,
1466 const cairo_polygon_t *polygon,
1467 cairo_fill_rule_t fill_rule)
1468 {
1469 int intersections;
1470 cairo_bo_start_event_t stack_events[CAIRO_STACK_ARRAY_LENGTH (cairo_bo_start_event_t)];
1471 cairo_bo_start_event_t *events;
1472 cairo_bo_event_t *stack_event_ptrs[ARRAY_LENGTH (stack_events) + 1];
1473 cairo_bo_event_t **event_ptrs;
1474 cairo_bo_start_event_t *stack_event_y[64];
1475 cairo_bo_start_event_t **event_y = NULL;
1476 int i, num_events, y, ymin, ymax;
1477 cairo_status_t status;
1478
1479 num_events = polygon->num_edges;
1480 if (unlikely (0 == num_events))
1481 return CAIRO_STATUS_SUCCESS;
1482
1483 if (polygon->num_limits) {
1484 ymin = _cairo_fixed_integer_floor (polygon->limit.p1.y);
1485 ymax = _cairo_fixed_integer_ceil (polygon->limit.p2.y) - ymin;
1486
1487 if (ymax > 64) {
1488 event_y = _cairo_malloc_ab(sizeof (cairo_bo_event_t*), ymax);
1489 if (unlikely (event_y == NULL))
1490 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
1491 } else {
1492 event_y = stack_event_y;
1493 }
1494 memset (event_y, 0, ymax * sizeof(cairo_bo_event_t *));
1495 }
1496
1497 events = stack_events;
1498 event_ptrs = stack_event_ptrs;
1499 if (num_events > ARRAY_LENGTH (stack_events)) {
1500 events = _cairo_malloc_ab_plus_c (num_events,
1501 sizeof (cairo_bo_start_event_t) +
1502 sizeof (cairo_bo_event_t *),
1503 sizeof (cairo_bo_event_t *));
1504 if (unlikely (events == NULL)) {
1505 if (event_y != stack_event_y)
1506 free (event_y);
1507 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
1508 }
1509
1510 event_ptrs = (cairo_bo_event_t **) (events + num_events);
1511 }
1512
1513 for (i = 0; i < num_events; i++) {
1514 events[i].type = CAIRO_BO_EVENT_TYPE_START;
1515 events[i].point.y = polygon->edges[i].top;
1516 events[i].point.x =
1517 _line_compute_intersection_x_for_y (&polygon->edges[i].line,
1518 events[i].point.y);
1519
1520 events[i].edge.edge = polygon->edges[i];
1521 events[i].edge.deferred_trap.right = NULL;
1522 events[i].edge.prev = NULL;
1523 events[i].edge.next = NULL;
1524 events[i].edge.colinear = NULL;
1525
1526 if (event_y) {
1527 y = _cairo_fixed_integer_floor (events[i].point.y) - ymin;
1528 events[i].edge.next = (cairo_bo_edge_t *) event_y[y];
1529 event_y[y] = (cairo_bo_start_event_t *) &events[i];
1530 } else
1531 event_ptrs[i] = (cairo_bo_event_t *) &events[i];
1532 }
1533
1534 if (event_y) {
1535 for (y = i = 0; y < ymax && i < num_events; y++) {
1536 cairo_bo_start_event_t *e;
1537 int j = i;
1538 for (e = event_y[y]; e; e = (cairo_bo_start_event_t *)e->edge.next)
1539 event_ptrs[i++] = (cairo_bo_event_t *) e;
1540 if (i > j + 1)
1541 _cairo_bo_event_queue_sort (event_ptrs+j, i-j);
1542 }
1543 if (event_y != stack_event_y)
1544 free (event_y);
1545 } else
1546 _cairo_bo_event_queue_sort (event_ptrs, i);
1547 event_ptrs[i] = NULL;
1548
1549 #if DEBUG_TRAPS
1550 dump_edges (events, num_events, "bo-polygon-edges.txt");
1551 #endif
1552
1553 /* XXX: This would be the convenient place to throw in multiple
1554 * passes of the Bentley-Ottmann algorithm. It would merely
1555 * require storing the results of each pass into a temporary
1556 * cairo_traps_t. */
1557 status = _cairo_bentley_ottmann_tessellate_bo_edges (event_ptrs, num_events,
1558 fill_rule, traps,
1559 &intersections);
1560 #if DEBUG_TRAPS
1561 dump_traps (traps, "bo-polygon-out.txt");
1562 #endif
1563
1564 if (events != stack_events)
1565 free (events);
1566
1567 return status;
1568 }
1569
1570 cairo_status_t
_cairo_bentley_ottmann_tessellate_traps(cairo_traps_t * traps,cairo_fill_rule_t fill_rule)1571 _cairo_bentley_ottmann_tessellate_traps (cairo_traps_t *traps,
1572 cairo_fill_rule_t fill_rule)
1573 {
1574 cairo_status_t status;
1575 cairo_polygon_t polygon;
1576 int i;
1577
1578 if (unlikely (0 == traps->num_traps))
1579 return CAIRO_STATUS_SUCCESS;
1580
1581 #if DEBUG_TRAPS
1582 dump_traps (traps, "bo-traps-in.txt");
1583 #endif
1584
1585 _cairo_polygon_init (&polygon, traps->limits, traps->num_limits);
1586
1587 for (i = 0; i < traps->num_traps; i++) {
1588 status = _cairo_polygon_add_line (&polygon,
1589 &traps->traps[i].left,
1590 traps->traps[i].top,
1591 traps->traps[i].bottom,
1592 1);
1593 if (unlikely (status))
1594 goto CLEANUP;
1595
1596 status = _cairo_polygon_add_line (&polygon,
1597 &traps->traps[i].right,
1598 traps->traps[i].top,
1599 traps->traps[i].bottom,
1600 -1);
1601 if (unlikely (status))
1602 goto CLEANUP;
1603 }
1604
1605 _cairo_traps_clear (traps);
1606 status = _cairo_bentley_ottmann_tessellate_polygon (traps,
1607 &polygon,
1608 fill_rule);
1609
1610 #if DEBUG_TRAPS
1611 dump_traps (traps, "bo-traps-out.txt");
1612 #endif
1613
1614 CLEANUP:
1615 _cairo_polygon_fini (&polygon);
1616
1617 return status;
1618 }
1619
1620 #if 0
1621 static cairo_bool_t
1622 edges_have_an_intersection_quadratic (cairo_bo_edge_t *edges,
1623 int num_edges)
1624
1625 {
1626 int i, j;
1627 cairo_bo_edge_t *a, *b;
1628 cairo_bo_point32_t intersection;
1629
1630 /* We must not be given any upside-down edges. */
1631 for (i = 0; i < num_edges; i++) {
1632 assert (_cairo_bo_point32_compare (&edges[i].top, &edges[i].bottom) < 0);
1633 edges[i].line.p1.x <<= CAIRO_BO_GUARD_BITS;
1634 edges[i].line.p1.y <<= CAIRO_BO_GUARD_BITS;
1635 edges[i].line.p2.x <<= CAIRO_BO_GUARD_BITS;
1636 edges[i].line.p2.y <<= CAIRO_BO_GUARD_BITS;
1637 }
1638
1639 for (i = 0; i < num_edges; i++) {
1640 for (j = 0; j < num_edges; j++) {
1641 if (i == j)
1642 continue;
1643
1644 a = &edges[i];
1645 b = &edges[j];
1646
1647 if (! _cairo_bo_edge_intersect (a, b, &intersection))
1648 continue;
1649
1650 printf ("Found intersection (%d,%d) between (%d,%d)-(%d,%d) and (%d,%d)-(%d,%d)\n",
1651 intersection.x,
1652 intersection.y,
1653 a->line.p1.x, a->line.p1.y,
1654 a->line.p2.x, a->line.p2.y,
1655 b->line.p1.x, b->line.p1.y,
1656 b->line.p2.x, b->line.p2.y);
1657
1658 return TRUE;
1659 }
1660 }
1661 return FALSE;
1662 }
1663
1664 #define TEST_MAX_EDGES 10
1665
1666 typedef struct test {
1667 const char *name;
1668 const char *description;
1669 int num_edges;
1670 cairo_bo_edge_t edges[TEST_MAX_EDGES];
1671 } test_t;
1672
1673 static test_t
1674 tests[] = {
1675 {
1676 "3 near misses",
1677 "3 edges all intersecting very close to each other",
1678 3,
1679 {
1680 { { 4, 2}, {0, 0}, { 9, 9}, NULL, NULL },
1681 { { 7, 2}, {0, 0}, { 2, 3}, NULL, NULL },
1682 { { 5, 2}, {0, 0}, { 1, 7}, NULL, NULL }
1683 }
1684 },
1685 {
1686 "inconsistent data",
1687 "Derived from random testing---was leading to skip list and edge list disagreeing.",
1688 2,
1689 {
1690 { { 2, 3}, {0, 0}, { 8, 9}, NULL, NULL },
1691 { { 2, 3}, {0, 0}, { 6, 7}, NULL, NULL }
1692 }
1693 },
1694 {
1695 "failed sort",
1696 "A test derived from random testing that leads to an inconsistent sort --- looks like we just can't attempt to validate the sweep line with edge_compare?",
1697 3,
1698 {
1699 { { 6, 2}, {0, 0}, { 6, 5}, NULL, NULL },
1700 { { 3, 5}, {0, 0}, { 5, 6}, NULL, NULL },
1701 { { 9, 2}, {0, 0}, { 5, 6}, NULL, NULL },
1702 }
1703 },
1704 {
1705 "minimal-intersection",
1706 "Intersection of a two from among the smallest possible edges.",
1707 2,
1708 {
1709 { { 0, 0}, {0, 0}, { 1, 1}, NULL, NULL },
1710 { { 1, 0}, {0, 0}, { 0, 1}, NULL, NULL }
1711 }
1712 },
1713 {
1714 "simple",
1715 "A simple intersection of two edges at an integer (2,2).",
1716 2,
1717 {
1718 { { 1, 1}, {0, 0}, { 3, 3}, NULL, NULL },
1719 { { 2, 1}, {0, 0}, { 2, 3}, NULL, NULL }
1720 }
1721 },
1722 {
1723 "bend-to-horizontal",
1724 "With intersection truncation one edge bends to horizontal",
1725 2,
1726 {
1727 { { 9, 1}, {0, 0}, {3, 7}, NULL, NULL },
1728 { { 3, 5}, {0, 0}, {9, 9}, NULL, NULL }
1729 }
1730 }
1731 };
1732
1733 /*
1734 {
1735 "endpoint",
1736 "An intersection that occurs at the endpoint of a segment.",
1737 {
1738 { { 4, 6}, { 5, 6}, NULL, { { NULL }} },
1739 { { 4, 5}, { 5, 7}, NULL, { { NULL }} },
1740 { { 0, 0}, { 0, 0}, NULL, { { NULL }} },
1741 }
1742 }
1743 {
1744 name = "overlapping",
1745 desc = "Parallel segments that share an endpoint, with different slopes.",
1746 edges = {
1747 { top = { x = 2, y = 0}, bottom = { x = 1, y = 1}},
1748 { top = { x = 2, y = 0}, bottom = { x = 0, y = 2}},
1749 { top = { x = 0, y = 3}, bottom = { x = 1, y = 3}},
1750 { top = { x = 0, y = 3}, bottom = { x = 2, y = 3}},
1751 { top = { x = 0, y = 4}, bottom = { x = 0, y = 6}},
1752 { top = { x = 0, y = 5}, bottom = { x = 0, y = 6}}
1753 }
1754 },
1755 {
1756 name = "hobby_stage_3",
1757 desc = "A particularly tricky part of the 3rd stage of the 'hobby' test below.",
1758 edges = {
1759 { top = { x = -1, y = -2}, bottom = { x = 4, y = 2}},
1760 { top = { x = 5, y = 3}, bottom = { x = 9, y = 5}},
1761 { top = { x = 5, y = 3}, bottom = { x = 6, y = 3}},
1762 }
1763 },
1764 {
1765 name = "hobby",
1766 desc = "Example from John Hobby's paper. Requires 3 passes of the iterative algorithm.",
1767 edges = {
1768 { top = { x = 0, y = 0}, bottom = { x = 9, y = 5}},
1769 { top = { x = 0, y = 0}, bottom = { x = 13, y = 6}},
1770 { top = { x = -1, y = -2}, bottom = { x = 9, y = 5}}
1771 }
1772 },
1773 {
1774 name = "slope",
1775 desc = "Edges with same start/stop points but different slopes",
1776 edges = {
1777 { top = { x = 4, y = 1}, bottom = { x = 6, y = 3}},
1778 { top = { x = 4, y = 1}, bottom = { x = 2, y = 3}},
1779 { top = { x = 2, y = 4}, bottom = { x = 4, y = 6}},
1780 { top = { x = 6, y = 4}, bottom = { x = 4, y = 6}}
1781 }
1782 },
1783 {
1784 name = "horizontal",
1785 desc = "Test of a horizontal edge",
1786 edges = {
1787 { top = { x = 1, y = 1}, bottom = { x = 6, y = 6}},
1788 { top = { x = 2, y = 3}, bottom = { x = 5, y = 3}}
1789 }
1790 },
1791 {
1792 name = "vertical",
1793 desc = "Test of a vertical edge",
1794 edges = {
1795 { top = { x = 5, y = 1}, bottom = { x = 5, y = 7}},
1796 { top = { x = 2, y = 4}, bottom = { x = 8, y = 5}}
1797 }
1798 },
1799 {
1800 name = "congruent",
1801 desc = "Two overlapping edges with the same slope",
1802 edges = {
1803 { top = { x = 5, y = 1}, bottom = { x = 5, y = 7}},
1804 { top = { x = 5, y = 2}, bottom = { x = 5, y = 6}},
1805 { top = { x = 2, y = 4}, bottom = { x = 8, y = 5}}
1806 }
1807 },
1808 {
1809 name = "multi",
1810 desc = "Several segments with a common intersection point",
1811 edges = {
1812 { top = { x = 1, y = 2}, bottom = { x = 5, y = 4} },
1813 { top = { x = 1, y = 1}, bottom = { x = 5, y = 5} },
1814 { top = { x = 2, y = 1}, bottom = { x = 4, y = 5} },
1815 { top = { x = 4, y = 1}, bottom = { x = 2, y = 5} },
1816 { top = { x = 5, y = 1}, bottom = { x = 1, y = 5} },
1817 { top = { x = 5, y = 2}, bottom = { x = 1, y = 4} }
1818 }
1819 }
1820 };
1821 */
1822
1823 static int
1824 run_test (const char *test_name,
1825 cairo_bo_edge_t *test_edges,
1826 int num_edges)
1827 {
1828 int i, intersections, passes;
1829 cairo_bo_edge_t *edges;
1830 cairo_array_t intersected_edges;
1831
1832 printf ("Testing: %s\n", test_name);
1833
1834 _cairo_array_init (&intersected_edges, sizeof (cairo_bo_edge_t));
1835
1836 intersections = _cairo_bentley_ottmann_intersect_edges (test_edges, num_edges, &intersected_edges);
1837 if (intersections)
1838 printf ("Pass 1 found %d intersections:\n", intersections);
1839
1840
1841 /* XXX: Multi-pass Bentley-Ottmmann. Preferable would be to add a
1842 * pass of Hobby's tolerance-square algorithm instead. */
1843 passes = 1;
1844 while (intersections) {
1845 int num_edges = _cairo_array_num_elements (&intersected_edges);
1846 passes++;
1847 edges = _cairo_malloc_ab (num_edges, sizeof (cairo_bo_edge_t));
1848 assert (edges != NULL);
1849 memcpy (edges, _cairo_array_index (&intersected_edges, 0), num_edges * sizeof (cairo_bo_edge_t));
1850 _cairo_array_fini (&intersected_edges);
1851 _cairo_array_init (&intersected_edges, sizeof (cairo_bo_edge_t));
1852 intersections = _cairo_bentley_ottmann_intersect_edges (edges, num_edges, &intersected_edges);
1853 free (edges);
1854
1855 if (intersections){
1856 printf ("Pass %d found %d remaining intersections:\n", passes, intersections);
1857 } else {
1858 if (passes > 3)
1859 for (i = 0; i < passes; i++)
1860 printf ("*");
1861 printf ("No remainining intersections found after pass %d\n", passes);
1862 }
1863 }
1864
1865 if (edges_have_an_intersection_quadratic (_cairo_array_index (&intersected_edges, 0),
1866 _cairo_array_num_elements (&intersected_edges)))
1867 printf ("*** FAIL ***\n");
1868 else
1869 printf ("PASS\n");
1870
1871 _cairo_array_fini (&intersected_edges);
1872
1873 return 0;
1874 }
1875
1876 #define MAX_RANDOM 300
1877
1878 int
1879 main (void)
1880 {
1881 char random_name[] = "random-XX";
1882 cairo_bo_edge_t random_edges[MAX_RANDOM], *edge;
1883 unsigned int i, num_random;
1884 test_t *test;
1885
1886 for (i = 0; i < ARRAY_LENGTH (tests); i++) {
1887 test = &tests[i];
1888 run_test (test->name, test->edges, test->num_edges);
1889 }
1890
1891 for (num_random = 0; num_random < MAX_RANDOM; num_random++) {
1892 srand (0);
1893 for (i = 0; i < num_random; i++) {
1894 do {
1895 edge = &random_edges[i];
1896 edge->line.p1.x = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0)));
1897 edge->line.p1.y = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0)));
1898 edge->line.p2.x = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0)));
1899 edge->line.p2.y = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0)));
1900 if (edge->line.p1.y > edge->line.p2.y) {
1901 int32_t tmp = edge->line.p1.y;
1902 edge->line.p1.y = edge->line.p2.y;
1903 edge->line.p2.y = tmp;
1904 }
1905 } while (edge->line.p1.y == edge->line.p2.y);
1906 }
1907
1908 sprintf (random_name, "random-%02d", num_random);
1909
1910 run_test (random_name, random_edges, num_random);
1911 }
1912
1913 return 0;
1914 }
1915 #endif
1916