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-error-private.h"
42 #include "cairo-freelist-private.h"
43 #include "cairo-combsort-inline.h"
44
45
46 typedef struct _cairo_bo_intersect_ordinate {
47 int32_t ordinate;
48 enum { EXCESS = -1, EXACT = 0, DEFAULT = 1 } approx;
49 } cairo_bo_intersect_ordinate_t;
50
51 typedef struct _cairo_bo_intersect_point {
52 cairo_bo_intersect_ordinate_t x;
53 cairo_bo_intersect_ordinate_t y;
54 } cairo_bo_intersect_point_t;
55
56 typedef struct _cairo_bo_edge cairo_bo_edge_t;
57
58 typedef struct _cairo_bo_deferred {
59 cairo_bo_edge_t *other;
60 int32_t top;
61 } cairo_bo_deferred_t;
62
63 struct _cairo_bo_edge {
64 int a_or_b;
65 cairo_edge_t edge;
66 cairo_bo_edge_t *prev;
67 cairo_bo_edge_t *next;
68 cairo_bo_deferred_t deferred;
69 };
70
71 /* the parent is always given by index/2 */
72 #define PQ_PARENT_INDEX(i) ((i) >> 1)
73 #define PQ_FIRST_ENTRY 1
74
75 /* left and right children are index * 2 and (index * 2) +1 respectively */
76 #define PQ_LEFT_CHILD_INDEX(i) ((i) << 1)
77
78 typedef enum {
79 CAIRO_BO_EVENT_TYPE_STOP = -1,
80 CAIRO_BO_EVENT_TYPE_INTERSECTION,
81 CAIRO_BO_EVENT_TYPE_START
82 } cairo_bo_event_type_t;
83
84 typedef struct _cairo_bo_event {
85 cairo_bo_event_type_t type;
86 cairo_bo_intersect_point_t point;
87 } cairo_bo_event_t;
88
89 typedef struct _cairo_bo_start_event {
90 cairo_bo_event_type_t type;
91 cairo_bo_intersect_point_t point;
92 cairo_bo_edge_t edge;
93 } cairo_bo_start_event_t;
94
95 typedef struct _cairo_bo_queue_event {
96 cairo_bo_event_type_t type;
97 cairo_bo_intersect_point_t point;
98 cairo_bo_edge_t *e1;
99 cairo_bo_edge_t *e2;
100 } cairo_bo_queue_event_t;
101
102 typedef struct _pqueue {
103 int size, max_size;
104
105 cairo_bo_event_t **elements;
106 cairo_bo_event_t *elements_embedded[1024];
107 } pqueue_t;
108
109 typedef struct _cairo_bo_event_queue {
110 cairo_freepool_t pool;
111 pqueue_t pqueue;
112 cairo_bo_event_t **start_events;
113 } cairo_bo_event_queue_t;
114
115 typedef struct _cairo_bo_sweep_line {
116 cairo_bo_edge_t *head;
117 int32_t current_y;
118 cairo_bo_edge_t *current_edge;
119 } cairo_bo_sweep_line_t;
120
121 static cairo_fixed_t
_line_compute_intersection_x_for_y(const cairo_line_t * line,cairo_fixed_t y)122 _line_compute_intersection_x_for_y (const cairo_line_t *line,
123 cairo_fixed_t y)
124 {
125 cairo_fixed_t x, dy;
126
127 if (y == line->p1.y)
128 return line->p1.x;
129 if (y == line->p2.y)
130 return line->p2.x;
131
132 x = line->p1.x;
133 dy = line->p2.y - line->p1.y;
134 if (dy != 0) {
135 x += _cairo_fixed_mul_div_floor (y - line->p1.y,
136 line->p2.x - line->p1.x,
137 dy);
138 }
139
140 return x;
141 }
142
143 static inline int
_cairo_bo_point32_compare(cairo_bo_intersect_point_t const * a,cairo_bo_intersect_point_t const * b)144 _cairo_bo_point32_compare (cairo_bo_intersect_point_t const *a,
145 cairo_bo_intersect_point_t const *b)
146 {
147 int cmp;
148
149 cmp = a->y.ordinate - b->y.ordinate;
150 if (cmp)
151 return cmp;
152
153 cmp = a->y.approx - b->y.approx;
154 if (cmp)
155 return cmp;
156
157 return a->x.ordinate - b->x.ordinate;
158 }
159
160 /* Compare the slope of a to the slope of b, returning 1, 0, -1 if the
161 * slope a is respectively greater than, equal to, or less than the
162 * slope of b.
163 *
164 * For each edge, consider the direction vector formed from:
165 *
166 * top -> bottom
167 *
168 * which is:
169 *
170 * (dx, dy) = (line.p2.x - line.p1.x, line.p2.y - line.p1.y)
171 *
172 * We then define the slope of each edge as dx/dy, (which is the
173 * inverse of the slope typically used in math instruction). We never
174 * compute a slope directly as the value approaches infinity, but we
175 * can derive a slope comparison without division as follows, (where
176 * the ? represents our compare operator).
177 *
178 * 1. slope(a) ? slope(b)
179 * 2. adx/ady ? bdx/bdy
180 * 3. (adx * bdy) ? (bdx * ady)
181 *
182 * Note that from step 2 to step 3 there is no change needed in the
183 * sign of the result since both ady and bdy are guaranteed to be
184 * greater than or equal to 0.
185 *
186 * When using this slope comparison to sort edges, some care is needed
187 * when interpreting the results. Since the slope compare operates on
188 * distance vectors from top to bottom it gives a correct left to
189 * right sort for edges that have a common top point, (such as two
190 * edges with start events at the same location). On the other hand,
191 * the sense of the result will be exactly reversed for two edges that
192 * have a common stop point.
193 */
194 static inline int
_slope_compare(const cairo_bo_edge_t * a,const cairo_bo_edge_t * b)195 _slope_compare (const cairo_bo_edge_t *a,
196 const cairo_bo_edge_t *b)
197 {
198 /* XXX: We're assuming here that dx and dy will still fit in 32
199 * bits. That's not true in general as there could be overflow. We
200 * should prevent that before the tessellation algorithm
201 * begins.
202 */
203 int32_t adx = a->edge.line.p2.x - a->edge.line.p1.x;
204 int32_t bdx = b->edge.line.p2.x - b->edge.line.p1.x;
205
206 /* Since the dy's are all positive by construction we can fast
207 * path several common cases.
208 */
209
210 /* First check for vertical lines. */
211 if (adx == 0)
212 return -bdx;
213 if (bdx == 0)
214 return adx;
215
216 /* Then where the two edges point in different directions wrt x. */
217 if ((adx ^ bdx) < 0)
218 return adx;
219
220 /* Finally we actually need to do the general comparison. */
221 {
222 int32_t ady = a->edge.line.p2.y - a->edge.line.p1.y;
223 int32_t bdy = b->edge.line.p2.y - b->edge.line.p1.y;
224 cairo_int64_t adx_bdy = _cairo_int32x32_64_mul (adx, bdy);
225 cairo_int64_t bdx_ady = _cairo_int32x32_64_mul (bdx, ady);
226
227 return _cairo_int64_cmp (adx_bdy, bdx_ady);
228 }
229 }
230
231 /*
232 * We need to compare the x-coordinates of a pair of lines for a particular y,
233 * without loss of precision.
234 *
235 * The x-coordinate along an edge for a given y is:
236 * X = A_x + (Y - A_y) * A_dx / A_dy
237 *
238 * So the inequality we wish to test is:
239 * A_x + (Y - A_y) * A_dx / A_dy ∘ B_x + (Y - B_y) * B_dx / B_dy,
240 * where ∘ is our inequality operator.
241 *
242 * By construction, we know that A_dy and B_dy (and (Y - A_y), (Y - B_y)) are
243 * all positive, so we can rearrange it thus without causing a sign change:
244 * A_dy * B_dy * (A_x - B_x) ∘ (Y - B_y) * B_dx * A_dy
245 * - (Y - A_y) * A_dx * B_dy
246 *
247 * Given the assumption that all the deltas fit within 32 bits, we can compute
248 * this comparison directly using 128 bit arithmetic. For certain, but common,
249 * input we can reduce this down to a single 32 bit compare by inspecting the
250 * deltas.
251 *
252 * (And put the burden of the work on developing fast 128 bit ops, which are
253 * required throughout the tessellator.)
254 *
255 * See the similar discussion for _slope_compare().
256 */
257 static int
edges_compare_x_for_y_general(const cairo_bo_edge_t * a,const cairo_bo_edge_t * b,int32_t y)258 edges_compare_x_for_y_general (const cairo_bo_edge_t *a,
259 const cairo_bo_edge_t *b,
260 int32_t y)
261 {
262 /* XXX: We're assuming here that dx and dy will still fit in 32
263 * bits. That's not true in general as there could be overflow. We
264 * should prevent that before the tessellation algorithm
265 * begins.
266 */
267 int32_t dx;
268 int32_t adx, ady;
269 int32_t bdx, bdy;
270 enum {
271 HAVE_NONE = 0x0,
272 HAVE_DX = 0x1,
273 HAVE_ADX = 0x2,
274 HAVE_DX_ADX = HAVE_DX | HAVE_ADX,
275 HAVE_BDX = 0x4,
276 HAVE_DX_BDX = HAVE_DX | HAVE_BDX,
277 HAVE_ADX_BDX = HAVE_ADX | HAVE_BDX,
278 HAVE_ALL = HAVE_DX | HAVE_ADX | HAVE_BDX
279 } have_dx_adx_bdx = HAVE_ALL;
280
281 /* don't bother solving for abscissa if the edges' bounding boxes
282 * can be used to order them. */
283 {
284 int32_t amin, amax;
285 int32_t bmin, bmax;
286 if (a->edge.line.p1.x < a->edge.line.p2.x) {
287 amin = a->edge.line.p1.x;
288 amax = a->edge.line.p2.x;
289 } else {
290 amin = a->edge.line.p2.x;
291 amax = a->edge.line.p1.x;
292 }
293 if (b->edge.line.p1.x < b->edge.line.p2.x) {
294 bmin = b->edge.line.p1.x;
295 bmax = b->edge.line.p2.x;
296 } else {
297 bmin = b->edge.line.p2.x;
298 bmax = b->edge.line.p1.x;
299 }
300 if (amax < bmin) return -1;
301 if (amin > bmax) return +1;
302 }
303
304 ady = a->edge.line.p2.y - a->edge.line.p1.y;
305 adx = a->edge.line.p2.x - a->edge.line.p1.x;
306 if (adx == 0)
307 have_dx_adx_bdx &= ~HAVE_ADX;
308
309 bdy = b->edge.line.p2.y - b->edge.line.p1.y;
310 bdx = b->edge.line.p2.x - b->edge.line.p1.x;
311 if (bdx == 0)
312 have_dx_adx_bdx &= ~HAVE_BDX;
313
314 dx = a->edge.line.p1.x - b->edge.line.p1.x;
315 if (dx == 0)
316 have_dx_adx_bdx &= ~HAVE_DX;
317
318 #define L _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (ady, bdy), dx)
319 #define A _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (adx, bdy), y - a->edge.line.p1.y)
320 #define B _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (bdx, ady), y - b->edge.line.p1.y)
321 switch (have_dx_adx_bdx) {
322 default:
323 case HAVE_NONE:
324 return 0;
325 case HAVE_DX:
326 /* A_dy * B_dy * (A_x - B_x) ∘ 0 */
327 return dx; /* ady * bdy is positive definite */
328 case HAVE_ADX:
329 /* 0 ∘ - (Y - A_y) * A_dx * B_dy */
330 return adx; /* bdy * (y - a->top.y) is positive definite */
331 case HAVE_BDX:
332 /* 0 ∘ (Y - B_y) * B_dx * A_dy */
333 return -bdx; /* ady * (y - b->top.y) is positive definite */
334 case HAVE_ADX_BDX:
335 /* 0 ∘ (Y - B_y) * B_dx * A_dy - (Y - A_y) * A_dx * B_dy */
336 if ((adx ^ bdx) < 0) {
337 return adx;
338 } else if (a->edge.line.p1.y == b->edge.line.p1.y) { /* common origin */
339 cairo_int64_t adx_bdy, bdx_ady;
340
341 /* ∴ A_dx * B_dy ∘ B_dx * A_dy */
342
343 adx_bdy = _cairo_int32x32_64_mul (adx, bdy);
344 bdx_ady = _cairo_int32x32_64_mul (bdx, ady);
345
346 return _cairo_int64_cmp (adx_bdy, bdx_ady);
347 } else
348 return _cairo_int128_cmp (A, B);
349 case HAVE_DX_ADX:
350 /* A_dy * (A_x - B_x) ∘ - (Y - A_y) * A_dx */
351 if ((-adx ^ dx) < 0) {
352 return dx;
353 } else {
354 cairo_int64_t ady_dx, dy_adx;
355
356 ady_dx = _cairo_int32x32_64_mul (ady, dx);
357 dy_adx = _cairo_int32x32_64_mul (a->edge.line.p1.y - y, adx);
358
359 return _cairo_int64_cmp (ady_dx, dy_adx);
360 }
361 case HAVE_DX_BDX:
362 /* B_dy * (A_x - B_x) ∘ (Y - B_y) * B_dx */
363 if ((bdx ^ dx) < 0) {
364 return dx;
365 } else {
366 cairo_int64_t bdy_dx, dy_bdx;
367
368 bdy_dx = _cairo_int32x32_64_mul (bdy, dx);
369 dy_bdx = _cairo_int32x32_64_mul (y - b->edge.line.p1.y, bdx);
370
371 return _cairo_int64_cmp (bdy_dx, dy_bdx);
372 }
373 case HAVE_ALL:
374 /* XXX try comparing (a->edge.line.p2.x - b->edge.line.p2.x) et al */
375 return _cairo_int128_cmp (L, _cairo_int128_sub (B, A));
376 }
377 #undef B
378 #undef A
379 #undef L
380 }
381
382 /*
383 * We need to compare the x-coordinate of a line for a particular y wrt to a
384 * given x, without loss of precision.
385 *
386 * The x-coordinate along an edge for a given y is:
387 * X = A_x + (Y - A_y) * A_dx / A_dy
388 *
389 * So the inequality we wish to test is:
390 * A_x + (Y - A_y) * A_dx / A_dy ∘ X
391 * where ∘ is our inequality operator.
392 *
393 * By construction, we know that A_dy (and (Y - A_y)) are
394 * all positive, so we can rearrange it thus without causing a sign change:
395 * (Y - A_y) * A_dx ∘ (X - A_x) * A_dy
396 *
397 * Given the assumption that all the deltas fit within 32 bits, we can compute
398 * this comparison directly using 64 bit arithmetic.
399 *
400 * See the similar discussion for _slope_compare() and
401 * edges_compare_x_for_y_general().
402 */
403 static int
edge_compare_for_y_against_x(const cairo_bo_edge_t * a,int32_t y,int32_t x)404 edge_compare_for_y_against_x (const cairo_bo_edge_t *a,
405 int32_t y,
406 int32_t x)
407 {
408 int32_t adx, ady;
409 int32_t dx, dy;
410 cairo_int64_t L, R;
411
412 if (x < a->edge.line.p1.x && x < a->edge.line.p2.x)
413 return 1;
414 if (x > a->edge.line.p1.x && x > a->edge.line.p2.x)
415 return -1;
416
417 adx = a->edge.line.p2.x - a->edge.line.p1.x;
418 dx = x - a->edge.line.p1.x;
419
420 if (adx == 0)
421 return -dx;
422 if (dx == 0 || (adx ^ dx) < 0)
423 return adx;
424
425 dy = y - a->edge.line.p1.y;
426 ady = a->edge.line.p2.y - a->edge.line.p1.y;
427
428 L = _cairo_int32x32_64_mul (dy, adx);
429 R = _cairo_int32x32_64_mul (dx, ady);
430
431 return _cairo_int64_cmp (L, R);
432 }
433
434 static int
edges_compare_x_for_y(const cairo_bo_edge_t * a,const cairo_bo_edge_t * b,int32_t y)435 edges_compare_x_for_y (const cairo_bo_edge_t *a,
436 const cairo_bo_edge_t *b,
437 int32_t y)
438 {
439 /* If the sweep-line is currently on an end-point of a line,
440 * then we know its precise x value (and considering that we often need to
441 * compare events at end-points, this happens frequently enough to warrant
442 * special casing).
443 */
444 enum {
445 HAVE_NEITHER = 0x0,
446 HAVE_AX = 0x1,
447 HAVE_BX = 0x2,
448 HAVE_BOTH = HAVE_AX | HAVE_BX
449 } have_ax_bx = HAVE_BOTH;
450 int32_t ax = 0, bx = 0;
451
452 if (y == a->edge.line.p1.y)
453 ax = a->edge.line.p1.x;
454 else if (y == a->edge.line.p2.y)
455 ax = a->edge.line.p2.x;
456 else
457 have_ax_bx &= ~HAVE_AX;
458
459 if (y == b->edge.line.p1.y)
460 bx = b->edge.line.p1.x;
461 else if (y == b->edge.line.p2.y)
462 bx = b->edge.line.p2.x;
463 else
464 have_ax_bx &= ~HAVE_BX;
465
466 switch (have_ax_bx) {
467 default:
468 case HAVE_NEITHER:
469 return edges_compare_x_for_y_general (a, b, y);
470 case HAVE_AX:
471 return -edge_compare_for_y_against_x (b, y, ax);
472 case HAVE_BX:
473 return edge_compare_for_y_against_x (a, y, bx);
474 case HAVE_BOTH:
475 return ax - bx;
476 }
477 }
478
479 static inline int
_line_equal(const cairo_line_t * a,const cairo_line_t * b)480 _line_equal (const cairo_line_t *a, const cairo_line_t *b)
481 {
482 return a->p1.x == b->p1.x && a->p1.y == b->p1.y &&
483 a->p2.x == b->p2.x && a->p2.y == b->p2.y;
484 }
485
486 static int
_cairo_bo_sweep_line_compare_edges(cairo_bo_sweep_line_t * sweep_line,const cairo_bo_edge_t * a,const cairo_bo_edge_t * b)487 _cairo_bo_sweep_line_compare_edges (cairo_bo_sweep_line_t *sweep_line,
488 const cairo_bo_edge_t *a,
489 const cairo_bo_edge_t *b)
490 {
491 int cmp;
492
493 /* compare the edges if not identical */
494 if (! _line_equal (&a->edge.line, &b->edge.line)) {
495 cmp = edges_compare_x_for_y (a, b, sweep_line->current_y);
496 if (cmp)
497 return cmp;
498
499 /* The two edges intersect exactly at y, so fall back on slope
500 * comparison. We know that this compare_edges function will be
501 * called only when starting a new edge, (not when stopping an
502 * edge), so we don't have to worry about conditionally inverting
503 * the sense of _slope_compare. */
504 cmp = _slope_compare (a, b);
505 if (cmp)
506 return cmp;
507 }
508
509 /* We've got two collinear edges now. */
510 return b->edge.bottom - a->edge.bottom;
511 }
512
513 static inline cairo_int64_t
det32_64(int32_t a,int32_t b,int32_t c,int32_t d)514 det32_64 (int32_t a, int32_t b,
515 int32_t c, int32_t d)
516 {
517 /* det = a * d - b * c */
518 return _cairo_int64_sub (_cairo_int32x32_64_mul (a, d),
519 _cairo_int32x32_64_mul (b, c));
520 }
521
522 static inline cairo_int128_t
det64x32_128(cairo_int64_t a,int32_t b,cairo_int64_t c,int32_t d)523 det64x32_128 (cairo_int64_t a, int32_t b,
524 cairo_int64_t c, int32_t d)
525 {
526 /* det = a * d - b * c */
527 return _cairo_int128_sub (_cairo_int64x32_128_mul (a, d),
528 _cairo_int64x32_128_mul (c, b));
529 }
530
531 static inline cairo_bo_intersect_ordinate_t
round_to_nearest(cairo_quorem64_t d,cairo_int64_t den)532 round_to_nearest (cairo_quorem64_t d,
533 cairo_int64_t den)
534 {
535 cairo_bo_intersect_ordinate_t ordinate;
536 int32_t quo = d.quo;
537 cairo_int64_t drem_2 = _cairo_int64_mul (d.rem, _cairo_int32_to_int64 (2));
538
539 /* assert (! _cairo_int64_negative (den));*/
540
541 if (_cairo_int64_lt (drem_2, _cairo_int64_negate (den))) {
542 quo -= 1;
543 drem_2 = _cairo_int64_negate (drem_2);
544 } else if (_cairo_int64_le (den, drem_2)) {
545 quo += 1;
546 drem_2 = _cairo_int64_negate (drem_2);
547 }
548
549 ordinate.ordinate = quo;
550 ordinate.approx = _cairo_int64_is_zero (drem_2) ? EXACT : _cairo_int64_negative (drem_2) ? EXCESS : DEFAULT;
551
552 return ordinate;
553 }
554
555 /* Compute the intersection of two lines as defined by two edges. The
556 * result is provided as a coordinate pair of 128-bit integers.
557 *
558 * Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection or
559 * %CAIRO_BO_STATUS_PARALLEL if the two lines are exactly parallel.
560 */
561 static cairo_bool_t
intersect_lines(cairo_bo_edge_t * a,cairo_bo_edge_t * b,cairo_bo_intersect_point_t * intersection)562 intersect_lines (cairo_bo_edge_t *a,
563 cairo_bo_edge_t *b,
564 cairo_bo_intersect_point_t *intersection)
565 {
566 cairo_int64_t a_det, b_det;
567
568 /* XXX: We're assuming here that dx and dy will still fit in 32
569 * bits. That's not true in general as there could be overflow. We
570 * should prevent that before the tessellation algorithm begins.
571 * What we're doing to mitigate this is to perform clamping in
572 * cairo_bo_tessellate_polygon().
573 */
574 int32_t dx1 = a->edge.line.p1.x - a->edge.line.p2.x;
575 int32_t dy1 = a->edge.line.p1.y - a->edge.line.p2.y;
576
577 int32_t dx2 = b->edge.line.p1.x - b->edge.line.p2.x;
578 int32_t dy2 = b->edge.line.p1.y - b->edge.line.p2.y;
579
580 cairo_int64_t den_det;
581 cairo_int64_t R;
582 cairo_quorem64_t qr;
583
584 den_det = det32_64 (dx1, dy1, dx2, dy2);
585
586 /* Q: Can we determine that the lines do not intersect (within range)
587 * much more cheaply than computing the intersection point i.e. by
588 * avoiding the division?
589 *
590 * X = ax + t * adx = bx + s * bdx;
591 * Y = ay + t * ady = by + s * bdy;
592 * ∴ t * (ady*bdx - bdy*adx) = bdx * (by - ay) + bdy * (ax - bx)
593 * => t * L = R
594 *
595 * Therefore we can reject any intersection (under the criteria for
596 * valid intersection events) if:
597 * L^R < 0 => t < 0, or
598 * L<R => t > 1
599 *
600 * (where top/bottom must at least extend to the line endpoints).
601 *
602 * A similar substitution can be performed for s, yielding:
603 * s * (ady*bdx - bdy*adx) = ady * (ax - bx) - adx * (ay - by)
604 */
605 R = det32_64 (dx2, dy2,
606 b->edge.line.p1.x - a->edge.line.p1.x,
607 b->edge.line.p1.y - a->edge.line.p1.y);
608 if (_cairo_int64_le (den_det, R))
609 return FALSE;
610
611 R = det32_64 (dy1, dx1,
612 a->edge.line.p1.y - b->edge.line.p1.y,
613 a->edge.line.p1.x - b->edge.line.p1.x);
614 if (_cairo_int64_le (den_det, R))
615 return FALSE;
616
617 /* We now know that the two lines should intersect within range. */
618
619 a_det = det32_64 (a->edge.line.p1.x, a->edge.line.p1.y,
620 a->edge.line.p2.x, a->edge.line.p2.y);
621 b_det = det32_64 (b->edge.line.p1.x, b->edge.line.p1.y,
622 b->edge.line.p2.x, b->edge.line.p2.y);
623
624 /* x = det (a_det, dx1, b_det, dx2) / den_det */
625 qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dx1,
626 b_det, dx2),
627 den_det);
628 if (_cairo_int64_eq (qr.rem, den_det))
629 return FALSE;
630
631 intersection->x = round_to_nearest (qr, den_det);
632
633 /* y = det (a_det, dy1, b_det, dy2) / den_det */
634 qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dy1,
635 b_det, dy2),
636 den_det);
637 if (_cairo_int64_eq (qr.rem, den_det))
638 return FALSE;
639
640 intersection->y = round_to_nearest (qr, den_det);
641
642 return TRUE;
643 }
644
645 static int
_cairo_bo_intersect_ordinate_32_compare(cairo_bo_intersect_ordinate_t a,int32_t b)646 _cairo_bo_intersect_ordinate_32_compare (cairo_bo_intersect_ordinate_t a,
647 int32_t b)
648 {
649 /* First compare the quotient */
650 if (a.ordinate > b)
651 return +1;
652 if (a.ordinate < b)
653 return -1;
654
655 return a.approx; /* == EXCESS ? -1 : a.approx == EXACT ? 0 : 1;*/
656 }
657
658 /* Does the given edge contain the given point. The point must already
659 * be known to be contained within the line determined by the edge,
660 * (most likely the point results from an intersection of this edge
661 * with another).
662 *
663 * If we had exact arithmetic, then this function would simply be a
664 * matter of examining whether the y value of the point lies within
665 * the range of y values of the edge. But since intersection points
666 * are not exact due to being rounded to the nearest integer within
667 * the available precision, we must also examine the x value of the
668 * point.
669 *
670 * The definition of "contains" here is that the given intersection
671 * point will be seen by the sweep line after the start event for the
672 * given edge and before the stop event for the edge. See the comments
673 * in the implementation for more details.
674 */
675 static cairo_bool_t
_cairo_bo_edge_contains_intersect_point(cairo_bo_edge_t * edge,cairo_bo_intersect_point_t * point)676 _cairo_bo_edge_contains_intersect_point (cairo_bo_edge_t *edge,
677 cairo_bo_intersect_point_t *point)
678 {
679 return _cairo_bo_intersect_ordinate_32_compare (point->y,
680 edge->edge.bottom) < 0;
681 }
682
683 /* Compute the intersection of two edges. The result is provided as a
684 * coordinate pair of 128-bit integers.
685 *
686 * Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection
687 * that is within both edges, %CAIRO_BO_STATUS_NO_INTERSECTION if the
688 * intersection of the lines defined by the edges occurs outside of
689 * one or both edges, and %CAIRO_BO_STATUS_PARALLEL if the two edges
690 * are exactly parallel.
691 *
692 * Note that when determining if a candidate intersection is "inside"
693 * an edge, we consider both the infinitesimal shortening and the
694 * infinitesimal tilt rules described by John Hobby. Specifically, if
695 * the intersection is exactly the same as an edge point, it is
696 * effectively outside (no intersection is returned). Also, if the
697 * intersection point has the same
698 */
699 static cairo_bool_t
_cairo_bo_edge_intersect(cairo_bo_edge_t * a,cairo_bo_edge_t * b,cairo_bo_intersect_point_t * intersection)700 _cairo_bo_edge_intersect (cairo_bo_edge_t *a,
701 cairo_bo_edge_t *b,
702 cairo_bo_intersect_point_t *intersection)
703 {
704 if (! intersect_lines (a, b, intersection))
705 return FALSE;
706
707 if (! _cairo_bo_edge_contains_intersect_point (a, intersection))
708 return FALSE;
709
710 if (! _cairo_bo_edge_contains_intersect_point (b, intersection))
711 return FALSE;
712
713 return TRUE;
714 }
715
716 static inline int
cairo_bo_event_compare(const cairo_bo_event_t * a,const cairo_bo_event_t * b)717 cairo_bo_event_compare (const cairo_bo_event_t *a,
718 const cairo_bo_event_t *b)
719 {
720 int cmp;
721
722 cmp = _cairo_bo_point32_compare (&a->point, &b->point);
723 if (cmp)
724 return cmp;
725
726 cmp = a->type - b->type;
727 if (cmp)
728 return cmp;
729
730 return a < b ? -1 : a == b ? 0 : 1;
731 }
732
733 static inline void
_pqueue_init(pqueue_t * pq)734 _pqueue_init (pqueue_t *pq)
735 {
736 pq->max_size = ARRAY_LENGTH (pq->elements_embedded);
737 pq->size = 0;
738
739 pq->elements = pq->elements_embedded;
740 }
741
742 static inline void
_pqueue_fini(pqueue_t * pq)743 _pqueue_fini (pqueue_t *pq)
744 {
745 if (pq->elements != pq->elements_embedded)
746 free (pq->elements);
747 }
748
749 static cairo_status_t
_pqueue_grow(pqueue_t * pq)750 _pqueue_grow (pqueue_t *pq)
751 {
752 cairo_bo_event_t **new_elements;
753 pq->max_size *= 2;
754
755 if (pq->elements == pq->elements_embedded) {
756 new_elements = _cairo_malloc_ab (pq->max_size,
757 sizeof (cairo_bo_event_t *));
758 if (unlikely (new_elements == NULL))
759 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
760
761 memcpy (new_elements, pq->elements_embedded,
762 sizeof (pq->elements_embedded));
763 } else {
764 new_elements = _cairo_realloc_ab (pq->elements,
765 pq->max_size,
766 sizeof (cairo_bo_event_t *));
767 if (unlikely (new_elements == NULL))
768 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
769 }
770
771 pq->elements = new_elements;
772 return CAIRO_STATUS_SUCCESS;
773 }
774
775 static inline cairo_status_t
_pqueue_push(pqueue_t * pq,cairo_bo_event_t * event)776 _pqueue_push (pqueue_t *pq, cairo_bo_event_t *event)
777 {
778 cairo_bo_event_t **elements;
779 int i, parent;
780
781 if (unlikely (pq->size + 1 == pq->max_size)) {
782 cairo_status_t status;
783
784 status = _pqueue_grow (pq);
785 if (unlikely (status))
786 return status;
787 }
788
789 elements = pq->elements;
790
791 for (i = ++pq->size;
792 i != PQ_FIRST_ENTRY &&
793 cairo_bo_event_compare (event,
794 elements[parent = PQ_PARENT_INDEX (i)]) < 0;
795 i = parent)
796 {
797 elements[i] = elements[parent];
798 }
799
800 elements[i] = event;
801
802 return CAIRO_STATUS_SUCCESS;
803 }
804
805 static inline void
_pqueue_pop(pqueue_t * pq)806 _pqueue_pop (pqueue_t *pq)
807 {
808 cairo_bo_event_t **elements = pq->elements;
809 cairo_bo_event_t *tail;
810 int child, i;
811
812 tail = elements[pq->size--];
813 if (pq->size == 0) {
814 elements[PQ_FIRST_ENTRY] = NULL;
815 return;
816 }
817
818 for (i = PQ_FIRST_ENTRY;
819 (child = PQ_LEFT_CHILD_INDEX (i)) <= pq->size;
820 i = child)
821 {
822 if (child != pq->size &&
823 cairo_bo_event_compare (elements[child+1],
824 elements[child]) < 0)
825 {
826 child++;
827 }
828
829 if (cairo_bo_event_compare (elements[child], tail) >= 0)
830 break;
831
832 elements[i] = elements[child];
833 }
834 elements[i] = tail;
835 }
836
837 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_bo_intersect_point_t * point)838 _cairo_bo_event_queue_insert (cairo_bo_event_queue_t *queue,
839 cairo_bo_event_type_t type,
840 cairo_bo_edge_t *e1,
841 cairo_bo_edge_t *e2,
842 const cairo_bo_intersect_point_t *point)
843 {
844 cairo_bo_queue_event_t *event;
845
846 event = _cairo_freepool_alloc (&queue->pool);
847 if (unlikely (event == NULL))
848 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
849
850 event->type = type;
851 event->e1 = e1;
852 event->e2 = e2;
853 event->point = *point;
854
855 return _pqueue_push (&queue->pqueue, (cairo_bo_event_t *) event);
856 }
857
858 static void
_cairo_bo_event_queue_delete(cairo_bo_event_queue_t * queue,cairo_bo_event_t * event)859 _cairo_bo_event_queue_delete (cairo_bo_event_queue_t *queue,
860 cairo_bo_event_t *event)
861 {
862 _cairo_freepool_free (&queue->pool, event);
863 }
864
865 static cairo_bo_event_t *
_cairo_bo_event_dequeue(cairo_bo_event_queue_t * event_queue)866 _cairo_bo_event_dequeue (cairo_bo_event_queue_t *event_queue)
867 {
868 cairo_bo_event_t *event, *cmp;
869
870 event = event_queue->pqueue.elements[PQ_FIRST_ENTRY];
871 cmp = *event_queue->start_events;
872 if (event == NULL ||
873 (cmp != NULL && cairo_bo_event_compare (cmp, event) < 0))
874 {
875 event = cmp;
876 event_queue->start_events++;
877 }
878 else
879 {
880 _pqueue_pop (&event_queue->pqueue);
881 }
882
883 return event;
884 }
885
CAIRO_COMBSORT_DECLARE(_cairo_bo_event_queue_sort,cairo_bo_event_t *,cairo_bo_event_compare)886 CAIRO_COMBSORT_DECLARE (_cairo_bo_event_queue_sort,
887 cairo_bo_event_t *,
888 cairo_bo_event_compare)
889
890 static void
891 _cairo_bo_event_queue_init (cairo_bo_event_queue_t *event_queue,
892 cairo_bo_event_t **start_events,
893 int num_events)
894 {
895 _cairo_bo_event_queue_sort (start_events, num_events);
896 start_events[num_events] = NULL;
897
898 event_queue->start_events = start_events;
899
900 _cairo_freepool_init (&event_queue->pool,
901 sizeof (cairo_bo_queue_event_t));
902 _pqueue_init (&event_queue->pqueue);
903 event_queue->pqueue.elements[PQ_FIRST_ENTRY] = NULL;
904 }
905
906 static cairo_status_t
event_queue_insert_stop(cairo_bo_event_queue_t * event_queue,cairo_bo_edge_t * edge)907 event_queue_insert_stop (cairo_bo_event_queue_t *event_queue,
908 cairo_bo_edge_t *edge)
909 {
910 cairo_bo_intersect_point_t point;
911
912 point.y.ordinate = edge->edge.bottom;
913 point.y.approx = EXACT;
914 point.x.ordinate = _line_compute_intersection_x_for_y (&edge->edge.line,
915 point.y.ordinate);
916 point.x.approx = EXACT;
917
918 return _cairo_bo_event_queue_insert (event_queue,
919 CAIRO_BO_EVENT_TYPE_STOP,
920 edge, NULL,
921 &point);
922 }
923
924 static void
_cairo_bo_event_queue_fini(cairo_bo_event_queue_t * event_queue)925 _cairo_bo_event_queue_fini (cairo_bo_event_queue_t *event_queue)
926 {
927 _pqueue_fini (&event_queue->pqueue);
928 _cairo_freepool_fini (&event_queue->pool);
929 }
930
931 static inline cairo_status_t
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)932 event_queue_insert_if_intersect_below_current_y (cairo_bo_event_queue_t *event_queue,
933 cairo_bo_edge_t *left,
934 cairo_bo_edge_t *right)
935 {
936 cairo_bo_intersect_point_t intersection;
937
938 if (_line_equal (&left->edge.line, &right->edge.line))
939 return CAIRO_STATUS_SUCCESS;
940
941 /* The names "left" and "right" here are correct descriptions of
942 * the order of the two edges within the active edge list. So if a
943 * slope comparison also puts left less than right, then we know
944 * that the intersection of these two segments has already
945 * occurred before the current sweep line position. */
946 if (_slope_compare (left, right) <= 0)
947 return CAIRO_STATUS_SUCCESS;
948
949 if (! _cairo_bo_edge_intersect (left, right, &intersection))
950 return CAIRO_STATUS_SUCCESS;
951
952 return _cairo_bo_event_queue_insert (event_queue,
953 CAIRO_BO_EVENT_TYPE_INTERSECTION,
954 left, right,
955 &intersection);
956 }
957
958 static void
_cairo_bo_sweep_line_init(cairo_bo_sweep_line_t * sweep_line)959 _cairo_bo_sweep_line_init (cairo_bo_sweep_line_t *sweep_line)
960 {
961 sweep_line->head = NULL;
962 sweep_line->current_y = INT32_MIN;
963 sweep_line->current_edge = NULL;
964 }
965
966 static cairo_status_t
sweep_line_insert(cairo_bo_sweep_line_t * sweep_line,cairo_bo_edge_t * edge)967 sweep_line_insert (cairo_bo_sweep_line_t *sweep_line,
968 cairo_bo_edge_t *edge)
969 {
970 if (sweep_line->current_edge != NULL) {
971 cairo_bo_edge_t *prev, *next;
972 int cmp;
973
974 cmp = _cairo_bo_sweep_line_compare_edges (sweep_line,
975 sweep_line->current_edge,
976 edge);
977 if (cmp < 0) {
978 prev = sweep_line->current_edge;
979 next = prev->next;
980 while (next != NULL &&
981 _cairo_bo_sweep_line_compare_edges (sweep_line,
982 next, edge) < 0)
983 {
984 prev = next, next = prev->next;
985 }
986
987 prev->next = edge;
988 edge->prev = prev;
989 edge->next = next;
990 if (next != NULL)
991 next->prev = edge;
992 } else if (cmp > 0) {
993 next = sweep_line->current_edge;
994 prev = next->prev;
995 while (prev != NULL &&
996 _cairo_bo_sweep_line_compare_edges (sweep_line,
997 prev, edge) > 0)
998 {
999 next = prev, prev = next->prev;
1000 }
1001
1002 next->prev = edge;
1003 edge->next = next;
1004 edge->prev = prev;
1005 if (prev != NULL)
1006 prev->next = edge;
1007 else
1008 sweep_line->head = edge;
1009 } else {
1010 prev = sweep_line->current_edge;
1011 edge->prev = prev;
1012 edge->next = prev->next;
1013 if (prev->next != NULL)
1014 prev->next->prev = edge;
1015 prev->next = edge;
1016 }
1017 } else {
1018 sweep_line->head = edge;
1019 }
1020
1021 sweep_line->current_edge = edge;
1022
1023 return CAIRO_STATUS_SUCCESS;
1024 }
1025
1026 static void
_cairo_bo_sweep_line_delete(cairo_bo_sweep_line_t * sweep_line,cairo_bo_edge_t * edge)1027 _cairo_bo_sweep_line_delete (cairo_bo_sweep_line_t *sweep_line,
1028 cairo_bo_edge_t *edge)
1029 {
1030 if (edge->prev != NULL)
1031 edge->prev->next = edge->next;
1032 else
1033 sweep_line->head = edge->next;
1034
1035 if (edge->next != NULL)
1036 edge->next->prev = edge->prev;
1037
1038 if (sweep_line->current_edge == edge)
1039 sweep_line->current_edge = edge->prev ? edge->prev : edge->next;
1040 }
1041
1042 static void
_cairo_bo_sweep_line_swap(cairo_bo_sweep_line_t * sweep_line,cairo_bo_edge_t * left,cairo_bo_edge_t * right)1043 _cairo_bo_sweep_line_swap (cairo_bo_sweep_line_t *sweep_line,
1044 cairo_bo_edge_t *left,
1045 cairo_bo_edge_t *right)
1046 {
1047 if (left->prev != NULL)
1048 left->prev->next = right;
1049 else
1050 sweep_line->head = right;
1051
1052 if (right->next != NULL)
1053 right->next->prev = left;
1054
1055 left->next = right->next;
1056 right->next = left;
1057
1058 right->prev = left->prev;
1059 left->prev = right;
1060 }
1061
1062 static inline cairo_bool_t
edges_colinear(const cairo_bo_edge_t * a,const cairo_bo_edge_t * b)1063 edges_colinear (const cairo_bo_edge_t *a, const cairo_bo_edge_t *b)
1064 {
1065 if (_line_equal (&a->edge.line, &b->edge.line))
1066 return TRUE;
1067
1068 if (_slope_compare (a, b))
1069 return FALSE;
1070
1071 /* The choice of y is not truly arbitrary since we must guarantee that it
1072 * is greater than the start of either line.
1073 */
1074 if (a->edge.line.p1.y == b->edge.line.p1.y) {
1075 return a->edge.line.p1.x == b->edge.line.p1.x;
1076 } else if (a->edge.line.p1.y < b->edge.line.p1.y) {
1077 return edge_compare_for_y_against_x (b,
1078 a->edge.line.p1.y,
1079 a->edge.line.p1.x) == 0;
1080 } else {
1081 return edge_compare_for_y_against_x (a,
1082 b->edge.line.p1.y,
1083 b->edge.line.p1.x) == 0;
1084 }
1085 }
1086
1087 static void
edges_end(cairo_bo_edge_t * left,int32_t bot,cairo_polygon_t * polygon)1088 edges_end (cairo_bo_edge_t *left,
1089 int32_t bot,
1090 cairo_polygon_t *polygon)
1091 {
1092 cairo_bo_deferred_t *l = &left->deferred;
1093 cairo_bo_edge_t *right = l->other;
1094
1095 assert(right->deferred.other == NULL);
1096 if (likely (l->top < bot)) {
1097 _cairo_polygon_add_line (polygon, &left->edge.line, l->top, bot, 1);
1098 _cairo_polygon_add_line (polygon, &right->edge.line, l->top, bot, -1);
1099 }
1100
1101 l->other = NULL;
1102 }
1103
1104 static inline void
edges_start_or_continue(cairo_bo_edge_t * left,cairo_bo_edge_t * right,int top,cairo_polygon_t * polygon)1105 edges_start_or_continue (cairo_bo_edge_t *left,
1106 cairo_bo_edge_t *right,
1107 int top,
1108 cairo_polygon_t *polygon)
1109 {
1110 assert (right != NULL);
1111 assert (right->deferred.other == NULL);
1112
1113 if (left->deferred.other == right)
1114 return;
1115
1116 if (left->deferred.other != NULL) {
1117 if (edges_colinear (left->deferred.other, right)) {
1118 cairo_bo_edge_t *old = left->deferred.other;
1119
1120 /* continuation on right, extend right to cover both */
1121 assert (old->deferred.other == NULL);
1122 assert (old->edge.line.p2.y > old->edge.line.p1.y);
1123
1124 if (old->edge.line.p1.y < right->edge.line.p1.y)
1125 right->edge.line.p1 = old->edge.line.p1;
1126 if (old->edge.line.p2.y > right->edge.line.p2.y)
1127 right->edge.line.p2 = old->edge.line.p2;
1128 left->deferred.other = right;
1129 return;
1130 }
1131
1132 edges_end (left, top, polygon);
1133 }
1134
1135 if (! edges_colinear (left, right)) {
1136 left->deferred.top = top;
1137 left->deferred.other = right;
1138 }
1139 }
1140
1141 #define is_zero(w) ((w)[0] == 0 || (w)[1] == 0)
1142
1143 static inline void
active_edges(cairo_bo_edge_t * left,int32_t top,cairo_polygon_t * polygon)1144 active_edges (cairo_bo_edge_t *left,
1145 int32_t top,
1146 cairo_polygon_t *polygon)
1147 {
1148 cairo_bo_edge_t *right;
1149 int winding[2] = {0, 0};
1150
1151 /* Yes, this is naive. Consider this a placeholder. */
1152
1153 while (left != NULL) {
1154 assert (is_zero (winding));
1155
1156 do {
1157 winding[left->a_or_b] += left->edge.dir;
1158 if (! is_zero (winding))
1159 break;
1160
1161 if unlikely ((left->deferred.other))
1162 edges_end (left, top, polygon);
1163
1164 left = left->next;
1165 if (! left)
1166 return;
1167 } while (1);
1168
1169 right = left->next;
1170 do {
1171 if unlikely ((right->deferred.other))
1172 edges_end (right, top, polygon);
1173
1174 winding[right->a_or_b] += right->edge.dir;
1175 if (is_zero (winding)) {
1176 if (right->next == NULL ||
1177 ! edges_colinear (right, right->next))
1178 break;
1179 }
1180
1181 right = right->next;
1182 } while (1);
1183
1184 edges_start_or_continue (left, right, top, polygon);
1185
1186 left = right->next;
1187 }
1188 }
1189
1190 static cairo_status_t
intersection_sweep(cairo_bo_event_t ** start_events,int num_events,cairo_polygon_t * polygon)1191 intersection_sweep (cairo_bo_event_t **start_events,
1192 int num_events,
1193 cairo_polygon_t *polygon)
1194 {
1195 cairo_status_t status = CAIRO_STATUS_SUCCESS; /* silence compiler */
1196 cairo_bo_event_queue_t event_queue;
1197 cairo_bo_sweep_line_t sweep_line;
1198 cairo_bo_event_t *event;
1199 cairo_bo_edge_t *left, *right;
1200 cairo_bo_edge_t *e1, *e2;
1201
1202 _cairo_bo_event_queue_init (&event_queue, start_events, num_events);
1203 _cairo_bo_sweep_line_init (&sweep_line);
1204
1205 while ((event = _cairo_bo_event_dequeue (&event_queue))) {
1206 if (event->point.y.ordinate != sweep_line.current_y) {
1207 active_edges (sweep_line.head,
1208 sweep_line.current_y,
1209 polygon);
1210 sweep_line.current_y = event->point.y.ordinate;
1211 }
1212
1213 switch (event->type) {
1214 case CAIRO_BO_EVENT_TYPE_START:
1215 e1 = &((cairo_bo_start_event_t *) event)->edge;
1216
1217 status = sweep_line_insert (&sweep_line, e1);
1218 if (unlikely (status))
1219 goto unwind;
1220
1221 status = event_queue_insert_stop (&event_queue, e1);
1222 if (unlikely (status))
1223 goto unwind;
1224
1225 left = e1->prev;
1226 right = e1->next;
1227
1228 if (left != NULL) {
1229 status = event_queue_insert_if_intersect_below_current_y (&event_queue, left, e1);
1230 if (unlikely (status))
1231 goto unwind;
1232 }
1233
1234 if (right != NULL) {
1235 status = event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right);
1236 if (unlikely (status))
1237 goto unwind;
1238 }
1239
1240 break;
1241
1242 case CAIRO_BO_EVENT_TYPE_STOP:
1243 e1 = ((cairo_bo_queue_event_t *) event)->e1;
1244 _cairo_bo_event_queue_delete (&event_queue, event);
1245
1246 if (e1->deferred.other)
1247 edges_end (e1, sweep_line.current_y, polygon);
1248
1249 left = e1->prev;
1250 right = e1->next;
1251
1252 _cairo_bo_sweep_line_delete (&sweep_line, e1);
1253
1254 if (left != NULL && right != NULL) {
1255 status = event_queue_insert_if_intersect_below_current_y (&event_queue, left, right);
1256 if (unlikely (status))
1257 goto unwind;
1258 }
1259
1260 break;
1261
1262 case CAIRO_BO_EVENT_TYPE_INTERSECTION:
1263 e1 = ((cairo_bo_queue_event_t *) event)->e1;
1264 e2 = ((cairo_bo_queue_event_t *) event)->e2;
1265 _cairo_bo_event_queue_delete (&event_queue, event);
1266
1267 /* skip this intersection if its edges are not adjacent */
1268 if (e2 != e1->next)
1269 break;
1270
1271 if (e1->deferred.other)
1272 edges_end (e1, sweep_line.current_y, polygon);
1273 if (e2->deferred.other)
1274 edges_end (e2, sweep_line.current_y, polygon);
1275
1276 left = e1->prev;
1277 right = e2->next;
1278
1279 _cairo_bo_sweep_line_swap (&sweep_line, e1, e2);
1280
1281 /* after the swap e2 is left of e1 */
1282
1283 if (left != NULL) {
1284 status = event_queue_insert_if_intersect_below_current_y (&event_queue, left, e2);
1285 if (unlikely (status))
1286 goto unwind;
1287 }
1288
1289 if (right != NULL) {
1290 status = event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right);
1291 if (unlikely (status))
1292 goto unwind;
1293 }
1294
1295 break;
1296 }
1297 }
1298
1299 unwind:
1300 _cairo_bo_event_queue_fini (&event_queue);
1301
1302 return status;
1303 }
1304
1305 cairo_status_t
_cairo_polygon_intersect(cairo_polygon_t * a,int winding_a,cairo_polygon_t * b,int winding_b)1306 _cairo_polygon_intersect (cairo_polygon_t *a, int winding_a,
1307 cairo_polygon_t *b, int winding_b)
1308 {
1309 cairo_status_t status;
1310 cairo_bo_start_event_t stack_events[CAIRO_STACK_ARRAY_LENGTH (cairo_bo_start_event_t)];
1311 cairo_bo_start_event_t *events;
1312 cairo_bo_event_t *stack_event_ptrs[ARRAY_LENGTH (stack_events) + 1];
1313 cairo_bo_event_t **event_ptrs;
1314 int num_events;
1315 int i, j;
1316
1317 /* XXX lazy */
1318 if (winding_a != CAIRO_FILL_RULE_WINDING) {
1319 status = _cairo_polygon_reduce (a, winding_a);
1320 if (unlikely (status))
1321 return status;
1322 }
1323
1324 if (winding_b != CAIRO_FILL_RULE_WINDING) {
1325 status = _cairo_polygon_reduce (b, winding_b);
1326 if (unlikely (status))
1327 return status;
1328 }
1329
1330 if (unlikely (0 == a->num_edges))
1331 return CAIRO_STATUS_SUCCESS;
1332
1333 if (unlikely (0 == b->num_edges)) {
1334 a->num_edges = 0;
1335 return CAIRO_STATUS_SUCCESS;
1336 }
1337
1338 events = stack_events;
1339 event_ptrs = stack_event_ptrs;
1340 num_events = a->num_edges + b->num_edges;
1341 if (num_events > ARRAY_LENGTH (stack_events)) {
1342 events = _cairo_malloc_ab_plus_c (num_events,
1343 sizeof (cairo_bo_start_event_t) +
1344 sizeof (cairo_bo_event_t *),
1345 sizeof (cairo_bo_event_t *));
1346 if (unlikely (events == NULL))
1347 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
1348
1349 event_ptrs = (cairo_bo_event_t **) (events + num_events);
1350 }
1351
1352 j = 0;
1353 for (i = 0; i < a->num_edges; i++) {
1354 event_ptrs[j] = (cairo_bo_event_t *) &events[j];
1355
1356 events[j].type = CAIRO_BO_EVENT_TYPE_START;
1357 events[j].point.y.ordinate = a->edges[i].top;
1358 events[j].point.y.approx = EXACT;
1359 events[j].point.x.ordinate =
1360 _line_compute_intersection_x_for_y (&a->edges[i].line,
1361 events[j].point.y.ordinate);
1362 events[j].point.x.approx = EXACT;
1363
1364 events[j].edge.a_or_b = 0;
1365 events[j].edge.edge = a->edges[i];
1366 events[j].edge.deferred.other = NULL;
1367 events[j].edge.prev = NULL;
1368 events[j].edge.next = NULL;
1369 j++;
1370 }
1371
1372 for (i = 0; i < b->num_edges; i++) {
1373 event_ptrs[j] = (cairo_bo_event_t *) &events[j];
1374
1375 events[j].type = CAIRO_BO_EVENT_TYPE_START;
1376 events[j].point.y.ordinate = b->edges[i].top;
1377 events[j].point.y.approx = EXACT;
1378 events[j].point.x.ordinate =
1379 _line_compute_intersection_x_for_y (&b->edges[i].line,
1380 events[j].point.y.ordinate);
1381 events[j].point.x.approx = EXACT;
1382
1383 events[j].edge.a_or_b = 1;
1384 events[j].edge.edge = b->edges[i];
1385 events[j].edge.deferred.other = NULL;
1386 events[j].edge.prev = NULL;
1387 events[j].edge.next = NULL;
1388 j++;
1389 }
1390 assert (j == num_events);
1391
1392 #if 0
1393 {
1394 FILE *file = fopen ("clip_a.txt", "w");
1395 _cairo_debug_print_polygon (file, a);
1396 fclose (file);
1397 }
1398 {
1399 FILE *file = fopen ("clip_b.txt", "w");
1400 _cairo_debug_print_polygon (file, b);
1401 fclose (file);
1402 }
1403 #endif
1404
1405 a->num_edges = 0;
1406 status = intersection_sweep (event_ptrs, num_events, a);
1407 if (events != stack_events)
1408 free (events);
1409
1410 #if 0
1411 {
1412 FILE *file = fopen ("clip_result.txt", "w");
1413 _cairo_debug_print_polygon (file, a);
1414 fclose (file);
1415 }
1416 #endif
1417
1418 return status;
1419 }
1420
1421 cairo_status_t
_cairo_polygon_intersect_with_boxes(cairo_polygon_t * polygon,cairo_fill_rule_t * winding,cairo_box_t * boxes,int num_boxes)1422 _cairo_polygon_intersect_with_boxes (cairo_polygon_t *polygon,
1423 cairo_fill_rule_t *winding,
1424 cairo_box_t *boxes,
1425 int num_boxes)
1426 {
1427 cairo_polygon_t b;
1428 cairo_status_t status;
1429 int n;
1430
1431 if (num_boxes == 0) {
1432 polygon->num_edges = 0;
1433 return CAIRO_STATUS_SUCCESS;
1434 }
1435
1436 for (n = 0; n < num_boxes; n++) {
1437 if (polygon->extents.p1.x >= boxes[n].p1.x &&
1438 polygon->extents.p2.x <= boxes[n].p2.x &&
1439 polygon->extents.p1.y >= boxes[n].p1.y &&
1440 polygon->extents.p2.y <= boxes[n].p2.y)
1441 {
1442 return CAIRO_STATUS_SUCCESS;
1443 }
1444 }
1445
1446 _cairo_polygon_init (&b, NULL, 0);
1447 for (n = 0; n < num_boxes; n++) {
1448 if (boxes[n].p2.x > polygon->extents.p1.x &&
1449 boxes[n].p1.x < polygon->extents.p2.x &&
1450 boxes[n].p2.y > polygon->extents.p1.y &&
1451 boxes[n].p1.y < polygon->extents.p2.y)
1452 {
1453 cairo_point_t p1, p2;
1454
1455 p1.y = boxes[n].p1.y;
1456 p2.y = boxes[n].p2.y;
1457
1458 p2.x = p1.x = boxes[n].p1.x;
1459 _cairo_polygon_add_external_edge (&b, &p1, &p2);
1460
1461 p2.x = p1.x = boxes[n].p2.x;
1462 _cairo_polygon_add_external_edge (&b, &p2, &p1);
1463 }
1464 }
1465
1466 status = _cairo_polygon_intersect (polygon, *winding,
1467 &b, CAIRO_FILL_RULE_WINDING);
1468 _cairo_polygon_fini (&b);
1469
1470 *winding = CAIRO_FILL_RULE_WINDING;
1471 return status;
1472 }
1473