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Diffstat (limited to 'src/cairo-bentley-ottmann.c')
| -rw-r--r-- | src/cairo-bentley-ottmann.c | 1909 |
1 files changed, 1909 insertions, 0 deletions
diff --git a/src/cairo-bentley-ottmann.c b/src/cairo-bentley-ottmann.c new file mode 100644 index 000000000..91e41f9c3 --- /dev/null +++ b/src/cairo-bentley-ottmann.c @@ -0,0 +1,1909 @@ +/* + * Copyright © 2004 Carl Worth + * Copyright © 2006 Red Hat, Inc. + * Copyright © 2008 Chris Wilson + * + * This library is free software; you can redistribute it and/or + * modify it either under the terms of the GNU Lesser General Public + * License version 2.1 as published by the Free Software Foundation + * (the "LGPL") or, at your option, under the terms of the Mozilla + * Public License Version 1.1 (the "MPL"). If you do not alter this + * notice, a recipient may use your version of this file under either + * the MPL or the LGPL. + * + * You should have received a copy of the LGPL along with this library + * in the file COPYING-LGPL-2.1; if not, write to the Free Software + * Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA + * You should have received a copy of the MPL along with this library + * in the file COPYING-MPL-1.1 + * + * The contents of this file are subject to the Mozilla Public License + * Version 1.1 (the "License"); you may not use this file except in + * compliance with the License. You may obtain a copy of the License at + * http://www.mozilla.org/MPL/ + * + * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY + * OF ANY KIND, either express or implied. See the LGPL or the MPL for + * the specific language governing rights and limitations. + * + * The Original Code is the cairo graphics library. + * + * The Initial Developer of the Original Code is Carl Worth + * + * Contributor(s): + * Carl D. Worth <cworth@cworth.org> + * Chris Wilson <chris@chris-wilson.co.uk> + */ + +/* Provide definitions for standalone compilation */ +#include "cairoint.h" + +#include "cairo-combsort-inline.h" +#include "cairo-error-private.h" +#include "cairo-freelist-private.h" +#include "cairo-line-inline.h" +#include "cairo-traps-private.h" + +#define DEBUG_PRINT_STATE 0 +#define DEBUG_EVENTS 0 +#define DEBUG_TRAPS 0 + +typedef cairo_point_t cairo_bo_point32_t; + +typedef struct _cairo_bo_intersect_ordinate { + int32_t ordinate; + enum { EXACT, INEXACT } exactness; +} cairo_bo_intersect_ordinate_t; + +typedef struct _cairo_bo_intersect_point { + cairo_bo_intersect_ordinate_t x; + cairo_bo_intersect_ordinate_t y; +} cairo_bo_intersect_point_t; + +typedef struct _cairo_bo_edge cairo_bo_edge_t; +typedef struct _cairo_bo_trap cairo_bo_trap_t; + +/* A deferred trapezoid of an edge */ +struct _cairo_bo_trap { + cairo_bo_edge_t *right; + int32_t top; +}; + +struct _cairo_bo_edge { + cairo_edge_t edge; + cairo_bo_edge_t *prev; + cairo_bo_edge_t *next; + cairo_bo_edge_t *colinear; + cairo_bo_trap_t deferred_trap; +}; + +/* the parent is always given by index/2 */ +#define PQ_PARENT_INDEX(i) ((i) >> 1) +#define PQ_FIRST_ENTRY 1 + +/* left and right children are index * 2 and (index * 2) +1 respectively */ +#define PQ_LEFT_CHILD_INDEX(i) ((i) << 1) + +typedef enum { + CAIRO_BO_EVENT_TYPE_STOP, + CAIRO_BO_EVENT_TYPE_INTERSECTION, + CAIRO_BO_EVENT_TYPE_START +} cairo_bo_event_type_t; + +typedef struct _cairo_bo_event { + cairo_bo_event_type_t type; + cairo_point_t point; +} cairo_bo_event_t; + +typedef struct _cairo_bo_start_event { + cairo_bo_event_type_t type; + cairo_point_t point; + cairo_bo_edge_t edge; +} cairo_bo_start_event_t; + +typedef struct _cairo_bo_queue_event { + cairo_bo_event_type_t type; + cairo_point_t point; + cairo_bo_edge_t *e1; + cairo_bo_edge_t *e2; +} cairo_bo_queue_event_t; + +typedef struct _pqueue { + int size, max_size; + + cairo_bo_event_t **elements; + cairo_bo_event_t *elements_embedded[1024]; +} pqueue_t; + +typedef struct _cairo_bo_event_queue { + cairo_freepool_t pool; + pqueue_t pqueue; + cairo_bo_event_t **start_events; +} cairo_bo_event_queue_t; + +typedef struct _cairo_bo_sweep_line { + cairo_bo_edge_t *head; + cairo_bo_edge_t *stopped; + int32_t current_y; + cairo_bo_edge_t *current_edge; +} cairo_bo_sweep_line_t; + +#if DEBUG_TRAPS +static void +dump_traps (cairo_traps_t *traps, const char *filename) +{ + FILE *file; + cairo_box_t extents; + int n; + + if (getenv ("CAIRO_DEBUG_TRAPS") == NULL) + return; + +#if 0 + if (traps->has_limits) { + printf ("%s: limits=(%d, %d, %d, %d)\n", + filename, + traps->limits.p1.x, traps->limits.p1.y, + traps->limits.p2.x, traps->limits.p2.y); + } +#endif + _cairo_traps_extents (traps, &extents); + printf ("%s: extents=(%d, %d, %d, %d)\n", + filename, + extents.p1.x, extents.p1.y, + extents.p2.x, extents.p2.y); + + file = fopen (filename, "a"); + if (file != NULL) { + for (n = 0; n < traps->num_traps; n++) { + fprintf (file, "%d %d L:(%d, %d), (%d, %d) R:(%d, %d), (%d, %d)\n", + traps->traps[n].top, + traps->traps[n].bottom, + traps->traps[n].left.p1.x, + traps->traps[n].left.p1.y, + traps->traps[n].left.p2.x, + traps->traps[n].left.p2.y, + traps->traps[n].right.p1.x, + traps->traps[n].right.p1.y, + traps->traps[n].right.p2.x, + traps->traps[n].right.p2.y); + } + fprintf (file, "\n"); + fclose (file); + } +} + +static void +dump_edges (cairo_bo_start_event_t *events, + int num_edges, + const char *filename) +{ + FILE *file; + int n; + + if (getenv ("CAIRO_DEBUG_TRAPS") == NULL) + return; + + file = fopen (filename, "a"); + if (file != NULL) { + for (n = 0; n < num_edges; n++) { + fprintf (file, "(%d, %d), (%d, %d) %d %d %d\n", + events[n].edge.edge.line.p1.x, + events[n].edge.edge.line.p1.y, + events[n].edge.edge.line.p2.x, + events[n].edge.edge.line.p2.y, + events[n].edge.edge.top, + events[n].edge.edge.bottom, + events[n].edge.edge.dir); + } + fprintf (file, "\n"); + fclose (file); + } +} +#endif + +static cairo_fixed_t +_line_compute_intersection_x_for_y (const cairo_line_t *line, + cairo_fixed_t y) +{ + cairo_fixed_t x, dy; + + if (y == line->p1.y) + return line->p1.x; + if (y == line->p2.y) + return line->p2.x; + + x = line->p1.x; + dy = line->p2.y - line->p1.y; + if (dy != 0) { + x += _cairo_fixed_mul_div_floor (y - line->p1.y, + line->p2.x - line->p1.x, + dy); + } + + return x; +} + +static inline int +_cairo_bo_point32_compare (cairo_bo_point32_t const *a, + cairo_bo_point32_t const *b) +{ + int cmp; + + cmp = a->y - b->y; + if (cmp) + return cmp; + + return a->x - b->x; +} + +/* Compare the slope of a to the slope of b, returning 1, 0, -1 if the + * slope a is respectively greater than, equal to, or less than the + * slope of b. + * + * For each edge, consider the direction vector formed from: + * + * top -> bottom + * + * which is: + * + * (dx, dy) = (line.p2.x - line.p1.x, line.p2.y - line.p1.y) + * + * We then define the slope of each edge as dx/dy, (which is the + * inverse of the slope typically used in math instruction). We never + * compute a slope directly as the value approaches infinity, but we + * can derive a slope comparison without division as follows, (where + * the ? represents our compare operator). + * + * 1. slope(a) ? slope(b) + * 2. adx/ady ? bdx/bdy + * 3. (adx * bdy) ? (bdx * ady) + * + * Note that from step 2 to step 3 there is no change needed in the + * sign of the result since both ady and bdy are guaranteed to be + * greater than or equal to 0. + * + * When using this slope comparison to sort edges, some care is needed + * when interpreting the results. Since the slope compare operates on + * distance vectors from top to bottom it gives a correct left to + * right sort for edges that have a common top point, (such as two + * edges with start events at the same location). On the other hand, + * the sense of the result will be exactly reversed for two edges that + * have a common stop point. + */ +static inline int +_slope_compare (const cairo_bo_edge_t *a, + const cairo_bo_edge_t *b) +{ + /* XXX: We're assuming here that dx and dy will still fit in 32 + * bits. That's not true in general as there could be overflow. We + * should prevent that before the tessellation algorithm + * begins. + */ + int32_t adx = a->edge.line.p2.x - a->edge.line.p1.x; + int32_t bdx = b->edge.line.p2.x - b->edge.line.p1.x; + + /* Since the dy's are all positive by construction we can fast + * path several common cases. + */ + + /* First check for vertical lines. */ + if (adx == 0) + return -bdx; + if (bdx == 0) + return adx; + + /* Then where the two edges point in different directions wrt x. */ + if ((adx ^ bdx) < 0) + return adx; + + /* Finally we actually need to do the general comparison. */ + { + int32_t ady = a->edge.line.p2.y - a->edge.line.p1.y; + int32_t bdy = b->edge.line.p2.y - b->edge.line.p1.y; + cairo_int64_t adx_bdy = _cairo_int32x32_64_mul (adx, bdy); + cairo_int64_t bdx_ady = _cairo_int32x32_64_mul (bdx, ady); + + return _cairo_int64_cmp (adx_bdy, bdx_ady); + } +} + + +/* + * We need to compare the x-coordinate of a line for a particular y wrt to a + * given x, without loss of precision. + * + * The x-coordinate along an edge for a given y is: + * X = A_x + (Y - A_y) * A_dx / A_dy + * + * So the inequality we wish to test is: + * A_x + (Y - A_y) * A_dx / A_dy ∘ X + * where ∘ is our inequality operator. + * + * By construction, we know that A_dy (and (Y - A_y)) are + * all positive, so we can rearrange it thus without causing a sign change: + * (Y - A_y) * A_dx ∘ (X - A_x) * A_dy + * + * Given the assumption that all the deltas fit within 32 bits, we can compute + * this comparison directly using 64 bit arithmetic. + * + * See the similar discussion for _slope_compare() and + * edges_compare_x_for_y_general(). + */ +static int +edge_compare_for_y_against_x (const cairo_bo_edge_t *a, + int32_t y, + int32_t x) +{ + int32_t adx, ady; + int32_t dx, dy; + cairo_int64_t L, R; + + if (x < a->edge.line.p1.x && x < a->edge.line.p2.x) + return 1; + if (x > a->edge.line.p1.x && x > a->edge.line.p2.x) + return -1; + + adx = a->edge.line.p2.x - a->edge.line.p1.x; + dx = x - a->edge.line.p1.x; + + if (adx == 0) + return -dx; + if (dx == 0 || (adx ^ dx) < 0) + return adx; + + dy = y - a->edge.line.p1.y; + ady = a->edge.line.p2.y - a->edge.line.p1.y; + + L = _cairo_int32x32_64_mul (dy, adx); + R = _cairo_int32x32_64_mul (dx, ady); + + return _cairo_int64_cmp (L, R); +} + +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) +{ + int cmp; + + cmp = cairo_lines_compare_at_y (&a->edge.line, + &b->edge.line, + sweep_line->current_y); + if (cmp) + return cmp; + + /* We've got two collinear edges now. */ + return b->edge.bottom - a->edge.bottom; +} + +static inline cairo_int64_t +det32_64 (int32_t a, int32_t b, + int32_t c, int32_t d) +{ + /* det = a * d - b * c */ + return _cairo_int64_sub (_cairo_int32x32_64_mul (a, d), + _cairo_int32x32_64_mul (b, c)); +} + +static inline cairo_int128_t +det64x32_128 (cairo_int64_t a, int32_t b, + cairo_int64_t c, int32_t d) +{ + /* det = a * d - b * c */ + return _cairo_int128_sub (_cairo_int64x32_128_mul (a, d), + _cairo_int64x32_128_mul (c, b)); +} + +/* Compute the intersection of two lines as defined by two edges. The + * result is provided as a coordinate pair of 128-bit integers. + * + * Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection or + * %CAIRO_BO_STATUS_PARALLEL if the two lines are exactly parallel. + */ +static cairo_bool_t +intersect_lines (cairo_bo_edge_t *a, + cairo_bo_edge_t *b, + cairo_bo_intersect_point_t *intersection) +{ + cairo_int64_t a_det, b_det; + + /* XXX: We're assuming here that dx and dy will still fit in 32 + * bits. That's not true in general as there could be overflow. We + * should prevent that before the tessellation algorithm begins. + * What we're doing to mitigate this is to perform clamping in + * cairo_bo_tessellate_polygon(). + */ + int32_t dx1 = a->edge.line.p1.x - a->edge.line.p2.x; + int32_t dy1 = a->edge.line.p1.y - a->edge.line.p2.y; + + int32_t dx2 = b->edge.line.p1.x - b->edge.line.p2.x; + int32_t dy2 = b->edge.line.p1.y - b->edge.line.p2.y; + + cairo_int64_t den_det; + cairo_int64_t R; + cairo_quorem64_t qr; + + den_det = det32_64 (dx1, dy1, dx2, dy2); + + /* Q: Can we determine that the lines do not intersect (within range) + * much more cheaply than computing the intersection point i.e. by + * avoiding the division? + * + * X = ax + t * adx = bx + s * bdx; + * Y = ay + t * ady = by + s * bdy; + * ∴ t * (ady*bdx - bdy*adx) = bdx * (by - ay) + bdy * (ax - bx) + * => t * L = R + * + * Therefore we can reject any intersection (under the criteria for + * valid intersection events) if: + * L^R < 0 => t < 0, or + * L<R => t > 1 + * + * (where top/bottom must at least extend to the line endpoints). + * + * A similar substitution can be performed for s, yielding: + * s * (ady*bdx - bdy*adx) = ady * (ax - bx) - adx * (ay - by) + */ + R = det32_64 (dx2, dy2, + b->edge.line.p1.x - a->edge.line.p1.x, + b->edge.line.p1.y - a->edge.line.p1.y); + if (_cairo_int64_negative (den_det)) { + if (_cairo_int64_ge (den_det, R)) + return FALSE; + } else { + if (_cairo_int64_le (den_det, R)) + return FALSE; + } + + R = det32_64 (dy1, dx1, + a->edge.line.p1.y - b->edge.line.p1.y, + a->edge.line.p1.x - b->edge.line.p1.x); + if (_cairo_int64_negative (den_det)) { + if (_cairo_int64_ge (den_det, R)) + return FALSE; + } else { + if (_cairo_int64_le (den_det, R)) + return FALSE; + } + + /* We now know that the two lines should intersect within range. */ + + a_det = det32_64 (a->edge.line.p1.x, a->edge.line.p1.y, + a->edge.line.p2.x, a->edge.line.p2.y); + b_det = det32_64 (b->edge.line.p1.x, b->edge.line.p1.y, + b->edge.line.p2.x, b->edge.line.p2.y); + + /* x = det (a_det, dx1, b_det, dx2) / den_det */ + qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dx1, + b_det, dx2), + den_det); + if (_cairo_int64_eq (qr.rem, den_det)) + return FALSE; +#if 0 + intersection->x.exactness = _cairo_int64_is_zero (qr.rem) ? EXACT : INEXACT; +#else + intersection->x.exactness = EXACT; + if (! _cairo_int64_is_zero (qr.rem)) { + if (_cairo_int64_negative (den_det) ^ _cairo_int64_negative (qr.rem)) + qr.rem = _cairo_int64_negate (qr.rem); + qr.rem = _cairo_int64_mul (qr.rem, _cairo_int32_to_int64 (2)); + if (_cairo_int64_ge (qr.rem, den_det)) { + qr.quo = _cairo_int64_add (qr.quo, + _cairo_int32_to_int64 (_cairo_int64_negative (qr.quo) ? -1 : 1)); + } else + intersection->x.exactness = INEXACT; + } +#endif + intersection->x.ordinate = _cairo_int64_to_int32 (qr.quo); + + /* y = det (a_det, dy1, b_det, dy2) / den_det */ + qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dy1, + b_det, dy2), + den_det); + if (_cairo_int64_eq (qr.rem, den_det)) + return FALSE; +#if 0 + intersection->y.exactness = _cairo_int64_is_zero (qr.rem) ? EXACT : INEXACT; +#else + intersection->y.exactness = EXACT; + if (! _cairo_int64_is_zero (qr.rem)) { + if (_cairo_int64_negative (den_det) ^ _cairo_int64_negative (qr.rem)) + qr.rem = _cairo_int64_negate (qr.rem); + qr.rem = _cairo_int64_mul (qr.rem, _cairo_int32_to_int64 (2)); + if (_cairo_int64_ge (qr.rem, den_det)) { + qr.quo = _cairo_int64_add (qr.quo, + _cairo_int32_to_int64 (_cairo_int64_negative (qr.quo) ? -1 : 1)); + } else + intersection->y.exactness = INEXACT; + } +#endif + intersection->y.ordinate = _cairo_int64_to_int32 (qr.quo); + + return TRUE; +} + +static int +_cairo_bo_intersect_ordinate_32_compare (cairo_bo_intersect_ordinate_t a, + int32_t b) +{ + /* First compare the quotient */ + if (a.ordinate > b) + return +1; + if (a.ordinate < b) + return -1; + /* With quotient identical, if remainder is 0 then compare equal */ + /* Otherwise, the non-zero remainder makes a > b */ + return INEXACT == a.exactness; +} + +/* Does the given edge contain the given point. The point must already + * be known to be contained within the line determined by the edge, + * (most likely the point results from an intersection of this edge + * with another). + * + * If we had exact arithmetic, then this function would simply be a + * matter of examining whether the y value of the point lies within + * the range of y values of the edge. But since intersection points + * are not exact due to being rounded to the nearest integer within + * the available precision, we must also examine the x value of the + * point. + * + * The definition of "contains" here is that the given intersection + * point will be seen by the sweep line after the start event for the + * given edge and before the stop event for the edge. See the comments + * in the implementation for more details. + */ +static cairo_bool_t +_cairo_bo_edge_contains_intersect_point (cairo_bo_edge_t *edge, + cairo_bo_intersect_point_t *point) +{ + int cmp_top, cmp_bottom; + + /* XXX: When running the actual algorithm, we don't actually need to + * compare against edge->top at all here, since any intersection above + * top is eliminated early via a slope comparison. We're leaving these + * here for now only for the sake of the quadratic-time intersection + * finder which needs them. + */ + + cmp_top = _cairo_bo_intersect_ordinate_32_compare (point->y, + edge->edge.top); + cmp_bottom = _cairo_bo_intersect_ordinate_32_compare (point->y, + edge->edge.bottom); + + if (cmp_top < 0 || cmp_bottom > 0) + { + return FALSE; + } + + if (cmp_top > 0 && cmp_bottom < 0) + { + return TRUE; + } + + /* At this stage, the point lies on the same y value as either + * edge->top or edge->bottom, so we have to examine the x value in + * order to properly determine containment. */ + + /* If the y value of the point is the same as the y value of the + * top of the edge, then the x value of the point must be greater + * to be considered as inside the edge. Similarly, if the y value + * of the point is the same as the y value of the bottom of the + * edge, then the x value of the point must be less to be + * considered as inside. */ + + if (cmp_top == 0) { + cairo_fixed_t top_x; + + top_x = _line_compute_intersection_x_for_y (&edge->edge.line, + edge->edge.top); + return _cairo_bo_intersect_ordinate_32_compare (point->x, top_x) > 0; + } else { /* cmp_bottom == 0 */ + cairo_fixed_t bot_x; + + bot_x = _line_compute_intersection_x_for_y (&edge->edge.line, + edge->edge.bottom); + return _cairo_bo_intersect_ordinate_32_compare (point->x, bot_x) < 0; + } +} + +/* Compute the intersection of two edges. The result is provided as a + * coordinate pair of 128-bit integers. + * + * Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection + * that is within both edges, %CAIRO_BO_STATUS_NO_INTERSECTION if the + * intersection of the lines defined by the edges occurs outside of + * one or both edges, and %CAIRO_BO_STATUS_PARALLEL if the two edges + * are exactly parallel. + * + * Note that when determining if a candidate intersection is "inside" + * an edge, we consider both the infinitesimal shortening and the + * infinitesimal tilt rules described by John Hobby. Specifically, if + * the intersection is exactly the same as an edge point, it is + * effectively outside (no intersection is returned). Also, if the + * intersection point has the same + */ +static cairo_bool_t +_cairo_bo_edge_intersect (cairo_bo_edge_t *a, + cairo_bo_edge_t *b, + cairo_bo_point32_t *intersection) +{ + cairo_bo_intersect_point_t quorem; + + if (! intersect_lines (a, b, &quorem)) + return FALSE; + + if (! _cairo_bo_edge_contains_intersect_point (a, &quorem)) + return FALSE; + + if (! _cairo_bo_edge_contains_intersect_point (b, &quorem)) + return FALSE; + + /* Now that we've correctly compared the intersection point and + * determined that it lies within the edge, then we know that we + * no longer need any more bits of storage for the intersection + * than we do for our edge coordinates. We also no longer need the + * remainder from the division. */ + intersection->x = quorem.x.ordinate; + intersection->y = quorem.y.ordinate; + + return TRUE; +} + +static inline int +cairo_bo_event_compare (const cairo_bo_event_t *a, + const cairo_bo_event_t *b) +{ + int cmp; + + cmp = _cairo_bo_point32_compare (&a->point, &b->point); + if (cmp) + return cmp; + + cmp = a->type - b->type; + if (cmp) + return cmp; + + return a - b; +} + +static inline void +_pqueue_init (pqueue_t *pq) +{ + pq->max_size = ARRAY_LENGTH (pq->elements_embedded); + pq->size = 0; + + pq->elements = pq->elements_embedded; +} + +static inline void +_pqueue_fini (pqueue_t *pq) +{ + if (pq->elements != pq->elements_embedded) + free (pq->elements); +} + +static cairo_status_t +_pqueue_grow (pqueue_t *pq) +{ + cairo_bo_event_t **new_elements; + pq->max_size *= 2; + + if (pq->elements == pq->elements_embedded) { + new_elements = _cairo_malloc_ab (pq->max_size, + sizeof (cairo_bo_event_t *)); + if (unlikely (new_elements == NULL)) + return _cairo_error (CAIRO_STATUS_NO_MEMORY); + + memcpy (new_elements, pq->elements_embedded, + sizeof (pq->elements_embedded)); + } else { + new_elements = _cairo_realloc_ab (pq->elements, + pq->max_size, + sizeof (cairo_bo_event_t *)); + if (unlikely (new_elements == NULL)) + return _cairo_error (CAIRO_STATUS_NO_MEMORY); + } + + pq->elements = new_elements; + return CAIRO_STATUS_SUCCESS; +} + +static inline cairo_status_t +_pqueue_push (pqueue_t *pq, cairo_bo_event_t *event) +{ + cairo_bo_event_t **elements; + int i, parent; + + if (unlikely (pq->size + 1 == pq->max_size)) { + cairo_status_t status; + + status = _pqueue_grow (pq); + if (unlikely (status)) + return status; + } + + elements = pq->elements; + + for (i = ++pq->size; + i != PQ_FIRST_ENTRY && + cairo_bo_event_compare (event, + elements[parent = PQ_PARENT_INDEX (i)]) < 0; + i = parent) + { + elements[i] = elements[parent]; + } + + elements[i] = event; + + return CAIRO_STATUS_SUCCESS; +} + +static inline void +_pqueue_pop (pqueue_t *pq) +{ + cairo_bo_event_t **elements = pq->elements; + cairo_bo_event_t *tail; + int child, i; + + tail = elements[pq->size--]; + if (pq->size == 0) { + elements[PQ_FIRST_ENTRY] = NULL; + return; + } + + for (i = PQ_FIRST_ENTRY; + (child = PQ_LEFT_CHILD_INDEX (i)) <= pq->size; + i = child) + { + if (child != pq->size && + cairo_bo_event_compare (elements[child+1], + elements[child]) < 0) + { + child++; + } + + if (cairo_bo_event_compare (elements[child], tail) >= 0) + break; + + elements[i] = elements[child]; + } + elements[i] = tail; +} + +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) +{ + cairo_bo_queue_event_t *event; + + event = _cairo_freepool_alloc (&queue->pool); + if (unlikely (event == NULL)) + return _cairo_error (CAIRO_STATUS_NO_MEMORY); + + event->type = type; + event->e1 = e1; + event->e2 = e2; + event->point = *point; + + return _pqueue_push (&queue->pqueue, (cairo_bo_event_t *) event); +} + +static void +_cairo_bo_event_queue_delete (cairo_bo_event_queue_t *queue, + cairo_bo_event_t *event) +{ + _cairo_freepool_free (&queue->pool, event); +} + +static cairo_bo_event_t * +_cairo_bo_event_dequeue (cairo_bo_event_queue_t *event_queue) +{ + cairo_bo_event_t *event, *cmp; + + event = event_queue->pqueue.elements[PQ_FIRST_ENTRY]; + cmp = *event_queue->start_events; + if (event == NULL || + (cmp != NULL && cairo_bo_event_compare (cmp, event) < 0)) + { + event = cmp; + event_queue->start_events++; + } + else + { + _pqueue_pop (&event_queue->pqueue); + } + + return event; +} + +CAIRO_COMBSORT_DECLARE (_cairo_bo_event_queue_sort, + cairo_bo_event_t *, + cairo_bo_event_compare) + +static void +_cairo_bo_event_queue_init (cairo_bo_event_queue_t *event_queue, + cairo_bo_event_t **start_events, + int num_events) +{ + event_queue->start_events = start_events; + + _cairo_freepool_init (&event_queue->pool, + sizeof (cairo_bo_queue_event_t)); + _pqueue_init (&event_queue->pqueue); + event_queue->pqueue.elements[PQ_FIRST_ENTRY] = NULL; +} + +static cairo_status_t +_cairo_bo_event_queue_insert_stop (cairo_bo_event_queue_t *event_queue, + cairo_bo_edge_t *edge) +{ + cairo_bo_point32_t point; + + point.y = edge->edge.bottom; + point.x = _line_compute_intersection_x_for_y (&edge->edge.line, + point.y); + return _cairo_bo_event_queue_insert (event_queue, + CAIRO_BO_EVENT_TYPE_STOP, + edge, NULL, + &point); +} + +static void +_cairo_bo_event_queue_fini (cairo_bo_event_queue_t *event_queue) +{ + _pqueue_fini (&event_queue->pqueue); + _cairo_freepool_fini (&event_queue->pool); +} + +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) +{ + cairo_bo_point32_t intersection; + + if (MAX (left->edge.line.p1.x, left->edge.line.p2.x) <= + MIN (right->edge.line.p1.x, right->edge.line.p2.x)) + return CAIRO_STATUS_SUCCESS; + + if (cairo_lines_equal (&left->edge.line, &right->edge.line)) + return CAIRO_STATUS_SUCCESS; + + /* The names "left" and "right" here are correct descriptions of + * the order of the two edges within the active edge list. So if a + * slope comparison also puts left less than right, then we know + * that the intersection of these two segments has already + * occurred before the current sweep line position. */ + if (_slope_compare (left, right) <= 0) + return CAIRO_STATUS_SUCCESS; + + if (! _cairo_bo_edge_intersect (left, right, &intersection)) + return CAIRO_STATUS_SUCCESS; + + return _cairo_bo_event_queue_insert (event_queue, + CAIRO_BO_EVENT_TYPE_INTERSECTION, + left, right, + &intersection); +} + +static void +_cairo_bo_sweep_line_init (cairo_bo_sweep_line_t *sweep_line) +{ + sweep_line->head = NULL; + sweep_line->stopped = NULL; + sweep_line->current_y = INT32_MIN; + sweep_line->current_edge = NULL; +} + +static void +_cairo_bo_sweep_line_insert (cairo_bo_sweep_line_t *sweep_line, + cairo_bo_edge_t *edge) +{ + if (sweep_line->current_edge != NULL) { + cairo_bo_edge_t *prev, *next; + int cmp; + + cmp = _cairo_bo_sweep_line_compare_edges (sweep_line, + sweep_line->current_edge, + edge); + if (cmp < 0) { + prev = sweep_line->current_edge; + next = prev->next; + while (next != NULL && + _cairo_bo_sweep_line_compare_edges (sweep_line, + next, edge) < 0) + { + prev = next, next = prev->next; + } + + prev->next = edge; + edge->prev = prev; + edge->next = next; + if (next != NULL) + next->prev = edge; + } else if (cmp > 0) { + next = sweep_line->current_edge; + prev = next->prev; + while (prev != NULL && + _cairo_bo_sweep_line_compare_edges (sweep_line, + prev, edge) > 0) + { + next = prev, prev = next->prev; + } + + next->prev = edge; + edge->next = next; + edge->prev = prev; + if (prev != NULL) + prev->next = edge; + else + sweep_line->head = edge; + } else { + prev = sweep_line->current_edge; + edge->prev = prev; + edge->next = prev->next; + if (prev->next != NULL) + prev->next->prev = edge; + prev->next = edge; + } + } else { + sweep_line->head = edge; + edge->next = NULL; + } + + sweep_line->current_edge = edge; +} + +static void +_cairo_bo_sweep_line_delete (cairo_bo_sweep_line_t *sweep_line, + cairo_bo_edge_t *edge) +{ + if (edge->prev != NULL) + edge->prev->next = edge->next; + else + sweep_line->head = edge->next; + + if (edge->next != NULL) + edge->next->prev = edge->prev; + + if (sweep_line->current_edge == edge) + sweep_line->current_edge = edge->prev ? edge->prev : edge->next; +} + +static void +_cairo_bo_sweep_line_swap (cairo_bo_sweep_line_t *sweep_line, + cairo_bo_edge_t *left, + cairo_bo_edge_t *right) +{ + if (left->prev != NULL) + left->prev->next = right; + else + sweep_line->head = right; + + if (right->next != NULL) + right->next->prev = left; + + left->next = right->next; + right->next = left; + + right->prev = left->prev; + left->prev = right; +} + +#if DEBUG_PRINT_STATE +static void +_cairo_bo_edge_print (cairo_bo_edge_t *edge) +{ + printf ("(0x%x, 0x%x)-(0x%x, 0x%x)", + edge->edge.line.p1.x, edge->edge.line.p1.y, + edge->edge.line.p2.x, edge->edge.line.p2.y); +} + +static void +_cairo_bo_event_print (cairo_bo_event_t *event) +{ + switch (event->type) { + case CAIRO_BO_EVENT_TYPE_START: + printf ("Start: "); + break; + case CAIRO_BO_EVENT_TYPE_STOP: + printf ("Stop: "); + break; + case CAIRO_BO_EVENT_TYPE_INTERSECTION: + printf ("Intersection: "); + break; + } + printf ("(%d, %d)\t", event->point.x, event->point.y); + _cairo_bo_edge_print (event->e1); + if (event->type == CAIRO_BO_EVENT_TYPE_INTERSECTION) { + printf (" X "); + _cairo_bo_edge_print (event->e2); + } + printf ("\n"); +} + +static void +_cairo_bo_event_queue_print (cairo_bo_event_queue_t *event_queue) +{ + /* XXX: fixme to print the start/stop array too. */ + printf ("Event queue:\n"); +} + +static void +_cairo_bo_sweep_line_print (cairo_bo_sweep_line_t *sweep_line) +{ + cairo_bool_t first = TRUE; + cairo_bo_edge_t *edge; + + printf ("Sweep line from edge list: "); + first = TRUE; + for (edge = sweep_line->head; + edge; + edge = edge->next) + { + if (!first) + printf (", "); + _cairo_bo_edge_print (edge); + first = FALSE; + } + printf ("\n"); +} + +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) +{ + printf ("%s ", msg); + _cairo_bo_event_print (event); + _cairo_bo_event_queue_print (event_queue); + _cairo_bo_sweep_line_print (sweep_line); + printf ("\n"); +} +#endif + +#if DEBUG_EVENTS +static void CAIRO_PRINTF_FORMAT (1, 2) +event_log (const char *fmt, ...) +{ + FILE *file; + + if (getenv ("CAIRO_DEBUG_EVENTS") == NULL) + return; + + file = fopen ("bo-events.txt", "a"); + if (file != NULL) { + va_list ap; + + va_start (ap, fmt); + vfprintf (file, fmt, ap); + va_end (ap); + + fclose (file); + } +} +#endif + +#define HAS_COLINEAR(a, b) ((cairo_bo_edge_t *)(((uintptr_t)(a))&~1) == (b)) +#define IS_COLINEAR(e) (((uintptr_t)(e))&1) +#define MARK_COLINEAR(e, v) ((cairo_bo_edge_t *)(((uintptr_t)(e))|(v))) + +static inline cairo_bool_t +edges_colinear (cairo_bo_edge_t *a, const cairo_bo_edge_t *b) +{ + unsigned p; + + if (HAS_COLINEAR(a->colinear, b)) + return IS_COLINEAR(a->colinear); + + if (HAS_COLINEAR(b->colinear, a)) { + p = IS_COLINEAR(b->colinear); + a->colinear = MARK_COLINEAR(b, p); + return p; + } + + p = 0; + p |= (a->edge.line.p1.x == b->edge.line.p1.x) << 0; + p |= (a->edge.line.p1.y == b->edge.line.p1.y) << 1; + p |= (a->edge.line.p2.x == b->edge.line.p2.x) << 3; + p |= (a->edge.line.p2.y == b->edge.line.p2.y) << 4; + if (p == ((1 << 0) | (1 << 1) | (1 << 3) | (1 << 4))) { + a->colinear = MARK_COLINEAR(b, 1); + return TRUE; + } + + if (_slope_compare (a, b)) { + a->colinear = MARK_COLINEAR(b, 0); + return FALSE; + } + + /* The choice of y is not truly arbitrary since we must guarantee that it + * is greater than the start of either line. + */ + if (p != 0) { + /* colinear if either end-point are coincident */ + p = (((p >> 1) & p) & 5) != 0; + } else if (a->edge.line.p1.y < b->edge.line.p1.y) { + p = edge_compare_for_y_against_x (b, + a->edge.line.p1.y, + a->edge.line.p1.x) == 0; + } else { + p = edge_compare_for_y_against_x (a, + b->edge.line.p1.y, + b->edge.line.p1.x) == 0; + } + + a->colinear = MARK_COLINEAR(b, p); + return p; +} + +/* Adds the trapezoid, if any, of the left edge to the #cairo_traps_t */ +static void +_cairo_bo_edge_end_trap (cairo_bo_edge_t *left, + int32_t bot, + cairo_traps_t *traps) +{ + cairo_bo_trap_t *trap = &left->deferred_trap; + + /* Only emit (trivial) non-degenerate trapezoids with positive height. */ + if (likely (trap->top < bot)) { + _cairo_traps_add_trap (traps, + trap->top, bot, + &left->edge.line, &trap->right->edge.line); + +#if DEBUG_PRINT_STATE + printf ("Deferred trap: left=(%x, %x)-(%x,%x) " + "right=(%x,%x)-(%x,%x) top=%x, bot=%x\n", + left->edge.line.p1.x, left->edge.line.p1.y, + left->edge.line.p2.x, left->edge.line.p2.y, + trap->right->edge.line.p1.x, trap->right->edge.line.p1.y, + trap->right->edge.line.p2.x, trap->right->edge.line.p2.y, + trap->top, bot); +#endif +#if DEBUG_EVENTS + event_log ("end trap: %lu %lu %d %d\n", + (long) left, + (long) trap->right, + trap->top, + bot); +#endif + } + + trap->right = NULL; +} + + +/* Start a new trapezoid at the given top y coordinate, whose edges + * are `edge' and `edge->next'. If `edge' already has a trapezoid, + * then either add it to the traps in `traps', if the trapezoid's + * right edge differs from `edge->next', or do nothing if the new + * trapezoid would be a continuation of the existing one. */ +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) +{ + if (left->deferred_trap.right == right) + return; + + assert (right); + if (left->deferred_trap.right != NULL) { + if (edges_colinear (left->deferred_trap.right, right)) + { + /* continuation on right, so just swap edges */ + left->deferred_trap.right = right; + return; + } + + _cairo_bo_edge_end_trap (left, top, traps); + } + + if (! edges_colinear (left, right)) { + left->deferred_trap.top = top; + left->deferred_trap.right = right; + +#if DEBUG_EVENTS + event_log ("begin trap: %lu %lu %d\n", + (long) left, + (long) right, + top); +#endif + } +} + +static inline void +_active_edges_to_traps (cairo_bo_edge_t *pos, + int32_t top, + unsigned mask, + cairo_traps_t *traps) +{ + cairo_bo_edge_t *left; + int in_out; + + +#if DEBUG_PRINT_STATE + printf ("Processing active edges for %x\n", top); +#endif + + in_out = 0; + left = pos; + while (pos != NULL) { + if (pos != left && pos->deferred_trap.right) { + /* XXX It shouldn't be possible to here with 2 deferred traps + * on colinear edges... See bug-bo-rictoz. + */ + if (left->deferred_trap.right == NULL && + edges_colinear (left, pos)) + { + /* continuation on left */ + left->deferred_trap = pos->deferred_trap; + pos->deferred_trap.right = NULL; + } + else + { + _cairo_bo_edge_end_trap (pos, top, traps); + } + } + + in_out += pos->edge.dir; + if ((in_out & mask) == 0) { + /* skip co-linear edges */ + if (pos->next == NULL || ! edges_colinear (pos, pos->next)) { + _cairo_bo_edge_start_or_continue_trap (left, pos, top, traps); + left = pos->next; + } + } + + pos = pos->next; + } +} + +/* Execute a single pass of the Bentley-Ottmann algorithm on edges, + * generating trapezoids according to the fill_rule and appending them + * to traps. */ +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) +{ + cairo_status_t status; + int intersection_count = 0; + cairo_bo_event_queue_t event_queue; + cairo_bo_sweep_line_t sweep_line; + cairo_bo_event_t *event; + cairo_bo_edge_t *left, *right; + cairo_bo_edge_t *e1, *e2; + + /* convert the fill_rule into a winding mask */ + if (fill_rule == CAIRO_FILL_RULE_WINDING) + fill_rule = (unsigned) -1; + else + fill_rule = 1; + +#if DEBUG_EVENTS + { + int i; + + for (i = 0; i < num_events; i++) { + cairo_bo_start_event_t *event = + ((cairo_bo_start_event_t **) start_events)[i]; + event_log ("edge: %lu (%d, %d) (%d, %d) (%d, %d) %d\n", + (long) &events[i].edge, + event->edge.edge.line.p1.x, + event->edge.edge.line.p1.y, + event->edge.edge.line.p2.x, + event->edge.edge.line.p2.y, + event->edge.top, + event->edge.bottom, + event->edge.edge.dir); + } + } +#endif + + _cairo_bo_event_queue_init (&event_queue, start_events, num_events); + _cairo_bo_sweep_line_init (&sweep_line); + + while ((event = _cairo_bo_event_dequeue (&event_queue))) { + if (event->point.y != sweep_line.current_y) { + for (e1 = sweep_line.stopped; e1; e1 = e1->next) { + if (e1->deferred_trap.right != NULL) { + _cairo_bo_edge_end_trap (e1, + e1->edge.bottom, + traps); + } + } + sweep_line.stopped = NULL; + + _active_edges_to_traps (sweep_line.head, + sweep_line.current_y, + fill_rule, traps); + + sweep_line.current_y = event->point.y; + } + +#if DEBUG_EVENTS + event_log ("event: %d (%ld, %ld) %lu, %lu\n", + event->type, + (long) event->point.x, + (long) event->point.y, + (long) event->e1, + (long) event->e2); +#endif + + switch (event->type) { + case CAIRO_BO_EVENT_TYPE_START: + e1 = &((cairo_bo_start_event_t *) event)->edge; + + _cairo_bo_sweep_line_insert (&sweep_line, e1); + + status = _cairo_bo_event_queue_insert_stop (&event_queue, e1); + if (unlikely (status)) + goto unwind; + + /* check to see if this is a continuation of a stopped edge */ + /* XXX change to an infinitesimal lengthening rule */ + for (left = sweep_line.stopped; left; left = left->next) { + if (e1->edge.top <= left->edge.bottom && + edges_colinear (e1, left)) + { + e1->deferred_trap = left->deferred_trap; + if (left->prev != NULL) + left->prev = left->next; + else + sweep_line.stopped = left->next; + if (left->next != NULL) + left->next->prev = left->prev; + break; + } + } + + left = e1->prev; + right = e1->next; + + if (left != NULL) { + status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, e1); + if (unlikely (status)) + goto unwind; + } + + if (right != NULL) { + status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right); + if (unlikely (status)) + goto unwind; + } + + break; + + case CAIRO_BO_EVENT_TYPE_STOP: + e1 = ((cairo_bo_queue_event_t *) event)->e1; + _cairo_bo_event_queue_delete (&event_queue, event); + + left = e1->prev; + right = e1->next; + + _cairo_bo_sweep_line_delete (&sweep_line, e1); + + /* first, check to see if we have a continuation via a fresh edge */ + if (e1->deferred_trap.right != NULL) { + e1->next = sweep_line.stopped; + if (sweep_line.stopped != NULL) + sweep_line.stopped->prev = e1; + sweep_line.stopped = e1; + e1->prev = NULL; + } + + if (left != NULL && right != NULL) { + status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, right); + if (unlikely (status)) + goto unwind; + } + + break; + + case CAIRO_BO_EVENT_TYPE_INTERSECTION: + e1 = ((cairo_bo_queue_event_t *) event)->e1; + e2 = ((cairo_bo_queue_event_t *) event)->e2; + _cairo_bo_event_queue_delete (&event_queue, event); + + /* skip this intersection if its edges are not adjacent */ + if (e2 != e1->next) + break; + + intersection_count++; + + left = e1->prev; + right = e2->next; + + _cairo_bo_sweep_line_swap (&sweep_line, e1, e2); + + /* after the swap e2 is left of e1 */ + + if (left != NULL) { + status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, e2); + if (unlikely (status)) + goto unwind; + } + + if (right != NULL) { + status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right); + if (unlikely (status)) + goto unwind; + } + + break; + } + } + + *num_intersections = intersection_count; + for (e1 = sweep_line.stopped; e1; e1 = e1->next) { + if (e1->deferred_trap.right != NULL) { + _cairo_bo_edge_end_trap (e1, e1->edge.bottom, traps); + } + } + status = traps->status; + unwind: + _cairo_bo_event_queue_fini (&event_queue); + +#if DEBUG_EVENTS + event_log ("\n"); +#endif + + return status; +} + +cairo_status_t +_cairo_bentley_ottmann_tessellate_polygon (cairo_traps_t *traps, + const cairo_polygon_t *polygon, + cairo_fill_rule_t fill_rule) +{ + int intersections; + cairo_bo_start_event_t stack_events[CAIRO_STACK_ARRAY_LENGTH (cairo_bo_start_event_t)]; + cairo_bo_start_event_t *events; + cairo_bo_event_t *stack_event_ptrs[ARRAY_LENGTH (stack_events) + 1]; + cairo_bo_event_t **event_ptrs; + cairo_bo_start_event_t *stack_event_y[64]; + cairo_bo_start_event_t **event_y = NULL; + int i, num_events, y, ymin, ymax; + cairo_status_t status; + + num_events = polygon->num_edges; + if (unlikely (0 == num_events)) + return CAIRO_STATUS_SUCCESS; + + if (polygon->num_limits) { + ymin = _cairo_fixed_integer_floor (polygon->limit.p1.y); + ymax = _cairo_fixed_integer_ceil (polygon->limit.p2.y) - ymin; + + if (ymax > 64) + event_y = _cairo_malloc_ab(sizeof (cairo_bo_event_t*), ymax); + else + event_y = stack_event_y; + memset (event_y, 0, ymax * sizeof(cairo_bo_event_t *)); + } + + events = stack_events; + event_ptrs = stack_event_ptrs; + if (num_events > ARRAY_LENGTH (stack_events)) { + events = _cairo_malloc_ab_plus_c (num_events, + sizeof (cairo_bo_start_event_t) + + sizeof (cairo_bo_event_t *), + sizeof (cairo_bo_event_t *)); + if (unlikely (events == NULL)) + return _cairo_error (CAIRO_STATUS_NO_MEMORY); + + event_ptrs = (cairo_bo_event_t **) (events + num_events); + } + + for (i = 0; i < num_events; i++) { + events[i].type = CAIRO_BO_EVENT_TYPE_START; + events[i].point.y = polygon->edges[i].top; + events[i].point.x = + _line_compute_intersection_x_for_y (&polygon->edges[i].line, + events[i].point.y); + + events[i].edge.edge = polygon->edges[i]; + events[i].edge.deferred_trap.right = NULL; + events[i].edge.prev = NULL; + events[i].edge.next = NULL; + events[i].edge.colinear = NULL; + + if (event_y) { + y = _cairo_fixed_integer_floor (events[i].point.y) - ymin; + events[i].edge.next = (cairo_bo_edge_t *) event_y[y]; + event_y[y] = (cairo_bo_start_event_t *) &events[i]; + } else + event_ptrs[i] = (cairo_bo_event_t *) &events[i]; + } + + if (event_y) { + for (y = i = 0; y < ymax && i < num_events; y++) { + cairo_bo_start_event_t *e; + int j = i; + for (e = event_y[y]; e; e = (cairo_bo_start_event_t *)e->edge.next) + event_ptrs[i++] = (cairo_bo_event_t *) e; + if (i > j + 1) + _cairo_bo_event_queue_sort (event_ptrs+j, i-j); + } + if (event_y != stack_event_y) + free (event_y); + } else + _cairo_bo_event_queue_sort (event_ptrs, i); + event_ptrs[i] = NULL; + +#if DEBUG_TRAPS + dump_edges (events, num_events, "bo-polygon-edges.txt"); +#endif + + /* XXX: This would be the convenient place to throw in multiple + * passes of the Bentley-Ottmann algorithm. It would merely + * require storing the results of each pass into a temporary + * cairo_traps_t. */ + status = _cairo_bentley_ottmann_tessellate_bo_edges (event_ptrs, num_events, + fill_rule, traps, + &intersections); +#if DEBUG_TRAPS + dump_traps (traps, "bo-polygon-out.txt"); +#endif + + if (events != stack_events) + free (events); + + return status; +} + +cairo_status_t +_cairo_bentley_ottmann_tessellate_traps (cairo_traps_t *traps, + cairo_fill_rule_t fill_rule) +{ + cairo_status_t status; + cairo_polygon_t polygon; + int i; + + if (unlikely (0 == traps->num_traps)) + return CAIRO_STATUS_SUCCESS; + +#if DEBUG_TRAPS + dump_traps (traps, "bo-traps-in.txt"); +#endif + + _cairo_polygon_init (&polygon, traps->limits, traps->num_limits); + + for (i = 0; i < traps->num_traps; i++) { + status = _cairo_polygon_add_line (&polygon, + &traps->traps[i].left, + traps->traps[i].top, + traps->traps[i].bottom, + 1); + if (unlikely (status)) + goto CLEANUP; + + status = _cairo_polygon_add_line (&polygon, + &traps->traps[i].right, + traps->traps[i].top, + traps->traps[i].bottom, + -1); + if (unlikely (status)) + goto CLEANUP; + } + + _cairo_traps_clear (traps); + status = _cairo_bentley_ottmann_tessellate_polygon (traps, + &polygon, + fill_rule); + +#if DEBUG_TRAPS + dump_traps (traps, "bo-traps-out.txt"); +#endif + + CLEANUP: + _cairo_polygon_fini (&polygon); + + return status; +} + +#if 0 +static cairo_bool_t +edges_have_an_intersection_quadratic (cairo_bo_edge_t *edges, + int num_edges) + +{ + int i, j; + cairo_bo_edge_t *a, *b; + cairo_bo_point32_t intersection; + + /* We must not be given any upside-down edges. */ + for (i = 0; i < num_edges; i++) { + assert (_cairo_bo_point32_compare (&edges[i].top, &edges[i].bottom) < 0); + edges[i].line.p1.x <<= CAIRO_BO_GUARD_BITS; + edges[i].line.p1.y <<= CAIRO_BO_GUARD_BITS; + edges[i].line.p2.x <<= CAIRO_BO_GUARD_BITS; + edges[i].line.p2.y <<= CAIRO_BO_GUARD_BITS; + } + + for (i = 0; i < num_edges; i++) { + for (j = 0; j < num_edges; j++) { + if (i == j) + continue; + + a = &edges[i]; + b = &edges[j]; + + if (! _cairo_bo_edge_intersect (a, b, &intersection)) + continue; + + printf ("Found intersection (%d,%d) between (%d,%d)-(%d,%d) and (%d,%d)-(%d,%d)\n", + intersection.x, + intersection.y, + a->line.p1.x, a->line.p1.y, + a->line.p2.x, a->line.p2.y, + b->line.p1.x, b->line.p1.y, + b->line.p2.x, b->line.p2.y); + + return TRUE; + } + } + return FALSE; +} + +#define TEST_MAX_EDGES 10 + +typedef struct test { + const char *name; + const char *description; + int num_edges; + cairo_bo_edge_t edges[TEST_MAX_EDGES]; +} test_t; + +static test_t +tests[] = { + { + "3 near misses", + "3 edges all intersecting very close to each other", + 3, + { + { { 4, 2}, {0, 0}, { 9, 9}, NULL, NULL }, + { { 7, 2}, {0, 0}, { 2, 3}, NULL, NULL }, + { { 5, 2}, {0, 0}, { 1, 7}, NULL, NULL } + } + }, + { + "inconsistent data", + "Derived from random testing---was leading to skip list and edge list disagreeing.", + 2, + { + { { 2, 3}, {0, 0}, { 8, 9}, NULL, NULL }, + { { 2, 3}, {0, 0}, { 6, 7}, NULL, NULL } + } + }, + { + "failed sort", + "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?", + 3, + { + { { 6, 2}, {0, 0}, { 6, 5}, NULL, NULL }, + { { 3, 5}, {0, 0}, { 5, 6}, NULL, NULL }, + { { 9, 2}, {0, 0}, { 5, 6}, NULL, NULL }, + } + }, + { + "minimal-intersection", + "Intersection of a two from among the smallest possible edges.", + 2, + { + { { 0, 0}, {0, 0}, { 1, 1}, NULL, NULL }, + { { 1, 0}, {0, 0}, { 0, 1}, NULL, NULL } + } + }, + { + "simple", + "A simple intersection of two edges at an integer (2,2).", + 2, + { + { { 1, 1}, {0, 0}, { 3, 3}, NULL, NULL }, + { { 2, 1}, {0, 0}, { 2, 3}, NULL, NULL } + } + }, + { + "bend-to-horizontal", + "With intersection truncation one edge bends to horizontal", + 2, + { + { { 9, 1}, {0, 0}, {3, 7}, NULL, NULL }, + { { 3, 5}, {0, 0}, {9, 9}, NULL, NULL } + } + } +}; + +/* + { + "endpoint", + "An intersection that occurs at the endpoint of a segment.", + { + { { 4, 6}, { 5, 6}, NULL, { { NULL }} }, + { { 4, 5}, { 5, 7}, NULL, { { NULL }} }, + { { 0, 0}, { 0, 0}, NULL, { { NULL }} }, + } + } + { + name = "overlapping", + desc = "Parallel segments that share an endpoint, with different slopes.", + edges = { + { top = { x = 2, y = 0}, bottom = { x = 1, y = 1}}, + { top = { x = 2, y = 0}, bottom = { x = 0, y = 2}}, + { top = { x = 0, y = 3}, bottom = { x = 1, y = 3}}, + { top = { x = 0, y = 3}, bottom = { x = 2, y = 3}}, + { top = { x = 0, y = 4}, bottom = { x = 0, y = 6}}, + { top = { x = 0, y = 5}, bottom = { x = 0, y = 6}} + } + }, + { + name = "hobby_stage_3", + desc = "A particularly tricky part of the 3rd stage of the 'hobby' test below.", + edges = { + { top = { x = -1, y = -2}, bottom = { x = 4, y = 2}}, + { top = { x = 5, y = 3}, bottom = { x = 9, y = 5}}, + { top = { x = 5, y = 3}, bottom = { x = 6, y = 3}}, + } + }, + { + name = "hobby", + desc = "Example from John Hobby's paper. Requires 3 passes of the iterative algorithm.", + edges = { + { top = { x = 0, y = 0}, bottom = { x = 9, y = 5}}, + { top = { x = 0, y = 0}, bottom = { x = 13, y = 6}}, + { top = { x = -1, y = -2}, bottom = { x = 9, y = 5}} + } + }, + { + name = "slope", + desc = "Edges with same start/stop points but different slopes", + edges = { + { top = { x = 4, y = 1}, bottom = { x = 6, y = 3}}, + { top = { x = 4, y = 1}, bottom = { x = 2, y = 3}}, + { top = { x = 2, y = 4}, bottom = { x = 4, y = 6}}, + { top = { x = 6, y = 4}, bottom = { x = 4, y = 6}} + } + }, + { + name = "horizontal", + desc = "Test of a horizontal edge", + edges = { + { top = { x = 1, y = 1}, bottom = { x = 6, y = 6}}, + { top = { x = 2, y = 3}, bottom = { x = 5, y = 3}} + } + }, + { + name = "vertical", + desc = "Test of a vertical edge", + edges = { + { top = { x = 5, y = 1}, bottom = { x = 5, y = 7}}, + { top = { x = 2, y = 4}, bottom = { x = 8, y = 5}} + } + }, + { + name = "congruent", + desc = "Two overlapping edges with the same slope", + edges = { + { top = { x = 5, y = 1}, bottom = { x = 5, y = 7}}, + { top = { x = 5, y = 2}, bottom = { x = 5, y = 6}}, + { top = { x = 2, y = 4}, bottom = { x = 8, y = 5}} + } + }, + { + name = "multi", + desc = "Several segments with a common intersection point", + edges = { + { top = { x = 1, y = 2}, bottom = { x = 5, y = 4} }, + { top = { x = 1, y = 1}, bottom = { x = 5, y = 5} }, + { top = { x = 2, y = 1}, bottom = { x = 4, y = 5} }, + { top = { x = 4, y = 1}, bottom = { x = 2, y = 5} }, + { top = { x = 5, y = 1}, bottom = { x = 1, y = 5} }, + { top = { x = 5, y = 2}, bottom = { x = 1, y = 4} } + } + } +}; +*/ + +static int +run_test (const char *test_name, + cairo_bo_edge_t *test_edges, + int num_edges) +{ + int i, intersections, passes; + cairo_bo_edge_t *edges; + cairo_array_t intersected_edges; + + printf ("Testing: %s\n", test_name); + + _cairo_array_init (&intersected_edges, sizeof (cairo_bo_edge_t)); + + intersections = _cairo_bentley_ottmann_intersect_edges (test_edges, num_edges, &intersected_edges); + if (intersections) + printf ("Pass 1 found %d intersections:\n", intersections); + + + /* XXX: Multi-pass Bentley-Ottmmann. Preferable would be to add a + * pass of Hobby's tolerance-square algorithm instead. */ + passes = 1; + while (intersections) { + int num_edges = _cairo_array_num_elements (&intersected_edges); + passes++; + edges = _cairo_malloc_ab (num_edges, sizeof (cairo_bo_edge_t)); + assert (edges != NULL); + memcpy (edges, _cairo_array_index (&intersected_edges, 0), num_edges * sizeof (cairo_bo_edge_t)); + _cairo_array_fini (&intersected_edges); + _cairo_array_init (&intersected_edges, sizeof (cairo_bo_edge_t)); + intersections = _cairo_bentley_ottmann_intersect_edges (edges, num_edges, &intersected_edges); + free (edges); + + if (intersections){ + printf ("Pass %d found %d remaining intersections:\n", passes, intersections); + } else { + if (passes > 3) + for (i = 0; i < passes; i++) + printf ("*"); + printf ("No remainining intersections found after pass %d\n", passes); + } + } + + if (edges_have_an_intersection_quadratic (_cairo_array_index (&intersected_edges, 0), + _cairo_array_num_elements (&intersected_edges))) + printf ("*** FAIL ***\n"); + else + printf ("PASS\n"); + + _cairo_array_fini (&intersected_edges); + + return 0; +} + +#define MAX_RANDOM 300 + +int +main (void) +{ + char random_name[] = "random-XX"; + cairo_bo_edge_t random_edges[MAX_RANDOM], *edge; + unsigned int i, num_random; + test_t *test; + + for (i = 0; i < ARRAY_LENGTH (tests); i++) { + test = &tests[i]; + run_test (test->name, test->edges, test->num_edges); + } + + for (num_random = 0; num_random < MAX_RANDOM; num_random++) { + srand (0); + for (i = 0; i < num_random; i++) { + do { + edge = &random_edges[i]; + edge->line.p1.x = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0))); + edge->line.p1.y = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0))); + edge->line.p2.x = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0))); + edge->line.p2.y = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0))); + if (edge->line.p1.y > edge->line.p2.y) { + int32_t tmp = edge->line.p1.y; + edge->line.p1.y = edge->line.p2.y; + edge->line.p2.y = tmp; + } + } while (edge->line.p1.y == edge->line.p2.y); + } + + sprintf (random_name, "random-%02d", num_random); + + run_test (random_name, random_edges, num_random); + } + + return 0; +} +#endif |