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+/*
+ * 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);
+ if (unlikely (event_y == NULL))
+ return _cairo_error (CAIRO_STATUS_NO_MEMORY);
+ } 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)) {
+ if (event_y != stack_event_y)
+ free (event_y);
+ 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