add cairo

1 files changed, 1915 insertions, 0 deletions

diff --git a/libs/cairo-1.16.0/src/cairo-bentley-ottmann.c b/libs/cairo-1.16.0/src/cairo-bentley-ottmann.c
new file mode 100644
index 0000000..2011e73
--- /dev/null
+++ b/libs/cairo-1.16.0/src/cairo-bentley-ottmann.c
@@ -0,0 +1,1915 @@
+/*
+ * 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