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authorhk57.kim <hk57.kim@samsung.com>2015-06-03 15:16:56 +0900
committerhk57.kim <hk57.kim@samsung.com>2015-06-03 15:16:56 +0900
commit4078c98a5d481778482f52d3aaf7a1777ffe6088 (patch)
treec18ae9d21e2b29c349231c5b61d742e9fca9c1d9 /src/cairo-polygon-intersect.c
parentcce6a0e298fac08c588204b085e7a807fa75813d (diff)
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Cairo 1.12.14
Change-Id: Ibc39e63896ec42cab29fbbbf615a46f2d58319a8 Signed-off-by: hk57.kim <hk57.kim@samsung.com>
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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-error-private.h"
+#include "cairo-freelist-private.h"
+#include "cairo-combsort-inline.h"
+
+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_deferred {
+ cairo_bo_edge_t *other;
+ int32_t top;
+} cairo_bo_deferred_t;
+
+struct _cairo_bo_edge {
+ int a_or_b;
+ cairo_edge_t edge;
+ cairo_bo_edge_t *prev;
+ cairo_bo_edge_t *next;
+ cairo_bo_deferred_t deferred;
+};
+
+/* 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;
+ int32_t current_y;
+ cairo_bo_edge_t *current_edge;
+} cairo_bo_sweep_line_t;
+
+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-coordinates of a pair of lines for a particular y,
+ * 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 ∘ B_x + (Y - B_y) * B_dx / B_dy,
+ * where ∘ is our inequality operator.
+ *
+ * By construction, we know that A_dy and B_dy (and (Y - A_y), (Y - B_y)) are
+ * all positive, so we can rearrange it thus without causing a sign change:
+ * A_dy * B_dy * (A_x - B_x) ∘ (Y - B_y) * B_dx * A_dy
+ * - (Y - A_y) * A_dx * B_dy
+ *
+ * Given the assumption that all the deltas fit within 32 bits, we can compute
+ * this comparison directly using 128 bit arithmetic. For certain, but common,
+ * input we can reduce this down to a single 32 bit compare by inspecting the
+ * deltas.
+ *
+ * (And put the burden of the work on developing fast 128 bit ops, which are
+ * required throughout the tessellator.)
+ *
+ * See the similar discussion for _slope_compare().
+ */
+static int
+edges_compare_x_for_y_general (const cairo_bo_edge_t *a,
+ const cairo_bo_edge_t *b,
+ int32_t y)
+{
+ /* 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 dx;
+ int32_t adx, ady;
+ int32_t bdx, bdy;
+ enum {
+ HAVE_NONE = 0x0,
+ HAVE_DX = 0x1,
+ HAVE_ADX = 0x2,
+ HAVE_DX_ADX = HAVE_DX | HAVE_ADX,
+ HAVE_BDX = 0x4,
+ HAVE_DX_BDX = HAVE_DX | HAVE_BDX,
+ HAVE_ADX_BDX = HAVE_ADX | HAVE_BDX,
+ HAVE_ALL = HAVE_DX | HAVE_ADX | HAVE_BDX
+ } have_dx_adx_bdx = HAVE_ALL;
+
+ /* don't bother solving for abscissa if the edges' bounding boxes
+ * can be used to order them. */
+ {
+ int32_t amin, amax;
+ int32_t bmin, bmax;
+ if (a->edge.line.p1.x < a->edge.line.p2.x) {
+ amin = a->edge.line.p1.x;
+ amax = a->edge.line.p2.x;
+ } else {
+ amin = a->edge.line.p2.x;
+ amax = a->edge.line.p1.x;
+ }
+ if (b->edge.line.p1.x < b->edge.line.p2.x) {
+ bmin = b->edge.line.p1.x;
+ bmax = b->edge.line.p2.x;
+ } else {
+ bmin = b->edge.line.p2.x;
+ bmax = b->edge.line.p1.x;
+ }
+ if (amax < bmin) return -1;
+ if (amin > bmax) return +1;
+ }
+
+ ady = a->edge.line.p2.y - a->edge.line.p1.y;
+ adx = a->edge.line.p2.x - a->edge.line.p1.x;
+ if (adx == 0)
+ have_dx_adx_bdx &= ~HAVE_ADX;
+
+ bdy = b->edge.line.p2.y - b->edge.line.p1.y;
+ bdx = b->edge.line.p2.x - b->edge.line.p1.x;
+ if (bdx == 0)
+ have_dx_adx_bdx &= ~HAVE_BDX;
+
+ dx = a->edge.line.p1.x - b->edge.line.p1.x;
+ if (dx == 0)
+ have_dx_adx_bdx &= ~HAVE_DX;
+
+#define L _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (ady, bdy), dx)
+#define A _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (adx, bdy), y - a->edge.line.p1.y)
+#define B _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (bdx, ady), y - b->edge.line.p1.y)
+ switch (have_dx_adx_bdx) {
+ default:
+ case HAVE_NONE:
+ return 0;
+ case HAVE_DX:
+ /* A_dy * B_dy * (A_x - B_x) ∘ 0 */
+ return dx; /* ady * bdy is positive definite */
+ case HAVE_ADX:
+ /* 0 ∘ - (Y - A_y) * A_dx * B_dy */
+ return adx; /* bdy * (y - a->top.y) is positive definite */
+ case HAVE_BDX:
+ /* 0 ∘ (Y - B_y) * B_dx * A_dy */
+ return -bdx; /* ady * (y - b->top.y) is positive definite */
+ case HAVE_ADX_BDX:
+ /* 0 ∘ (Y - B_y) * B_dx * A_dy - (Y - A_y) * A_dx * B_dy */
+ if ((adx ^ bdx) < 0) {
+ return adx;
+ } else if (a->edge.line.p1.y == b->edge.line.p1.y) { /* common origin */
+ cairo_int64_t adx_bdy, bdx_ady;
+
+ /* ∴ A_dx * B_dy ∘ B_dx * A_dy */
+
+ adx_bdy = _cairo_int32x32_64_mul (adx, bdy);
+ bdx_ady = _cairo_int32x32_64_mul (bdx, ady);
+
+ return _cairo_int64_cmp (adx_bdy, bdx_ady);
+ } else
+ return _cairo_int128_cmp (A, B);
+ case HAVE_DX_ADX:
+ /* A_dy * (A_x - B_x) ∘ - (Y - A_y) * A_dx */
+ if ((-adx ^ dx) < 0) {
+ return dx;
+ } else {
+ cairo_int64_t ady_dx, dy_adx;
+
+ ady_dx = _cairo_int32x32_64_mul (ady, dx);
+ dy_adx = _cairo_int32x32_64_mul (a->edge.line.p1.y - y, adx);
+
+ return _cairo_int64_cmp (ady_dx, dy_adx);
+ }
+ case HAVE_DX_BDX:
+ /* B_dy * (A_x - B_x) ∘ (Y - B_y) * B_dx */
+ if ((bdx ^ dx) < 0) {
+ return dx;
+ } else {
+ cairo_int64_t bdy_dx, dy_bdx;
+
+ bdy_dx = _cairo_int32x32_64_mul (bdy, dx);
+ dy_bdx = _cairo_int32x32_64_mul (y - b->edge.line.p1.y, bdx);
+
+ return _cairo_int64_cmp (bdy_dx, dy_bdx);
+ }
+ case HAVE_ALL:
+ /* XXX try comparing (a->edge.line.p2.x - b->edge.line.p2.x) et al */
+ return _cairo_int128_cmp (L, _cairo_int128_sub (B, A));
+ }
+#undef B
+#undef A
+#undef L
+}
+
+/*
+ * 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 int
+edges_compare_x_for_y (const cairo_bo_edge_t *a,
+ const cairo_bo_edge_t *b,
+ int32_t y)
+{
+ /* If the sweep-line is currently on an end-point of a line,
+ * then we know its precise x value (and considering that we often need to
+ * compare events at end-points, this happens frequently enough to warrant
+ * special casing).
+ */
+ enum {
+ HAVE_NEITHER = 0x0,
+ HAVE_AX = 0x1,
+ HAVE_BX = 0x2,
+ HAVE_BOTH = HAVE_AX | HAVE_BX
+ } have_ax_bx = HAVE_BOTH;
+ int32_t ax, bx;
+
+ if (y == a->edge.line.p1.y)
+ ax = a->edge.line.p1.x;
+ else if (y == a->edge.line.p2.y)
+ ax = a->edge.line.p2.x;
+ else
+ have_ax_bx &= ~HAVE_AX;
+
+ if (y == b->edge.line.p1.y)
+ bx = b->edge.line.p1.x;
+ else if (y == b->edge.line.p2.y)
+ bx = b->edge.line.p2.x;
+ else
+ have_ax_bx &= ~HAVE_BX;
+
+ switch (have_ax_bx) {
+ default:
+ case HAVE_NEITHER:
+ return edges_compare_x_for_y_general (a, b, y);
+ case HAVE_AX:
+ return -edge_compare_for_y_against_x (b, y, ax);
+ case HAVE_BX:
+ return edge_compare_for_y_against_x (a, y, bx);
+ case HAVE_BOTH:
+ return ax - bx;
+ }
+}
+
+static inline int
+_line_equal (const cairo_line_t *a, const cairo_line_t *b)
+{
+ return a->p1.x == b->p1.x && a->p1.y == b->p1.y &&
+ a->p2.x == b->p2.x && a->p2.y == b->p2.y;
+}
+
+static int
+_cairo_bo_sweep_line_compare_edges (cairo_bo_sweep_line_t *sweep_line,
+ const cairo_bo_edge_t *a,
+ const cairo_bo_edge_t *b)
+{
+ int cmp;
+
+ /* compare the edges if not identical */
+ if (! _line_equal (&a->edge.line, &b->edge.line)) {
+ cmp = edges_compare_x_for_y (a, b, sweep_line->current_y);
+ if (cmp)
+ return cmp;
+
+ /* The two edges intersect exactly at y, so fall back on slope
+ * comparison. We know that this compare_edges function will be
+ * called only when starting a new edge, (not when stopping an
+ * edge), so we don't have to worry about conditionally inverting
+ * the sense of _slope_compare. */
+ cmp = _slope_compare (a, b);
+ 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)
+{
+ _cairo_bo_event_queue_sort (start_events, num_events);
+ start_events[num_events] = NULL;
+
+ 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
+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
+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 (_line_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->current_y = INT32_MIN;
+ sweep_line->current_edge = NULL;
+}
+
+static cairo_status_t
+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;
+ }
+
+ sweep_line->current_edge = edge;
+
+ return CAIRO_STATUS_SUCCESS;
+}
+
+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;
+}
+
+static inline cairo_bool_t
+edges_colinear (const cairo_bo_edge_t *a, const cairo_bo_edge_t *b)
+{
+ if (_line_equal (&a->edge.line, &b->edge.line))
+ return TRUE;
+
+ if (_slope_compare (a, b))
+ 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 (a->edge.line.p1.y == b->edge.line.p1.y) {
+ return a->edge.line.p1.x == b->edge.line.p1.x;
+ } else if (a->edge.line.p1.y < b->edge.line.p1.y) {
+ return edge_compare_for_y_against_x (b,
+ a->edge.line.p1.y,
+ a->edge.line.p1.x) == 0;
+ } else {
+ return edge_compare_for_y_against_x (a,
+ b->edge.line.p1.y,
+ b->edge.line.p1.x) == 0;
+ }
+}
+
+static void
+edges_end (cairo_bo_edge_t *left,
+ int32_t bot,
+ cairo_polygon_t *polygon)
+{
+ cairo_bo_deferred_t *l = &left->deferred;
+ cairo_bo_edge_t *right = l->other;
+
+ assert(right->deferred.other == NULL);
+ if (likely (l->top < bot)) {
+ _cairo_polygon_add_line (polygon, &left->edge.line, l->top, bot, 1);
+ _cairo_polygon_add_line (polygon, &right->edge.line, l->top, bot, -1);
+ }
+
+ l->other = NULL;
+}
+
+static inline void
+edges_start_or_continue (cairo_bo_edge_t *left,
+ cairo_bo_edge_t *right,
+ int top,
+ cairo_polygon_t *polygon)
+{
+ assert (right->deferred.other == NULL);
+
+ if (left->deferred.other == right)
+ return;
+
+ if (left->deferred.other != NULL) {
+ if (right != NULL && edges_colinear (left->deferred.other, right)) {
+ cairo_bo_edge_t *old = left->deferred.other;
+
+ /* continuation on right, extend right to cover both */
+ assert (old->deferred.other == NULL);
+ assert (old->edge.line.p2.y > old->edge.line.p1.y);
+
+ if (old->edge.line.p1.y < right->edge.line.p1.y)
+ right->edge.line.p1 = old->edge.line.p1;
+ if (old->edge.line.p2.y > right->edge.line.p2.y)
+ right->edge.line.p2 = old->edge.line.p2;
+ left->deferred.other = right;
+ return;
+ }
+
+ edges_end (left, top, polygon);
+ }
+
+ if (right != NULL && ! edges_colinear (left, right)) {
+ left->deferred.top = top;
+ left->deferred.other = right;
+ }
+}
+
+#define is_zero(w) ((w)[0] == 0 || (w)[1] == 0)
+
+static inline void
+active_edges (cairo_bo_edge_t *left,
+ int32_t top,
+ cairo_polygon_t *polygon)
+{
+ cairo_bo_edge_t *right;
+ int winding[2] = {0, 0};
+
+ /* Yes, this is naive. Consider this a placeholder. */
+
+ while (left != NULL) {
+ assert (is_zero (winding));
+
+ do {
+ winding[left->a_or_b] += left->edge.dir;
+ if (! is_zero (winding))
+ break;
+
+ if unlikely ((left->deferred.other))
+ edges_end (left, top, polygon);
+
+ left = left->next;
+ if (! left)
+ return;
+ } while (1);
+
+ right = left->next;
+ do {
+ if unlikely ((right->deferred.other))
+ edges_end (right, top, polygon);
+
+ winding[right->a_or_b] += right->edge.dir;
+ if (is_zero (winding)) {
+ if (right->next == NULL ||
+ ! edges_colinear (right, right->next))
+ break;
+ }
+
+ right = right->next;
+ } while (1);
+
+ edges_start_or_continue (left, right, top, polygon);
+
+ left = right->next;
+ }
+}
+
+static cairo_status_t
+intersection_sweep (cairo_bo_event_t **start_events,
+ int num_events,
+ cairo_polygon_t *polygon)
+{
+ cairo_status_t status = CAIRO_STATUS_SUCCESS; /* silence compiler */
+ 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;
+
+ _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) {
+ active_edges (sweep_line.head,
+ sweep_line.current_y,
+ polygon);
+ sweep_line.current_y = event->point.y;
+ }
+
+ switch (event->type) {
+ case CAIRO_BO_EVENT_TYPE_START:
+ e1 = &((cairo_bo_start_event_t *) event)->edge;
+
+ status = sweep_line_insert (&sweep_line, e1);
+ if (unlikely (status))
+ goto unwind;
+
+ status = event_queue_insert_stop (&event_queue, e1);
+ if (unlikely (status))
+ goto unwind;
+
+ left = e1->prev;
+ right = e1->next;
+
+ if (left != NULL) {
+ status = event_queue_insert_if_intersect_below_current_y (&event_queue, left, e1);
+ if (unlikely (status))
+ goto unwind;
+ }
+
+ if (right != NULL) {
+ status = 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);
+
+ if (e1->deferred.other)
+ edges_end (e1, sweep_line.current_y, polygon);
+
+ left = e1->prev;
+ right = e1->next;
+
+ _cairo_bo_sweep_line_delete (&sweep_line, e1);
+
+ if (left != NULL && right != NULL) {
+ status = 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;
+
+ if (e1->deferred.other)
+ edges_end (e1, sweep_line.current_y, polygon);
+ if (e2->deferred.other)
+ edges_end (e2, sweep_line.current_y, polygon);
+
+ 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 = event_queue_insert_if_intersect_below_current_y (&event_queue, left, e2);
+ if (unlikely (status))
+ goto unwind;
+ }
+
+ if (right != NULL) {
+ status = event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right);
+ if (unlikely (status))
+ goto unwind;
+ }
+
+ break;
+ }
+ }
+
+ unwind:
+ _cairo_bo_event_queue_fini (&event_queue);
+
+ return status;
+}
+
+cairo_status_t
+_cairo_polygon_intersect (cairo_polygon_t *a, int winding_a,
+ cairo_polygon_t *b, int winding_b)
+{
+ cairo_status_t status;
+ 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;
+ int num_events;
+ int i, j;
+
+ /* XXX lazy */
+ if (winding_a != CAIRO_FILL_RULE_WINDING) {
+ status = _cairo_polygon_reduce (a, winding_a);
+ if (unlikely (status))
+ return status;
+ }
+
+ if (winding_b != CAIRO_FILL_RULE_WINDING) {
+ status = _cairo_polygon_reduce (b, winding_b);
+ if (unlikely (status))
+ return status;
+ }
+
+ if (unlikely (0 == a->num_edges))
+ return CAIRO_STATUS_SUCCESS;
+
+ if (unlikely (0 == b->num_edges)) {
+ a->num_edges = 0;
+ return CAIRO_STATUS_SUCCESS;
+ }
+
+ events = stack_events;
+ event_ptrs = stack_event_ptrs;
+ num_events = a->num_edges + b->num_edges;
+ if (num_events > ARRAY_LENGTH (stack_events)) {
+ events = _cairo_malloc_ab_plus_c (num_events,
+ sizeof (cairo_bo_start_event_t) +
+ sizeof (cairo_bo_event_t *),
+ sizeof (cairo_bo_event_t *));
+ if (unlikely (events == NULL))
+ return _cairo_error (CAIRO_STATUS_NO_MEMORY);
+
+ event_ptrs = (cairo_bo_event_t **) (events + num_events);
+ }
+
+ j = 0;
+ for (i = 0; i < a->num_edges; i++) {
+ event_ptrs[j] = (cairo_bo_event_t *) &events[j];
+
+ events[j].type = CAIRO_BO_EVENT_TYPE_START;
+ events[j].point.y = a->edges[i].top;
+ events[j].point.x =
+ _line_compute_intersection_x_for_y (&a->edges[i].line,
+ events[j].point.y);
+
+ events[j].edge.a_or_b = 0;
+ events[j].edge.edge = a->edges[i];
+ events[j].edge.deferred.other = NULL;
+ events[j].edge.prev = NULL;
+ events[j].edge.next = NULL;
+ j++;
+ }
+
+ for (i = 0; i < b->num_edges; i++) {
+ event_ptrs[j] = (cairo_bo_event_t *) &events[j];
+
+ events[j].type = CAIRO_BO_EVENT_TYPE_START;
+ events[j].point.y = b->edges[i].top;
+ events[j].point.x =
+ _line_compute_intersection_x_for_y (&b->edges[i].line,
+ events[j].point.y);
+
+ events[j].edge.a_or_b = 1;
+ events[j].edge.edge = b->edges[i];
+ events[j].edge.deferred.other = NULL;
+ events[j].edge.prev = NULL;
+ events[j].edge.next = NULL;
+ j++;
+ }
+ assert (j == num_events);
+
+#if 0
+ {
+ FILE *file = fopen ("clip_a.txt", "w");
+ _cairo_debug_print_polygon (file, a);
+ fclose (file);
+ }
+ {
+ FILE *file = fopen ("clip_b.txt", "w");
+ _cairo_debug_print_polygon (file, b);
+ fclose (file);
+ }
+#endif
+
+ a->num_edges = 0;
+ status = intersection_sweep (event_ptrs, num_events, a);
+ if (events != stack_events)
+ free (events);
+
+#if 0
+ {
+ FILE *file = fopen ("clip_result.txt", "w");
+ _cairo_debug_print_polygon (file, a);
+ fclose (file);
+ }
+#endif
+
+ return status;
+}
+
+cairo_status_t
+_cairo_polygon_intersect_with_boxes (cairo_polygon_t *polygon,
+ cairo_fill_rule_t *winding,
+ cairo_box_t *boxes,
+ int num_boxes)
+{
+ cairo_polygon_t b;
+ cairo_status_t status;
+ int n;
+
+ if (num_boxes == 0) {
+ polygon->num_edges = 0;
+ return CAIRO_STATUS_SUCCESS;
+ }
+
+ for (n = 0; n < num_boxes; n++) {
+ if (polygon->extents.p1.x >= boxes[n].p1.x &&
+ polygon->extents.p2.x <= boxes[n].p2.x &&
+ polygon->extents.p1.y >= boxes[n].p1.y &&
+ polygon->extents.p2.y <= boxes[n].p2.y)
+ {
+ return CAIRO_STATUS_SUCCESS;
+ }
+ }
+
+ _cairo_polygon_init (&b, NULL, 0);
+ for (n = 0; n < num_boxes; n++) {
+ if (boxes[n].p2.x > polygon->extents.p1.x &&
+ boxes[n].p1.x < polygon->extents.p2.x &&
+ boxes[n].p2.y > polygon->extents.p1.y &&
+ boxes[n].p1.y < polygon->extents.p2.y)
+ {
+ cairo_point_t p1, p2;
+
+ p1.y = boxes[n].p1.y;
+ p2.y = boxes[n].p2.y;
+
+ p2.x = p1.x = boxes[n].p1.x;
+ _cairo_polygon_add_external_edge (&b, &p1, &p2);
+
+ p2.x = p1.x = boxes[n].p2.x;
+ _cairo_polygon_add_external_edge (&b, &p2, &p1);
+ }
+ }
+
+ status = _cairo_polygon_intersect (polygon, *winding,
+ &b, CAIRO_FILL_RULE_WINDING);
+ _cairo_polygon_fini (&b);
+
+ *winding = CAIRO_FILL_RULE_WINDING;
+ return status;
+}