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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"
#define DEBUG_POLYGON 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_deferred {
cairo_bo_edge_t *right;
int32_t top;
} cairo_bo_deferred_t;
struct _cairo_bo_edge {
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
_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 (_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
_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;
}
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.p2.y == b->edge.line.p2.y) {
return a->edge.line.p2.x == b->edge.line.p2.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
_cairo_bo_edge_end (cairo_bo_edge_t *left,
int32_t bot,
cairo_polygon_t *polygon)
{
cairo_bo_deferred_t *d = &left->deferred;
if (likely (d->top < bot)) {
_cairo_polygon_add_line (polygon,
&left->edge.line,
d->top, bot,
1);
_cairo_polygon_add_line (polygon,
&d->right->edge.line,
d->top, bot,
-1);
}
d->right = NULL;
}
static inline void
_cairo_bo_edge_start_or_continue (cairo_bo_edge_t *left,
cairo_bo_edge_t *right,
int top,
cairo_polygon_t *polygon)
{
if (left->deferred.right == right)
return;
if (left->deferred.right != NULL) {
if (right != NULL && edges_colinear (left->deferred.right, right))
{
/* continuation on right, so just swap edges */
left->deferred.right = right;
return;
}
_cairo_bo_edge_end (left, top, polygon);
}
if (right != NULL && ! edges_colinear (left, right)) {
left->deferred.top = top;
left->deferred.right = right;
}
}
static inline void
_active_edges_to_polygon (cairo_bo_edge_t *left,
int32_t top,
cairo_fill_rule_t fill_rule,
cairo_polygon_t *polygon)
{
cairo_bo_edge_t *right;
unsigned int mask;
if (fill_rule == CAIRO_FILL_RULE_WINDING)
mask = ~0;
else
mask = 1;
while (left != NULL) {
int in_out = left->edge.dir;
right = left->next;
if (left->deferred.right == NULL) {
while (right != NULL && right->deferred.right == NULL)
right = right->next;
if (right != NULL && edges_colinear (left, right)) {
/* continuation on left */
left->deferred = right->deferred;
right->deferred.right = NULL;
}
}
right = left->next;
while (right != NULL) {
if (right->deferred.right != NULL)
_cairo_bo_edge_end (right, top, polygon);
in_out += right->edge.dir;
if ((in_out & mask) == 0) {
/* skip co-linear edges */
if (right->next == NULL || !edges_colinear (right, right->next))
break;
}
right = right->next;
}
_cairo_bo_edge_start_or_continue (left, right, top, polygon);
left = right;
if (left != NULL)
left = left->next;
}
}
static cairo_status_t
_cairo_bentley_ottmann_tessellate_bo_edges (cairo_bo_event_t **start_events,
int num_events,
cairo_fill_rule_t fill_rule,
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_to_polygon (sweep_line.head,
sweep_line.current_y,
fill_rule, 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 = _cairo_bo_sweep_line_insert (&sweep_line, e1);
if (unlikely (status))
goto unwind;
status = _cairo_bo_event_queue_insert_stop (&event_queue, e1);
if (unlikely (status))
goto unwind;
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);
if (e1->deferred.right != NULL)
_cairo_bo_edge_end (e1, e1->edge.bottom, polygon);
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;
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;
}
}
unwind:
_cairo_bo_event_queue_fini (&event_queue);
return status;
}
cairo_status_t
_cairo_polygon_reduce (cairo_polygon_t *polygon,
cairo_fill_rule_t fill_rule)
{
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_limits;
int num_events;
int i;
num_events = polygon->num_edges;
if (unlikely (0 == num_events))
return CAIRO_STATUS_SUCCESS;
if (DEBUG_POLYGON) {
FILE *file = fopen ("reduce_in.txt", "w");
_cairo_debug_print_polygon (file, polygon);
fclose (file);
}
events = stack_events;
event_ptrs = stack_event_ptrs;
if (num_events > ARRAY_LENGTH (stack_events)) {
events = _cairo_malloc_ab_plus_c (num_events,
sizeof (cairo_bo_start_event_t) +
sizeof (cairo_bo_event_t *),
sizeof (cairo_bo_event_t *));
if (unlikely (events == NULL))
return _cairo_error (CAIRO_STATUS_NO_MEMORY);
event_ptrs = (cairo_bo_event_t **) (events + num_events);
}
for (i = 0; i < num_events; i++) {
event_ptrs[i] = (cairo_bo_event_t *) &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.right = NULL;
events[i].edge.prev = NULL;
events[i].edge.next = NULL;
}
num_limits = polygon->num_limits; polygon->num_limits = 0;
polygon->num_edges = 0;
status = _cairo_bentley_ottmann_tessellate_bo_edges (event_ptrs,
num_events,
fill_rule,
polygon);
polygon->num_limits = num_limits;
if (events != stack_events)
free (events);
if (DEBUG_POLYGON) {
FILE *file = fopen ("reduce_out.txt", "w");
_cairo_debug_print_polygon (file, polygon);
fclose (file);
}
return status;
}