0,0 → 1,2127 |
/* |
* 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" |
#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-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 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; |
|
/* compare the edges if not identical */ |
if (! _line_equal (&a->edge.line, &b->edge.line)) { |
if (MAX (a->edge.line.p1.x, a->edge.line.p2.x) < |
MIN (b->edge.line.p1.x, b->edge.line.p2.x)) |
return -1; |
else if (MIN (a->edge.line.p1.x, a->edge.line.p2.x) > |
MAX (b->edge.line.p1.x, b->edge.line.p2.x)) |
return 1; |
|
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) |
{ |
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 (_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->stopped = NULL; |
sweep_line->current_y = INT32_MIN; |
sweep_line->current_edge = NULL; |
} |
|
static void |
_cairo_bo_sweep_line_insert (cairo_bo_sweep_line_t *sweep_line, |
cairo_bo_edge_t *edge) |
{ |
if (sweep_line->current_edge != NULL) { |
cairo_bo_edge_t *prev, *next; |
int cmp; |
|
cmp = _cairo_bo_sweep_line_compare_edges (sweep_line, |
sweep_line->current_edge, |
edge); |
if (cmp < 0) { |
prev = sweep_line->current_edge; |
next = prev->next; |
while (next != NULL && |
_cairo_bo_sweep_line_compare_edges (sweep_line, |
next, edge) < 0) |
{ |
prev = next, next = prev->next; |
} |
|
prev->next = edge; |
edge->prev = prev; |
edge->next = next; |
if (next != NULL) |
next->prev = edge; |
} else if (cmp > 0) { |
next = sweep_line->current_edge; |
prev = next->prev; |
while (prev != NULL && |
_cairo_bo_sweep_line_compare_edges (sweep_line, |
prev, edge) > 0) |
{ |
next = prev, prev = next->prev; |
} |
|
next->prev = edge; |
edge->next = next; |
edge->prev = prev; |
if (prev != NULL) |
prev->next = edge; |
else |
sweep_line->head = edge; |
} else { |
prev = sweep_line->current_edge; |
edge->prev = prev; |
edge->next = prev->next; |
if (prev->next != NULL) |
prev->next->prev = edge; |
prev->next = edge; |
} |
} else { |
sweep_line->head = edge; |
edge->next = NULL; |
} |
|
sweep_line->current_edge = edge; |
} |
|
static void |
_cairo_bo_sweep_line_delete (cairo_bo_sweep_line_t *sweep_line, |
cairo_bo_edge_t *edge) |
{ |
if (edge->prev != NULL) |
edge->prev->next = edge->next; |
else |
sweep_line->head = edge->next; |
|
if (edge->next != NULL) |
edge->next->prev = edge->prev; |
|
if (sweep_line->current_edge == edge) |
sweep_line->current_edge = edge->prev ? edge->prev : edge->next; |
} |
|
static void |
_cairo_bo_sweep_line_swap (cairo_bo_sweep_line_t *sweep_line, |
cairo_bo_edge_t *left, |
cairo_bo_edge_t *right) |
{ |
if (left->prev != NULL) |
left->prev->next = right; |
else |
sweep_line->head = right; |
|
if (right->next != NULL) |
right->next->prev = left; |
|
left->next = right->next; |
right->next = left; |
|
right->prev = left->prev; |
left->prev = right; |
} |
|
#if DEBUG_PRINT_STATE |
static void |
_cairo_bo_edge_print (cairo_bo_edge_t *edge) |
{ |
printf ("(0x%x, 0x%x)-(0x%x, 0x%x)", |
edge->edge.line.p1.x, edge->edge.line.p1.y, |
edge->edge.line.p2.x, edge->edge.line.p2.y); |
} |
|
static void |
_cairo_bo_event_print (cairo_bo_event_t *event) |
{ |
switch (event->type) { |
case CAIRO_BO_EVENT_TYPE_START: |
printf ("Start: "); |
break; |
case CAIRO_BO_EVENT_TYPE_STOP: |
printf ("Stop: "); |
break; |
case CAIRO_BO_EVENT_TYPE_INTERSECTION: |
printf ("Intersection: "); |
break; |
} |
printf ("(%d, %d)\t", event->point.x, event->point.y); |
_cairo_bo_edge_print (event->e1); |
if (event->type == CAIRO_BO_EVENT_TYPE_INTERSECTION) { |
printf (" X "); |
_cairo_bo_edge_print (event->e2); |
} |
printf ("\n"); |
} |
|
static void |
_cairo_bo_event_queue_print (cairo_bo_event_queue_t *event_queue) |
{ |
/* XXX: fixme to print the start/stop array too. */ |
printf ("Event queue:\n"); |
} |
|
static void |
_cairo_bo_sweep_line_print (cairo_bo_sweep_line_t *sweep_line) |
{ |
cairo_bool_t first = TRUE; |
cairo_bo_edge_t *edge; |
|
printf ("Sweep line from edge list: "); |
first = TRUE; |
for (edge = sweep_line->head; |
edge; |
edge = edge->next) |
{ |
if (!first) |
printf (", "); |
_cairo_bo_edge_print (edge); |
first = FALSE; |
} |
printf ("\n"); |
} |
|
static void |
print_state (const char *msg, |
cairo_bo_event_t *event, |
cairo_bo_event_queue_t *event_queue, |
cairo_bo_sweep_line_t *sweep_line) |
{ |
printf ("%s ", msg); |
_cairo_bo_event_print (event); |
_cairo_bo_event_queue_print (event_queue); |
_cairo_bo_sweep_line_print (sweep_line); |
printf ("\n"); |
} |
#endif |
|
#if DEBUG_EVENTS |
static void CAIRO_PRINTF_FORMAT (1, 2) |
event_log (const char *fmt, ...) |
{ |
FILE *file; |
|
if (getenv ("CAIRO_DEBUG_EVENTS") == NULL) |
return; |
|
file = fopen ("bo-events.txt", "a"); |
if (file != NULL) { |
va_list ap; |
|
va_start (ap, fmt); |
vfprintf (file, fmt, ap); |
va_end (ap); |
|
fclose (file); |
} |
} |
#endif |
|
#define HAS_COLINEAR(a, b) ((cairo_bo_edge_t *)(((uintptr_t)(a))&~1) == (b)) |
#define IS_COLINEAR(e) (((uintptr_t)(e))&1) |
#define MARK_COLINEAR(e, v) ((cairo_bo_edge_t *)(((uintptr_t)(e))|(v))) |
|
static inline cairo_bool_t |
edges_colinear (cairo_bo_edge_t *a, const cairo_bo_edge_t *b) |
{ |
unsigned p; |
|
if (HAS_COLINEAR(a->colinear, b)) |
return IS_COLINEAR(a->colinear); |
|
if (HAS_COLINEAR(b->colinear, a)) { |
p = IS_COLINEAR(b->colinear); |
a->colinear = MARK_COLINEAR(b, p); |
return p; |
} |
|
p = 0; |
p |= (a->edge.line.p1.x == b->edge.line.p1.x) << 0; |
p |= (a->edge.line.p1.y == b->edge.line.p1.y) << 1; |
p |= (a->edge.line.p2.x == b->edge.line.p2.x) << 3; |
p |= (a->edge.line.p2.y == b->edge.line.p2.y) << 4; |
if (p == ((1 << 0) | (1 << 1) | (1 << 3) | (1 << 4))) { |
a->colinear = MARK_COLINEAR(b, 1); |
return TRUE; |
} |
|
if (_slope_compare (a, b)) { |
a->colinear = MARK_COLINEAR(b, 0); |
return FALSE; |
} |
|
/* The choice of y is not truly arbitrary since we must guarantee that it |
* is greater than the start of either line. |
*/ |
if (p != 0) { |
/* colinear if either end-point are coincident */ |
p = (((p >> 1) & p) & 5) != 0; |
} else if (a->edge.line.p1.y < b->edge.line.p1.y) { |
p = edge_compare_for_y_against_x (b, |
a->edge.line.p1.y, |
a->edge.line.p1.x) == 0; |
} else { |
p = edge_compare_for_y_against_x (a, |
b->edge.line.p1.y, |
b->edge.line.p1.x) == 0; |
} |
|
a->colinear = MARK_COLINEAR(b, p); |
return p; |
} |
|
/* Adds the trapezoid, if any, of the left edge to the #cairo_traps_t */ |
static void |
_cairo_bo_edge_end_trap (cairo_bo_edge_t *left, |
int32_t bot, |
cairo_traps_t *traps) |
{ |
cairo_bo_trap_t *trap = &left->deferred_trap; |
|
/* Only emit (trivial) non-degenerate trapezoids with positive height. */ |
if (likely (trap->top < bot)) { |
_cairo_traps_add_trap (traps, |
trap->top, bot, |
&left->edge.line, &trap->right->edge.line); |
|
#if DEBUG_PRINT_STATE |
printf ("Deferred trap: left=(%x, %x)-(%x,%x) " |
"right=(%x,%x)-(%x,%x) top=%x, bot=%x\n", |
left->edge.line.p1.x, left->edge.line.p1.y, |
left->edge.line.p2.x, left->edge.line.p2.y, |
trap->right->edge.line.p1.x, trap->right->edge.line.p1.y, |
trap->right->edge.line.p2.x, trap->right->edge.line.p2.y, |
trap->top, bot); |
#endif |
#if DEBUG_EVENTS |
event_log ("end trap: %lu %lu %d %d\n", |
(long) left, |
(long) trap->right, |
trap->top, |
bot); |
#endif |
} |
|
trap->right = NULL; |
} |
|
|
/* Start a new trapezoid at the given top y coordinate, whose edges |
* are `edge' and `edge->next'. If `edge' already has a trapezoid, |
* then either add it to the traps in `traps', if the trapezoid's |
* right edge differs from `edge->next', or do nothing if the new |
* trapezoid would be a continuation of the existing one. */ |
static inline void |
_cairo_bo_edge_start_or_continue_trap (cairo_bo_edge_t *left, |
cairo_bo_edge_t *right, |
int top, |
cairo_traps_t *traps) |
{ |
if (left->deferred_trap.right == right) |
return; |
|
assert (right); |
if (left->deferred_trap.right != NULL) { |
if (edges_colinear (left->deferred_trap.right, right)) |
{ |
/* continuation on right, so just swap edges */ |
left->deferred_trap.right = right; |
return; |
} |
|
_cairo_bo_edge_end_trap (left, top, traps); |
} |
|
if (! edges_colinear (left, right)) { |
left->deferred_trap.top = top; |
left->deferred_trap.right = right; |
|
#if DEBUG_EVENTS |
event_log ("begin trap: %lu %lu %d\n", |
(long) left, |
(long) right, |
top); |
#endif |
} |
} |
|
static inline void |
_active_edges_to_traps (cairo_bo_edge_t *pos, |
int32_t top, |
unsigned mask, |
cairo_traps_t *traps) |
{ |
cairo_bo_edge_t *left; |
int in_out; |
|
|
#if DEBUG_PRINT_STATE |
printf ("Processing active edges for %x\n", top); |
#endif |
|
in_out = 0; |
left = pos; |
while (pos != NULL) { |
if (pos != left && pos->deferred_trap.right) { |
/* XXX It shouldn't be possible to here with 2 deferred traps |
* on colinear edges... See bug-bo-rictoz. |
*/ |
if (left->deferred_trap.right == NULL && |
edges_colinear (left, pos)) |
{ |
/* continuation on left */ |
left->deferred_trap = pos->deferred_trap; |
pos->deferred_trap.right = NULL; |
} |
else |
{ |
_cairo_bo_edge_end_trap (pos, top, traps); |
} |
} |
|
in_out += pos->edge.dir; |
if ((in_out & mask) == 0) { |
/* skip co-linear edges */ |
if (pos->next == NULL || ! edges_colinear (pos, pos->next)) { |
_cairo_bo_edge_start_or_continue_trap (left, pos, top, traps); |
left = pos->next; |
} |
} |
|
pos = pos->next; |
} |
} |
|
/* Execute a single pass of the Bentley-Ottmann algorithm on edges, |
* generating trapezoids according to the fill_rule and appending them |
* to traps. */ |
static cairo_status_t |
_cairo_bentley_ottmann_tessellate_bo_edges (cairo_bo_event_t **start_events, |
int num_events, |
unsigned fill_rule, |
cairo_traps_t *traps, |
int *num_intersections) |
{ |
cairo_status_t status; |
int intersection_count = 0; |
cairo_bo_event_queue_t event_queue; |
cairo_bo_sweep_line_t sweep_line; |
cairo_bo_event_t *event; |
cairo_bo_edge_t *left, *right; |
cairo_bo_edge_t *e1, *e2; |
|
/* convert the fill_rule into a winding mask */ |
if (fill_rule == CAIRO_FILL_RULE_WINDING) |
fill_rule = (unsigned) -1; |
else |
fill_rule = 1; |
|
#if DEBUG_EVENTS |
{ |
int i; |
|
for (i = 0; i < num_events; i++) { |
cairo_bo_start_event_t *event = |
((cairo_bo_start_event_t **) start_events)[i]; |
event_log ("edge: %lu (%d, %d) (%d, %d) (%d, %d) %d\n", |
(long) &events[i].edge, |
event->edge.edge.line.p1.x, |
event->edge.edge.line.p1.y, |
event->edge.edge.line.p2.x, |
event->edge.edge.line.p2.y, |
event->edge.top, |
event->edge.bottom, |
event->edge.edge.dir); |
} |
} |
#endif |
|
_cairo_bo_event_queue_init (&event_queue, start_events, num_events); |
_cairo_bo_sweep_line_init (&sweep_line); |
|
while ((event = _cairo_bo_event_dequeue (&event_queue))) { |
if (event->point.y != sweep_line.current_y) { |
for (e1 = sweep_line.stopped; e1; e1 = e1->next) { |
if (e1->deferred_trap.right != NULL) { |
_cairo_bo_edge_end_trap (e1, |
e1->edge.bottom, |
traps); |
} |
} |
sweep_line.stopped = NULL; |
|
_active_edges_to_traps (sweep_line.head, |
sweep_line.current_y, |
fill_rule, traps); |
|
sweep_line.current_y = event->point.y; |
} |
|
#if DEBUG_EVENTS |
event_log ("event: %d (%ld, %ld) %lu, %lu\n", |
event->type, |
(long) event->point.x, |
(long) event->point.y, |
(long) event->e1, |
(long) event->e2); |
#endif |
|
switch (event->type) { |
case CAIRO_BO_EVENT_TYPE_START: |
e1 = &((cairo_bo_start_event_t *) event)->edge; |
|
_cairo_bo_sweep_line_insert (&sweep_line, e1); |
|
status = _cairo_bo_event_queue_insert_stop (&event_queue, e1); |
if (unlikely (status)) |
goto unwind; |
|
/* check to see if this is a continuation of a stopped edge */ |
/* XXX change to an infinitesimal lengthening rule */ |
for (left = sweep_line.stopped; left; left = left->next) { |
if (e1->edge.top <= left->edge.bottom && |
edges_colinear (e1, left)) |
{ |
e1->deferred_trap = left->deferred_trap; |
if (left->prev != NULL) |
left->prev = left->next; |
else |
sweep_line.stopped = left->next; |
if (left->next != NULL) |
left->next->prev = left->prev; |
break; |
} |
} |
|
left = e1->prev; |
right = e1->next; |
|
if (left != NULL) { |
status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, e1); |
if (unlikely (status)) |
goto unwind; |
} |
|
if (right != NULL) { |
status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right); |
if (unlikely (status)) |
goto unwind; |
} |
|
break; |
|
case CAIRO_BO_EVENT_TYPE_STOP: |
e1 = ((cairo_bo_queue_event_t *) event)->e1; |
_cairo_bo_event_queue_delete (&event_queue, event); |
|
left = e1->prev; |
right = e1->next; |
|
_cairo_bo_sweep_line_delete (&sweep_line, e1); |
|
/* first, check to see if we have a continuation via a fresh edge */ |
if (e1->deferred_trap.right != NULL) { |
e1->next = sweep_line.stopped; |
if (sweep_line.stopped != NULL) |
sweep_line.stopped->prev = e1; |
sweep_line.stopped = e1; |
e1->prev = NULL; |
} |
|
if (left != NULL && right != NULL) { |
status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, right); |
if (unlikely (status)) |
goto unwind; |
} |
|
break; |
|
case CAIRO_BO_EVENT_TYPE_INTERSECTION: |
e1 = ((cairo_bo_queue_event_t *) event)->e1; |
e2 = ((cairo_bo_queue_event_t *) event)->e2; |
_cairo_bo_event_queue_delete (&event_queue, event); |
|
/* skip this intersection if its edges are not adjacent */ |
if (e2 != e1->next) |
break; |
|
intersection_count++; |
|
left = e1->prev; |
right = e2->next; |
|
_cairo_bo_sweep_line_swap (&sweep_line, e1, e2); |
|
/* after the swap e2 is left of e1 */ |
|
if (left != NULL) { |
status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, e2); |
if (unlikely (status)) |
goto unwind; |
} |
|
if (right != NULL) { |
status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right); |
if (unlikely (status)) |
goto unwind; |
} |
|
break; |
} |
} |
|
*num_intersections = intersection_count; |
for (e1 = sweep_line.stopped; e1; e1 = e1->next) { |
if (e1->deferred_trap.right != NULL) { |
_cairo_bo_edge_end_trap (e1, e1->edge.bottom, traps); |
} |
} |
status = traps->status; |
unwind: |
_cairo_bo_event_queue_fini (&event_queue); |
|
#if DEBUG_EVENTS |
event_log ("\n"); |
#endif |
|
return status; |
} |
|
cairo_status_t |
_cairo_bentley_ottmann_tessellate_polygon (cairo_traps_t *traps, |
const cairo_polygon_t *polygon, |
cairo_fill_rule_t fill_rule) |
{ |
int intersections; |
cairo_bo_start_event_t stack_events[CAIRO_STACK_ARRAY_LENGTH (cairo_bo_start_event_t)]; |
cairo_bo_start_event_t *events; |
cairo_bo_event_t *stack_event_ptrs[ARRAY_LENGTH (stack_events) + 1]; |
cairo_bo_event_t **event_ptrs; |
cairo_bo_start_event_t *stack_event_y[64]; |
cairo_bo_start_event_t **event_y = NULL; |
int i, num_events, y, ymin, ymax; |
cairo_status_t status; |
|
num_events = polygon->num_edges; |
if (unlikely (0 == num_events)) |
return CAIRO_STATUS_SUCCESS; |
|
if (polygon->num_limits) { |
ymin = _cairo_fixed_integer_floor (polygon->limit.p1.y); |
ymax = _cairo_fixed_integer_ceil (polygon->limit.p2.y) - ymin; |
|
if (ymax > 64) |
event_y = _cairo_malloc_ab(sizeof (cairo_bo_event_t*), ymax); |
else |
event_y = stack_event_y; |
memset (event_y, 0, ymax * sizeof(cairo_bo_event_t *)); |
} |
|
events = stack_events; |
event_ptrs = stack_event_ptrs; |
if (num_events > ARRAY_LENGTH (stack_events)) { |
events = _cairo_malloc_ab_plus_c (num_events, |
sizeof (cairo_bo_start_event_t) + |
sizeof (cairo_bo_event_t *), |
sizeof (cairo_bo_event_t *)); |
if (unlikely (events == NULL)) |
return _cairo_error (CAIRO_STATUS_NO_MEMORY); |
|
event_ptrs = (cairo_bo_event_t **) (events + num_events); |
} |
|
for (i = 0; i < num_events; i++) { |
events[i].type = CAIRO_BO_EVENT_TYPE_START; |
events[i].point.y = polygon->edges[i].top; |
events[i].point.x = |
_line_compute_intersection_x_for_y (&polygon->edges[i].line, |
events[i].point.y); |
|
events[i].edge.edge = polygon->edges[i]; |
events[i].edge.deferred_trap.right = NULL; |
events[i].edge.prev = NULL; |
events[i].edge.next = NULL; |
events[i].edge.colinear = NULL; |
|
if (event_y) { |
y = _cairo_fixed_integer_floor (events[i].point.y) - ymin; |
events[i].edge.next = (cairo_bo_edge_t *) event_y[y]; |
event_y[y] = (cairo_bo_start_event_t *) &events[i]; |
} else |
event_ptrs[i] = (cairo_bo_event_t *) &events[i]; |
} |
|
if (event_y) { |
for (y = i = 0; y < ymax && i < num_events; y++) { |
cairo_bo_start_event_t *e; |
int j = i; |
for (e = event_y[y]; e; e = (cairo_bo_start_event_t *)e->edge.next) |
event_ptrs[i++] = (cairo_bo_event_t *) e; |
if (i > j + 1) |
_cairo_bo_event_queue_sort (event_ptrs+j, i-j); |
} |
if (event_y != stack_event_y) |
free (event_y); |
} else |
_cairo_bo_event_queue_sort (event_ptrs, i); |
event_ptrs[i] = NULL; |
|
#if DEBUG_TRAPS |
dump_edges (events, num_events, "bo-polygon-edges.txt"); |
#endif |
|
/* XXX: This would be the convenient place to throw in multiple |
* passes of the Bentley-Ottmann algorithm. It would merely |
* require storing the results of each pass into a temporary |
* cairo_traps_t. */ |
status = _cairo_bentley_ottmann_tessellate_bo_edges (event_ptrs, num_events, |
fill_rule, traps, |
&intersections); |
#if DEBUG_TRAPS |
dump_traps (traps, "bo-polygon-out.txt"); |
#endif |
|
if (events != stack_events) |
free (events); |
|
return status; |
} |
|
cairo_status_t |
_cairo_bentley_ottmann_tessellate_traps (cairo_traps_t *traps, |
cairo_fill_rule_t fill_rule) |
{ |
cairo_status_t status; |
cairo_polygon_t polygon; |
int i; |
|
if (unlikely (0 == traps->num_traps)) |
return CAIRO_STATUS_SUCCESS; |
|
#if DEBUG_TRAPS |
dump_traps (traps, "bo-traps-in.txt"); |
#endif |
|
_cairo_polygon_init (&polygon, traps->limits, traps->num_limits); |
|
for (i = 0; i < traps->num_traps; i++) { |
status = _cairo_polygon_add_line (&polygon, |
&traps->traps[i].left, |
traps->traps[i].top, |
traps->traps[i].bottom, |
1); |
if (unlikely (status)) |
goto CLEANUP; |
|
status = _cairo_polygon_add_line (&polygon, |
&traps->traps[i].right, |
traps->traps[i].top, |
traps->traps[i].bottom, |
-1); |
if (unlikely (status)) |
goto CLEANUP; |
} |
|
_cairo_traps_clear (traps); |
status = _cairo_bentley_ottmann_tessellate_polygon (traps, |
&polygon, |
fill_rule); |
|
#if DEBUG_TRAPS |
dump_traps (traps, "bo-traps-out.txt"); |
#endif |
|
CLEANUP: |
_cairo_polygon_fini (&polygon); |
|
return status; |
} |
|
#if 0 |
static cairo_bool_t |
edges_have_an_intersection_quadratic (cairo_bo_edge_t *edges, |
int num_edges) |
|
{ |
int i, j; |
cairo_bo_edge_t *a, *b; |
cairo_bo_point32_t intersection; |
|
/* We must not be given any upside-down edges. */ |
for (i = 0; i < num_edges; i++) { |
assert (_cairo_bo_point32_compare (&edges[i].top, &edges[i].bottom) < 0); |
edges[i].line.p1.x <<= CAIRO_BO_GUARD_BITS; |
edges[i].line.p1.y <<= CAIRO_BO_GUARD_BITS; |
edges[i].line.p2.x <<= CAIRO_BO_GUARD_BITS; |
edges[i].line.p2.y <<= CAIRO_BO_GUARD_BITS; |
} |
|
for (i = 0; i < num_edges; i++) { |
for (j = 0; j < num_edges; j++) { |
if (i == j) |
continue; |
|
a = &edges[i]; |
b = &edges[j]; |
|
if (! _cairo_bo_edge_intersect (a, b, &intersection)) |
continue; |
|
printf ("Found intersection (%d,%d) between (%d,%d)-(%d,%d) and (%d,%d)-(%d,%d)\n", |
intersection.x, |
intersection.y, |
a->line.p1.x, a->line.p1.y, |
a->line.p2.x, a->line.p2.y, |
b->line.p1.x, b->line.p1.y, |
b->line.p2.x, b->line.p2.y); |
|
return TRUE; |
} |
} |
return FALSE; |
} |
|
#define TEST_MAX_EDGES 10 |
|
typedef struct test { |
const char *name; |
const char *description; |
int num_edges; |
cairo_bo_edge_t edges[TEST_MAX_EDGES]; |
} test_t; |
|
static test_t |
tests[] = { |
{ |
"3 near misses", |
"3 edges all intersecting very close to each other", |
3, |
{ |
{ { 4, 2}, {0, 0}, { 9, 9}, NULL, NULL }, |
{ { 7, 2}, {0, 0}, { 2, 3}, NULL, NULL }, |
{ { 5, 2}, {0, 0}, { 1, 7}, NULL, NULL } |
} |
}, |
{ |
"inconsistent data", |
"Derived from random testing---was leading to skip list and edge list disagreeing.", |
2, |
{ |
{ { 2, 3}, {0, 0}, { 8, 9}, NULL, NULL }, |
{ { 2, 3}, {0, 0}, { 6, 7}, NULL, NULL } |
} |
}, |
{ |
"failed sort", |
"A test derived from random testing that leads to an inconsistent sort --- looks like we just can't attempt to validate the sweep line with edge_compare?", |
3, |
{ |
{ { 6, 2}, {0, 0}, { 6, 5}, NULL, NULL }, |
{ { 3, 5}, {0, 0}, { 5, 6}, NULL, NULL }, |
{ { 9, 2}, {0, 0}, { 5, 6}, NULL, NULL }, |
} |
}, |
{ |
"minimal-intersection", |
"Intersection of a two from among the smallest possible edges.", |
2, |
{ |
{ { 0, 0}, {0, 0}, { 1, 1}, NULL, NULL }, |
{ { 1, 0}, {0, 0}, { 0, 1}, NULL, NULL } |
} |
}, |
{ |
"simple", |
"A simple intersection of two edges at an integer (2,2).", |
2, |
{ |
{ { 1, 1}, {0, 0}, { 3, 3}, NULL, NULL }, |
{ { 2, 1}, {0, 0}, { 2, 3}, NULL, NULL } |
} |
}, |
{ |
"bend-to-horizontal", |
"With intersection truncation one edge bends to horizontal", |
2, |
{ |
{ { 9, 1}, {0, 0}, {3, 7}, NULL, NULL }, |
{ { 3, 5}, {0, 0}, {9, 9}, NULL, NULL } |
} |
} |
}; |
|
/* |
{ |
"endpoint", |
"An intersection that occurs at the endpoint of a segment.", |
{ |
{ { 4, 6}, { 5, 6}, NULL, { { NULL }} }, |
{ { 4, 5}, { 5, 7}, NULL, { { NULL }} }, |
{ { 0, 0}, { 0, 0}, NULL, { { NULL }} }, |
} |
} |
{ |
name = "overlapping", |
desc = "Parallel segments that share an endpoint, with different slopes.", |
edges = { |
{ top = { x = 2, y = 0}, bottom = { x = 1, y = 1}}, |
{ top = { x = 2, y = 0}, bottom = { x = 0, y = 2}}, |
{ top = { x = 0, y = 3}, bottom = { x = 1, y = 3}}, |
{ top = { x = 0, y = 3}, bottom = { x = 2, y = 3}}, |
{ top = { x = 0, y = 4}, bottom = { x = 0, y = 6}}, |
{ top = { x = 0, y = 5}, bottom = { x = 0, y = 6}} |
} |
}, |
{ |
name = "hobby_stage_3", |
desc = "A particularly tricky part of the 3rd stage of the 'hobby' test below.", |
edges = { |
{ top = { x = -1, y = -2}, bottom = { x = 4, y = 2}}, |
{ top = { x = 5, y = 3}, bottom = { x = 9, y = 5}}, |
{ top = { x = 5, y = 3}, bottom = { x = 6, y = 3}}, |
} |
}, |
{ |
name = "hobby", |
desc = "Example from John Hobby's paper. Requires 3 passes of the iterative algorithm.", |
edges = { |
{ top = { x = 0, y = 0}, bottom = { x = 9, y = 5}}, |
{ top = { x = 0, y = 0}, bottom = { x = 13, y = 6}}, |
{ top = { x = -1, y = -2}, bottom = { x = 9, y = 5}} |
} |
}, |
{ |
name = "slope", |
desc = "Edges with same start/stop points but different slopes", |
edges = { |
{ top = { x = 4, y = 1}, bottom = { x = 6, y = 3}}, |
{ top = { x = 4, y = 1}, bottom = { x = 2, y = 3}}, |
{ top = { x = 2, y = 4}, bottom = { x = 4, y = 6}}, |
{ top = { x = 6, y = 4}, bottom = { x = 4, y = 6}} |
} |
}, |
{ |
name = "horizontal", |
desc = "Test of a horizontal edge", |
edges = { |
{ top = { x = 1, y = 1}, bottom = { x = 6, y = 6}}, |
{ top = { x = 2, y = 3}, bottom = { x = 5, y = 3}} |
} |
}, |
{ |
name = "vertical", |
desc = "Test of a vertical edge", |
edges = { |
{ top = { x = 5, y = 1}, bottom = { x = 5, y = 7}}, |
{ top = { x = 2, y = 4}, bottom = { x = 8, y = 5}} |
} |
}, |
{ |
name = "congruent", |
desc = "Two overlapping edges with the same slope", |
edges = { |
{ top = { x = 5, y = 1}, bottom = { x = 5, y = 7}}, |
{ top = { x = 5, y = 2}, bottom = { x = 5, y = 6}}, |
{ top = { x = 2, y = 4}, bottom = { x = 8, y = 5}} |
} |
}, |
{ |
name = "multi", |
desc = "Several segments with a common intersection point", |
edges = { |
{ top = { x = 1, y = 2}, bottom = { x = 5, y = 4} }, |
{ top = { x = 1, y = 1}, bottom = { x = 5, y = 5} }, |
{ top = { x = 2, y = 1}, bottom = { x = 4, y = 5} }, |
{ top = { x = 4, y = 1}, bottom = { x = 2, y = 5} }, |
{ top = { x = 5, y = 1}, bottom = { x = 1, y = 5} }, |
{ top = { x = 5, y = 2}, bottom = { x = 1, y = 4} } |
} |
} |
}; |
*/ |
|
static int |
run_test (const char *test_name, |
cairo_bo_edge_t *test_edges, |
int num_edges) |
{ |
int i, intersections, passes; |
cairo_bo_edge_t *edges; |
cairo_array_t intersected_edges; |
|
printf ("Testing: %s\n", test_name); |
|
_cairo_array_init (&intersected_edges, sizeof (cairo_bo_edge_t)); |
|
intersections = _cairo_bentley_ottmann_intersect_edges (test_edges, num_edges, &intersected_edges); |
if (intersections) |
printf ("Pass 1 found %d intersections:\n", intersections); |
|
|
/* XXX: Multi-pass Bentley-Ottmmann. Preferable would be to add a |
* pass of Hobby's tolerance-square algorithm instead. */ |
passes = 1; |
while (intersections) { |
int num_edges = _cairo_array_num_elements (&intersected_edges); |
passes++; |
edges = _cairo_malloc_ab (num_edges, sizeof (cairo_bo_edge_t)); |
assert (edges != NULL); |
memcpy (edges, _cairo_array_index (&intersected_edges, 0), num_edges * sizeof (cairo_bo_edge_t)); |
_cairo_array_fini (&intersected_edges); |
_cairo_array_init (&intersected_edges, sizeof (cairo_bo_edge_t)); |
intersections = _cairo_bentley_ottmann_intersect_edges (edges, num_edges, &intersected_edges); |
free (edges); |
|
if (intersections){ |
printf ("Pass %d found %d remaining intersections:\n", passes, intersections); |
} else { |
if (passes > 3) |
for (i = 0; i < passes; i++) |
printf ("*"); |
printf ("No remainining intersections found after pass %d\n", passes); |
} |
} |
|
if (edges_have_an_intersection_quadratic (_cairo_array_index (&intersected_edges, 0), |
_cairo_array_num_elements (&intersected_edges))) |
printf ("*** FAIL ***\n"); |
else |
printf ("PASS\n"); |
|
_cairo_array_fini (&intersected_edges); |
|
return 0; |
} |
|
#define MAX_RANDOM 300 |
|
int |
main (void) |
{ |
char random_name[] = "random-XX"; |
cairo_bo_edge_t random_edges[MAX_RANDOM], *edge; |
unsigned int i, num_random; |
test_t *test; |
|
for (i = 0; i < ARRAY_LENGTH (tests); i++) { |
test = &tests[i]; |
run_test (test->name, test->edges, test->num_edges); |
} |
|
for (num_random = 0; num_random < MAX_RANDOM; num_random++) { |
srand (0); |
for (i = 0; i < num_random; i++) { |
do { |
edge = &random_edges[i]; |
edge->line.p1.x = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0))); |
edge->line.p1.y = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0))); |
edge->line.p2.x = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0))); |
edge->line.p2.y = (int32_t) (10.0 * (rand() / (RAND_MAX + 1.0))); |
if (edge->line.p1.y > edge->line.p2.y) { |
int32_t tmp = edge->line.p1.y; |
edge->line.p1.y = edge->line.p2.y; |
edge->line.p2.y = tmp; |
} |
} while (edge->line.p1.y == edge->line.p2.y); |
} |
|
sprintf (random_name, "random-%02d", num_random); |
|
run_test (random_name, random_edges, num_random); |
} |
|
return 0; |
} |
#endif |