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/*
* Copyright © 2004 Carl Worth
* Copyright © 2006 Red Hat, Inc.
* Copyright © 2009 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-boxes-private.h"
#include "cairo-error-private.h"
#include "cairo-combsort-inline.h"
#include "cairo-list-private.h"
#include "cairo-traps-private.h"
#include <setjmp.h>
typedef struct _rectangle rectangle_t;
typedef struct _edge edge_t;
struct _edge {
edge_t *next, *prev;
edge_t *right;
cairo_fixed_t x, top;
int dir;
};
struct _rectangle {
edge_t left, right;
int32_t top, bottom;
#define UNROLL3(x) x x x
/* 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 struct _sweep_line {
rectangle_t **rectangles;
rectangle_t **stop;
edge_t head, tail, *insert, *cursor;
int32_t current_y;
int32_t last_y;
int stop_size;
int32_t insert_x;
cairo_fill_rule_t fill_rule;
cairo_bool_t do_traps;
void *container;
jmp_buf unwind;
} sweep_line_t;
#define DEBUG_TRAPS 0
#if DEBUG_TRAPS
static void
dump_traps (cairo_traps_t *traps, 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 < 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);
#else
#define dump_traps(traps, filename)
#endif
static inline int
rectangle_compare_start (const rectangle_t *a,
const rectangle_t *b)
return a->top - b->top;
rectangle_compare_stop (const rectangle_t *a,
return a->bottom - b->bottom;
static inline void
pqueue_push (sweep_line_t *sweep, rectangle_t *rectangle)
rectangle_t **elements;
int i, parent;
elements = sweep->stop;
for (i = ++sweep->stop_size;
i != PQ_FIRST_ENTRY &&
rectangle_compare_stop (rectangle,
elements[parent = PQ_PARENT_INDEX (i)]) < 0;
i = parent)
elements[i] = elements[parent];
elements[i] = rectangle;
rectangle_pop_stop (sweep_line_t *sweep)
rectangle_t **elements = sweep->stop;
rectangle_t *tail;
int child, i;
tail = elements[sweep->stop_size--];
if (sweep->stop_size == 0) {
elements[PQ_FIRST_ENTRY] = NULL;
for (i = PQ_FIRST_ENTRY;
(child = PQ_LEFT_CHILD_INDEX (i)) <= sweep->stop_size;
i = child)
if (child != sweep->stop_size &&
rectangle_compare_stop (elements[child+1],
elements[child]) < 0)
child++;
if (rectangle_compare_stop (elements[child], tail) >= 0)
break;
elements[i] = elements[child];
elements[i] = tail;
static inline rectangle_t *
rectangle_pop_start (sweep_line_t *sweep_line)
return *sweep_line->rectangles++;
rectangle_peek_stop (sweep_line_t *sweep_line)
return sweep_line->stop[PQ_FIRST_ENTRY];
CAIRO_COMBSORT_DECLARE (_rectangle_sort,
rectangle_t *,
rectangle_compare_start)
sweep_line_init (sweep_line_t *sweep_line,
rectangle_t **rectangles,
int num_rectangles,
cairo_fill_rule_t fill_rule,
cairo_bool_t do_traps,
void *container)
rectangles[-2] = NULL;
rectangles[-1] = NULL;
rectangles[num_rectangles] = NULL;
sweep_line->rectangles = rectangles;
sweep_line->stop = rectangles - 2;
sweep_line->stop_size = 0;
sweep_line->insert = NULL;
sweep_line->insert_x = INT_MAX;
sweep_line->cursor = &sweep_line->tail;
sweep_line->head.dir = 0;
sweep_line->head.x = INT32_MIN;
sweep_line->head.right = NULL;
sweep_line->head.prev = NULL;
sweep_line->head.next = &sweep_line->tail;
sweep_line->tail.prev = &sweep_line->head;
sweep_line->tail.next = NULL;
sweep_line->tail.right = NULL;
sweep_line->tail.x = INT32_MAX;
sweep_line->tail.dir = 0;
sweep_line->current_y = INT32_MIN;
sweep_line->last_y = INT32_MIN;
sweep_line->fill_rule = fill_rule;
sweep_line->container = container;
sweep_line->do_traps = do_traps;
edge_end_box (sweep_line_t *sweep_line, edge_t *left, int32_t bot)
cairo_status_t status = CAIRO_STATUS_SUCCESS;
/* Only emit (trivial) non-degenerate trapezoids with positive height. */
if (likely (left->top < bot)) {
if (sweep_line->do_traps) {
cairo_line_t _left = {
{ left->x, left->top },
{ left->x, bot },
}, _right = {
{ left->right->x, left->top },
{ left->right->x, bot },
_cairo_traps_add_trap (sweep_line->container, left->top, bot, &_left, &_right);
status = _cairo_traps_status ((cairo_traps_t *) sweep_line->container);
} else {
cairo_box_t box;
box.p1.x = left->x;
box.p1.y = left->top;
box.p2.x = left->right->x;
box.p2.y = bot;
status = _cairo_boxes_add (sweep_line->container,
CAIRO_ANTIALIAS_DEFAULT,
&box);
if (unlikely (status))
longjmp (sweep_line->unwind, status);
left->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. */
edge_start_or_continue_box (sweep_line_t *sweep_line,
edge_t *left,
edge_t *right,
int top)
if (left->right == right)
if (left->right != NULL) {
if (left->right->x == right->x) {
/* continuation on right, so just swap edges */
left->right = right;
edge_end_box (sweep_line, left, top);
if (left->x != right->x) {
left->top = top;
* Merge two sorted edge lists.
* Input:
* - head_a: The head of the first list.
* - head_b: The head of the second list; head_b cannot be NULL.
* Output:
* Returns the head of the merged list.
* Implementation notes:
* To make it fast (in particular, to reduce to an insertion sort whenever
* one of the two input lists only has a single element) we iterate through
* a list until its head becomes greater than the head of the other list,
* then we switch their roles. As soon as one of the two lists is empty, we
* just attach the other one to the current list and exit.
* Writes to memory are only needed to "switch" lists (as it also requires
* attaching to the output list the list which we will be iterating next) and
* to attach the last non-empty list.
static edge_t *
merge_sorted_edges (edge_t *head_a, edge_t *head_b)
edge_t *head, *prev;
int32_t x;
prev = head_a->prev;
if (head_a->x <= head_b->x) {
head = head_a;
head_b->prev = prev;
head = head_b;
goto start_with_b;
do {
x = head_b->x;
while (head_a != NULL && head_a->x <= x) {
prev = head_a;
head_a = head_a->next;
prev->next = head_b;
if (head_a == NULL)
return head;
start_with_b:
x = head_a->x;
while (head_b != NULL && head_b->x <= x) {
prev = head_b;
head_b = head_b->next;
head_a->prev = prev;
prev->next = head_a;
if (head_b == NULL)
} while (1);
* Sort (part of) a list.
* - list: The list to be sorted; list cannot be NULL.
* - limit: Recursion limit.
* - head_out: The head of the sorted list containing the first 2^(level+1) elements of the
* input list; if the input list has fewer elements, head_out be a sorted list
* containing all the elements of the input list.
* Returns the head of the list of unprocessed elements (NULL if the sorted list contains
* all the elements of the input list).
* Special case single element list, unroll/inline the sorting of the first two elements.
* Some tail recursion is used since we iterate on the bottom-up solution of the problem
* (we start with a small sorted list and keep merging other lists of the same size to it).
sort_edges (edge_t *list,
unsigned int level,
edge_t **head_out)
edge_t *head_other, *remaining;
unsigned int i;
head_other = list->next;
if (head_other == NULL) {
*head_out = list;
return NULL;
remaining = head_other->next;
if (list->x <= head_other->x) {
head_other->next = NULL;
*head_out = head_other;
head_other->prev = list->prev;
head_other->next = list;
list->prev = head_other;
list->next = NULL;
for (i = 0; i < level && remaining; i++) {
remaining = sort_edges (remaining, i, &head_other);
*head_out = merge_sorted_edges (*head_out, head_other);
return remaining;
merge_unsorted_edges (edge_t *head, edge_t *unsorted)
sort_edges (unsorted, UINT_MAX, &unsorted);
return merge_sorted_edges (head, unsorted);
active_edges_insert (sweep_line_t *sweep)
edge_t *prev;
int x;
x = sweep->insert_x;
prev = sweep->cursor;
if (prev->x > x) {
prev = prev->prev;
} while (prev->x > x);
while (prev->next->x < x)
prev = prev->next;
prev->next = merge_unsorted_edges (prev->next, sweep->insert);
sweep->cursor = sweep->insert;
sweep->insert = NULL;
sweep->insert_x = INT_MAX;
active_edges_to_traps (sweep_line_t *sweep)
int top = sweep->current_y;
edge_t *pos;
if (sweep->last_y == sweep->current_y)
if (sweep->insert)
active_edges_insert (sweep);
pos = sweep->head.next;
if (pos == &sweep->tail)
if (sweep->fill_rule == CAIRO_FILL_RULE_WINDING) {
edge_t *left, *right;
int winding;
left = pos;
winding = left->dir;
right = left->next;
/* Check if there is a co-linear edge with an existing trap */
while (right->x == left->x) {
if (right->right != NULL) {
assert (left->right == NULL);
/* continuation on left */
left->top = right->top;
left->right = right->right;
right->right = NULL;
winding += right->dir;
right = right->next;
if (winding == 0) {
if (left->right != NULL)
edge_end_box (sweep, left, top);
pos = right;
continue;
/* End all subsumed traps */
if (unlikely (right->right != NULL))
edge_end_box (sweep, right, top);
/* Greedily search for the closing edge, so that we generate
* the * maximal span width with the minimal number of
* boxes.
if (winding == 0 && right->x != right->next->x)
} while (TRUE);
edge_start_or_continue_box (sweep, left, right, top);
pos = right->next;
} while (pos != &sweep->tail);
edge_t *right = pos->next;
int count = 0;
/* skip co-linear edges */
if (++count & 1 && right->x != right->next->x)
edge_start_or_continue_box (sweep, pos, right, top);
sweep->last_y = sweep->current_y;
sweep_line_delete_edge (sweep_line_t *sweep, edge_t *edge)
if (edge->right != NULL) {
edge_t *next = edge->next;
if (next->x == edge->x) {
next->top = edge->top;
next->right = edge->right;
} else
edge_end_box (sweep, edge, sweep->current_y);
if (sweep->cursor == edge)
sweep->cursor = edge->prev;
edge->prev->next = edge->next;
edge->next->prev = edge->prev;
static inline cairo_bool_t
sweep_line_delete (sweep_line_t *sweep, rectangle_t *rectangle)
cairo_bool_t update;
update = TRUE;
if (sweep->fill_rule == CAIRO_FILL_RULE_WINDING &&
rectangle->left.prev->dir == rectangle->left.dir)
update = rectangle->left.next != &rectangle->right;
sweep_line_delete_edge (sweep, &rectangle->left);
sweep_line_delete_edge (sweep, &rectangle->right);
rectangle_pop_stop (sweep);
return update;
sweep_line_insert (sweep_line_t *sweep, rectangle_t *rectangle)
sweep->insert->prev = &rectangle->right;
rectangle->right.next = sweep->insert;
rectangle->right.prev = &rectangle->left;
rectangle->left.next = &rectangle->right;
rectangle->left.prev = NULL;
sweep->insert = &rectangle->left;
if (rectangle->left.x < sweep->insert_x)
sweep->insert_x = rectangle->left.x;
pqueue_push (sweep, rectangle);
static cairo_status_t
_cairo_bentley_ottmann_tessellate_rectangular (rectangle_t **rectangles,
sweep_line_t sweep_line;
rectangle_t *rectangle;
cairo_status_t status;
sweep_line_init (&sweep_line,
rectangles, num_rectangles,
fill_rule,
do_traps, container);
if ((status = setjmp (sweep_line.unwind)))
return status;
update = FALSE;
rectangle = rectangle_pop_start (&sweep_line);
if (rectangle->top != sweep_line.current_y) {
rectangle_t *stop;
stop = rectangle_peek_stop (&sweep_line);
while (stop != NULL && stop->bottom < rectangle->top) {
if (stop->bottom != sweep_line.current_y) {
if (update) {
active_edges_to_traps (&sweep_line);
sweep_line.current_y = stop->bottom;
update |= sweep_line_delete (&sweep_line, stop);
sweep_line.current_y = rectangle->top;
sweep_line_insert (&sweep_line, rectangle);
} while ((rectangle = rectangle_pop_start (&sweep_line)) != NULL &&
sweep_line.current_y == rectangle->top);
} while (rectangle);
while ((rectangle = rectangle_peek_stop (&sweep_line)) != NULL) {
if (rectangle->bottom != sweep_line.current_y) {
sweep_line.current_y = rectangle->bottom;
update |= sweep_line_delete (&sweep_line, rectangle);
return CAIRO_STATUS_SUCCESS;
cairo_status_t
_cairo_bentley_ottmann_tessellate_rectangular_traps (cairo_traps_t *traps,
cairo_fill_rule_t fill_rule)
rectangle_t stack_rectangles[CAIRO_STACK_ARRAY_LENGTH (rectangle_t)];
rectangle_t *stack_rectangles_ptrs[ARRAY_LENGTH (stack_rectangles) + 3];
rectangle_t *rectangles, **rectangles_ptrs;
int i;
assert (traps->is_rectangular);
if (unlikely (traps->num_traps <= 1)) {
if (traps->num_traps == 1) {
cairo_trapezoid_t *trap = traps->traps;
if (trap->left.p1.x > trap->right.p1.x) {
cairo_line_t tmp = trap->left;
trap->left = trap->right;
trap->right = tmp;
dump_traps (traps, "bo-rects-traps-in.txt");
rectangles = stack_rectangles;
rectangles_ptrs = stack_rectangles_ptrs;
if (traps->num_traps > ARRAY_LENGTH (stack_rectangles)) {
rectangles = _cairo_malloc_ab_plus_c (traps->num_traps,
sizeof (rectangle_t) +
sizeof (rectangle_t *),
3*sizeof (rectangle_t *));
if (unlikely (rectangles == NULL))
return _cairo_error (CAIRO_STATUS_NO_MEMORY);
rectangles_ptrs = (rectangle_t **) (rectangles + traps->num_traps);
for (i = 0; i < traps->num_traps; i++) {
if (traps->traps[i].left.p1.x < traps->traps[i].right.p1.x) {
rectangles[i].left.x = traps->traps[i].left.p1.x;
rectangles[i].left.dir = 1;
rectangles[i].right.x = traps->traps[i].right.p1.x;
rectangles[i].right.dir = -1;
rectangles[i].right.x = traps->traps[i].left.p1.x;
rectangles[i].right.dir = 1;
rectangles[i].left.x = traps->traps[i].right.p1.x;
rectangles[i].left.dir = -1;
rectangles[i].left.right = NULL;
rectangles[i].right.right = NULL;
rectangles[i].top = traps->traps[i].top;
rectangles[i].bottom = traps->traps[i].bottom;
rectangles_ptrs[i+2] = &rectangles[i];
/* XXX incremental sort */
_rectangle_sort (rectangles_ptrs+2, i);
_cairo_traps_clear (traps);
status = _cairo_bentley_ottmann_tessellate_rectangular (rectangles_ptrs+2, i,
TRUE, traps);
traps->is_rectilinear = TRUE;
traps->is_rectangular = TRUE;
if (rectangles != stack_rectangles)
free (rectangles);
dump_traps (traps, "bo-rects-traps-out.txt");
_cairo_bentley_ottmann_tessellate_boxes (const cairo_boxes_t *in,
cairo_boxes_t *out)
rectangle_t *stack_rectangles_chain[CAIRO_STACK_ARRAY_LENGTH (rectangle_t *) ];
rectangle_t **rectangles_chain = NULL;
const struct _cairo_boxes_chunk *chunk;
int i, j, y_min, y_max;
if (unlikely (in->num_boxes == 0)) {
_cairo_boxes_clear (out);
if (in->num_boxes == 1) {
if (in == out) {
cairo_box_t *box = &in->chunks.base[0];
if (box->p1.x > box->p2.x) {
cairo_fixed_t tmp = box->p1.x;
box->p1.x = box->p2.x;
box->p2.x = tmp;
cairo_box_t box = in->chunks.base[0];
if (box.p1.x > box.p2.x) {
cairo_fixed_t tmp = box.p1.x;
box.p1.x = box.p2.x;
box.p2.x = tmp;
status = _cairo_boxes_add (out, CAIRO_ANTIALIAS_DEFAULT, &box);
assert (status == CAIRO_STATUS_SUCCESS);
y_min = INT_MAX; y_max = INT_MIN;
for (chunk = &in->chunks; chunk != NULL; chunk = chunk->next) {
const cairo_box_t *box = chunk->base;
for (i = 0; i < chunk->count; i++) {
if (box[i].p1.y < y_min)
y_min = box[i].p1.y;
if (box[i].p1.y > y_max)
y_max = box[i].p1.y;
y_min = _cairo_fixed_integer_floor (y_min);
y_max = _cairo_fixed_integer_floor (y_max) + 1;
y_max -= y_min;
if (y_max < in->num_boxes) {
rectangles_chain = stack_rectangles_chain;
if (y_max > ARRAY_LENGTH (stack_rectangles_chain)) {
rectangles_chain = _cairo_malloc_ab (y_max, sizeof (rectangle_t *));
if (unlikely (rectangles_chain == NULL))
memset (rectangles_chain, 0, y_max * sizeof (rectangle_t*));
if (in->num_boxes > ARRAY_LENGTH (stack_rectangles)) {
rectangles = _cairo_malloc_ab_plus_c (in->num_boxes,
if (unlikely (rectangles == NULL)) {
if (rectangles_chain != stack_rectangles_chain)
free (rectangles_chain);
rectangles_ptrs = (rectangle_t **) (rectangles + in->num_boxes);
j = 0;
int h;
if (box[i].p1.x < box[i].p2.x) {
rectangles[j].left.x = box[i].p1.x;
rectangles[j].left.dir = 1;
rectangles[j].right.x = box[i].p2.x;
rectangles[j].right.dir = -1;
rectangles[j].right.x = box[i].p1.x;
rectangles[j].right.dir = 1;
rectangles[j].left.x = box[i].p2.x;
rectangles[j].left.dir = -1;
rectangles[j].left.right = NULL;
rectangles[j].right.right = NULL;
rectangles[j].top = box[i].p1.y;
rectangles[j].bottom = box[i].p2.y;
if (rectangles_chain) {
h = _cairo_fixed_integer_floor (box[i].p1.y) - y_min;
rectangles[j].left.next = (edge_t *)rectangles_chain[h];
rectangles_chain[h] = &rectangles[j];
rectangles_ptrs[j+2] = &rectangles[j];
j++;
j = 2;
for (y_min = 0; y_min < y_max; y_min++) {
rectangle_t *r;
int start = j;
for (r = rectangles_chain[y_min]; r; r = (rectangle_t *)r->left.next)
rectangles_ptrs[j++] = r;
if (j > start + 1)
_rectangle_sort (rectangles_ptrs + start, j - start);
j -= 2;
_rectangle_sort (rectangles_ptrs + 2, j);
status = _cairo_bentley_ottmann_tessellate_rectangular (rectangles_ptrs+2, j,
FALSE, out);