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/* cairo - a vector graphics library with display and print output
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 *
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 * Copyright © 2003 University of Southern California
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 *
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 * This library is free software; you can redistribute it and/or
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 * modify it either under the terms of the GNU Lesser General Public
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 * License version 2.1 as published by the Free Software Foundation
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 * (the "LGPL") or, at your option, under the terms of the Mozilla
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 * Public License Version 1.1 (the "MPL"). If you do not alter this
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 * notice, a recipient may use your version of this file under either
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 * the MPL or the LGPL.
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 *
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 * You should have received a copy of the LGPL along with this library
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 * in the file COPYING-LGPL-2.1; if not, write to the Free Software
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 * Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA
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 * You should have received a copy of the MPL along with this library
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 * in the file COPYING-MPL-1.1
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 *
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 * The contents of this file are subject to the Mozilla Public License
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 * Version 1.1 (the "License"); you may not use this file except in
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 * compliance with the License. You may obtain a copy of the License at
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 * http://www.mozilla.org/MPL/
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 *
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 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
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 * OF ANY KIND, either express or implied. See the LGPL or the MPL for
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 * the specific language governing rights and limitations.
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 *
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 * The Original Code is the cairo graphics library.
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 *
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 * The Initial Developer of the Original Code is University of Southern
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 * California.
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 *
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 * Contributor(s):
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 *	Carl D. Worth <cworth@cworth.org>
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 */
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#include "cairoint.h"
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#include "cairo-error-private.h"
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#include "cairo-slope-private.h"
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typedef struct cairo_hull {
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    cairo_point_t point;
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    cairo_slope_t slope;
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    int discard;
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    int id;
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} cairo_hull_t;
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static void
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_cairo_hull_init (cairo_hull_t			*hull,
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	          cairo_pen_vertex_t		*vertices,
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		  int				 num_vertices)
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{
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    cairo_point_t *p, *extremum, tmp;
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    int i;
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    extremum = &vertices[0].point;
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    for (i = 1; i < num_vertices; i++) {
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	p = &vertices[i].point;
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	if (p->y < extremum->y || (p->y == extremum->y && p->x < extremum->x))
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	    extremum = p;
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    }
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    /* Put the extremal point at the beginning of the array */
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    tmp = *extremum;
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    *extremum = vertices[0].point;
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    vertices[0].point = tmp;
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    for (i = 0; i < num_vertices; i++) {
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	hull[i].point = vertices[i].point;
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	_cairo_slope_init (&hull[i].slope, &hull[0].point, &hull[i].point);
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        /* give each point a unique id for later comparison */
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        hull[i].id = i;
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        /* Don't discard by default */
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        hull[i].discard = 0;
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	/* Discard all points coincident with the extremal point */
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	if (i != 0 && hull[i].slope.dx == 0 && hull[i].slope.dy == 0)
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	    hull[i].discard = 1;
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    }
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}
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static inline cairo_int64_t
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_slope_length (cairo_slope_t *slope)
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{
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    return _cairo_int64_add (_cairo_int32x32_64_mul (slope->dx, slope->dx),
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			     _cairo_int32x32_64_mul (slope->dy, slope->dy));
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}
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static int
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_cairo_hull_vertex_compare (const void *av, const void *bv)
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{
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    cairo_hull_t *a = (cairo_hull_t *) av;
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    cairo_hull_t *b = (cairo_hull_t *) bv;
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    int ret;
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    /* Some libraries are reported to actually compare identical
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     * pointers and require the result to be 0. This is the crazy world we
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     * have to live in.
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     */
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    if (a == b)
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	return 0;
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    ret = _cairo_slope_compare (&a->slope, &b->slope);
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    /*
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     * In the case of two vertices with identical slope from the
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     * extremal point discard the nearer point.
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     */
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    if (ret == 0) {
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	int cmp;
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	cmp = _cairo_int64_cmp (_slope_length (&a->slope),
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				_slope_length (&b->slope));
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	/*
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	 * Use the points' ids to ensure a well-defined ordering,
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	 * and avoid setting discard on both points.
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	 */
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	if (cmp < 0 || (cmp == 0 && a->id < b->id)) {
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	    a->discard = 1;
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	    ret = -1;
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	} else {
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	    b->discard = 1;
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	    ret = 1;
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	}
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    }
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    return ret;
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}
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static int
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_cairo_hull_prev_valid (cairo_hull_t *hull, int num_hull, int index)
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{
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    /* hull[0] is always valid, and we never need to wraparound, (if
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     * we are passed an index of 0 here, then the calling loop is just
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     * about to terminate). */
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    if (index == 0)
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	return 0;
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    do {
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	index--;
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    } while (hull[index].discard);
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    return index;
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}
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static int
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_cairo_hull_next_valid (cairo_hull_t *hull, int num_hull, int index)
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{
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    do {
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	index = (index + 1) % num_hull;
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    } while (hull[index].discard);
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    return index;
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}
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static void
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_cairo_hull_eliminate_concave (cairo_hull_t *hull, int num_hull)
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{
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    int i, j, k;
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    cairo_slope_t slope_ij, slope_jk;
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    i = 0;
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    j = _cairo_hull_next_valid (hull, num_hull, i);
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    k = _cairo_hull_next_valid (hull, num_hull, j);
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    do {
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	_cairo_slope_init (&slope_ij, &hull[i].point, &hull[j].point);
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	_cairo_slope_init (&slope_jk, &hull[j].point, &hull[k].point);
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	/* Is the angle formed by ij and jk concave? */
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	if (_cairo_slope_compare (&slope_ij, &slope_jk) >= 0) {
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	    if (i == k)
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		return;
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	    hull[j].discard = 1;
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	    j = i;
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	    i = _cairo_hull_prev_valid (hull, num_hull, j);
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	} else {
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	    i = j;
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	    j = k;
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	    k = _cairo_hull_next_valid (hull, num_hull, j);
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	}
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    } while (j != 0);
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}
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static void
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_cairo_hull_to_pen (cairo_hull_t *hull, cairo_pen_vertex_t *vertices, int *num_vertices)
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{
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    int i, j = 0;
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    for (i = 0; i < *num_vertices; i++) {
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	if (hull[i].discard)
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	    continue;
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	vertices[j++].point = hull[i].point;
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    }
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    *num_vertices = j;
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}
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/* Given a set of vertices, compute the convex hull using the Graham
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   scan algorithm. */
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cairo_status_t
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_cairo_hull_compute (cairo_pen_vertex_t *vertices, int *num_vertices)
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{
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    cairo_hull_t hull_stack[CAIRO_STACK_ARRAY_LENGTH (cairo_hull_t)];
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    cairo_hull_t *hull;
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    int num_hull = *num_vertices;
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    if (CAIRO_INJECT_FAULT ())
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	return _cairo_error (CAIRO_STATUS_NO_MEMORY);
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    if (num_hull > ARRAY_LENGTH (hull_stack)) {
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	hull = _cairo_malloc_ab (num_hull, sizeof (cairo_hull_t));
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	if (unlikely (hull == NULL))
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	    return _cairo_error (CAIRO_STATUS_NO_MEMORY);
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    } else {
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	hull = hull_stack;
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    }
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    _cairo_hull_init (hull, vertices, num_hull);
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    qsort (hull + 1, num_hull - 1,
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	   sizeof (cairo_hull_t), _cairo_hull_vertex_compare);
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    _cairo_hull_eliminate_concave (hull, num_hull);
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    _cairo_hull_to_pen (hull, vertices, num_vertices);
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    if (hull != hull_stack)
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	free (hull);
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    return CAIRO_STATUS_SUCCESS;
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}