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/* cairo - a vector graphics library with display and print output

 *

 * Copyright © 2003 University of Southern California

 *

 * 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 University of Southern

 * California.

 *

 * Contributor(s):

 *	Carl D. Worth 

 */

#include "cairoint.h"

#include "cairo-error-private.h"

#include "cairo-slope-private.h"

typedef struct cairo_hull {

    cairo_point_t point;

    cairo_slope_t slope;

    int discard;

    int id;

} cairo_hull_t;

static void

_cairo_hull_init (cairo_hull_t			*hull,

	          cairo_pen_vertex_t		*vertices,

		  int				 num_vertices)

{

    cairo_point_t *p, *extremum, tmp;

    int i;

    extremum = &vertices[0].point;

    for (i = 1; i < num_vertices; i++) {

	p = &vertices[i].point;

	if (p->y < extremum->y || (p->y == extremum->y && p->x < extremum->x))

	    extremum = p;

    }

    /* Put the extremal point at the beginning of the array */

    tmp = *extremum;

    *extremum = vertices[0].point;

    vertices[0].point = tmp;

    for (i = 0; i < num_vertices; i++) {

	hull[i].point = vertices[i].point;

	_cairo_slope_init (&hull[i].slope, &hull[0].point, &hull[i].point);

        /* give each point a unique id for later comparison */

        hull[i].id = i;

        /* Don't discard by default */

        hull[i].discard = 0;

	/* Discard all points coincident with the extremal point */

	if (i != 0 && hull[i].slope.dx == 0 && hull[i].slope.dy == 0)

	    hull[i].discard = 1;

    }

}

static inline cairo_int64_t

_slope_length (cairo_slope_t *slope)

{

    return _cairo_int64_add (_cairo_int32x32_64_mul (slope->dx, slope->dx),

			     _cairo_int32x32_64_mul (slope->dy, slope->dy));

}

static int

_cairo_hull_vertex_compare (const void *av, const void *bv)

{

    cairo_hull_t *a = (cairo_hull_t *) av;

    cairo_hull_t *b = (cairo_hull_t *) bv;

    int ret;

    /* Some libraries are reported to actually compare identical

     * pointers and require the result to be 0. This is the crazy world we

     * have to live in.

     */

    if (a == b)

	return 0;

    ret = _cairo_slope_compare (&a->slope, &b->slope);

    /*

     * In the case of two vertices with identical slope from the

     * extremal point discard the nearer point.

     */

    if (ret == 0) {

	int cmp;

	cmp = _cairo_int64_cmp (_slope_length (&a->slope),

				_slope_length (&b->slope));

	/*

	 * Use the points' ids to ensure a well-defined ordering,

	 * and avoid setting discard on both points.

	 */

	if (cmp < 0 || (cmp == 0 && a->id < b->id)) {

	    a->discard = 1;

	    ret = -1;

	} else {

	    b->discard = 1;

	    ret = 1;

	}

    }

    return ret;

}

static int

_cairo_hull_prev_valid (cairo_hull_t *hull, int num_hull, int index)

{

    /* hull[0] is always valid, and we never need to wraparound, (if

     * we are passed an index of 0 here, then the calling loop is just

     * about to terminate). */

    if (index == 0)

	return 0;

    do {

	index--;

    } while (hull[index].discard);

    return index;

}

static int

_cairo_hull_next_valid (cairo_hull_t *hull, int num_hull, int index)

{

    do {

	index = (index + 1) % num_hull;

    } while (hull[index].discard);

    return index;

}

static void

_cairo_hull_eliminate_concave (cairo_hull_t *hull, int num_hull)

{

    int i, j, k;

    cairo_slope_t slope_ij, slope_jk;

    i = 0;

    j = _cairo_hull_next_valid (hull, num_hull, i);

    k = _cairo_hull_next_valid (hull, num_hull, j);

    do {

	_cairo_slope_init (&slope_ij, &hull[i].point, &hull[j].point);

	_cairo_slope_init (&slope_jk, &hull[j].point, &hull[k].point);

	/* Is the angle formed by ij and jk concave? */

	if (_cairo_slope_compare (&slope_ij, &slope_jk) >= 0) {

	    if (i == k)

		return;

	    hull[j].discard = 1;

	    j = i;

	    i = _cairo_hull_prev_valid (hull, num_hull, j);

	} else {

	    i = j;

	    j = k;

	    k = _cairo_hull_next_valid (hull, num_hull, j);

	}

    } while (j != 0);

}

static void

_cairo_hull_to_pen (cairo_hull_t *hull, cairo_pen_vertex_t *vertices, int *num_vertices)

{

    int i, j = 0;

    for (i = 0; i < *num_vertices; i++) {

	if (hull[i].discard)

	    continue;

	vertices[j++].point = hull[i].point;

    }

    *num_vertices = j;

}

/* Given a set of vertices, compute the convex hull using the Graham

   scan algorithm. */

cairo_status_t

_cairo_hull_compute (cairo_pen_vertex_t *vertices, int *num_vertices)

{

    cairo_hull_t hull_stack[CAIRO_STACK_ARRAY_LENGTH (cairo_hull_t)];

    cairo_hull_t *hull;

    int num_hull = *num_vertices;

    if (CAIRO_INJECT_FAULT ())

	return _cairo_error (CAIRO_STATUS_NO_MEMORY);

    if (num_hull > ARRAY_LENGTH (hull_stack)) {

	hull = _cairo_malloc_ab (num_hull, sizeof (cairo_hull_t));

	if (unlikely (hull == NULL))

	    return _cairo_error (CAIRO_STATUS_NO_MEMORY);

    } else {

	hull = hull_stack;

    }

    _cairo_hull_init (hull, vertices, num_hull);

    qsort (hull + 1, num_hull - 1,

	   sizeof (cairo_hull_t), _cairo_hull_vertex_compare);

    _cairo_hull_eliminate_concave (hull, num_hull);

    _cairo_hull_to_pen (hull, vertices, num_vertices);

    if (hull != hull_stack)

	free (hull);

    return CAIRO_STATUS_SUCCESS;

}