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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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 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 <cworth@cworth.org>
*/
#include "cairoint.h"
typedef struct cairo_hull
{
cairo_point_t point;
cairo_slope_t slope;
int discard;
int id;
} cairo_hull_t;
static cairo_hull_t *
_cairo_hull_create (cairo_pen_vertex_t *vertices, int num_vertices)
{
int i;
cairo_hull_t *hull;
cairo_point_t *p, *extremum, tmp;
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;
hull = _cairo_malloc_ab (num_vertices, sizeof (cairo_hull_t));
if (hull == NULL) {
_cairo_error_throw (CAIRO_STATUS_NO_MEMORY);
return NULL;
}
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;
}
return hull;
}
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;
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) {
cairo_fixed_48_16_t a_dist, b_dist;
a_dist = ((cairo_fixed_48_16_t) a->slope.dx * a->slope.dx +
(cairo_fixed_48_16_t) a->slope.dy * a->slope.dy);
b_dist = ((cairo_fixed_48_16_t) b->slope.dx * b->slope.dx +
(cairo_fixed_48_16_t) b->slope.dy * b->slope.dy);
/*
* Use the point's ids to ensure a total ordering.
* a well-defined ordering, and avoid setting discard on
* both points.
*/
if (a_dist < b_dist || (a_dist == b_dist && 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)
{
do {
/* hull[0] is always valid, so don't test and wraparound */
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 cairo_status_t
_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 CAIRO_STATUS_SUCCESS;
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);
return CAIRO_STATUS_SUCCESS;
}
static cairo_status_t
_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;
return CAIRO_STATUS_SUCCESS;
}
/* 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;
int num_hull = *num_vertices;
hull = _cairo_hull_create (vertices, num_hull);
if (hull == NULL)
return CAIRO_STATUS_NO_MEMORY;
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);
free (hull);
return CAIRO_STATUS_SUCCESS;
}
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