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/*
* Copyright © 2003 University of Southern California
*
* Permission to use, copy, modify, distribute, and sell this software
* and its documentation for any purpose is hereby granted without
* fee, provided that the above copyright notice appear in all copies
* and that both that copyright notice and this permission notice
* appear in supporting documentation, and that the name of the
* University of Southern California not be used in advertising or
* publicity pertaining to distribution of the software without
* specific, written prior permission. The University of Southern
* California makes no representations about the suitability of this
* software for any purpose. It is provided "as is" without express
* or implied warranty.
*
* THE UNIVERSITY OF SOUTHERN CALIFORNIA DISCLAIMS ALL WARRANTIES WITH
* REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL THE UNIVERSITY OF
* SOUTHERN CALIFORNIA BE LIABLE FOR ANY SPECIAL, INDIRECT OR
* CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
* OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,
* NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*
* Author: Carl D. Worth <cworth@isi.edu>
*/
#include "cairoint.h"
typedef struct cairo_hull
{
cairo_point_t point;
cairo_slope_t slope;
int discard;
} 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 = malloc (num_vertices * sizeof (cairo_hull_t));
if (hull == NULL)
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);
/* 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;
else
hull[i].discard = 0;
}
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);
if (a_dist < b_dist)
a->discard = 1;
else
b->discard = 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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