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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
*
* 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"
#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;
}