1 /* cairo - a vector graphics library with display and print output
3 * Copyright © 2003 University of Southern California
5 * This library is free software; you can redistribute it and/or
6 * modify it either under the terms of the GNU Lesser General Public
7 * License version 2.1 as published by the Free Software Foundation
8 * (the "LGPL") or, at your option, under the terms of the Mozilla
9 * Public License Version 1.1 (the "MPL"). If you do not alter this
10 * notice, a recipient may use your version of this file under either
11 * the MPL or the LGPL.
13 * You should have received a copy of the LGPL along with this library
14 * in the file COPYING-LGPL-2.1; if not, write to the Free Software
15 * Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA
16 * You should have received a copy of the MPL along with this library
17 * in the file COPYING-MPL-1.1
19 * The contents of this file are subject to the Mozilla Public License
20 * Version 1.1 (the "License"); you may not use this file except in
21 * compliance with the License. You may obtain a copy of the License at
22 * http://www.mozilla.org/MPL/
24 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
25 * OF ANY KIND, either express or implied. See the LGPL or the MPL for
26 * the specific language governing rights and limitations.
28 * The Original Code is the cairo graphics library.
30 * The Initial Developer of the Original Code is University of Southern
34 * Carl D. Worth <cworth@cworth.org>
39 #include "cairo-error-private.h"
40 #include "cairo-slope-private.h"
42 typedef struct cairo_hull {
50 _cairo_hull_init (cairo_hull_t *hull,
51 cairo_pen_vertex_t *vertices,
54 cairo_point_t *p, *extremum, tmp;
57 extremum = &vertices[0].point;
58 for (i = 1; i < num_vertices; i++) {
59 p = &vertices[i].point;
60 if (p->y < extremum->y || (p->y == extremum->y && p->x < extremum->x))
63 /* Put the extremal point at the beginning of the array */
65 *extremum = vertices[0].point;
66 vertices[0].point = tmp;
68 for (i = 0; i < num_vertices; i++) {
69 hull[i].point = vertices[i].point;
70 _cairo_slope_init (&hull[i].slope, &hull[0].point, &hull[i].point);
72 /* give each point a unique id for later comparison */
75 /* Don't discard by default */
78 /* Discard all points coincident with the extremal point */
79 if (i != 0 && hull[i].slope.dx == 0 && hull[i].slope.dy == 0)
84 static inline cairo_int64_t
85 _slope_length (cairo_slope_t *slope)
87 return _cairo_int64_add (_cairo_int32x32_64_mul (slope->dx, slope->dx),
88 _cairo_int32x32_64_mul (slope->dy, slope->dy));
92 _cairo_hull_vertex_compare (const void *av, const void *bv)
94 cairo_hull_t *a = (cairo_hull_t *) av;
95 cairo_hull_t *b = (cairo_hull_t *) bv;
98 /* Some libraries are reported to actually compare identical
99 * pointers and require the result to be 0. This is the crazy world we
105 ret = _cairo_slope_compare (&a->slope, &b->slope);
108 * In the case of two vertices with identical slope from the
109 * extremal point discard the nearer point.
114 cmp = _cairo_int64_cmp (_slope_length (&a->slope),
115 _slope_length (&b->slope));
118 * Use the points' ids to ensure a well-defined ordering,
119 * and avoid setting discard on both points.
121 if (cmp < 0 || (cmp == 0 && a->id < b->id)) {
134 _cairo_hull_prev_valid (cairo_hull_t *hull, int num_hull, int index)
136 /* hull[0] is always valid, and we never need to wraparound, (if
137 * we are passed an index of 0 here, then the calling loop is just
138 * about to terminate). */
144 } while (hull[index].discard);
150 _cairo_hull_next_valid (cairo_hull_t *hull, int num_hull, int index)
153 index = (index + 1) % num_hull;
154 } while (hull[index].discard);
160 _cairo_hull_eliminate_concave (cairo_hull_t *hull, int num_hull)
163 cairo_slope_t slope_ij, slope_jk;
166 j = _cairo_hull_next_valid (hull, num_hull, i);
167 k = _cairo_hull_next_valid (hull, num_hull, j);
170 _cairo_slope_init (&slope_ij, &hull[i].point, &hull[j].point);
171 _cairo_slope_init (&slope_jk, &hull[j].point, &hull[k].point);
173 /* Is the angle formed by ij and jk concave? */
174 if (_cairo_slope_compare (&slope_ij, &slope_jk) >= 0) {
179 i = _cairo_hull_prev_valid (hull, num_hull, j);
183 k = _cairo_hull_next_valid (hull, num_hull, j);
189 _cairo_hull_to_pen (cairo_hull_t *hull, cairo_pen_vertex_t *vertices, int *num_vertices)
193 for (i = 0; i < *num_vertices; i++) {
196 vertices[j++].point = hull[i].point;
202 /* Given a set of vertices, compute the convex hull using the Graham
205 _cairo_hull_compute (cairo_pen_vertex_t *vertices, int *num_vertices)
207 cairo_hull_t hull_stack[CAIRO_STACK_ARRAY_LENGTH (cairo_hull_t)];
209 int num_hull = *num_vertices;
211 if (CAIRO_INJECT_FAULT ())
212 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
214 if (num_hull > ARRAY_LENGTH (hull_stack)) {
215 hull = _cairo_malloc_ab (num_hull, sizeof (cairo_hull_t));
216 if (unlikely (hull == NULL))
217 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
222 _cairo_hull_init (hull, vertices, num_hull);
224 qsort (hull + 1, num_hull - 1,
225 sizeof (cairo_hull_t), _cairo_hull_vertex_compare);
227 _cairo_hull_eliminate_concave (hull, num_hull);
229 _cairo_hull_to_pen (hull, vertices, num_vertices);
231 if (hull != hull_stack)
234 return CAIRO_STATUS_SUCCESS;