Line data Source code
1 : /* cairo - a vector graphics library with display and print output
2 : *
3 : * Copyright © 2003 University of Southern California
4 : *
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.
12 : *
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
18 : *
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/
23 : *
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.
27 : *
28 : * The Original Code is the cairo graphics library.
29 : *
30 : * The Initial Developer of the Original Code is University of Southern
31 : * California.
32 : *
33 : * Contributor(s):
34 : * Carl D. Worth <cworth@cworth.org>
35 : */
36 :
37 : #include "cairoint.h"
38 :
39 : #include "cairo-error-private.h"
40 : #include "cairo-slope-private.h"
41 :
42 : typedef struct cairo_hull {
43 : cairo_point_t point;
44 : cairo_slope_t slope;
45 : int discard;
46 : int id;
47 : } cairo_hull_t;
48 :
49 : static void
50 0 : _cairo_hull_init (cairo_hull_t *hull,
51 : cairo_pen_vertex_t *vertices,
52 : int num_vertices)
53 : {
54 : cairo_point_t *p, *extremum, tmp;
55 : int i;
56 :
57 0 : extremum = &vertices[0].point;
58 0 : for (i = 1; i < num_vertices; i++) {
59 0 : p = &vertices[i].point;
60 0 : if (p->y < extremum->y || (p->y == extremum->y && p->x < extremum->x))
61 0 : extremum = p;
62 : }
63 : /* Put the extremal point at the beginning of the array */
64 0 : tmp = *extremum;
65 0 : *extremum = vertices[0].point;
66 0 : vertices[0].point = tmp;
67 :
68 0 : for (i = 0; i < num_vertices; i++) {
69 0 : hull[i].point = vertices[i].point;
70 0 : _cairo_slope_init (&hull[i].slope, &hull[0].point, &hull[i].point);
71 :
72 : /* give each point a unique id for later comparison */
73 0 : hull[i].id = i;
74 :
75 : /* Don't discard by default */
76 0 : hull[i].discard = 0;
77 :
78 : /* Discard all points coincident with the extremal point */
79 0 : if (i != 0 && hull[i].slope.dx == 0 && hull[i].slope.dy == 0)
80 0 : hull[i].discard = 1;
81 : }
82 0 : }
83 :
84 : static inline cairo_int64_t
85 0 : _slope_length (cairo_slope_t *slope)
86 : {
87 0 : return _cairo_int64_add (_cairo_int32x32_64_mul (slope->dx, slope->dx),
88 : _cairo_int32x32_64_mul (slope->dy, slope->dy));
89 : }
90 :
91 : static int
92 0 : _cairo_hull_vertex_compare (const void *av, const void *bv)
93 : {
94 0 : cairo_hull_t *a = (cairo_hull_t *) av;
95 0 : cairo_hull_t *b = (cairo_hull_t *) bv;
96 : int ret;
97 :
98 : /* Some libraries are reported to actually compare identical
99 : * pointers and require the result to be 0. This is the crazy world we
100 : * have to live in.
101 : */
102 0 : if (a == b)
103 0 : return 0;
104 :
105 0 : ret = _cairo_slope_compare (&a->slope, &b->slope);
106 :
107 : /*
108 : * In the case of two vertices with identical slope from the
109 : * extremal point discard the nearer point.
110 : */
111 0 : if (ret == 0) {
112 : int cmp;
113 :
114 0 : cmp = _cairo_int64_cmp (_slope_length (&a->slope),
115 : _slope_length (&b->slope));
116 :
117 : /*
118 : * Use the points' ids to ensure a well-defined ordering,
119 : * and avoid setting discard on both points.
120 : */
121 0 : if (cmp < 0 || (cmp == 0 && a->id < b->id)) {
122 0 : a->discard = 1;
123 0 : ret = -1;
124 : } else {
125 0 : b->discard = 1;
126 0 : ret = 1;
127 : }
128 : }
129 :
130 0 : return ret;
131 : }
132 :
133 : static int
134 0 : _cairo_hull_prev_valid (cairo_hull_t *hull, int num_hull, int index)
135 : {
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). */
139 0 : if (index == 0)
140 0 : return 0;
141 :
142 : do {
143 0 : index--;
144 0 : } while (hull[index].discard);
145 :
146 0 : return index;
147 : }
148 :
149 : static int
150 0 : _cairo_hull_next_valid (cairo_hull_t *hull, int num_hull, int index)
151 : {
152 : do {
153 0 : index = (index + 1) % num_hull;
154 0 : } while (hull[index].discard);
155 :
156 0 : return index;
157 : }
158 :
159 : static void
160 0 : _cairo_hull_eliminate_concave (cairo_hull_t *hull, int num_hull)
161 : {
162 : int i, j, k;
163 : cairo_slope_t slope_ij, slope_jk;
164 :
165 0 : i = 0;
166 0 : j = _cairo_hull_next_valid (hull, num_hull, i);
167 0 : k = _cairo_hull_next_valid (hull, num_hull, j);
168 :
169 : do {
170 0 : _cairo_slope_init (&slope_ij, &hull[i].point, &hull[j].point);
171 0 : _cairo_slope_init (&slope_jk, &hull[j].point, &hull[k].point);
172 :
173 : /* Is the angle formed by ij and jk concave? */
174 0 : if (_cairo_slope_compare (&slope_ij, &slope_jk) >= 0) {
175 0 : if (i == k)
176 0 : return;
177 0 : hull[j].discard = 1;
178 0 : j = i;
179 0 : i = _cairo_hull_prev_valid (hull, num_hull, j);
180 : } else {
181 0 : i = j;
182 0 : j = k;
183 0 : k = _cairo_hull_next_valid (hull, num_hull, j);
184 : }
185 0 : } while (j != 0);
186 : }
187 :
188 : static void
189 0 : _cairo_hull_to_pen (cairo_hull_t *hull, cairo_pen_vertex_t *vertices, int *num_vertices)
190 : {
191 0 : int i, j = 0;
192 :
193 0 : for (i = 0; i < *num_vertices; i++) {
194 0 : if (hull[i].discard)
195 0 : continue;
196 0 : vertices[j++].point = hull[i].point;
197 : }
198 :
199 0 : *num_vertices = j;
200 0 : }
201 :
202 : /* Given a set of vertices, compute the convex hull using the Graham
203 : scan algorithm. */
204 : cairo_status_t
205 0 : _cairo_hull_compute (cairo_pen_vertex_t *vertices, int *num_vertices)
206 : {
207 : cairo_hull_t hull_stack[CAIRO_STACK_ARRAY_LENGTH (cairo_hull_t)];
208 : cairo_hull_t *hull;
209 0 : int num_hull = *num_vertices;
210 :
211 : if (CAIRO_INJECT_FAULT ())
212 : return _cairo_error (CAIRO_STATUS_NO_MEMORY);
213 :
214 0 : if (num_hull > ARRAY_LENGTH (hull_stack)) {
215 0 : hull = _cairo_malloc_ab (num_hull, sizeof (cairo_hull_t));
216 0 : if (unlikely (hull == NULL))
217 0 : return _cairo_error (CAIRO_STATUS_NO_MEMORY);
218 : } else {
219 0 : hull = hull_stack;
220 : }
221 :
222 0 : _cairo_hull_init (hull, vertices, num_hull);
223 :
224 0 : qsort (hull + 1, num_hull - 1,
225 : sizeof (cairo_hull_t), _cairo_hull_vertex_compare);
226 :
227 0 : _cairo_hull_eliminate_concave (hull, num_hull);
228 :
229 0 : _cairo_hull_to_pen (hull, vertices, num_vertices);
230 :
231 0 : if (hull != hull_stack)
232 0 : free (hull);
233 :
234 0 : return CAIRO_STATUS_SUCCESS;
235 : }
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