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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
+ * 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"
+
+#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;
+}