From 5dbe17cc125bf7d9e96b45c02bdfbd00b6103bdf Mon Sep 17 00:00:00 2001 From: Campbell Barton Date: Tue, 10 Sep 2013 07:52:10 +0000 Subject: add 2d convex hull utility function, BLI_convexhull_2d(), and python api mathutils.geometry.convex_hull_2d() uses Andrew's monotone chain 2D convex hull algorithm. --- source/blender/blenlib/intern/convexhull2d.c | 221 +++++++++++++++++++++++++++ 1 file changed, 221 insertions(+) create mode 100644 source/blender/blenlib/intern/convexhull2d.c (limited to 'source/blender/blenlib/intern/convexhull2d.c') diff --git a/source/blender/blenlib/intern/convexhull2d.c b/source/blender/blenlib/intern/convexhull2d.c new file mode 100644 index 00000000000..9909f470e02 --- /dev/null +++ b/source/blender/blenlib/intern/convexhull2d.c @@ -0,0 +1,221 @@ +/* + * ***** BEGIN GPL LICENSE BLOCK ***** + * + * This program is free software; you can redistribute it and/or + * modify it under the terms of the GNU General Public License + * as published by the Free Software Foundation; either version 2 + * of the License, or (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software Foundation, + * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. + * + * ***** END GPL LICENSE BLOCK ***** + */ + +#include +#include + +#include "MEM_guardedalloc.h" + +#include "BLI_convexhull2d.h" + +#include "BLI_strict_flags.h" + + +/* Copyright 2001, softSurfer (www.softsurfer.com) + * This code may be freely used and modified for any purpose + * providing that this copyright notice is included with it. + * SoftSurfer makes no warranty for this code, and cannot be held + * liable for any real or imagined damage resulting from its use. + * Users of this code must verify correctness for their application. + * http://softsurfer.com/Archive/algorithm_0203/algorithm_0203.htm + */ + +/** + * tests if a point is Left|On|Right of an infinite line. + * Input: three points P0, P1, and P2 + * \returns > 0.0 for P2 left of the line through P0 and P1. + * = 0.0 for P2 on the line. + * < 0.0 for P2 right of the line. + */ +static float is_left(const float p0[2], const float p1[2], const float p2[2]) +{ + return (p1[0] - p0[0]) * (p2[1] - p0[1]) - (p2[0] - p0[0]) * (p1[1] - p0[1]); +} + +/** + * A.M. Andrew's monotone chain 2D convex hull algorithm + * + * \param points An array of 2D points presorted by increasing x and y-coords. + * \param n The number of points in points. + * \param r_points An array of the convex hull vertex indices (max is n). + * \returns the number of points in r_points. + */ +int BLI_convexhull_2d_presorted(const float (*points)[2], const int n, int r_points[]) +{ + /* the output array r_points[] will be used as the stack */ + int bot = 0; + int top = -1; /* indices for bottom and top of the stack */ + int i; /* array scan index */ + int minmin, minmax; + int maxmin, maxmax; + float xmax; + + /* Get the indices of points with min x-coord and min|max y-coord */ + float xmin = points[0][0]; + for (i = 1; i < n; i++) { + if (points[i][0] != xmin) { + break; + } + } + + minmin = 0; + minmax = i - 1; + if (minmax == n - 1) { /* degenerate case: all x-coords == xmin */ + r_points[++top] = minmin; + if (points[minmax][1] != points[minmin][1]) /* a nontrivial segment */ + r_points[++top] = minmax; + r_points[++top] = minmin; /* add polygon endpoint */ + return top + 1; + } + + /* Get the indices of points with max x-coord and min|max y-coord */ + + maxmax = n - 1; + xmax = points[n - 1][0]; + for (i = n - 2; i >= 0; i--) { + if (points[i][0] != xmax) { + break; + } + } + maxmin = i + 1; + + /* Compute the lower hull on the stack r_points */ + r_points[++top] = minmin; /* push minmin point onto stack */ + i = minmax; + while (++i <= maxmin) { + /* the lower line joins points[minmin] with points[maxmin] */ + if (is_left(points[minmin], points[maxmin], points[i]) >= 0 && i < maxmin) { + continue; /* ignore points[i] above or on the lower line */ + } + + while (top > 0) { /* there are at least 2 points on the stack */ + /* test if points[i] is left of the line at the stack top */ + if (is_left(points[r_points[top - 1]], points[r_points[top]], points[i]) > 0.0f) { + break; /* points[i] is a new hull vertex */ + } + else { + top--; /* pop top point off stack */ + } + } + + r_points[++top] = i; /* push points[i] onto stack */ + } + + /* Next, compute the upper hull on the stack r_points above the bottom hull */ + if (maxmax != maxmin) { /* if distinct xmax points */ + r_points[++top] = maxmax; /* push maxmax point onto stack */ + } + + bot = top; /* the bottom point of the upper hull stack */ + i = maxmin; + while (--i >= minmax) { + /* the upper line joins points[maxmax] with points[minmax] */ + if (is_left(points[maxmax], points[minmax], points[i]) >= 0 && i > minmax) { + continue; /* ignore points[i] below or on the upper line */ + } + + while (top > bot) { /* at least 2 points on the upper stack */ + /* test if points[i] is left of the line at the stack top */ + if (is_left(points[r_points[top - 1]], points[r_points[top]], points[i]) > 0.0f) { + break; /* points[i] is a new hull vertex */ + } + else { + top--; /* pop top point off stack */ + } + } + + if (points[i][0] == points[r_points[0]][0] && points[i][1] == points[r_points[0]][1]) { + return top + 1; /* special case (mgomes) */ + } + + r_points[++top] = i; /* push points[i] onto stack */ + } + + if (minmax != minmin) { + r_points[++top] = minmin; /* push joining endpoint onto stack */ + } + + return top + 1; +} + +struct PointRef { + const float *pt; /* 2d vector */ +}; + +static int pointref_cmp_x(const void *a_, const void *b_) +{ + const struct PointRef *a = a_; + const struct PointRef *b = b_; + if (a->pt[0] > b->pt[0]) return 1; + else if (a->pt[0] < b->pt[0]) return -1; + else return 0; +} + +static int pointref_cmp_y(const void *a_, const void *b_) +{ + const struct PointRef *a = a_; + const struct PointRef *b = b_; + if (a->pt[1] > b->pt[1]) return 1; + else if (a->pt[1] < b->pt[1]) return -1; + else return 0; +} + +/** + * A.M. Andrew's monotone chain 2D convex hull algorithm + * + * \param points An array of 2D points. + * \param n The number of points in points. + * \param r_points An array of the convex hull vertex indices (max is n). + * \returns the number of points in r_points. + */ +int BLI_convexhull_2d(const float (*points)[2], const int n, int r_points[]) +{ + struct PointRef *points_ref = MEM_mallocN(sizeof(*points_ref) * (size_t)n, __func__); + float (*points_sort)[2] = MEM_mallocN(sizeof(*points_sort) * (size_t)n, __func__); + int *points_map; + int tot, i; + + for (i = 0; i < n; i++) { + points_ref[i].pt = points[i]; + } + + /* Sort the points by X, then by Y (required by the algorithm) */ + qsort(points_ref, (size_t)n, sizeof(struct PointRef), pointref_cmp_x); + qsort(points_ref, (size_t)n, sizeof(struct PointRef), pointref_cmp_y); + + for (i = 0; i < n; i++) { + memcpy(points_sort[i], points_ref[i].pt, sizeof(float[2])); + } + + tot = BLI_convexhull_2d_presorted((const float (*)[2])points_sort, n, r_points); + + /* map back to the original index values */ + points_map = (int *)points_sort; /* abuse float array for temp storage */ + for (i = 0; i < tot; i++) { + points_map[i] = (int)((const float(*)[2])points_ref[r_points[i]].pt - points); + } + + memcpy(r_points, points_map, (size_t)tot * sizeof(*points_map)); + + MEM_freeN(points_ref); + MEM_freeN(points_sort); + + return tot; +} -- cgit v1.2.3