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.

1 files changed, 221 insertions, 0 deletions

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 <stdlib.h>
+#include <string.h>
+
+#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;
+}