143 lines
4.8 KiB
C#
143 lines
4.8 KiB
C#
using System.Collections.Generic;
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using Microsoft.Xna.Framework;
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namespace FarseerPhysics.Common.ConvexHull
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{
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/// <summary>
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/// Andrew's Monotone Chain Convex Hull algorithm.
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/// Used to get the convex hull of a point cloud.
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///
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/// Source: http://www.softsurfer.com/Archive/algorithm_0109/algorithm_0109.htm
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/// </summary>
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public static class ChainHull
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{
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//Copyright 2001, softSurfer (www.softsurfer.com)
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private static PointComparer _pointComparer = new PointComparer();
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/// <summary>
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/// Returns the convex hull from the given vertices..
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/// </summary>
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public static Vertices GetConvexHull(Vertices vertices)
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{
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if (vertices.Count <= 3)
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return vertices;
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Vertices pointSet = new Vertices(vertices);
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//Sort by X-axis
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pointSet.Sort(_pointComparer);
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Vector2[] h = new Vector2[pointSet.Count];
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Vertices res;
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int top = -1; // indices for bottom and top of the stack
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int i; // array scan index
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// Get the indices of points with min x-coord and min|max y-coord
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const int minmin = 0;
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float xmin = pointSet[0].X;
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for (i = 1; i < pointSet.Count; i++)
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{
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if (pointSet[i].X != xmin)
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break;
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}
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// degenerate case: all x-coords == xmin
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int minmax = i - 1;
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if (minmax == pointSet.Count - 1)
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{
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h[++top] = pointSet[minmin];
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if (pointSet[minmax].Y != pointSet[minmin].Y) // a nontrivial segment
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h[++top] = pointSet[minmax];
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h[++top] = pointSet[minmin]; // add polygon endpoint
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res = new Vertices(top + 1);
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for (int j = 0; j < top + 1; j++)
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{
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res.Add(h[j]);
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}
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return res;
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}
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top = -1;
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// Get the indices of points with max x-coord and min|max y-coord
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int maxmax = pointSet.Count - 1;
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float xmax = pointSet[pointSet.Count - 1].X;
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for (i = pointSet.Count - 2; i >= 0; i--)
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{
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if (pointSet[i].X != xmax)
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break;
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}
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int maxmin = i + 1;
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// Compute the lower hull on the stack H
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h[++top] = pointSet[minmin]; // push minmin point onto stack
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i = minmax;
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while (++i <= maxmin)
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{
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// the lower line joins P[minmin] with P[maxmin]
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if (MathUtils.Area(pointSet[minmin], pointSet[maxmin], pointSet[i]) >= 0 && i < maxmin)
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continue; // ignore P[i] above or on the lower line
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while (top > 0) // there are at least 2 points on the stack
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{
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// test if P[i] is left of the line at the stack top
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if (MathUtils.Area(h[top - 1], h[top], pointSet[i]) > 0)
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break; // P[i] is a new hull vertex
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top--; // pop top point off stack
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}
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h[++top] = pointSet[i]; // push P[i] onto stack
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}
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// Next, compute the upper hull on the stack H above the bottom hull
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if (maxmax != maxmin) // if distinct xmax points
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h[++top] = pointSet[maxmax]; // push maxmax point onto stack
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int bot = top;
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i = maxmin;
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while (--i >= minmax)
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{
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// the upper line joins P[maxmax] with P[minmax]
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if (MathUtils.Area(pointSet[maxmax], pointSet[minmax], pointSet[i]) >= 0 && i > minmax)
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continue; // ignore P[i] below or on the upper line
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while (top > bot) // at least 2 points on the upper stack
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{
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// test if P[i] is left of the line at the stack top
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if (MathUtils.Area(h[top - 1], h[top], pointSet[i]) > 0)
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break; // P[i] is a new hull vertex
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top--; // pop top point off stack
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}
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h[++top] = pointSet[i]; // push P[i] onto stack
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}
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if (minmax != minmin)
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h[++top] = pointSet[minmin]; // push joining endpoint onto stack
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res = new Vertices(top + 1);
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for (int j = 0; j < top + 1; j++)
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{
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res.Add(h[j]);
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}
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return res;
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}
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private class PointComparer : Comparer<Vector2>
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{
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public override int Compare(Vector2 a, Vector2 b)
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{
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int f = a.X.CompareTo(b.X);
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return f != 0 ? f : a.Y.CompareTo(b.Y);
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}
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}
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}
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} |