253 lines
10 KiB
C#
253 lines
10 KiB
C#
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using System.Collections.Generic;
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using FarseerPhysics.Common.PolygonManipulation;
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using Microsoft.Xna.Framework;
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namespace FarseerPhysics.Common.Decomposition
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{
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//From phed rev 36
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/// <summary>
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/// Convex decomposition algorithm created by Mark Bayazit (http://mnbayazit.com/)
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/// For more information about this algorithm, see http://mnbayazit.com/406/bayazit
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/// </summary>
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public static class BayazitDecomposer
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{
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private static Vector2 At(int i, Vertices vertices)
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{
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int s = vertices.Count;
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return vertices[i < 0 ? s - (-i % s) : i % s];
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}
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private static Vertices Copy(int i, int j, Vertices vertices)
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{
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Vertices p = new Vertices();
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while (j < i) j += vertices.Count;
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//p.reserve(j - i + 1);
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for (; i <= j; ++i)
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{
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p.Add(At(i, vertices));
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}
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return p;
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}
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/// <summary>
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/// Decompose the polygon into several smaller non-concave polygon.
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/// If the polygon is already convex, it will return the original polygon, unless it is over Settings.MaxPolygonVertices.
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/// Precondition: Counter Clockwise polygon
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/// </summary>
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/// <param name="vertices"></param>
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/// <returns></returns>
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public static List<Vertices> ConvexPartition(Vertices vertices)
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{
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//We force it to CCW as it is a precondition in this algorithm.
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vertices.ForceCounterClockWise();
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List<Vertices> list = new List<Vertices>();
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float d, lowerDist, upperDist;
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Vector2 p;
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Vector2 lowerInt = new Vector2();
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Vector2 upperInt = new Vector2(); // intersection points
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int lowerIndex = 0, upperIndex = 0;
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Vertices lowerPoly, upperPoly;
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for (int i = 0; i < vertices.Count; ++i)
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{
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if (Reflex(i, vertices))
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{
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lowerDist = upperDist = float.MaxValue; // std::numeric_limits<qreal>::max();
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for (int j = 0; j < vertices.Count; ++j)
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{
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// if line intersects with an edge
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if (Left(At(i - 1, vertices), At(i, vertices), At(j, vertices)) &&
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RightOn(At(i - 1, vertices), At(i, vertices), At(j - 1, vertices)))
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{
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// find the point of intersection
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p = LineTools.LineIntersect(At(i - 1, vertices), At(i, vertices), At(j, vertices),
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At(j - 1, vertices));
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if (Right(At(i + 1, vertices), At(i, vertices), p))
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{
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// make sure it's inside the poly
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d = SquareDist(At(i, vertices), p);
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if (d < lowerDist)
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{
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// keep only the closest intersection
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lowerDist = d;
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lowerInt = p;
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lowerIndex = j;
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}
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}
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}
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if (Left(At(i + 1, vertices), At(i, vertices), At(j + 1, vertices)) &&
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RightOn(At(i + 1, vertices), At(i, vertices), At(j, vertices)))
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{
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p = LineTools.LineIntersect(At(i + 1, vertices), At(i, vertices), At(j, vertices),
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At(j + 1, vertices));
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if (Left(At(i - 1, vertices), At(i, vertices), p))
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{
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d = SquareDist(At(i, vertices), p);
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if (d < upperDist)
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{
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upperDist = d;
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upperIndex = j;
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upperInt = p;
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}
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}
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}
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}
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// if there are no vertices to connect to, choose a point in the middle
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if (lowerIndex == (upperIndex + 1) % vertices.Count)
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{
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Vector2 sp = ((lowerInt + upperInt) / 2);
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lowerPoly = Copy(i, upperIndex, vertices);
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lowerPoly.Add(sp);
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upperPoly = Copy(lowerIndex, i, vertices);
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upperPoly.Add(sp);
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}
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else
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{
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double highestScore = 0, bestIndex = lowerIndex;
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while (upperIndex < lowerIndex) upperIndex += vertices.Count;
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for (int j = lowerIndex; j <= upperIndex; ++j)
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{
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if (CanSee(i, j, vertices))
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{
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double score = 1 / (SquareDist(At(i, vertices), At(j, vertices)) + 1);
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if (Reflex(j, vertices))
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{
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if (RightOn(At(j - 1, vertices), At(j, vertices), At(i, vertices)) &&
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LeftOn(At(j + 1, vertices), At(j, vertices), At(i, vertices)))
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{
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score += 3;
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}
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else
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{
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score += 2;
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}
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}
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else
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{
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score += 1;
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}
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if (score > highestScore)
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{
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bestIndex = j;
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highestScore = score;
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}
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}
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}
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lowerPoly = Copy(i, (int)bestIndex, vertices);
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upperPoly = Copy((int)bestIndex, i, vertices);
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}
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list.AddRange(ConvexPartition(lowerPoly));
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list.AddRange(ConvexPartition(upperPoly));
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return list;
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}
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}
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// polygon is already convex
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if (vertices.Count > Settings.MaxPolygonVertices)
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{
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lowerPoly = Copy(0, vertices.Count / 2, vertices);
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upperPoly = Copy(vertices.Count / 2, 0, vertices);
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list.AddRange(ConvexPartition(lowerPoly));
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list.AddRange(ConvexPartition(upperPoly));
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}
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else
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list.Add(vertices);
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//The polygons are not guaranteed to be without collinear points. We remove
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//them to be sure.
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for (int i = 0; i < list.Count; i++)
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{
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list[i] = SimplifyTools.CollinearSimplify(list[i], 0);
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}
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//Remove empty vertice collections
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for (int i = list.Count - 1; i >= 0; i--)
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{
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if (list[i].Count == 0)
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list.RemoveAt(i);
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}
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return list;
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}
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private static bool CanSee(int i, int j, Vertices vertices)
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{
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if (Reflex(i, vertices))
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{
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if (LeftOn(At(i, vertices), At(i - 1, vertices), At(j, vertices)) &&
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RightOn(At(i, vertices), At(i + 1, vertices), At(j, vertices))) return false;
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}
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else
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{
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if (RightOn(At(i, vertices), At(i + 1, vertices), At(j, vertices)) ||
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LeftOn(At(i, vertices), At(i - 1, vertices), At(j, vertices))) return false;
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}
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if (Reflex(j, vertices))
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{
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if (LeftOn(At(j, vertices), At(j - 1, vertices), At(i, vertices)) &&
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RightOn(At(j, vertices), At(j + 1, vertices), At(i, vertices))) return false;
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}
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else
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{
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if (RightOn(At(j, vertices), At(j + 1, vertices), At(i, vertices)) ||
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LeftOn(At(j, vertices), At(j - 1, vertices), At(i, vertices))) return false;
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}
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for (int k = 0; k < vertices.Count; ++k)
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{
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if ((k + 1) % vertices.Count == i || k == i || (k + 1) % vertices.Count == j || k == j)
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{
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continue; // ignore incident edges
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}
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Vector2 intersectionPoint;
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if (LineTools.LineIntersect(At(i, vertices), At(j, vertices), At(k, vertices), At(k + 1, vertices), out intersectionPoint))
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{
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return false;
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}
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}
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return true;
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}
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// precondition: ccw
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private static bool Reflex(int i, Vertices vertices)
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{
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return Right(i, vertices);
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}
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private static bool Right(int i, Vertices vertices)
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{
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return Right(At(i - 1, vertices), At(i, vertices), At(i + 1, vertices));
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}
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private static bool Left(Vector2 a, Vector2 b, Vector2 c)
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{
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return MathUtils.Area(ref a, ref b, ref c) > 0;
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}
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private static bool LeftOn(Vector2 a, Vector2 b, Vector2 c)
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{
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return MathUtils.Area(ref a, ref b, ref c) >= 0;
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}
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private static bool Right(Vector2 a, Vector2 b, Vector2 c)
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{
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return MathUtils.Area(ref a, ref b, ref c) < 0;
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}
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private static bool RightOn(Vector2 a, Vector2 b, Vector2 c)
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{
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return MathUtils.Area(ref a, ref b, ref c) <= 0;
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}
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private static float SquareDist(Vector2 a, Vector2 b)
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{
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float dx = b.X - a.X;
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float dy = b.Y - a.Y;
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return dx * dx + dy * dy;
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}
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}
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}
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