403 lines
15 KiB
C#
403 lines
15 KiB
C#
/*
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* C# Version Ported by Matt Bettcher and Ian Qvist 2009-2010
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*
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* Original C++ Version Copyright (c) 2007 Eric Jordan
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*
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* This software is provided 'as-is', without any express or implied
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* warranty. In no event will the authors be held liable for any damages
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* arising from the use of this software.
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* Permission is granted to anyone to use this software for any purpose,
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* including commercial applications, and to alter it and redistribute it
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* freely, subject to the following restrictions:
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* 1. The origin of this software must not be misrepresented; you must not
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* claim that you wrote the original software. If you use this software
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* in a product, an acknowledgment in the product documentation would be
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* appreciated but is not required.
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* 2. Altered source versions must be plainly marked as such, and must not be
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* misrepresented as being the original software.
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* 3. This notice may not be removed or altered from any source distribution.
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*/
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using System;
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using System.Collections.Generic;
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using System.Diagnostics;
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using Microsoft.Xna.Framework;
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namespace FarseerPhysics.Common.Decomposition
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{
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/// <summary>
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/// Convex decomposition algorithm using ear clipping
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///
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/// Properties:
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/// - Only works on simple polygons.
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/// - Does not support holes.
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/// - Running time is O(n^2), n = number of vertices.
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///
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/// Source: http://www.ewjordan.com/earClip/
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/// </summary>
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internal static class EarclipDecomposer
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{
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//box2D rev 32 - for details, see http://www.box2d.org/forum/viewtopic.php?f=4&t=83&start=50
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/// <summary>
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/// Decompose the polygon into several smaller non-concave polygon.
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/// Each resulting polygon will have no more than Settings.MaxPolygonVertices vertices.
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/// </summary>
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/// <param name="vertices">The vertices.</param>
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/// <param name="tolerance">The tolerance.</param>
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public static List<Vertices> ConvexPartition(Vertices vertices, float tolerance = 0.001f)
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{
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Debug.Assert(vertices.Count > 3);
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Debug.Assert(!vertices.IsCounterClockWise());
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return TriangulatePolygon(vertices, tolerance);
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}
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/// <summary>
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/// Triangulates a polygon using simple ear-clipping algorithm. Returns
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/// size of Triangle array unless the polygon can't be triangulated.
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/// This should only happen if the polygon self-intersects,
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/// though it will not _always_ return null for a bad polygon - it is the
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/// caller's responsibility to check for self-intersection, and if it
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/// doesn't, it should at least check that the return value is non-null
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/// before using. You're warned!
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///
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/// Triangles may be degenerate, especially if you have identical points
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/// in the input to the algorithm. Check this before you use them.
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///
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/// This is totally unoptimized, so for large polygons it should not be part
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/// of the simulation loop.
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/// </summary>
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/// <remarks>
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/// Only works on simple polygons.
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/// </remarks>
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private static List<Vertices> TriangulatePolygon(Vertices vertices, float tolerance)
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{
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//FPE note: Check is needed as invalid triangles can be returned in recursive calls.
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if (vertices.Count < 3)
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return new List<Vertices>();
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List<Vertices> results = new List<Vertices>();
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//Recurse and split on pinch points
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Vertices pA, pB;
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Vertices pin = new Vertices(vertices);
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if (ResolvePinchPoint(pin, out pA, out pB, tolerance))
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{
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List<Vertices> mergeA = TriangulatePolygon(pA, tolerance);
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List<Vertices> mergeB = TriangulatePolygon(pB, tolerance);
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if (mergeA.Count == -1 || mergeB.Count == -1)
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throw new Exception("Can't triangulate your polygon.");
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for (int i = 0; i < mergeA.Count; ++i)
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{
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results.Add(new Vertices(mergeA[i]));
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}
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for (int i = 0; i < mergeB.Count; ++i)
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{
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results.Add(new Vertices(mergeB[i]));
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}
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return results;
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}
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Vertices[] buffer = new Vertices[vertices.Count - 2];
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int bufferSize = 0;
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float[] xrem = new float[vertices.Count];
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float[] yrem = new float[vertices.Count];
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for (int i = 0; i < vertices.Count; ++i)
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{
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xrem[i] = vertices[i].X;
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yrem[i] = vertices[i].Y;
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}
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int vNum = vertices.Count;
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while (vNum > 3)
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{
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// Find an ear
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int earIndex = -1;
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float earMaxMinCross = -10.0f;
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for (int i = 0; i < vNum; ++i)
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{
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if (IsEar(i, xrem, yrem, vNum))
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{
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int lower = Remainder(i - 1, vNum);
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int upper = Remainder(i + 1, vNum);
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Vector2 d1 = new Vector2(xrem[upper] - xrem[i], yrem[upper] - yrem[i]);
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Vector2 d2 = new Vector2(xrem[i] - xrem[lower], yrem[i] - yrem[lower]);
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Vector2 d3 = new Vector2(xrem[lower] - xrem[upper], yrem[lower] - yrem[upper]);
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d1.Normalize();
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d2.Normalize();
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d3.Normalize();
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float cross12;
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MathUtils.Cross(ref d1, ref d2, out cross12);
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cross12 = Math.Abs(cross12);
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float cross23;
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MathUtils.Cross(ref d2, ref d3, out cross23);
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cross23 = Math.Abs(cross23);
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float cross31;
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MathUtils.Cross(ref d3, ref d1, out cross31);
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cross31 = Math.Abs(cross31);
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//Find the maximum minimum angle
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float minCross = Math.Min(cross12, Math.Min(cross23, cross31));
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if (minCross > earMaxMinCross)
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{
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earIndex = i;
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earMaxMinCross = minCross;
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}
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}
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}
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// If we still haven't found an ear, we're screwed.
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// Note: sometimes this is happening because the
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// remaining points are collinear. Really these
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// should just be thrown out without halting triangulation.
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if (earIndex == -1)
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{
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for (int i = 0; i < bufferSize; i++)
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{
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results.Add(buffer[i]);
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}
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return results;
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}
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// Clip off the ear:
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// - remove the ear tip from the list
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--vNum;
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float[] newx = new float[vNum];
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float[] newy = new float[vNum];
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int currDest = 0;
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for (int i = 0; i < vNum; ++i)
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{
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if (currDest == earIndex) ++currDest;
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newx[i] = xrem[currDest];
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newy[i] = yrem[currDest];
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++currDest;
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}
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// - add the clipped triangle to the triangle list
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int under = (earIndex == 0) ? (vNum) : (earIndex - 1);
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int over = (earIndex == vNum) ? 0 : (earIndex + 1);
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Triangle toAdd = new Triangle(xrem[earIndex], yrem[earIndex], xrem[over], yrem[over], xrem[under],
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yrem[under]);
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buffer[bufferSize] = toAdd;
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++bufferSize;
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// - replace the old list with the new one
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xrem = newx;
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yrem = newy;
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}
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Triangle tooAdd = new Triangle(xrem[1], yrem[1], xrem[2], yrem[2], xrem[0], yrem[0]);
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buffer[bufferSize] = tooAdd;
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++bufferSize;
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for (int i = 0; i < bufferSize; i++)
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{
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results.Add(new Vertices(buffer[i]));
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}
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return results;
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}
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/// <summary>
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/// Finds and fixes "pinch points," points where two polygon
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/// vertices are at the same point.
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///
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/// If a pinch point is found, pin is broken up into poutA and poutB
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/// and true is returned; otherwise, returns false.
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///
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/// Mostly for internal use.
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///
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/// O(N^2) time, which sucks...
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/// </summary>
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/// <param name="pin">The pin.</param>
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/// <param name="poutA">The pout A.</param>
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/// <param name="poutB">The pout B.</param>
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/// <param name="tolerance"></param>
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private static bool ResolvePinchPoint(Vertices pin, out Vertices poutA, out Vertices poutB, float tolerance)
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{
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poutA = new Vertices();
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poutB = new Vertices();
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if (pin.Count < 3)
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return false;
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bool hasPinchPoint = false;
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int pinchIndexA = -1;
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int pinchIndexB = -1;
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for (int i = 0; i < pin.Count; ++i)
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{
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for (int j = i + 1; j < pin.Count; ++j)
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{
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//Don't worry about pinch points where the points
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//are actually just dupe neighbors
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if (Math.Abs(pin[i].X - pin[j].X) < tolerance && Math.Abs(pin[i].Y - pin[j].Y) < tolerance && j != i + 1)
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{
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pinchIndexA = i;
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pinchIndexB = j;
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hasPinchPoint = true;
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break;
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}
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}
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if (hasPinchPoint) break;
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}
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if (hasPinchPoint)
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{
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int sizeA = pinchIndexB - pinchIndexA;
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if (sizeA == pin.Count) return false; //has dupe points at wraparound, not a problem here
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for (int i = 0; i < sizeA; ++i)
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{
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int ind = Remainder(pinchIndexA + i, pin.Count); // is this right
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poutA.Add(pin[ind]);
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}
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int sizeB = pin.Count - sizeA;
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for (int i = 0; i < sizeB; ++i)
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{
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int ind = Remainder(pinchIndexB + i, pin.Count); // is this right
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poutB.Add(pin[ind]);
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}
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}
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return hasPinchPoint;
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}
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/// <summary>
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/// Fix for obnoxious behavior for the % operator for negative numbers...
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/// </summary>
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/// <param name="x">The x.</param>
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/// <param name="modulus">The modulus.</param>
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/// <returns></returns>
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private static int Remainder(int x, int modulus)
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{
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int rem = x % modulus;
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while (rem < 0)
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{
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rem += modulus;
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}
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return rem;
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}
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/// <summary>
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/// Checks if vertex i is the tip of an ear in polygon defined by xv[] and yv[].
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/// </summary>
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/// <param name="i">The i.</param>
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/// <param name="xv">The xv.</param>
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/// <param name="yv">The yv.</param>
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/// <param name="xvLength">Length of the xv.</param>
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/// <remarks>
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/// Assumes clockwise orientation of polygon.
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/// </remarks>
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/// <returns>
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/// <c>true</c> if the specified i is ear; otherwise, <c>false</c>.
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/// </returns>
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private static bool IsEar(int i, float[] xv, float[] yv, int xvLength)
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{
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float dx0, dy0, dx1, dy1;
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if (i >= xvLength || i < 0 || xvLength < 3)
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{
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return false;
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}
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int upper = i + 1;
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int lower = i - 1;
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if (i == 0)
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{
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dx0 = xv[0] - xv[xvLength - 1];
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dy0 = yv[0] - yv[xvLength - 1];
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dx1 = xv[1] - xv[0];
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dy1 = yv[1] - yv[0];
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lower = xvLength - 1;
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}
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else if (i == xvLength - 1)
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{
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dx0 = xv[i] - xv[i - 1];
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dy0 = yv[i] - yv[i - 1];
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dx1 = xv[0] - xv[i];
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dy1 = yv[0] - yv[i];
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upper = 0;
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}
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else
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{
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dx0 = xv[i] - xv[i - 1];
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dy0 = yv[i] - yv[i - 1];
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dx1 = xv[i + 1] - xv[i];
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dy1 = yv[i + 1] - yv[i];
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}
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float cross = dx0 * dy1 - dx1 * dy0;
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if (cross > 0)
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return false;
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Triangle myTri = new Triangle(xv[i], yv[i], xv[upper], yv[upper], xv[lower], yv[lower]);
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for (int j = 0; j < xvLength; ++j)
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{
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if (j == i || j == lower || j == upper)
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continue;
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if (myTri.IsInside(xv[j], yv[j]))
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return false;
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}
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return true;
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}
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private class Triangle : Vertices
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{
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//Constructor automatically fixes orientation to ccw
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public Triangle(float x1, float y1, float x2, float y2, float x3, float y3)
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{
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float cross = (x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1);
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if (cross > 0)
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{
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Add(new Vector2(x1, y1));
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Add(new Vector2(x2, y2));
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Add(new Vector2(x3, y3));
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}
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else
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{
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Add(new Vector2(x1, y1));
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Add(new Vector2(x3, y3));
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Add(new Vector2(x2, y2));
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}
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}
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public bool IsInside(float x, float y)
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{
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Vector2 a = this[0];
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Vector2 b = this[1];
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Vector2 c = this[2];
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if (x < a.X && x < b.X && x < c.X) return false;
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if (x > a.X && x > b.X && x > c.X) return false;
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if (y < a.Y && y < b.Y && y < c.Y) return false;
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if (y > a.Y && y > b.Y && y > c.Y) return false;
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float vx2 = x - a.X;
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float vy2 = y - a.Y;
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float vx1 = b.X - a.X;
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float vy1 = b.Y - a.Y;
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float vx0 = c.X - a.X;
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float vy0 = c.Y - a.Y;
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float dot00 = vx0 * vx0 + vy0 * vy0;
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float dot01 = vx0 * vx1 + vy0 * vy1;
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float dot02 = vx0 * vx2 + vy0 * vy2;
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float dot11 = vx1 * vx1 + vy1 * vy1;
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float dot12 = vx1 * vx2 + vy1 * vy2;
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float invDenom = 1.0f / (dot00 * dot11 - dot01 * dot01);
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float u = (dot11 * dot02 - dot01 * dot12) * invDenom;
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float v = (dot00 * dot12 - dot01 * dot02) * invDenom;
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return ((u > 0) && (v > 0) && (u + v < 1));
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}
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}
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}
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} |