500 lines
19 KiB
C#
500 lines
19 KiB
C#
/*
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* Farseer Physics Engine based on Box2D.XNA port:
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* Copyright (c) 2010 Ian Qvist
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*
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* Box2D.XNA port of Box2D:
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* Copyright (c) 2009 Brandon Furtwangler, Nathan Furtwangler
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*
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* Original source Box2D:
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* Copyright (c) 2006-2009 Erin Catto http://www.gphysics.com
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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.Diagnostics;
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using FarseerPhysics.Common;
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using Microsoft.Xna.Framework;
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namespace FarseerPhysics.Collision
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{
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/// <summary>
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/// Input parameters for CalculateTimeOfImpact
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/// </summary>
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public class TOIInput
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{
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public DistanceProxy ProxyA = new DistanceProxy();
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public DistanceProxy ProxyB = new DistanceProxy();
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public Sweep SweepA;
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public Sweep SweepB;
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public float TMax; // defines sweep interval [0, tMax]
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}
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public enum TOIOutputState
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{
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Unknown,
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Failed,
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Overlapped,
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Touching,
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Seperated,
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}
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public struct TOIOutput
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{
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public TOIOutputState State;
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public float T;
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}
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public enum SeparationFunctionType
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{
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Points,
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FaceA,
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FaceB
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}
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public static class SeparationFunction
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{
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private static Vector2 _axis;
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private static Vector2 _localPoint;
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private static DistanceProxy _proxyA = new DistanceProxy();
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private static DistanceProxy _proxyB = new DistanceProxy();
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private static Sweep _sweepA, _sweepB;
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private static SeparationFunctionType _type;
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public static void Set(ref SimplexCache cache,
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DistanceProxy proxyA, ref Sweep sweepA,
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DistanceProxy proxyB, ref Sweep sweepB,
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float t1)
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{
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_localPoint = Vector2.Zero;
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_proxyA = proxyA;
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_proxyB = proxyB;
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int count = cache.Count;
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Debug.Assert(0 < count && count < 3);
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_sweepA = sweepA;
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_sweepB = sweepB;
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Transform xfA, xfB;
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_sweepA.GetTransform(out xfA, t1);
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_sweepB.GetTransform(out xfB, t1);
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if (count == 1)
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{
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_type = SeparationFunctionType.Points;
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Vector2 localPointA = _proxyA.Vertices[cache.IndexA[0]];
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Vector2 localPointB = _proxyB.Vertices[cache.IndexB[0]];
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Vector2 pointA = MathUtils.Multiply(ref xfA, localPointA);
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Vector2 pointB = MathUtils.Multiply(ref xfB, localPointB);
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_axis = pointB - pointA;
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_axis.Normalize();
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return;
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}
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else if (cache.IndexA[0] == cache.IndexA[1])
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{
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// Two points on B and one on A.
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_type = SeparationFunctionType.FaceB;
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Vector2 localPointB1 = proxyB.Vertices[cache.IndexB[0]];
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Vector2 localPointB2 = proxyB.Vertices[cache.IndexB[1]];
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Vector2 a = localPointB2 - localPointB1;
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_axis = new Vector2(a.Y, -a.X);
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_axis.Normalize();
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Vector2 normal = MathUtils.Multiply(ref xfB.R, _axis);
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_localPoint = 0.5f * (localPointB1 + localPointB2);
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Vector2 pointB = MathUtils.Multiply(ref xfB, _localPoint);
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Vector2 localPointA = proxyA.Vertices[cache.IndexA[0]];
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Vector2 pointA = MathUtils.Multiply(ref xfA, localPointA);
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float s = Vector2.Dot(pointA - pointB, normal);
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if (s < 0.0f)
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{
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_axis = -_axis;
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s = -s;
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}
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return;
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}
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else
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{
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// Two points on A and one or two points on B.
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_type = SeparationFunctionType.FaceA;
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Vector2 localPointA1 = _proxyA.Vertices[cache.IndexA[0]];
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Vector2 localPointA2 = _proxyA.Vertices[cache.IndexA[1]];
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Vector2 a = localPointA2 - localPointA1;
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_axis = new Vector2(a.Y, -a.X);
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_axis.Normalize();
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Vector2 normal = MathUtils.Multiply(ref xfA.R, _axis);
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_localPoint = 0.5f * (localPointA1 + localPointA2);
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Vector2 pointA = MathUtils.Multiply(ref xfA, _localPoint);
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Vector2 localPointB = _proxyB.Vertices[cache.IndexB[0]];
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Vector2 pointB = MathUtils.Multiply(ref xfB, localPointB);
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float s = Vector2.Dot(pointB - pointA, normal);
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if (s < 0.0f)
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{
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_axis = -_axis;
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s = -s;
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}
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return;
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}
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}
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public static float FindMinSeparation(out int indexA, out int indexB, float t)
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{
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Transform xfA, xfB;
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_sweepA.GetTransform(out xfA, t);
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_sweepB.GetTransform(out xfB, t);
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switch (_type)
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{
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case SeparationFunctionType.Points:
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{
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Vector2 axisA = MathUtils.MultiplyT(ref xfA.R, _axis);
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Vector2 axisB = MathUtils.MultiplyT(ref xfB.R, -_axis);
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indexA = _proxyA.GetSupport(axisA);
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indexB = _proxyB.GetSupport(axisB);
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Vector2 localPointA = _proxyA.Vertices[indexA];
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Vector2 localPointB = _proxyB.Vertices[indexB];
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Vector2 pointA = MathUtils.Multiply(ref xfA, localPointA);
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Vector2 pointB = MathUtils.Multiply(ref xfB, localPointB);
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float separation = Vector2.Dot(pointB - pointA, _axis);
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return separation;
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}
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case SeparationFunctionType.FaceA:
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{
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Vector2 normal = MathUtils.Multiply(ref xfA.R, _axis);
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Vector2 pointA = MathUtils.Multiply(ref xfA, _localPoint);
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Vector2 axisB = MathUtils.MultiplyT(ref xfB.R, -normal);
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indexA = -1;
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indexB = _proxyB.GetSupport(axisB);
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Vector2 localPointB = _proxyB.Vertices[indexB];
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Vector2 pointB = MathUtils.Multiply(ref xfB, localPointB);
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float separation = Vector2.Dot(pointB - pointA, normal);
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return separation;
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}
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case SeparationFunctionType.FaceB:
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{
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Vector2 normal = MathUtils.Multiply(ref xfB.R, _axis);
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Vector2 pointB = MathUtils.Multiply(ref xfB, _localPoint);
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Vector2 axisA = MathUtils.MultiplyT(ref xfA.R, -normal);
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indexB = -1;
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indexA = _proxyA.GetSupport(axisA);
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Vector2 localPointA = _proxyA.Vertices[indexA];
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Vector2 pointA = MathUtils.Multiply(ref xfA, localPointA);
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float separation = Vector2.Dot(pointA - pointB, normal);
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return separation;
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}
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default:
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Debug.Assert(false);
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indexA = -1;
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indexB = -1;
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return 0.0f;
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}
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}
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public static float Evaluate(int indexA, int indexB, float t)
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{
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Transform xfA, xfB;
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_sweepA.GetTransform(out xfA, t);
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_sweepB.GetTransform(out xfB, t);
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switch (_type)
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{
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case SeparationFunctionType.Points:
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{
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Vector2 axisA = MathUtils.MultiplyT(ref xfA.R, _axis);
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Vector2 axisB = MathUtils.MultiplyT(ref xfB.R, -_axis);
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Vector2 localPointA = _proxyA.Vertices[indexA];
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Vector2 localPointB = _proxyB.Vertices[indexB];
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Vector2 pointA = MathUtils.Multiply(ref xfA, localPointA);
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Vector2 pointB = MathUtils.Multiply(ref xfB, localPointB);
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float separation = Vector2.Dot(pointB - pointA, _axis);
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return separation;
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}
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case SeparationFunctionType.FaceA:
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{
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Vector2 normal = MathUtils.Multiply(ref xfA.R, _axis);
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Vector2 pointA = MathUtils.Multiply(ref xfA, _localPoint);
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Vector2 axisB = MathUtils.MultiplyT(ref xfB.R, -normal);
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Vector2 localPointB = _proxyB.Vertices[indexB];
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Vector2 pointB = MathUtils.Multiply(ref xfB, localPointB);
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float separation = Vector2.Dot(pointB - pointA, normal);
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return separation;
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}
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case SeparationFunctionType.FaceB:
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{
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Vector2 normal = MathUtils.Multiply(ref xfB.R, _axis);
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Vector2 pointB = MathUtils.Multiply(ref xfB, _localPoint);
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Vector2 axisA = MathUtils.MultiplyT(ref xfA.R, -normal);
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Vector2 localPointA = _proxyA.Vertices[indexA];
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Vector2 pointA = MathUtils.Multiply(ref xfA, localPointA);
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float separation = Vector2.Dot(pointA - pointB, normal);
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return separation;
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}
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default:
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Debug.Assert(false);
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return 0.0f;
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}
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}
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}
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public static class TimeOfImpact
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{
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// CCD via the local separating axis method. This seeks progression
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// by computing the largest time at which separation is maintained.
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public static int TOICalls, TOIIters, TOIMaxIters;
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public static int TOIRootIters, TOIMaxRootIters;
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private static DistanceInput _distanceInput = new DistanceInput();
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/// <summary>
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/// Compute the upper bound on time before two shapes penetrate. Time is represented as
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/// a fraction between [0,tMax]. This uses a swept separating axis and may miss some intermediate,
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/// non-tunneling collision. If you change the time interval, you should call this function
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/// again.
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/// Note: use Distance() to compute the contact point and normal at the time of impact.
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/// </summary>
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/// <param name="output">The output.</param>
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/// <param name="input">The input.</param>
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public static void CalculateTimeOfImpact(out TOIOutput output, TOIInput input)
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{
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++TOICalls;
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output = new TOIOutput();
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output.State = TOIOutputState.Unknown;
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output.T = input.TMax;
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Sweep sweepA = input.SweepA;
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Sweep sweepB = input.SweepB;
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// Large rotations can make the root finder fail, so we normalize the
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// sweep angles.
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sweepA.Normalize();
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sweepB.Normalize();
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float tMax = input.TMax;
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float totalRadius = input.ProxyA.Radius + input.ProxyB.Radius;
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float target = Math.Max(Settings.LinearSlop, totalRadius - 3.0f * Settings.LinearSlop);
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const float tolerance = 0.25f * Settings.LinearSlop;
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Debug.Assert(target > tolerance);
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float t1 = 0.0f;
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const int k_maxIterations = 20;
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int iter = 0;
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// Prepare input for distance query.
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SimplexCache cache;
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_distanceInput.ProxyA = input.ProxyA;
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_distanceInput.ProxyB = input.ProxyB;
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_distanceInput.UseRadii = false;
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// The outer loop progressively attempts to compute new separating axes.
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// This loop terminates when an axis is repeated (no progress is made).
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for (; ; )
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{
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Transform xfA, xfB;
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sweepA.GetTransform(out xfA, t1);
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sweepB.GetTransform(out xfB, t1);
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// Get the distance between shapes. We can also use the results
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// to get a separating axis.
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_distanceInput.TransformA = xfA;
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_distanceInput.TransformB = xfB;
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DistanceOutput distanceOutput;
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Distance.ComputeDistance(out distanceOutput, out cache, _distanceInput);
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// If the shapes are overlapped, we give up on continuous collision.
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if (distanceOutput.Distance <= 0.0f)
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{
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// Failure!
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output.State = TOIOutputState.Overlapped;
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output.T = 0.0f;
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break;
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}
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if (distanceOutput.Distance < target + tolerance)
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{
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// Victory!
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output.State = TOIOutputState.Touching;
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output.T = t1;
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break;
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}
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SeparationFunction.Set(ref cache, input.ProxyA, ref sweepA, input.ProxyB, ref sweepB, t1);
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// Compute the TOI on the separating axis. We do this by successively
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// resolving the deepest point. This loop is bounded by the number of vertices.
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bool done = false;
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float t2 = tMax;
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int pushBackIter = 0;
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for (; ; )
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{
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// Find the deepest point at t2. Store the witness point indices.
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int indexA, indexB;
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float s2 = SeparationFunction.FindMinSeparation(out indexA, out indexB, t2);
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// Is the final configuration separated?
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if (s2 > target + tolerance)
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{
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// Victory!
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output.State = TOIOutputState.Seperated;
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output.T = tMax;
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done = true;
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break;
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}
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// Has the separation reached tolerance?
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if (s2 > target - tolerance)
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{
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// Advance the sweeps
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t1 = t2;
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break;
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}
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// Compute the initial separation of the witness points.
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float s1 = SeparationFunction.Evaluate(indexA, indexB, t1);
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// Check for initial overlap. This might happen if the root finder
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// runs out of iterations.
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if (s1 < target - tolerance)
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{
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output.State = TOIOutputState.Failed;
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output.T = t1;
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done = true;
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break;
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}
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// Check for touching
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if (s1 <= target + tolerance)
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{
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// Victory! t1 should hold the TOI (could be 0.0).
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output.State = TOIOutputState.Touching;
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output.T = t1;
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done = true;
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break;
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}
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// Compute 1D root of: f(x) - target = 0
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int rootIterCount = 0;
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float a1 = t1, a2 = t2;
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for (; ; )
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{
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// Use a mix of the secant rule and bisection.
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float t;
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if ((rootIterCount & 1) != 0)
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{
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// Secant rule to improve convergence.
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t = a1 + (target - s1) * (a2 - a1) / (s2 - s1);
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}
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else
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{
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// Bisection to guarantee progress.
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t = 0.5f * (a1 + a2);
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}
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float s = SeparationFunction.Evaluate(indexA, indexB, t);
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if (Math.Abs(s - target) < tolerance)
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{
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// t2 holds a tentative value for t1
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t2 = t;
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break;
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}
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// Ensure we continue to bracket the root.
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if (s > target)
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{
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a1 = t;
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s1 = s;
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}
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else
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{
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a2 = t;
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s2 = s;
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}
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++rootIterCount;
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++TOIRootIters;
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if (rootIterCount == 50)
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{
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break;
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}
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}
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TOIMaxRootIters = Math.Max(TOIMaxRootIters, rootIterCount);
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++pushBackIter;
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if (pushBackIter == Settings.MaxPolygonVertices)
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{
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break;
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}
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}
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++iter;
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++TOIIters;
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if (done)
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{
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break;
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}
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if (iter == k_maxIterations)
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{
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// Root finder got stuck. Semi-victory.
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output.State = TOIOutputState.Failed;
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output.T = t1;
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break;
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}
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}
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TOIMaxIters = Math.Max(TOIMaxIters, iter);
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}
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}
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} |