979 lines
38 KiB
C#
979 lines
38 KiB
C#
/*
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* Farseer Physics Engine:
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* Copyright (c) 2012 Ian Qvist
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*
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* Original source Box2D:
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* Copyright (c) 2006-2011 Erin Catto http://www.box2d.org
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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.Collision;
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using FarseerPhysics.Collision.Shapes;
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using FarseerPhysics.Common;
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using Microsoft.Xna.Framework;
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namespace FarseerPhysics.Dynamics.Contacts
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{
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public sealed class ContactPositionConstraint
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{
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public Vector2[] localPoints = new Vector2[Settings.MaxManifoldPoints];
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public Vector2 localNormal;
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public Vector2 localPoint;
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public int indexA;
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public int indexB;
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public float invMassA, invMassB;
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public Vector2 localCenterA, localCenterB;
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public float invIA, invIB;
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public ManifoldType type;
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public float radiusA, radiusB;
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public int pointCount;
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}
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public sealed class VelocityConstraintPoint
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{
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public Vector2 rA;
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public Vector2 rB;
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public float normalImpulse;
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public float tangentImpulse;
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public float normalMass;
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public float tangentMass;
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public float velocityBias;
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}
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public sealed class ContactVelocityConstraint
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{
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public VelocityConstraintPoint[] points = new VelocityConstraintPoint[Settings.MaxManifoldPoints];
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public Vector2 normal;
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public Mat22 normalMass;
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public Mat22 K;
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public int indexA;
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public int indexB;
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public float invMassA, invMassB;
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public float invIA, invIB;
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public float friction;
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public float restitution;
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public float tangentSpeed;
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public int pointCount;
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public int contactIndex;
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public ContactVelocityConstraint()
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{
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for (int i = 0; i < Settings.MaxManifoldPoints; i++)
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{
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points[i] = new VelocityConstraintPoint();
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}
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}
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}
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public class ContactSolver
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{
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public TimeStep _step;
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public Position[] _positions;
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public Velocity[] _velocities;
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public ContactPositionConstraint[] _positionConstraints;
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public ContactVelocityConstraint[] _velocityConstraints;
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public Contact[] _contacts;
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public int _count;
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public void Reset(TimeStep step, int count, Contact[] contacts, Position[] positions, Velocity[] velocities, bool warmstarting = Settings.EnableWarmstarting)
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{
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_step = step;
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_count = count;
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_positions = positions;
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_velocities = velocities;
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_contacts = contacts;
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// grow the array
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if (_velocityConstraints == null || _velocityConstraints.Length < count)
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{
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_velocityConstraints = new ContactVelocityConstraint[count * 2];
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_positionConstraints = new ContactPositionConstraint[count * 2];
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for (int i = 0; i < _velocityConstraints.Length; i++)
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{
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_velocityConstraints[i] = new ContactVelocityConstraint();
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}
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for (int i = 0; i < _positionConstraints.Length; i++)
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{
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_positionConstraints[i] = new ContactPositionConstraint();
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}
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}
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// Initialize position independent portions of the constraints.
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for (int i = 0; i < _count; ++i)
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{
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Contact contact = contacts[i];
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Fixture fixtureA = contact.FixtureA;
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Fixture fixtureB = contact.FixtureB;
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Shape shapeA = fixtureA.Shape;
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Shape shapeB = fixtureB.Shape;
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float radiusA = shapeA.Radius;
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float radiusB = shapeB.Radius;
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Body bodyA = fixtureA.Body;
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Body bodyB = fixtureB.Body;
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Manifold manifold = contact.Manifold;
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int pointCount = manifold.PointCount;
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Debug.Assert(pointCount > 0);
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ContactVelocityConstraint vc = _velocityConstraints[i];
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vc.friction = contact.Friction;
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vc.restitution = contact.Restitution;
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vc.tangentSpeed = contact.TangentSpeed;
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vc.indexA = bodyA.IslandIndex;
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vc.indexB = bodyB.IslandIndex;
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vc.invMassA = bodyA._invMass;
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vc.invMassB = bodyB._invMass;
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vc.invIA = bodyA._invI;
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vc.invIB = bodyB._invI;
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vc.contactIndex = i;
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vc.pointCount = pointCount;
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vc.K.SetZero();
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vc.normalMass.SetZero();
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ContactPositionConstraint pc = _positionConstraints[i];
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pc.indexA = bodyA.IslandIndex;
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pc.indexB = bodyB.IslandIndex;
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pc.invMassA = bodyA._invMass;
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pc.invMassB = bodyB._invMass;
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pc.localCenterA = bodyA._sweep.LocalCenter;
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pc.localCenterB = bodyB._sweep.LocalCenter;
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pc.invIA = bodyA._invI;
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pc.invIB = bodyB._invI;
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pc.localNormal = manifold.LocalNormal;
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pc.localPoint = manifold.LocalPoint;
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pc.pointCount = pointCount;
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pc.radiusA = radiusA;
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pc.radiusB = radiusB;
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pc.type = manifold.Type;
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for (int j = 0; j < pointCount; ++j)
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{
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ManifoldPoint cp = manifold.Points[j];
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VelocityConstraintPoint vcp = vc.points[j];
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if (Settings.EnableWarmstarting)
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{
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vcp.normalImpulse = _step.dtRatio * cp.NormalImpulse;
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vcp.tangentImpulse = _step.dtRatio * cp.TangentImpulse;
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}
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else
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{
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vcp.normalImpulse = 0.0f;
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vcp.tangentImpulse = 0.0f;
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}
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vcp.rA = Vector2.Zero;
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vcp.rB = Vector2.Zero;
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vcp.normalMass = 0.0f;
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vcp.tangentMass = 0.0f;
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vcp.velocityBias = 0.0f;
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pc.localPoints[j] = cp.LocalPoint;
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}
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}
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}
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public void InitializeVelocityConstraints()
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{
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for (int i = 0; i < _count; ++i)
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{
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ContactVelocityConstraint vc = _velocityConstraints[i];
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ContactPositionConstraint pc = _positionConstraints[i];
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float radiusA = pc.radiusA;
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float radiusB = pc.radiusB;
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Manifold manifold = _contacts[vc.contactIndex].Manifold;
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int indexA = vc.indexA;
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int indexB = vc.indexB;
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float mA = vc.invMassA;
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float mB = vc.invMassB;
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float iA = vc.invIA;
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float iB = vc.invIB;
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Vector2 localCenterA = pc.localCenterA;
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Vector2 localCenterB = pc.localCenterB;
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Vector2 cA = _positions[indexA].c;
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float aA = _positions[indexA].a;
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Vector2 vA = _velocities[indexA].v;
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float wA = _velocities[indexA].w;
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Vector2 cB = _positions[indexB].c;
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float aB = _positions[indexB].a;
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Vector2 vB = _velocities[indexB].v;
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float wB = _velocities[indexB].w;
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Debug.Assert(manifold.PointCount > 0);
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Transform xfA = new Transform();
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Transform xfB = new Transform();
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xfA.q.Set(aA);
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xfB.q.Set(aB);
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xfA.p = cA - MathUtils.Mul(xfA.q, localCenterA);
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xfB.p = cB - MathUtils.Mul(xfB.q, localCenterB);
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Vector2 normal;
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FixedArray2<Vector2> points;
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WorldManifold.Initialize(ref manifold, ref xfA, radiusA, ref xfB, radiusB, out normal, out points);
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vc.normal = normal;
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int pointCount = vc.pointCount;
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for (int j = 0; j < pointCount; ++j)
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{
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VelocityConstraintPoint vcp = vc.points[j];
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vcp.rA = points[j] - cA;
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vcp.rB = points[j] - cB;
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float rnA = MathUtils.Cross(vcp.rA, vc.normal);
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float rnB = MathUtils.Cross(vcp.rB, vc.normal);
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float kNormal = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
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vcp.normalMass = kNormal > 0.0f ? 1.0f / kNormal : 0.0f;
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Vector2 tangent = MathUtils.Cross(vc.normal, 1.0f);
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float rtA = MathUtils.Cross(vcp.rA, tangent);
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float rtB = MathUtils.Cross(vcp.rB, tangent);
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float kTangent = mA + mB + iA * rtA * rtA + iB * rtB * rtB;
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vcp.tangentMass = kTangent > 0.0f ? 1.0f / kTangent : 0.0f;
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// Setup a velocity bias for restitution.
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vcp.velocityBias = 0.0f;
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float vRel = Vector2.Dot(vc.normal, vB + MathUtils.Cross(wB, vcp.rB) - vA - MathUtils.Cross(wA, vcp.rA));
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if (vRel < -Settings.VelocityThreshold)
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{
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vcp.velocityBias = -vc.restitution * vRel;
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}
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}
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// If we have two points, then prepare the block solver.
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if (vc.pointCount == 2)
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{
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VelocityConstraintPoint vcp1 = vc.points[0];
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VelocityConstraintPoint vcp2 = vc.points[1];
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float rn1A = MathUtils.Cross(vcp1.rA, vc.normal);
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float rn1B = MathUtils.Cross(vcp1.rB, vc.normal);
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float rn2A = MathUtils.Cross(vcp2.rA, vc.normal);
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float rn2B = MathUtils.Cross(vcp2.rB, vc.normal);
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float k11 = mA + mB + iA * rn1A * rn1A + iB * rn1B * rn1B;
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float k22 = mA + mB + iA * rn2A * rn2A + iB * rn2B * rn2B;
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float k12 = mA + mB + iA * rn1A * rn2A + iB * rn1B * rn2B;
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// Ensure a reasonable condition number.
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const float k_maxConditionNumber = 1000.0f;
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if (k11 * k11 < k_maxConditionNumber * (k11 * k22 - k12 * k12))
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{
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// K is safe to invert.
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vc.K.ex = new Vector2(k11, k12);
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vc.K.ey = new Vector2(k12, k22);
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vc.normalMass = vc.K.Inverse;
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}
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else
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{
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// The constraints are redundant, just use one.
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// TODO_ERIN use deepest?
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vc.pointCount = 1;
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}
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}
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}
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}
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public void WarmStart()
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{
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// Warm start.
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for (int i = 0; i < _count; ++i)
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{
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ContactVelocityConstraint vc = _velocityConstraints[i];
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int indexA = vc.indexA;
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int indexB = vc.indexB;
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float mA = vc.invMassA;
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float iA = vc.invIA;
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float mB = vc.invMassB;
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float iB = vc.invIB;
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int pointCount = vc.pointCount;
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Vector2 vA = _velocities[indexA].v;
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float wA = _velocities[indexA].w;
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Vector2 vB = _velocities[indexB].v;
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float wB = _velocities[indexB].w;
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Vector2 normal = vc.normal;
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Vector2 tangent = MathUtils.Cross(normal, 1.0f);
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for (int j = 0; j < pointCount; ++j)
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{
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VelocityConstraintPoint vcp = vc.points[j];
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Vector2 P = vcp.normalImpulse * normal + vcp.tangentImpulse * tangent;
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wA -= iA * MathUtils.Cross(vcp.rA, P);
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vA -= mA * P;
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wB += iB * MathUtils.Cross(vcp.rB, P);
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vB += mB * P;
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}
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_velocities[indexA].v = vA;
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_velocities[indexA].w = wA;
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_velocities[indexB].v = vB;
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_velocities[indexB].w = wB;
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}
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}
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public void SolveVelocityConstraints()
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{
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for (int i = 0; i < _count; ++i)
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{
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ContactVelocityConstraint vc = _velocityConstraints[i];
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int indexA = vc.indexA;
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int indexB = vc.indexB;
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float mA = vc.invMassA;
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float iA = vc.invIA;
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float mB = vc.invMassB;
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float iB = vc.invIB;
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int pointCount = vc.pointCount;
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Vector2 vA = _velocities[indexA].v;
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float wA = _velocities[indexA].w;
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Vector2 vB = _velocities[indexB].v;
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float wB = _velocities[indexB].w;
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Vector2 normal = vc.normal;
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Vector2 tangent = MathUtils.Cross(normal, 1.0f);
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float friction = vc.friction;
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Debug.Assert(pointCount == 1 || pointCount == 2);
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// Solve tangent constraints first because non-penetration is more important
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// than friction.
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for (int j = 0; j < pointCount; ++j)
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{
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VelocityConstraintPoint vcp = vc.points[j];
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// Relative velocity at contact
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Vector2 dv = vB + MathUtils.Cross(wB, vcp.rB) - vA - MathUtils.Cross(wA, vcp.rA);
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// Compute tangent force
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float vt = Vector2.Dot(dv, tangent) - vc.tangentSpeed;
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float lambda = vcp.tangentMass * (-vt);
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// b2Clamp the accumulated force
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float maxFriction = friction * vcp.normalImpulse;
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float newImpulse = MathUtils.Clamp(vcp.tangentImpulse + lambda, -maxFriction, maxFriction);
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lambda = newImpulse - vcp.tangentImpulse;
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vcp.tangentImpulse = newImpulse;
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// Apply contact impulse
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Vector2 P = lambda * tangent;
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vA -= mA * P;
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wA -= iA * MathUtils.Cross(vcp.rA, P);
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vB += mB * P;
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wB += iB * MathUtils.Cross(vcp.rB, P);
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}
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// Solve normal constraints
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if (vc.pointCount == 1)
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{
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VelocityConstraintPoint vcp = vc.points[0];
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// Relative velocity at contact
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Vector2 dv = vB + MathUtils.Cross(wB, vcp.rB) - vA - MathUtils.Cross(wA, vcp.rA);
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// Compute normal impulse
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float vn = Vector2.Dot(dv, normal);
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float lambda = -vcp.normalMass * (vn - vcp.velocityBias);
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// b2Clamp the accumulated impulse
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float newImpulse = Math.Max(vcp.normalImpulse + lambda, 0.0f);
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lambda = newImpulse - vcp.normalImpulse;
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vcp.normalImpulse = newImpulse;
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// Apply contact impulse
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Vector2 P = lambda * normal;
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vA -= mA * P;
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wA -= iA * MathUtils.Cross(vcp.rA, P);
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vB += mB * P;
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wB += iB * MathUtils.Cross(vcp.rB, P);
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}
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else
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{
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// Block solver developed in collaboration with Dirk Gregorius (back in 01/07 on Box2D_Lite).
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// Build the mini LCP for this contact patch
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//
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// vn = A * x + b, vn >= 0, , vn >= 0, x >= 0 and vn_i * x_i = 0 with i = 1..2
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//
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// A = J * W * JT and J = ( -n, -r1 x n, n, r2 x n )
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// b = vn0 - velocityBias
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//
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// The system is solved using the "Total enumeration method" (s. Murty). The complementary constraint vn_i * x_i
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// implies that we must have in any solution either vn_i = 0 or x_i = 0. So for the 2D contact problem the cases
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// vn1 = 0 and vn2 = 0, x1 = 0 and x2 = 0, x1 = 0 and vn2 = 0, x2 = 0 and vn1 = 0 need to be tested. The first valid
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// solution that satisfies the problem is chosen.
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//
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// In order to account of the accumulated impulse 'a' (because of the iterative nature of the solver which only requires
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// that the accumulated impulse is clamped and not the incremental impulse) we change the impulse variable (x_i).
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//
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// Substitute:
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//
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// x = a + d
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//
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// a := old total impulse
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// x := new total impulse
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// d := incremental impulse
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//
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// For the current iteration we extend the formula for the incremental impulse
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// to compute the new total impulse:
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//
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// vn = A * d + b
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// = A * (x - a) + b
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// = A * x + b - A * a
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// = A * x + b'
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// b' = b - A * a;
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VelocityConstraintPoint cp1 = vc.points[0];
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VelocityConstraintPoint cp2 = vc.points[1];
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Vector2 a = new Vector2(cp1.normalImpulse, cp2.normalImpulse);
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Debug.Assert(a.X >= 0.0f && a.Y >= 0.0f);
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// Relative velocity at contact
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Vector2 dv1 = vB + MathUtils.Cross(wB, cp1.rB) - vA - MathUtils.Cross(wA, cp1.rA);
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Vector2 dv2 = vB + MathUtils.Cross(wB, cp2.rB) - vA - MathUtils.Cross(wA, cp2.rA);
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// Compute normal velocity
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float vn1 = Vector2.Dot(dv1, normal);
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float vn2 = Vector2.Dot(dv2, normal);
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Vector2 b = new Vector2();
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b.X = vn1 - cp1.velocityBias;
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b.Y = vn2 - cp2.velocityBias;
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// Compute b'
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b -= MathUtils.Mul(ref vc.K, a);
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const float k_errorTol = 1e-3f;
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//B2_NOT_USED(k_errorTol);
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for (; ; )
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{
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//
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// Case 1: vn = 0
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//
|
|
// 0 = A * x + b'
|
|
//
|
|
// Solve for x:
|
|
//
|
|
// x = - inv(A) * b'
|
|
//
|
|
Vector2 x = -MathUtils.Mul(ref vc.normalMass, b);
|
|
|
|
if (x.X >= 0.0f && x.Y >= 0.0f)
|
|
{
|
|
// Get the incremental impulse
|
|
Vector2 d = x - a;
|
|
|
|
// Apply incremental impulse
|
|
Vector2 P1 = d.X * normal;
|
|
Vector2 P2 = d.Y * normal;
|
|
vA -= mA * (P1 + P2);
|
|
wA -= iA * (MathUtils.Cross(cp1.rA, P1) + MathUtils.Cross(cp2.rA, P2));
|
|
|
|
vB += mB * (P1 + P2);
|
|
wB += iB * (MathUtils.Cross(cp1.rB, P1) + MathUtils.Cross(cp2.rB, P2));
|
|
|
|
// Accumulate
|
|
cp1.normalImpulse = x.X;
|
|
cp2.normalImpulse = x.Y;
|
|
|
|
#if B2_DEBUG_SOLVER
|
|
// Postconditions
|
|
dv1 = vB + MathUtils.Cross(wB, cp1.rB) - vA - MathUtils.Cross(wA, cp1.rA);
|
|
dv2 = vB + MathUtils.Cross(wB, cp2.rB) - vA - MathUtils.Cross(wA, cp2.rA);
|
|
|
|
// Compute normal velocity
|
|
vn1 = Vector2.Dot(dv1, normal);
|
|
vn2 = Vector2.Dot(dv2, normal);
|
|
|
|
b2Assert(b2Abs(vn1 - cp1.velocityBias) < k_errorTol);
|
|
b2Assert(b2Abs(vn2 - cp2.velocityBias) < k_errorTol);
|
|
#endif
|
|
break;
|
|
}
|
|
|
|
//
|
|
// Case 2: vn1 = 0 and x2 = 0
|
|
//
|
|
// 0 = a11 * x1 + a12 * 0 + b1'
|
|
// vn2 = a21 * x1 + a22 * 0 + b2'
|
|
//
|
|
x.X = -cp1.normalMass * b.X;
|
|
x.Y = 0.0f;
|
|
vn1 = 0.0f;
|
|
vn2 = vc.K.ex.Y * x.X + b.Y;
|
|
|
|
if (x.X >= 0.0f && vn2 >= 0.0f)
|
|
{
|
|
// Get the incremental impulse
|
|
Vector2 d = x - a;
|
|
|
|
// Apply incremental impulse
|
|
Vector2 P1 = d.X * normal;
|
|
Vector2 P2 = d.Y * normal;
|
|
vA -= mA * (P1 + P2);
|
|
wA -= iA * (MathUtils.Cross(cp1.rA, P1) + MathUtils.Cross(cp2.rA, P2));
|
|
|
|
vB += mB * (P1 + P2);
|
|
wB += iB * (MathUtils.Cross(cp1.rB, P1) + MathUtils.Cross(cp2.rB, P2));
|
|
|
|
// Accumulate
|
|
cp1.normalImpulse = x.X;
|
|
cp2.normalImpulse = x.Y;
|
|
|
|
#if B2_DEBUG_SOLVER
|
|
// Postconditions
|
|
dv1 = vB + MathUtils.Cross(wB, cp1.rB) - vA - MathUtils.Cross(wA, cp1.rA);
|
|
|
|
// Compute normal velocity
|
|
vn1 = Vector2.Dot(dv1, normal);
|
|
|
|
b2Assert(b2Abs(vn1 - cp1.velocityBias) < k_errorTol);
|
|
#endif
|
|
break;
|
|
}
|
|
|
|
|
|
//
|
|
// Case 3: vn2 = 0 and x1 = 0
|
|
//
|
|
// vn1 = a11 * 0 + a12 * x2 + b1'
|
|
// 0 = a21 * 0 + a22 * x2 + b2'
|
|
//
|
|
x.X = 0.0f;
|
|
x.Y = -cp2.normalMass * b.Y;
|
|
vn1 = vc.K.ey.X * x.Y + b.X;
|
|
vn2 = 0.0f;
|
|
|
|
if (x.Y >= 0.0f && vn1 >= 0.0f)
|
|
{
|
|
// Resubstitute for the incremental impulse
|
|
Vector2 d = x - a;
|
|
|
|
// Apply incremental impulse
|
|
Vector2 P1 = d.X * normal;
|
|
Vector2 P2 = d.Y * normal;
|
|
vA -= mA * (P1 + P2);
|
|
wA -= iA * (MathUtils.Cross(cp1.rA, P1) + MathUtils.Cross(cp2.rA, P2));
|
|
|
|
vB += mB * (P1 + P2);
|
|
wB += iB * (MathUtils.Cross(cp1.rB, P1) + MathUtils.Cross(cp2.rB, P2));
|
|
|
|
// Accumulate
|
|
cp1.normalImpulse = x.X;
|
|
cp2.normalImpulse = x.Y;
|
|
|
|
#if B2_DEBUG_SOLVER
|
|
// Postconditions
|
|
dv2 = vB + MathUtils.Cross(wB, cp2.rB) - vA - MathUtils.Cross(wA, cp2.rA);
|
|
|
|
// Compute normal velocity
|
|
vn2 = Vector2.Dot(dv2, normal);
|
|
|
|
b2Assert(b2Abs(vn2 - cp2.velocityBias) < k_errorTol);
|
|
#endif
|
|
break;
|
|
}
|
|
|
|
//
|
|
// Case 4: x1 = 0 and x2 = 0
|
|
//
|
|
// vn1 = b1
|
|
// vn2 = b2;
|
|
x.X = 0.0f;
|
|
x.Y = 0.0f;
|
|
vn1 = b.X;
|
|
vn2 = b.Y;
|
|
|
|
if (vn1 >= 0.0f && vn2 >= 0.0f)
|
|
{
|
|
// Resubstitute for the incremental impulse
|
|
Vector2 d = x - a;
|
|
|
|
// Apply incremental impulse
|
|
Vector2 P1 = d.X * normal;
|
|
Vector2 P2 = d.Y * normal;
|
|
vA -= mA * (P1 + P2);
|
|
wA -= iA * (MathUtils.Cross(cp1.rA, P1) + MathUtils.Cross(cp2.rA, P2));
|
|
|
|
vB += mB * (P1 + P2);
|
|
wB += iB * (MathUtils.Cross(cp1.rB, P1) + MathUtils.Cross(cp2.rB, P2));
|
|
|
|
// Accumulate
|
|
cp1.normalImpulse = x.X;
|
|
cp2.normalImpulse = x.Y;
|
|
|
|
break;
|
|
}
|
|
|
|
// No solution, give up. This is hit sometimes, but it doesn't seem to matter.
|
|
break;
|
|
}
|
|
}
|
|
|
|
_velocities[indexA].v = vA;
|
|
_velocities[indexA].w = wA;
|
|
_velocities[indexB].v = vB;
|
|
_velocities[indexB].w = wB;
|
|
}
|
|
}
|
|
|
|
public void StoreImpulses()
|
|
{
|
|
for (int i = 0; i < _count; ++i)
|
|
{
|
|
ContactVelocityConstraint vc = _velocityConstraints[i];
|
|
Manifold manifold = _contacts[vc.contactIndex].Manifold;
|
|
|
|
for (int j = 0; j < vc.pointCount; ++j)
|
|
{
|
|
ManifoldPoint point = manifold.Points[j];
|
|
point.NormalImpulse = vc.points[j].normalImpulse;
|
|
point.TangentImpulse = vc.points[j].tangentImpulse;
|
|
manifold.Points[j] = point;
|
|
}
|
|
|
|
_contacts[vc.contactIndex].Manifold = manifold;
|
|
}
|
|
}
|
|
|
|
public bool SolvePositionConstraints()
|
|
{
|
|
float minSeparation = 0.0f;
|
|
|
|
for (int i = 0; i < _count; ++i)
|
|
{
|
|
ContactPositionConstraint pc = _positionConstraints[i];
|
|
|
|
int indexA = pc.indexA;
|
|
int indexB = pc.indexB;
|
|
Vector2 localCenterA = pc.localCenterA;
|
|
float mA = pc.invMassA;
|
|
float iA = pc.invIA;
|
|
Vector2 localCenterB = pc.localCenterB;
|
|
float mB = pc.invMassB;
|
|
float iB = pc.invIB;
|
|
int pointCount = pc.pointCount;
|
|
|
|
Vector2 cA = _positions[indexA].c;
|
|
float aA = _positions[indexA].a;
|
|
|
|
Vector2 cB = _positions[indexB].c;
|
|
float aB = _positions[indexB].a;
|
|
|
|
// Solve normal constraints
|
|
for (int j = 0; j < pointCount; ++j)
|
|
{
|
|
Transform xfA = new Transform();
|
|
Transform xfB = new Transform();
|
|
xfA.q.Set(aA);
|
|
xfB.q.Set(aB);
|
|
xfA.p = cA - MathUtils.Mul(xfA.q, localCenterA);
|
|
xfB.p = cB - MathUtils.Mul(xfB.q, localCenterB);
|
|
|
|
Vector2 normal;
|
|
Vector2 point;
|
|
float separation;
|
|
|
|
PositionSolverManifold.Initialize(pc, xfA, xfB, j, out normal, out point, out separation);
|
|
|
|
Vector2 rA = point - cA;
|
|
Vector2 rB = point - cB;
|
|
|
|
// Track max constraint error.
|
|
minSeparation = Math.Min(minSeparation, separation);
|
|
|
|
// Prevent large corrections and allow slop.
|
|
float C = MathUtils.Clamp(Settings.Baumgarte * (separation + Settings.LinearSlop), -Settings.MaxLinearCorrection, 0.0f);
|
|
|
|
// Compute the effective mass.
|
|
float rnA = MathUtils.Cross(rA, normal);
|
|
float rnB = MathUtils.Cross(rB, normal);
|
|
float K = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
|
|
|
|
// Compute normal impulse
|
|
float impulse = K > 0.0f ? -C / K : 0.0f;
|
|
|
|
Vector2 P = impulse * normal;
|
|
|
|
cA -= mA * P;
|
|
aA -= iA * MathUtils.Cross(rA, P);
|
|
|
|
cB += mB * P;
|
|
aB += iB * MathUtils.Cross(rB, P);
|
|
}
|
|
|
|
_positions[indexA].c = cA;
|
|
_positions[indexA].a = aA;
|
|
|
|
_positions[indexB].c = cB;
|
|
_positions[indexB].a = aB;
|
|
}
|
|
|
|
// We can't expect minSpeparation >= -b2_linearSlop because we don't
|
|
// push the separation above -b2_linearSlop.
|
|
return minSeparation >= -3.0f * Settings.LinearSlop;
|
|
}
|
|
|
|
// Sequential position solver for position constraints.
|
|
public bool SolveTOIPositionConstraints(int toiIndexA, int toiIndexB)
|
|
{
|
|
float minSeparation = 0.0f;
|
|
|
|
for (int i = 0; i < _count; ++i)
|
|
{
|
|
ContactPositionConstraint pc = _positionConstraints[i];
|
|
|
|
int indexA = pc.indexA;
|
|
int indexB = pc.indexB;
|
|
Vector2 localCenterA = pc.localCenterA;
|
|
Vector2 localCenterB = pc.localCenterB;
|
|
int pointCount = pc.pointCount;
|
|
|
|
float mA = 0.0f;
|
|
float iA = 0.0f;
|
|
if (indexA == toiIndexA || indexA == toiIndexB)
|
|
{
|
|
mA = pc.invMassA;
|
|
iA = pc.invIA;
|
|
}
|
|
|
|
float mB = 0.0f;
|
|
float iB = 0.0f;
|
|
if (indexB == toiIndexA || indexB == toiIndexB)
|
|
{
|
|
mB = pc.invMassB;
|
|
iB = pc.invIB;
|
|
}
|
|
|
|
Vector2 cA = _positions[indexA].c;
|
|
float aA = _positions[indexA].a;
|
|
|
|
Vector2 cB = _positions[indexB].c;
|
|
float aB = _positions[indexB].a;
|
|
|
|
// Solve normal constraints
|
|
for (int j = 0; j < pointCount; ++j)
|
|
{
|
|
Transform xfA = new Transform();
|
|
Transform xfB = new Transform();
|
|
xfA.q.Set(aA);
|
|
xfB.q.Set(aB);
|
|
xfA.p = cA - MathUtils.Mul(xfA.q, localCenterA);
|
|
xfB.p = cB - MathUtils.Mul(xfB.q, localCenterB);
|
|
|
|
Vector2 normal;
|
|
Vector2 point;
|
|
float separation;
|
|
|
|
PositionSolverManifold.Initialize(pc, xfA, xfB, j, out normal, out point, out separation);
|
|
|
|
Vector2 rA = point - cA;
|
|
Vector2 rB = point - cB;
|
|
|
|
// Track max constraint error.
|
|
minSeparation = Math.Min(minSeparation, separation);
|
|
|
|
// Prevent large corrections and allow slop.
|
|
float C = MathUtils.Clamp(Settings.Baumgarte * (separation + Settings.LinearSlop), -Settings.MaxLinearCorrection, 0.0f);
|
|
|
|
// Compute the effective mass.
|
|
float rnA = MathUtils.Cross(rA, normal);
|
|
float rnB = MathUtils.Cross(rB, normal);
|
|
float K = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
|
|
|
|
// Compute normal impulse
|
|
float impulse = K > 0.0f ? -C / K : 0.0f;
|
|
|
|
Vector2 P = impulse * normal;
|
|
|
|
cA -= mA * P;
|
|
aA -= iA * MathUtils.Cross(rA, P);
|
|
|
|
cB += mB * P;
|
|
aB += iB * MathUtils.Cross(rB, P);
|
|
}
|
|
|
|
_positions[indexA].c = cA;
|
|
_positions[indexA].a = aA;
|
|
|
|
_positions[indexB].c = cB;
|
|
_positions[indexB].a = aB;
|
|
}
|
|
|
|
// We can't expect minSpeparation >= -b2_linearSlop because we don't
|
|
// push the separation above -b2_linearSlop.
|
|
return minSeparation >= -1.5f * Settings.LinearSlop;
|
|
}
|
|
|
|
public static class WorldManifold
|
|
{
|
|
/// <summary>
|
|
/// Evaluate the manifold with supplied transforms. This assumes
|
|
/// modest motion from the original state. This does not change the
|
|
/// point count, impulses, etc. The radii must come from the Shapes
|
|
/// that generated the manifold.
|
|
/// </summary>
|
|
/// <param name="manifold">The manifold.</param>
|
|
/// <param name="xfA">The transform for A.</param>
|
|
/// <param name="radiusA">The radius for A.</param>
|
|
/// <param name="xfB">The transform for B.</param>
|
|
/// <param name="radiusB">The radius for B.</param>
|
|
/// <param name="normal">World vector pointing from A to B</param>
|
|
/// <param name="points">Torld contact point (point of intersection).</param>
|
|
public static void Initialize(ref Manifold manifold, ref Transform xfA, float radiusA, ref Transform xfB, float radiusB, out Vector2 normal, out FixedArray2<Vector2> points)
|
|
{
|
|
normal = Vector2.Zero;
|
|
points = new FixedArray2<Vector2>();
|
|
|
|
if (manifold.PointCount == 0)
|
|
{
|
|
return;
|
|
}
|
|
|
|
switch (manifold.Type)
|
|
{
|
|
case ManifoldType.Circles:
|
|
{
|
|
normal = new Vector2(1.0f, 0.0f);
|
|
Vector2 pointA = MathUtils.Mul(ref xfA, manifold.LocalPoint);
|
|
Vector2 pointB = MathUtils.Mul(ref xfB, manifold.Points[0].LocalPoint);
|
|
if (Vector2.DistanceSquared(pointA, pointB) > Settings.Epsilon * Settings.Epsilon)
|
|
{
|
|
normal = pointB - pointA;
|
|
normal.Normalize();
|
|
}
|
|
|
|
Vector2 cA = pointA + radiusA * normal;
|
|
Vector2 cB = pointB - radiusB * normal;
|
|
points[0] = 0.5f * (cA + cB);
|
|
}
|
|
break;
|
|
|
|
case ManifoldType.FaceA:
|
|
{
|
|
normal = MathUtils.Mul(xfA.q, manifold.LocalNormal);
|
|
Vector2 planePoint = MathUtils.Mul(ref xfA, manifold.LocalPoint);
|
|
|
|
for (int i = 0; i < manifold.PointCount; ++i)
|
|
{
|
|
Vector2 clipPoint = MathUtils.Mul(ref xfB, manifold.Points[i].LocalPoint);
|
|
Vector2 cA = clipPoint + (radiusA - Vector2.Dot(clipPoint - planePoint, normal)) * normal;
|
|
Vector2 cB = clipPoint - radiusB * normal;
|
|
points[i] = 0.5f * (cA + cB);
|
|
}
|
|
}
|
|
break;
|
|
|
|
case ManifoldType.FaceB:
|
|
{
|
|
normal = MathUtils.Mul(xfB.q, manifold.LocalNormal);
|
|
Vector2 planePoint = MathUtils.Mul(ref xfB, manifold.LocalPoint);
|
|
|
|
for (int i = 0; i < manifold.PointCount; ++i)
|
|
{
|
|
Vector2 clipPoint = MathUtils.Mul(ref xfA, manifold.Points[i].LocalPoint);
|
|
Vector2 cB = clipPoint + (radiusB - Vector2.Dot(clipPoint - planePoint, normal)) * normal;
|
|
Vector2 cA = clipPoint - radiusA * normal;
|
|
points[i] = 0.5f * (cA + cB);
|
|
}
|
|
|
|
// Ensure normal points from A to B.
|
|
normal = -normal;
|
|
}
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
private static class PositionSolverManifold
|
|
{
|
|
public static void Initialize(ContactPositionConstraint pc, Transform xfA, Transform xfB, int index, out Vector2 normal, out Vector2 point, out float separation)
|
|
{
|
|
Debug.Assert(pc.pointCount > 0);
|
|
|
|
|
|
switch (pc.type)
|
|
{
|
|
case ManifoldType.Circles:
|
|
{
|
|
Vector2 pointA = MathUtils.Mul(ref xfA, pc.localPoint);
|
|
Vector2 pointB = MathUtils.Mul(ref xfB, pc.localPoints[0]);
|
|
normal = pointB - pointA;
|
|
normal.Normalize();
|
|
point = 0.5f * (pointA + pointB);
|
|
separation = Vector2.Dot(pointB - pointA, normal) - pc.radiusA - pc.radiusB;
|
|
}
|
|
break;
|
|
|
|
case ManifoldType.FaceA:
|
|
{
|
|
normal = MathUtils.Mul(xfA.q, pc.localNormal);
|
|
Vector2 planePoint = MathUtils.Mul(ref xfA, pc.localPoint);
|
|
|
|
Vector2 clipPoint = MathUtils.Mul(ref xfB, pc.localPoints[index]);
|
|
separation = Vector2.Dot(clipPoint - planePoint, normal) - pc.radiusA - pc.radiusB;
|
|
point = clipPoint;
|
|
}
|
|
break;
|
|
|
|
case ManifoldType.FaceB:
|
|
{
|
|
normal = MathUtils.Mul(xfB.q, pc.localNormal);
|
|
Vector2 planePoint = MathUtils.Mul(ref xfB, pc.localPoint);
|
|
|
|
Vector2 clipPoint = MathUtils.Mul(ref xfA, pc.localPoints[index]);
|
|
separation = Vector2.Dot(clipPoint - planePoint, normal) - pc.radiusA - pc.radiusB;
|
|
point = clipPoint;
|
|
|
|
// Ensure normal points from A to B
|
|
normal = -normal;
|
|
}
|
|
break;
|
|
default:
|
|
normal = Vector2.Zero;
|
|
point = Vector2.Zero;
|
|
separation = 0;
|
|
break;
|
|
|
|
}
|
|
}
|
|
}
|
|
}
|
|
} |