// Copyright (c) 2017 Kastellanos Nikolaos /* Original source Farseer Physics Engine: * Copyright (c) 2014 Ian Qvist, http://farseerphysics.codeplex.com * Microsoft Permissive License (Ms-PL) v1.1 */ /* * Farseer Physics Engine: * Copyright (c) 2012 Ian Qvist * * Original source Box2D: * Copyright (c) 2006-2011 Erin Catto http://www.box2d.org * * This software is provided 'as-is', without any express or implied * warranty. In no event will the authors be held liable for any damages * arising from the use of this software. * Permission is granted to anyone to use this software for any purpose, * including commercial applications, and to alter it and redistribute it * freely, subject to the following restrictions: * 1. The origin of this software must not be misrepresented; you must not * claim that you wrote the original software. If you use this software * in a product, an acknowledgment in the product documentation would be * appreciated but is not required. * 2. Altered source versions must be plainly marked as such, and must not be * misrepresented as being the original software. * 3. This notice may not be removed or altered from any source distribution. */ using System; using System.Diagnostics; using FarseerPhysics.Collision; using FarseerPhysics.Collision.Shapes; using FarseerPhysics.Common; using FarseerPhysics.Common.Maths; using Microsoft.Xna.Framework; #if NET40 || NET45 || PORTABLE40 || PORTABLE45 || W10 || W8_1 || WP8_1 using System.Threading; using System.Threading.Tasks; #endif namespace FarseerPhysics.Dynamics.Contacts { public sealed class ContactPositionConstraint { public Vector2[] localPoints = new Vector2[Settings.MaxManifoldPoints]; public Vector2 localNormal; public Vector2 localPoint; public int indexA; public int indexB; public float invMassA, invMassB; public Vector2 localCenterA, localCenterB; public float invIA, invIB; public ManifoldType type; public float radiusA, radiusB; public int pointCount; } public sealed class VelocityConstraintPoint { public Vector2 rA; public Vector2 rB; public float normalImpulse; public float tangentImpulse; public float normalMass; public float tangentMass; public float velocityBias; } public sealed class ContactVelocityConstraint { public VelocityConstraintPoint[] points = new VelocityConstraintPoint[Settings.MaxManifoldPoints]; public Vector2 normal; public Mat22 normalMass; public Mat22 K; public int indexA; public int indexB; public float invMassA, invMassB; public float invIA, invIB; public float friction; public float restitution; public float tangentSpeed; public int pointCount; public int contactIndex; public ContactVelocityConstraint() { for (int i = 0; i < Settings.MaxManifoldPoints; i++) { points[i] = new VelocityConstraintPoint(); } } } public class ContactSolver { public Position[] _positions; public Velocity[] _velocities; public ContactPositionConstraint[] _positionConstraints; public ContactVelocityConstraint[] _velocityConstraints; public Contact[] _contacts; public int _count; int _velocityConstraintsMultithreadThreshold; int _positionConstraintsMultithreadThreshold; public void Reset(ref TimeStep step, int count, Contact[] contacts, Position[] positions, Velocity[] velocities, int velocityConstraintsMultithreadThreshold, int positionConstraintsMultithreadThreshold) { _count = count; _positions = positions; _velocities = velocities; _contacts = contacts; _velocityConstraintsMultithreadThreshold = velocityConstraintsMultithreadThreshold; _positionConstraintsMultithreadThreshold = positionConstraintsMultithreadThreshold; // grow the array if (_velocityConstraints == null || _velocityConstraints.Length < count) { _velocityConstraints = new ContactVelocityConstraint[count * 2]; _positionConstraints = new ContactPositionConstraint[count * 2]; for (int i = 0; i < _velocityConstraints.Length; i++) { _velocityConstraints[i] = new ContactVelocityConstraint(); } for (int i = 0; i < _positionConstraints.Length; i++) { _positionConstraints[i] = new ContactPositionConstraint(); } } // Initialize position independent portions of the constraints. for (int i = 0; i < _count; ++i) { Contact contact = contacts[i]; Fixture fixtureA = contact.FixtureA; Fixture fixtureB = contact.FixtureB; Shape shapeA = fixtureA.Shape; Shape shapeB = fixtureB.Shape; float radiusA = shapeA.Radius; float radiusB = shapeB.Radius; Body bodyA = fixtureA.Body; Body bodyB = fixtureB.Body; Manifold manifold = contact.Manifold; int pointCount = manifold.PointCount; Debug.Assert(pointCount > 0); ContactVelocityConstraint vc = _velocityConstraints[i]; vc.friction = contact.Friction; vc.restitution = contact.Restitution; vc.tangentSpeed = contact.TangentSpeed; vc.indexA = bodyA.IslandIndex; vc.indexB = bodyB.IslandIndex; vc.invMassA = bodyA._invMass; vc.invMassB = bodyB._invMass; vc.invIA = bodyA._invI; vc.invIB = bodyB._invI; vc.contactIndex = i; vc.pointCount = pointCount; vc.K.SetZero(); vc.normalMass.SetZero(); ContactPositionConstraint pc = _positionConstraints[i]; pc.indexA = bodyA.IslandIndex; pc.indexB = bodyB.IslandIndex; pc.invMassA = bodyA._invMass; pc.invMassB = bodyB._invMass; pc.localCenterA = bodyA._sweep.LocalCenter; pc.localCenterB = bodyB._sweep.LocalCenter; pc.invIA = bodyA._invI; pc.invIB = bodyB._invI; pc.localNormal = manifold.LocalNormal; pc.localPoint = manifold.LocalPoint; pc.pointCount = pointCount; pc.radiusA = radiusA; pc.radiusB = radiusB; pc.type = manifold.Type; for (int j = 0; j < pointCount; ++j) { ManifoldPoint cp = manifold.Points[j]; VelocityConstraintPoint vcp = vc.points[j]; if (step.warmStarting) { vcp.normalImpulse = step.dtRatio * cp.NormalImpulse; vcp.tangentImpulse = step.dtRatio * cp.TangentImpulse; } else { vcp.normalImpulse = 0.0f; vcp.tangentImpulse = 0.0f; } vcp.rA = Vector2.Zero; vcp.rB = Vector2.Zero; vcp.normalMass = 0.0f; vcp.tangentMass = 0.0f; vcp.velocityBias = 0.0f; pc.localPoints[j] = cp.LocalPoint; } } } public void InitializeVelocityConstraints() { for (int i = 0; i < _count; ++i) { ContactVelocityConstraint vc = _velocityConstraints[i]; ContactPositionConstraint pc = _positionConstraints[i]; float radiusA = pc.radiusA; float radiusB = pc.radiusB; Manifold manifold = _contacts[vc.contactIndex].Manifold; int indexA = vc.indexA; int indexB = vc.indexB; float mA = vc.invMassA; float mB = vc.invMassB; float iA = vc.invIA; float iB = vc.invIB; Vector2 localCenterA = pc.localCenterA; Vector2 localCenterB = pc.localCenterB; Vector2 cA = _positions[indexA].c; float aA = _positions[indexA].a; Vector2 vA = _velocities[indexA].v; float wA = _velocities[indexA].w; Vector2 cB = _positions[indexB].c; float aB = _positions[indexB].a; Vector2 vB = _velocities[indexB].v; float wB = _velocities[indexB].w; Debug.Assert(manifold.PointCount > 0); Transform xfA = new Transform(Vector2.Zero, aA); Transform xfB = new Transform(Vector2.Zero, aB); xfA.p = cA - Complex.Multiply(ref localCenterA, ref xfA.q); xfB.p = cB - Complex.Multiply(ref localCenterB, ref xfB.q); Vector2 normal; FixedArray2 points; WorldManifold.Initialize(ref manifold, ref xfA, radiusA, ref xfB, radiusB, out normal, out points); vc.normal = normal; Vector2 tangent = MathUtils.Rot270(ref vc.normal); int pointCount = vc.pointCount; for (int j = 0; j < pointCount; ++j) { VelocityConstraintPoint vcp = vc.points[j]; vcp.rA = points[j] - cA; vcp.rB = points[j] - cB; float rnA = MathUtils.Cross(ref vcp.rA, ref vc.normal); float rnB = MathUtils.Cross(ref vcp.rB, ref vc.normal); float kNormal = mA + mB + iA * rnA * rnA + iB * rnB * rnB; vcp.normalMass = kNormal > 0.0f ? 1.0f / kNormal : 0.0f; float rtA = MathUtils.Cross(ref vcp.rA, ref tangent); float rtB = MathUtils.Cross(ref vcp.rB, ref tangent); float kTangent = mA + mB + iA * rtA * rtA + iB * rtB * rtB; vcp.tangentMass = kTangent > 0.0f ? 1.0f / kTangent : 0.0f; // Setup a velocity bias for restitution. vcp.velocityBias = 0.0f; float vRel = Vector2.Dot(vc.normal, vB + MathUtils.Cross(wB, ref vcp.rB) - vA - MathUtils.Cross(wA, ref vcp.rA)); if (vRel < -Settings.VelocityThreshold) { vcp.velocityBias = -vc.restitution * vRel; } } // If we have two points, then prepare the block solver. if (vc.pointCount == 2) { VelocityConstraintPoint vcp1 = vc.points[0]; VelocityConstraintPoint vcp2 = vc.points[1]; float rn1A = MathUtils.Cross(ref vcp1.rA, ref vc.normal); float rn1B = MathUtils.Cross(ref vcp1.rB, ref vc.normal); float rn2A = MathUtils.Cross(ref vcp2.rA, ref vc.normal); float rn2B = MathUtils.Cross(ref vcp2.rB, ref vc.normal); float k11 = mA + mB + iA * rn1A * rn1A + iB * rn1B * rn1B; float k22 = mA + mB + iA * rn2A * rn2A + iB * rn2B * rn2B; float k12 = mA + mB + iA * rn1A * rn2A + iB * rn1B * rn2B; // Ensure a reasonable condition number. const float k_maxConditionNumber = 1000.0f; if (k11 * k11 < k_maxConditionNumber * (k11 * k22 - k12 * k12)) { // K is safe to invert. vc.K.ex = new Vector2(k11, k12); vc.K.ey = new Vector2(k12, k22); vc.normalMass = vc.K.Inverse; } else { // The constraints are redundant, just use one. // TODO_ERIN use deepest? vc.pointCount = 1; } } } } public void WarmStart() { // Warm start. for (int i = 0; i < _count; ++i) { ContactVelocityConstraint vc = _velocityConstraints[i]; int indexA = vc.indexA; int indexB = vc.indexB; float mA = vc.invMassA; float iA = vc.invIA; float mB = vc.invMassB; float iB = vc.invIB; int pointCount = vc.pointCount; Vector2 vA = _velocities[indexA].v; float wA = _velocities[indexA].w; Vector2 vB = _velocities[indexB].v; float wB = _velocities[indexB].w; Vector2 normal = vc.normal; Vector2 tangent = MathUtils.Rot270(ref normal); for (int j = 0; j < pointCount; ++j) { VelocityConstraintPoint vcp = vc.points[j]; Vector2 P = vcp.normalImpulse * normal + vcp.tangentImpulse * tangent; wA -= iA * MathUtils.Cross(ref vcp.rA, ref P); vA -= mA * P; wB += iB * MathUtils.Cross(ref vcp.rB, ref P); vB += mB * P; } _velocities[indexA].v = vA; _velocities[indexA].w = wA; _velocities[indexB].v = vB; _velocities[indexB].w = wB; } } public void SolveVelocityConstraints() { if (_count >= _velocityConstraintsMultithreadThreshold && System.Environment.ProcessorCount > 1) { if (_count == 0) return; var batchSize = (int)Math.Ceiling((float)_count / System.Environment.ProcessorCount); var batches = (int)Math.Ceiling((float)_count / batchSize); #if NET40 || NET45 SolveVelocityConstraintsWaitLock.Reset(batches); for (int i = 0; i < batches; i++) { var start = i * batchSize; var end = Math.Min(start + batchSize, _count); ThreadPool.QueueUserWorkItem( SolveVelocityConstraintsCallback, SolveVelocityConstraintsState.Get(this, start,end)); } // We avoid SolveVelocityConstraintsWaitLock.Wait(); because it spins a few milliseconds before going into sleep. Going into sleep(0) directly in a while loop is faster. while (SolveVelocityConstraintsWaitLock.CurrentCount > 0) Thread.Sleep(0); #elif PORTABLE40 || PORTABLE45 || W10 || W8_1 || WP8_1 Parallel.For(0, batches, (i) => { var start = i * batchSize; var end = Math.Min(start + batchSize, _count); SolveVelocityConstraints(start, end); }); #else SolveVelocityConstraints(0, _count); #endif } else { SolveVelocityConstraints(0, _count); } return; } #if NET40 || NET45 CountdownEvent SolveVelocityConstraintsWaitLock = new CountdownEvent(0); static void SolveVelocityConstraintsCallback(object state) { var svcState = (SolveVelocityConstraintsState)state; svcState.ContactSolver.SolveVelocityConstraints(svcState.Start, svcState.End); SolveVelocityConstraintsState.Return(svcState); svcState.ContactSolver.SolveVelocityConstraintsWaitLock.Signal(); } private class SolveVelocityConstraintsState { private static System.Collections.Concurrent.ConcurrentQueue _queue = new System.Collections.Concurrent.ConcurrentQueue(); // pool public ContactSolver ContactSolver; public int Start { get; private set; } public int End { get; private set; } private SolveVelocityConstraintsState() { } internal static object Get(ContactSolver contactSolver, int start, int end) { SolveVelocityConstraintsState result; if (!_queue.TryDequeue(out result)) result = new SolveVelocityConstraintsState(); result.ContactSolver = contactSolver; result.Start = start; result.End = end; return result; } internal static void Return(object state) { _queue.Enqueue((SolveVelocityConstraintsState)state); } } #endif private void SolveVelocityConstraints(int start, int end) { for (int i = start; i < end; ++i) { ContactVelocityConstraint vc = _velocityConstraints[i]; #if NET40 || NET45 || PORTABLE40 || PORTABLE45 || W10 || W8_1 || WP8_1 // find lower order item int orderedIndexA = vc.indexA; int orderedIndexB = vc.indexB; if (orderedIndexB < orderedIndexA) { orderedIndexA = vc.indexB; orderedIndexB = vc.indexA; } for (; ; ) { if (Interlocked.CompareExchange(ref _velocities[orderedIndexA].Lock, 1, 0) == 0) { if (Interlocked.CompareExchange(ref _velocities[orderedIndexB].Lock, 1, 0) == 0) break; System.Threading.Interlocked.Exchange(ref _velocities[orderedIndexA].Lock, 0); } #if NET40 || NET45 Thread.Sleep(0); #endif } #endif int indexA = vc.indexA; int indexB = vc.indexB; float mA = vc.invMassA; float iA = vc.invIA; float mB = vc.invMassB; float iB = vc.invIB; int pointCount = vc.pointCount; Vector2 vA = _velocities[indexA].v; float wA = _velocities[indexA].w; Vector2 vB = _velocities[indexB].v; float wB = _velocities[indexB].w; Vector2 normal = vc.normal; Vector2 tangent = MathUtils.Rot270(ref normal); float friction = vc.friction; Debug.Assert(pointCount == 1 || pointCount == 2); // Solve tangent constraints first because non-penetration is more important // than friction. for (int j = 0; j < pointCount; ++j) { VelocityConstraintPoint vcp = vc.points[j]; // Relative velocity at contact Vector2 dv = vB + MathUtils.Cross(wB, ref vcp.rB) - vA - MathUtils.Cross(wA, ref vcp.rA); // Compute tangent force float vt = Vector2.Dot(dv, tangent) - vc.tangentSpeed; float lambda = vcp.tangentMass * (-vt); // b2Clamp the accumulated force float maxFriction = friction * vcp.normalImpulse; float newImpulse = MathUtils.Clamp(vcp.tangentImpulse + lambda, -maxFriction, maxFriction); lambda = newImpulse - vcp.tangentImpulse; vcp.tangentImpulse = newImpulse; // Apply contact impulse Vector2 P = lambda * tangent; vA -= mA * P; wA -= iA * MathUtils.Cross(ref vcp.rA, ref P); vB += mB * P; wB += iB * MathUtils.Cross(ref vcp.rB, ref P); } // Solve normal constraints if (vc.pointCount == 1) { VelocityConstraintPoint vcp = vc.points[0]; // Relative velocity at contact Vector2 dv = vB + MathUtils.Cross(wB, ref vcp.rB) - vA - MathUtils.Cross(wA, ref vcp.rA); // Compute normal impulse float vn = Vector2.Dot(dv, normal); float lambda = -vcp.normalMass * (vn - vcp.velocityBias); // b2Clamp the accumulated impulse float newImpulse = Math.Max(vcp.normalImpulse + lambda, 0.0f); lambda = newImpulse - vcp.normalImpulse; vcp.normalImpulse = newImpulse; // Apply contact impulse Vector2 P = lambda * normal; vA -= mA * P; wA -= iA * MathUtils.Cross(ref vcp.rA, ref P); vB += mB * P; wB += iB * MathUtils.Cross(ref vcp.rB, ref P); } else { // Block solver developed in collaboration with Dirk Gregorius (back in 01/07 on Box2D_Lite). // Build the mini LCP for this contact patch // // vn = A * x + b, vn >= 0, , vn >= 0, x >= 0 and vn_i * x_i = 0 with i = 1..2 // // A = J * W * JT and J = ( -n, -r1 x n, n, r2 x n ) // b = vn0 - velocityBias // // The system is solved using the "Total enumeration method" (s. Murty). The complementary constraint vn_i * x_i // implies that we must have in any solution either vn_i = 0 or x_i = 0. So for the 2D contact problem the cases // 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 // solution that satisfies the problem is chosen. // // In order to account of the accumulated impulse 'a' (because of the iterative nature of the solver which only requires // that the accumulated impulse is clamped and not the incremental impulse) we change the impulse variable (x_i). // // Substitute: // // x = a + d // // a := old total impulse // x := new total impulse // d := incremental impulse // // For the current iteration we extend the formula for the incremental impulse // to compute the new total impulse: // // vn = A * d + b // = A * (x - a) + b // = A * x + b - A * a // = A * x + b' // b' = b - A * a; VelocityConstraintPoint cp1 = vc.points[0]; VelocityConstraintPoint cp2 = vc.points[1]; Vector2 a = new Vector2(cp1.normalImpulse, cp2.normalImpulse); Debug.Assert(a.X >= 0.0f && a.Y >= 0.0f); // Relative velocity at contact Vector2 dv1 = vB + MathUtils.Cross(wB, ref cp1.rB) - vA - MathUtils.Cross(wA, ref cp1.rA); Vector2 dv2 = vB + MathUtils.Cross(wB, ref cp2.rB) - vA - MathUtils.Cross(wA, ref cp2.rA); // Compute normal velocity float vn1 = Vector2.Dot(dv1, normal); float vn2 = Vector2.Dot(dv2, normal); Vector2 b = new Vector2(); b.X = vn1 - cp1.velocityBias; b.Y = vn2 - cp2.velocityBias; // Compute b' b -= MathUtils.Mul(ref vc.K, ref a); const float k_errorTol = 1e-3f; //B2_NOT_USED(k_errorTol); for (; ; ) { // // Case 1: vn = 0 // // 0 = A * x + b' // // Solve for x: // // x = - inv(A) * b' // Vector2 x = -MathUtils.Mul(ref vc.normalMass, ref 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(ref cp1.rA, ref P1) + MathUtils.Cross(ref cp2.rA, ref P2)); vB += mB * (P1 + P2); wB += iB * (MathUtils.Cross(ref cp1.rB, ref P1) + MathUtils.Cross(ref cp2.rB, ref 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(ref cp1.rA, ref P1) + MathUtils.Cross(ref cp2.rA, ref P2)); vB += mB * (P1 + P2); wB += iB * (MathUtils.Cross(ref cp1.rB, ref P1) + MathUtils.Cross(ref cp2.rB, ref 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(ref cp1.rA, ref P1) + MathUtils.Cross(ref cp2.rA, ref P2)); vB += mB * (P1 + P2); wB += iB * (MathUtils.Cross(ref cp1.rB, ref P1) + MathUtils.Cross(ref cp2.rB, ref 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(ref cp1.rA, ref P1) + MathUtils.Cross(ref cp2.rA, ref P2)); vB += mB * (P1 + P2); wB += iB * (MathUtils.Cross(ref cp1.rB, ref P1) + MathUtils.Cross(ref cp2.rB, ref 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; #if NET40 || NET45 || PORTABLE40 || PORTABLE45 || W10 || W8_1 || WP8_1 System.Threading.Interlocked.Exchange(ref _velocities[orderedIndexB].Lock, 0); System.Threading.Interlocked.Exchange(ref _velocities[orderedIndexA].Lock, 0); #endif } } 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() { bool contactsOkay = false; if (_count >= _positionConstraintsMultithreadThreshold && System.Environment.ProcessorCount > 1) { if (_count == 0) return true; var batchSize = (int)Math.Ceiling((float)_count / System.Environment.ProcessorCount); var batches = (int)Math.Ceiling((float)_count / batchSize); #if NET40 || NET45 || PORTABLE40 || PORTABLE45 || W10 || W8_1 || WP8_1 Parallel.For(0, batches, (i) => { var start = i * batchSize; var end = Math.Min(start + batchSize, _count); var res = SolvePositionConstraints(start, end); lock (this) { contactsOkay = contactsOkay || res; } }); #else contactsOkay = SolvePositionConstraints(0, _count); #endif } else { contactsOkay = SolvePositionConstraints(0, _count); } return contactsOkay; } private bool SolvePositionConstraints(int start, int end) { float minSeparation = 0.0f; for (int i = start; i < end; ++i) { ContactPositionConstraint pc = _positionConstraints[i]; #if NET40 || NET45 || PORTABLE40 || PORTABLE45 || W10 || W8_1 || WP8_1 // Find lower order item. int orderedIndexA = pc.indexA; int orderedIndexB = pc.indexB; if (orderedIndexB < orderedIndexA) { orderedIndexA = pc.indexB; orderedIndexB = pc.indexA; } // Lock bodies. for (; ; ) { if (Interlocked.CompareExchange(ref _positions[orderedIndexA].Lock, 1, 0) == 0) { if (Interlocked.CompareExchange(ref _positions[orderedIndexB].Lock, 1, 0) == 0) break; System.Threading.Interlocked.Exchange(ref _positions[orderedIndexA].Lock, 0); } #if NET40 || NET45 Thread.Sleep(0); #endif } #endif 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(Vector2.Zero, aA); Transform xfB = new Transform(Vector2.Zero, aB); xfA.p = cA - Complex.Multiply(ref localCenterA, ref xfA.q); xfB.p = cB - Complex.Multiply(ref localCenterB, ref xfB.q); Vector2 normal; Vector2 point; float separation; PositionSolverManifold.Initialize(pc, ref xfA, ref 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(ref rA, ref normal); float rnB = MathUtils.Cross(ref rB, ref 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(ref rA, ref P); cB += mB * P; aB += iB * MathUtils.Cross(ref rB, ref P); } _positions[indexA].c = cA; _positions[indexA].a = aA; _positions[indexB].c = cB; _positions[indexB].a = aB; #if NET40 || NET45 || PORTABLE40 || PORTABLE45 || W10 || W8_1 || WP8_1 // Unlock bodies. System.Threading.Interlocked.Exchange(ref _positions[orderedIndexB].Lock, 0); System.Threading.Interlocked.Exchange(ref _positions[orderedIndexA].Lock, 0); #endif } // 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(Vector2.Zero, aA); Transform xfB = new Transform(Vector2.Zero, aB); xfA.p = cA - Complex.Multiply(ref localCenterA, ref xfA.q); xfB.p = cB - Complex.Multiply(ref localCenterB, ref xfB.q); Vector2 normal; Vector2 point; float separation; PositionSolverManifold.Initialize(pc, ref xfA, ref 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(ref rA, ref normal); float rnB = MathUtils.Cross(ref rB, ref 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(ref rA, ref P); cB += mB * P; aB += iB * MathUtils.Cross(ref rB, ref 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 { /// /// 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. /// /// The manifold. /// The transform for A. /// The radius for A. /// The transform for B. /// The radius for B. /// World vector pointing from A to B /// Torld contact point (point of intersection). public static void Initialize(ref Manifold manifold, ref Transform xfA, float radiusA, ref Transform xfB, float radiusB, out Vector2 normal, out FixedArray2 points) { normal = Vector2.Zero; points = new FixedArray2(); if (manifold.PointCount == 0) { return; } switch (manifold.Type) { case ManifoldType.Circles: { normal = new Vector2(1.0f, 0.0f); Vector2 pointA = Transform.Multiply(ref manifold.LocalPoint, ref xfA); Vector2 pointB = Transform.Multiply(manifold.Points[0].LocalPoint, ref xfB); 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 = Complex.Multiply(ref manifold.LocalNormal, ref xfA.q); Vector2 planePoint = Transform.Multiply(ref manifold.LocalPoint, ref xfA); for (int i = 0; i < manifold.PointCount; ++i) { Vector2 clipPoint = Transform.Multiply(manifold.Points[i].LocalPoint, ref xfB); 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 = Complex.Multiply(ref manifold.LocalNormal, ref xfB.q); Vector2 planePoint = Transform.Multiply(ref manifold.LocalPoint, ref xfB); for (int i = 0; i < manifold.PointCount; ++i) { Vector2 clipPoint = Transform.Multiply(manifold.Points[i].LocalPoint, ref xfA); 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, ref Transform xfA, ref 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 = Transform.Multiply(ref pc.localPoint, ref xfA); Vector2 pointB = Transform.Multiply(pc.localPoints[0], ref xfB); normal = pointB - pointA; // Handle zero normalization if (normal != Vector2.Zero) normal.Normalize(); point = 0.5f * (pointA + pointB); separation = Vector2.Dot(pointB - pointA, normal) - pc.radiusA - pc.radiusB; } break; case ManifoldType.FaceA: { Complex.Multiply(ref pc.localNormal, ref xfA.q, out normal); Vector2 planePoint = Transform.Multiply(ref pc.localPoint, ref xfA); Vector2 clipPoint = Transform.Multiply(pc.localPoints[index], ref xfB); separation = Vector2.Dot(clipPoint - planePoint, normal) - pc.radiusA - pc.radiusB; point = clipPoint; } break; case ManifoldType.FaceB: { Complex.Multiply(ref pc.localNormal, ref xfB.q, out normal); Vector2 planePoint = Transform.Multiply(ref pc.localPoint, ref xfB); Vector2 clipPoint = Transform.Multiply(pc.localPoints[index], ref xfA); 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; } } } } }