RobustToolbox/Robust.Shared/Physics/Dynamics/Contacts/ContactSolver.cs

/*
* 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 Robust.Shared.Configuration;
using Robust.Shared.IoC;
using Robust.Shared.Maths;
using Robust.Shared.Physics.Collision;
using Robust.Shared.Utility;

namespace Robust.Shared.Physics.Dynamics.Contacts
{
    internal sealed class ContactSolver
    {
        [Dependency] private readonly IConfigurationManager _configManager = default!;

        private bool _warmStarting;
        private float _velocityThreshold;
        private float _baumgarte;
        private float _linearSlop;
        private float _maxLinearCorrection;

        private Vector2[] _linearVelocities = Array.Empty<Vector2>();
        private float[] _angularVelocities = Array.Empty<float>();

        private Vector2[] _positions = Array.Empty<Vector2>();
        private float[] _angles = Array.Empty<float>();

        private Contact[] _contacts = Array.Empty<Contact>();
        private int _contactCount;

        private ContactVelocityConstraint[] _velocityConstraints = Array.Empty<ContactVelocityConstraint>();
        private ContactPositionConstraint[] _positionConstraints = Array.Empty<ContactPositionConstraint>();

        public void Initialize()
        {
            IoCManager.InjectDependencies(this);

            _warmStarting = _configManager.GetCVar(CVars.WarmStarting);
            _configManager.OnValueChanged(CVars.WarmStarting, value => _warmStarting = value);

            _velocityThreshold = _configManager.GetCVar(CVars.VelocityThreshold);
            _configManager.OnValueChanged(CVars.VelocityThreshold, value => _velocityThreshold = value);

            _baumgarte = _configManager.GetCVar(CVars.Baumgarte);
            _configManager.OnValueChanged(CVars.Baumgarte, value => _baumgarte = value);

            _linearSlop = _configManager.GetCVar(CVars.LinearSlop);
            _configManager.OnValueChanged(CVars.LinearSlop, value => _linearSlop = value);

            _maxLinearCorrection = _configManager.GetCVar(CVars.MaxLinearCorrection);
            _configManager.OnValueChanged(CVars.MaxLinearCorrection, value => _maxLinearCorrection = value);
        }

        public void Reset(SolverData data, int contactCount, Contact[] contacts)
        {
            _linearVelocities = data.LinearVelocities;
            _angularVelocities = data.AngularVelocities;

            _positions = data.Positions;
            _positions = data.Positions;
            _angles = data.Angles;

            _contactCount = contactCount;
            _contacts = contacts;

            // If we need more constraints then grow the cached arrays
            if (_velocityConstraints.Length < contactCount)
            {
                var oldLength = _velocityConstraints.Length;

                Array.Resize(ref _velocityConstraints, contactCount * 2);
                Array.Resize(ref _positionConstraints, contactCount * 2);

                for (var i = oldLength; i < _velocityConstraints.Length; i++)
                {
                    _velocityConstraints[i] = new ContactVelocityConstraint();
                    _positionConstraints[i] = new ContactPositionConstraint();
                }
            }

            // Build constraints
            // For now these are going to be bare but will change
            for (var i = 0; i < _contactCount; i++)
            {
                var contact = contacts[i];
                Fixture fixtureA = contact.FixtureA!;
                Fixture fixtureB = contact.FixtureB!;
                var shapeA = fixtureA.Shape;
                var shapeB = fixtureB.Shape;
                float radiusA = shapeA.Radius;
                float radiusB = shapeB.Radius;
                var bodyA = fixtureA.Body;
                var bodyB = fixtureB.Body;
                var manifold = contact.Manifold;

                int pointCount = manifold.PointCount;
                DebugTools.Assert(pointCount > 0);

                var velocityConstraint = _velocityConstraints[i];
                velocityConstraint.Friction = contact.Friction;
                velocityConstraint.Restitution = contact.Restitution;
                velocityConstraint.TangentSpeed = contact.TangentSpeed;
                velocityConstraint.IndexA = bodyA.IslandIndex;
                velocityConstraint.IndexB = bodyB.IslandIndex;
                velocityConstraint.InvMassA = bodyA.InvMass;
                velocityConstraint.InvMassB = bodyB.InvMass;
                velocityConstraint.InvIA = bodyA.InvI;
                velocityConstraint.InvIB = bodyB.InvI;
                velocityConstraint.ContactIndex = i;
                velocityConstraint.PointCount = pointCount;

                for (var x = 0; x < 2; x++)
                {
                    velocityConstraint.K[x] = Vector2.Zero;
                    velocityConstraint.NormalMass[x] = Vector2.Zero;
                }

                var positionConstraint = _positionConstraints[i];
                positionConstraint.IndexA = bodyA.IslandIndex;
                positionConstraint.IndexB = bodyB.IslandIndex;
                positionConstraint.InvMassA = bodyA.InvMass;
                positionConstraint.InvMassB = bodyB.InvMass;
                // TODO: Dis
                // positionConstraint.LocalCenterA = bodyA._sweep.LocalCenter;
                // positionConstraint.LocalCenterB = bodyB._sweep.LocalCenter;
                positionConstraint.LocalCenterA = bodyA.LocalCenter;
                positionConstraint.LocalCenterB = bodyB.LocalCenter;

                positionConstraint.InvIA = bodyA.InvI;
                positionConstraint.InvIB = bodyB.InvI;
                positionConstraint.LocalNormal = manifold.LocalNormal;
                positionConstraint.LocalPoint = manifold.LocalPoint;
                positionConstraint.PointCount = pointCount;
                positionConstraint.RadiusA = radiusA;
                positionConstraint.RadiusB = radiusB;
                positionConstraint.Type = manifold.Type;

                for (int j = 0; j < pointCount; ++j)
                {
                    var contactPoint = manifold.Points[j];
                    var constraintPoint = velocityConstraint.Points[j];

                    if (_warmStarting)
                    {
                        constraintPoint.NormalImpulse = data.DtRatio * contactPoint.NormalImpulse;
                        constraintPoint.TangentImpulse = data.DtRatio * contactPoint.TangentImpulse;
                    }
                    else
                    {
                        constraintPoint.NormalImpulse = 0.0f;
                        constraintPoint.TangentImpulse = 0.0f;
                    }

                    constraintPoint.RelativeVelocityA = Vector2.Zero;
                    constraintPoint.RelativeVelocityB = Vector2.Zero;
                    constraintPoint.NormalMass = 0.0f;
                    constraintPoint.TangentMass = 0.0f;
                    constraintPoint.VelocityBias = 0.0f;

                    positionConstraint.LocalPoints[j] = contactPoint.LocalPoint;
                }
            }
        }

        public void InitializeVelocityConstraints()
        {
            for (var i = 0; i < _contactCount; ++i)
            {
                var velocityConstraint = _velocityConstraints[i];
                var positionConstraint = _positionConstraints[i];

                var radiusA = positionConstraint.RadiusA;
                var radiusB = positionConstraint.RadiusB;
                var manifold = _contacts[velocityConstraint.ContactIndex].Manifold;

                var indexA = velocityConstraint.IndexA;
                var indexB = velocityConstraint.IndexB;

                var invMassA = velocityConstraint.InvMassA;
                var invMassB = velocityConstraint.InvMassB;
                var invIA = velocityConstraint.InvIA;
                var invIB = velocityConstraint.InvIB;
                var localCenterA = positionConstraint.LocalCenterA;
                var localCenterB = positionConstraint.LocalCenterB;

                var centerA = _positions[indexA];
                var angleA = _angles[indexA];
                var linVelocityA = _linearVelocities[indexA];
                var angVelocityA = _angularVelocities[indexA];

                var centerB = _positions[indexB];
                var angleB = _angles[indexB];
                var linVelocityB = _linearVelocities[indexB];
                var angVelocityB = _angularVelocities[indexB];

                DebugTools.Assert(manifold.PointCount > 0);

                Transform xfA = new Transform(angleA);
                Transform xfB = new Transform(angleB);
                xfA.Position = centerA - Transform.Mul(xfA.Quaternion2D, localCenterA);
                xfB.Position = centerB - Transform.Mul(xfB.Quaternion2D, localCenterB);

                Vector2 normal;
                var points = new Vector2[2];
                InitializeManifold(manifold, xfA, xfB, radiusA, radiusB, out normal, out points);

                velocityConstraint.Normal = normal;

                int pointCount = velocityConstraint.PointCount;

                for (int j = 0; j < pointCount; ++j)
                {
                    VelocityConstraintPoint vcp = velocityConstraint.Points[j];

                    vcp.RelativeVelocityA = points[j] - centerA;
                    vcp.RelativeVelocityB = points[j] - centerB;

                    float rnA = Vector2.Cross(vcp.RelativeVelocityA, velocityConstraint.Normal);
                    float rnB = Vector2.Cross(vcp.RelativeVelocityB, velocityConstraint.Normal);

                    float kNormal = invMassA + invMassB + invIA * rnA * rnA + invIB * rnB * rnB;

                    vcp.NormalMass = kNormal > 0.0f ? 1.0f / kNormal : 0.0f;

                    Vector2 tangent = Vector2.Cross(velocityConstraint.Normal, 1.0f);

                    float rtA = Vector2.Cross(vcp.RelativeVelocityA, tangent);
                    float rtB = Vector2.Cross(vcp.RelativeVelocityB, tangent);

                    float kTangent = invMassA + invMassB + invIA * rtA * rtA + invIB * 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(velocityConstraint.Normal, linVelocityB + Vector2.Cross(angVelocityB, vcp.RelativeVelocityB) - linVelocityA - Vector2.Cross(angVelocityA, vcp.RelativeVelocityA));
                    if (vRel < -_velocityThreshold)
                    {
                        vcp.VelocityBias = -velocityConstraint.Restitution * vRel;
                    }
                }

                // If we have two points, then prepare the block solver.
                if (velocityConstraint.PointCount == 2)
                {
                    var vcp1 = velocityConstraint.Points[0];
                    var vcp2 = velocityConstraint.Points[1];

                    var rn1A = Vector2.Cross(vcp1.RelativeVelocityA, velocityConstraint.Normal);
                    var rn1B = Vector2.Cross(vcp1.RelativeVelocityB, velocityConstraint.Normal);
                    var rn2A = Vector2.Cross(vcp2.RelativeVelocityA, velocityConstraint.Normal);
                    var rn2B = Vector2.Cross(vcp2.RelativeVelocityB, velocityConstraint.Normal);

                    var k11 = invMassA + invMassB + invIA * rn1A * rn1A + invIB * rn1B * rn1B;
                    var k22 = invMassA + invMassB + invIA * rn2A * rn2A + invIB * rn2B * rn2B;
                    var k12 = invMassA + invMassB + invIA * rn1A * rn2A + invIB * 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.
                        velocityConstraint.K[0] = new Vector2(k11, k12);
                        velocityConstraint.K[1] = new Vector2(k12, k22);
                        velocityConstraint.NormalMass = velocityConstraint.K.Inverse();
                    }
                    else
                    {
                        // The constraints are redundant, just use one.
                        // TODO_ERIN use deepest?
                        velocityConstraint.PointCount = 1;
                    }
                }
            }
        }

        public void WarmStart()
        {
            for (var i = 0; i < _contactCount; ++i)
            {
                var velocityConstraint = _velocityConstraints[i];

                var indexA = velocityConstraint.IndexA;
                var indexB = velocityConstraint.IndexB;
                var invMassA = velocityConstraint.InvMassA;
                var invIA = velocityConstraint.InvIA;
                var invMassB = velocityConstraint.InvMassB;
                var invIB = velocityConstraint.InvIB;
                var pointCount = velocityConstraint.PointCount;

                var linVelocityA = _linearVelocities[indexA];
                var angVelocityA = _angularVelocities[indexA];
                var linVelocityB = _linearVelocities[indexB];
                var angVelocityB = _angularVelocities[indexB];

                var normal = velocityConstraint.Normal;
                var tangent = Vector2.Cross(normal, 1.0f);

                for (var j = 0; j < pointCount; ++j)
                {
                    var constraintPoint = velocityConstraint.Points[j];
                    var P = normal * constraintPoint.NormalImpulse + tangent * constraintPoint.TangentImpulse;
                    angVelocityA -= invIA * Vector2.Cross(constraintPoint.RelativeVelocityA, P);
                    linVelocityA -= P * invMassA;
                    angVelocityB += invIB * Vector2.Cross(constraintPoint.RelativeVelocityB, P);
                    linVelocityB += P * invMassB;
                }

                _linearVelocities[indexA] = linVelocityA;
                _angularVelocities[indexA] = angVelocityA;
                _linearVelocities[indexB] = linVelocityB;
                _angularVelocities[indexB] = angVelocityB;
            }
        }

        public void SolveVelocityConstraints()
        {
            // Here be dragons
            for (var i = 0; i < _contactCount; ++i)
            {
                var velocityConstraint = _velocityConstraints[i];

                var indexA = velocityConstraint.IndexA;
                var indexB = velocityConstraint.IndexB;
                var mA = velocityConstraint.InvMassA;
                var iA = velocityConstraint.InvIA;
                var mB = velocityConstraint.InvMassB;
                var iB = velocityConstraint.InvIB;
                var pointCount = velocityConstraint.PointCount;

                var vA = _linearVelocities[indexA];
                var wA = _angularVelocities[indexA];
                var vB = _linearVelocities[indexB];
                var wB = _angularVelocities[indexB];

                var normal = velocityConstraint.Normal;
                var tangent = Vector2.Cross(normal, 1.0f);
                var friction = velocityConstraint.Friction;

                DebugTools.Assert(pointCount == 1 || pointCount == 2);

                // Solve tangent constraints first because non-penetration is more important
                // than friction.
                for (var j = 0; j < pointCount; ++j)
                {
                    VelocityConstraintPoint velConstraintPoint = velocityConstraint.Points[j];

                    // Relative velocity at contact
                    var dv = vB + Vector2.Cross(wB, velConstraintPoint.RelativeVelocityB) - vA - Vector2.Cross(wA, velConstraintPoint.RelativeVelocityA);

                    // Compute tangent force
                    float vt = Vector2.Dot(dv, tangent) - velocityConstraint.TangentSpeed;
                    float lambda = velConstraintPoint.TangentMass * (-vt);

                    // b2Clamp the accumulated force
                    var maxFriction = friction * velConstraintPoint.NormalImpulse;
                    var newImpulse = Math.Clamp(velConstraintPoint.TangentImpulse + lambda, -maxFriction, maxFriction);
                    lambda = newImpulse - velConstraintPoint.TangentImpulse;
                    velConstraintPoint.TangentImpulse = newImpulse;

                    // Apply contact impulse
                    Vector2 P = tangent * lambda;

                    vA -= P * mA;
                    wA -= iA * Vector2.Cross(velConstraintPoint.RelativeVelocityA, P);

                    vB += P * mB;
                    wB += iB * Vector2.Cross(velConstraintPoint.RelativeVelocityB, P);
                }

                // Solve normal constraints
                if (velocityConstraint.PointCount == 1)
                {
                    VelocityConstraintPoint vcp = velocityConstraint.Points[0];

                    // Relative velocity at contact
                    Vector2 dv = vB + Vector2.Cross(wB, vcp.RelativeVelocityB) - vA - Vector2.Cross(wA, vcp.RelativeVelocityA);

                    // 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 = normal * lambda;
                    vA -= P * mA;
                    wA -= iA * Vector2.Cross(vcp.RelativeVelocityA, P);

                    vB += P * mB;
                    wB += iB * Vector2.Cross(vcp.RelativeVelocityB, 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 = velocityConstraint.Points[0];
                    VelocityConstraintPoint cp2 = velocityConstraint.Points[1];

                    Vector2 a = new Vector2(cp1.NormalImpulse, cp2.NormalImpulse);
                    DebugTools.Assert(a.X >= 0.0f && a.Y >= 0.0f);

                    // Relative velocity at contact
                    Vector2 dv1 = vB + Vector2.Cross(wB, cp1.RelativeVelocityB) - vA - Vector2.Cross(wA, cp1.RelativeVelocityA);
                    Vector2 dv2 = vB + Vector2.Cross(wB, cp2.RelativeVelocityB) - vA - Vector2.Cross(wA, cp2.RelativeVelocityA);

                    // Compute normal velocity
                    float vn1 = Vector2.Dot(dv1, normal);
                    float vn2 = Vector2.Dot(dv2, normal);

                    Vector2 b = new Vector2
                    {
                        X = vn1 - cp1.VelocityBias,
                        Y = vn2 - cp2.VelocityBias
                    };

                    // Compute b'
                    b -= Transform.Mul(velocityConstraint.K, 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 = -Transform.Mul(velocityConstraint.NormalMass, b);

                        if (x.X >= 0.0f && x.Y >= 0.0f)
                        {
                            // Get the incremental impulse
                            Vector2 d = x - a;

                            // Apply incremental impulse
                            Vector2 P1 = normal * d.X;
                            Vector2 P2 = normal * d.Y;
                            vA -= (P1 + P2) * mA;
                            wA -= iA * (Vector2.Cross(cp1.RelativeVelocityA, P1) + Vector2.Cross(cp2.RelativeVelocityA, P2));

                            vB += (P1 + P2) * mB;
                            wB += iB * (Vector2.Cross(cp1.RelativeVelocityB, P1) + Vector2.Cross(cp2.RelativeVelocityB, P2));

                            // Accumulate
                            cp1.NormalImpulse = x.X;
                            cp2.NormalImpulse = x.Y;

                            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 = velocityConstraint.K[0].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 = normal * d.X;
                            Vector2 P2 = normal * d.Y;
                            vA -= (P1 + P2) * mA;
                            wA -= iA * (Vector2.Cross(cp1.RelativeVelocityA, P1) + Vector2.Cross(cp2.RelativeVelocityA, P2));

                            vB += (P1 + P2) * mB;
                            wB += iB * (Vector2.Cross(cp1.RelativeVelocityB, P1) + Vector2.Cross(cp2.RelativeVelocityB, P2));

                            // Accumulate
                            cp1.NormalImpulse = x.X;
                            cp2.NormalImpulse = x.Y;

                            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 = velocityConstraint.K[1].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 = normal * d.X;
                            Vector2 P2 = normal * d.Y;
                            vA -= (P1 + P2) * mA;
                            wA -= iA * (Vector2.Cross(cp1.RelativeVelocityA, P1) + Vector2.Cross(cp2.RelativeVelocityA, P2));

                            vB += (P1 + P2) * mB;
                            wB += iB * (Vector2.Cross(cp1.RelativeVelocityB, P1) + Vector2.Cross(cp2.RelativeVelocityB, P2));

                            // Accumulate
                            cp1.NormalImpulse = x.X;
                            cp2.NormalImpulse = x.Y;

                            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 = normal * d.X;
                            Vector2 P2 = normal * d.Y;
                            vA -= (P1 + P2) * mA;
                            wA -= iA * (Vector2.Cross(cp1.RelativeVelocityA, P1) + Vector2.Cross(cp2.RelativeVelocityA, P2));

                            vB += (P1 + P2) * mB;
                            wB += iB * (Vector2.Cross(cp1.RelativeVelocityB, P1) + Vector2.Cross(cp2.RelativeVelocityB, 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;
                    }
                }

                _linearVelocities[indexA] = vA;
                _angularVelocities[indexA] = wA;
                _linearVelocities[indexB] = vB;
                _angularVelocities[indexB] = wB;
            }
        }

        public void StoreImpulses()
        {
            for (int i = 0; i < _contactCount; ++i)
            {
                ContactVelocityConstraint velocityConstraint = _velocityConstraints[i];
                Collision.Manifold manifold = _contacts[velocityConstraint.ContactIndex].Manifold;

                for (int j = 0; j < velocityConstraint.PointCount; ++j)
                {
                    ManifoldPoint point = manifold.Points[j];
                    point.NormalImpulse = velocityConstraint.Points[j].NormalImpulse;
                    point.TangentImpulse = velocityConstraint.Points[j].TangentImpulse;
                    manifold.Points[j] = point;
                }

                _contacts[velocityConstraint.ContactIndex].Manifold = manifold;
            }
        }

        /// <summary>
        ///     Tries to solve positions for all contacts specified.
        /// </summary>
        /// <returns>true if all positions solved</returns>
        public bool SolvePositionConstraints()
        {
            float minSeparation = 0.0f;

            for (int i = 0; i < _contactCount; ++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 centerA = _positions[indexA];
                float angleA = _angles[indexA];

                Vector2 centerB = _positions[indexB];
                float angleB = _angles[indexB];

                // Solve normal constraints
                for (int j = 0; j < pointCount; ++j)
                {
                    Transform xfA = new Transform(angleA);
                    Transform xfB = new Transform(angleB);
                    xfA.Position = centerA - Transform.Mul(xfA.Quaternion2D, localCenterA);
                    xfB.Position = centerB - Transform.Mul(xfB.Quaternion2D, localCenterB);

                    Vector2 normal;
                    Vector2 point;
                    float separation;

                    PositionSolverManifoldInitialize(pc, j, xfA, xfB, out normal, out point, out separation);

                    Vector2 rA = point - centerA;
                    Vector2 rB = point - centerB;

                    // Track max constraint error.
                    minSeparation = Math.Min(minSeparation, separation);

                    // Prevent large corrections and allow slop.
                    float C = Math.Clamp(_baumgarte * (separation + _linearSlop), -_maxLinearCorrection, 0.0f);

                    // Compute the effective mass.
                    float rnA = Vector2.Cross(rA, normal);
                    float rnB = Vector2.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 = normal * impulse;

                    centerA -= P * mA;
                    angleA -= iA * Vector2.Cross(rA, P);

                    centerB += P * mB;
                    angleB += iB * Vector2.Cross(rB, P);
                }

                _positions[indexA] = centerA;
                _angles[indexA] = angleA;

                _positions[indexB] = centerB;
                _angles[indexB] = angleB;
            }

            // We can't expect minSpeparation >= -b2_linearSlop because we don't
            // push the separation above -b2_linearSlop.
            return minSeparation >= -3.0f * _linearSlop;
        }

        /// <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>
        internal static void InitializeManifold(
            in Collision.Manifold manifold,
            in Transform xfA,
            in Transform xfB,
            float radiusA,
            float radiusB,
            out Vector2 normal,
            out Vector2[] points)
        {
            normal = Vector2.Zero;
            points = new Vector2[2];

            if (manifold.PointCount == 0)
            {
                return;
            }

            switch (manifold.Type)
            {
                case ManifoldType.Circles:
                {
                    normal = new Vector2(1.0f, 0.0f);
                    Vector2 pointA = Transform.Mul(xfA, manifold.LocalPoint);
                    Vector2 pointB = Transform.Mul(xfB, manifold.Points[0].LocalPoint);

                    if ((pointA - pointB).LengthSquared > float.Epsilon * float.Epsilon)
                    {
                        normal = pointB - pointA;
                        normal = normal.Normalized;
                    }

                    Vector2 cA = pointA + normal * radiusA;
                    Vector2 cB = pointB - normal * radiusB;
                    points[0] = (cA + cB) * 0.5f;
                }
                break;

                case ManifoldType.FaceA:
                {
                    normal = Transform.Mul(xfA.Quaternion2D, manifold.LocalNormal);
                    Vector2 planePoint = Transform.Mul(xfA, manifold.LocalPoint);

                    for (int i = 0; i < manifold.PointCount; ++i)
                    {
                        Vector2 clipPoint = Transform.Mul(xfB, manifold.Points[i].LocalPoint);
                        Vector2 cA = clipPoint + normal * (radiusA - Vector2.Dot(clipPoint - planePoint, normal));
                        Vector2 cB = clipPoint - normal * radiusB;
                        points[i] = (cA + cB) * 0.5f;
                    }
                }
                break;

                case ManifoldType.FaceB:
                {
                    normal = Transform.Mul(xfB.Quaternion2D, manifold.LocalNormal);
                    Vector2 planePoint = Transform.Mul(xfB, manifold.LocalPoint);

                    for (int i = 0; i < manifold.PointCount; ++i)
                    {
                        Vector2 clipPoint = Transform.Mul(xfA, manifold.Points[i].LocalPoint);
                        Vector2 cB = clipPoint + normal * (radiusB - Vector2.Dot(clipPoint - planePoint, normal));
                        Vector2 cA = clipPoint - normal * radiusA;
                        points[i] = (cA + cB) * 0.5f;
                    }

                    // Ensure normal points from A to B.
                    normal = -normal;
                }
                break;
                default:
                    // Shouldn't happentm
                    throw new InvalidOperationException();

            }
        }

        private static void PositionSolverManifoldInitialize(
            in ContactPositionConstraint pc,
            int index,
            in Transform xfA,
            in Transform xfB,
            out Vector2 normal,
            out Vector2 point,
            out float separation)
        {
            DebugTools.Assert(pc.PointCount > 0);

                switch (pc.Type)
                {
                    case ManifoldType.Circles:
                        {
                            Vector2 pointA = Transform.Mul(xfA, pc.LocalPoint);
                            Vector2 pointB = Transform.Mul(xfB, pc.LocalPoints[0]);
                            normal = pointB - pointA;

                            //FPE: Fix to handle zero normalization
                            if (normal != Vector2.Zero)
                                normal = normal.Normalized;

                            point = (pointA + pointB) * 0.5f;
                            separation = Vector2.Dot(pointB - pointA, normal) - pc.RadiusA - pc.RadiusB;
                        }
                        break;

                    case ManifoldType.FaceA:
                        {
                            normal = Transform.Mul(xfA.Quaternion2D, pc.LocalNormal);
                            Vector2 planePoint = Transform.Mul(xfA, pc.LocalPoint);

                            Vector2 clipPoint = Transform.Mul(xfB, pc.LocalPoints[index]);
                            separation = Vector2.Dot(clipPoint - planePoint, normal) - pc.RadiusA - pc.RadiusB;
                            point = clipPoint;
                        }
                        break;

                    case ManifoldType.FaceB:
                        {
                            normal = Transform.Mul(xfB.Quaternion2D, pc.LocalNormal);
                            Vector2 planePoint = Transform.Mul(xfB, pc.LocalPoint);

                            Vector2 clipPoint = Transform.Mul(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;

                }
        }
    }
}