Beispiel #1
0
        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;
            }
        }
Beispiel #2
0
        public void InitializeVelocityConstraints()
        {
            Span <Vector2> points = stackalloc Vector2[2];

            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;
                InitializeManifold(ref manifold, xfA, xfB, radiusA, radiusB, out normal, 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;
                    }
                }
            }
        }