public void InitVelocityConstraints(TimeStep step) { unsafe { // Warm start. for (int i = 0; i < _constraintCount; ++i) { ContactConstraint c = _constraints[i]; Body bodyA = c.BodyA; Body bodyB = c.BodyB; float invMassA = bodyA._invMass; float invIA = bodyA._invI; float invMassB = bodyB._invMass; float invIB = bodyB._invI; Vec2 normal = c.Normal; Vec2 tangent = Vec2.Cross(normal, 1.0f); fixed(ContactConstraintPoint *pointsPtr = c.Points) { if (step.WarmStarting) { for (int j = 0; j < c.PointCount; ++j) { ContactConstraintPoint *ccp = &pointsPtr[j]; ccp->NormalImpulse *= step.DtRatio; ccp->TangentImpulse *= step.DtRatio; Vec2 P = ccp->NormalImpulse * normal + ccp->TangentImpulse * tangent; bodyA._angularVelocity -= invIA * Vec2.Cross(ccp->RA, P); bodyA._linearVelocity -= invMassA * P; bodyB._angularVelocity += invIB * Vec2.Cross(ccp->RB, P); bodyB._linearVelocity += invMassB * P; } } else { for (int j = 0; j < c.PointCount; ++j) { ContactConstraintPoint *ccp = &pointsPtr[j]; ccp->NormalImpulse = 0.0f; ccp->TangentImpulse = 0.0f; } } } } } }
public void SolveVelocityConstraints() { for (int i = 0; i < _constraintCount; ++i) { ContactConstraint c = _constraints[i]; Body bodyA = c.BodyA; Body bodyB = c.BodyB; float wA = bodyA._angularVelocity; float wB = bodyB._angularVelocity; Vector2 vA = bodyA._linearVelocity; Vector2 vB = bodyB._linearVelocity; float invMassA = bodyA._invMass; float invIA = bodyA._invI; float invMassB = bodyB._invMass; float invIB = bodyB._invI; Vector2 normal = c.Normal; Vector2 tangent = normal.CrossScalarPostMultiply(1.0f); float friction = c.Friction; #if ALLOWUNSAFE unsafe { fixed(ContactConstraintPoint *pointsPtr = c.Points) { // Solve tangent constraints for (int j = 0; j < c.PointCount; ++j) { ContactConstraintPoint *ccp = &pointsPtr[j]; // Relative velocity at contact Vector2 dv = vB + ccp->RB.CrossScalarPreMultiply(wB) - vA - ccp->RA.CrossScalarPreMultiply(wA); // Compute tangent force float vt = Vector2.Dot(dv, tangent); float lambda = ccp->TangentMass * (-vt); // b2Clamp the accumulated force float maxFriction = friction * ccp->NormalImpulse; float newImpulse = Mathf.Clamp(ccp->TangentImpulse + lambda, -maxFriction, maxFriction); lambda = newImpulse - ccp->TangentImpulse; // Apply contact impulse Vector2 P = lambda * tangent; vA -= invMassA * P; wA -= invIA * ccp->RA.Cross(P); vB += invMassB * P; wB += invIB * ccp->RB.Cross(P); ccp->TangentImpulse = newImpulse; } // Solve normal constraints if (c.PointCount == 1) { ContactConstraintPoint ccp = c.Points[0]; // Relative velocity at contact Vector2 dv = vB + ccp.RB.CrossScalarPreMultiply(wB) - vA - ccp.RA.CrossScalarPreMultiply(wA); // Compute normal impulse float vn = Vector2.Dot(dv, normal); float lambda = -ccp.NormalMass * (vn - ccp.VelocityBias); // Clamp the accumulated impulse float newImpulse = Common.Math.Max(ccp.NormalImpulse + lambda, 0.0f); lambda = newImpulse - ccp.NormalImpulse; // Apply contact impulse Vector2 P = lambda * normal; vA -= invMassA * P; wA -= invIA * ccp.RA.Cross(P); vB += invMassB * P; wB += invIB * ccp.RB.Cross(P); ccp.NormalImpulse = newImpulse; } 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 = vn_0 - 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 = x' - a // // Plug into above equation: // // vn = A * x + b // = A * (x' - a) + b // = A * x' + b - A * a // = A * x' + b' // b' = b - A * a; ContactConstraintPoint *cp1 = &pointsPtr[0]; ContactConstraintPoint *cp2 = &pointsPtr[1]; Vector2 a = new Vector2(cp1->NormalImpulse, cp2->NormalImpulse); // Relative velocity at contact Vector2 dv1 = vB + cp1->RB.CrossScalarPreMultiply(wB) - vA - cp1->RA.CrossScalarPreMultiply(wA); Vector2 dv2 = vB + cp2->RB.CrossScalarPreMultiply(wB) - vA - cp2->RA.CrossScalarPreMultiply(wA); // Compute normal velocity float vn1 = Vector2.Dot(dv1, normal); float vn2 = Vector2.Dot(dv2, normal); Vector2 b = new Vector2(vn1 - cp1->VelocityBias, vn2 - cp2->VelocityBias); b -= c.K.Multiply(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 = -c.NormalMass.Multiply(b); if (x.x >= 0.0f && x.y >= 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 -= invMassA * (P1 + P2); wA -= invIA * (cp1->RA.Cross(P1) + cp2->RA.Cross(P2)); vB += invMassB * (P1 + P2); wB += invIB * (cp1->RB.Cross(P1) + cp2->RB.Cross(P2)); // Accumulate cp1->NormalImpulse = x.x; cp2->NormalImpulse = x.y; #if DEBUG_SOLVER // Postconditions dv1 = vB + Vec2.Cross(wB, cp1->RB) - vA - Vec2.Cross(wA, cp1->RA); dv2 = vB + Vec2.Cross(wB, cp2->RB) - vA - Vec2.Cross(wA, cp2->RA); // Compute normal velocity vn1 = Vec2.Dot(dv1, normal); vn2 = Vec2.Dot(dv2, normal); #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 = c.K.Col1.y * x.x + b.y; if (x.x >= 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 -= invMassA * (P1 + P2); wA -= invIA * (cp1->RA.Cross(P1) + cp2->RA.Cross(P2)); vB += invMassB * (P1 + P2); wB += invIB * (cp1->RB.Cross(P1) + cp2->RB.Cross(P2)); // Accumulate cp1->NormalImpulse = x.x; cp2->NormalImpulse = x.y; #if DEBUG_SOLVER // Postconditions dv1 = vB + Vec2.Cross(wB, cp1->RB) - vA - Vec2.Cross(wA, cp1->RA); // Compute normal velocity vn1 = Vec2.Dot(dv1, normal); #endif break; } // // Case 3: w2 = 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 = c.K.Col2.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 -= invMassA * (P1 + P2); wA -= invIA * (cp1->RA.Cross(P1) + cp2->RA.Cross(P2)); vB += invMassB * (P1 + P2); wB += invIB * (cp1->RB.Cross(P1) + cp2->RB.Cross(P2)); // Accumulate cp1->NormalImpulse = x.x; cp2->NormalImpulse = x.y; #if DEBUG_SOLVER // Postconditions dv2 = vB + Vec2.Cross(wB, cp2->RB) - vA - Vec2.Cross(wA, cp2->RA); // Compute normal velocity vn2 = Vec2.Dot(dv2, normal); #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 -= invMassA * (P1 + P2); wA -= invIA * (cp1->RA.Cross(P1) + cp2->RA.Cross(P2)); vB += invMassB * (P1 + P2); wB += invIB * (cp1->RB.Cross(P1) + cp2->RB.Cross(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; } } bodyA._linearVelocity = vA; bodyA._angularVelocity = wA; bodyB._linearVelocity = vB; bodyB._angularVelocity = wB; } } #else ContactConstraintPoint[] pointsPtr = c.Points; // Solve tangent constraints for (int j = 0; j < c.PointCount; ++j) { ContactConstraintPoint ccp = pointsPtr[j]; // Relative velocity at contact Vector2 dv = vB + ccp.RB.CrossScalarPreMultiply(wB) - vA - ccp.RA.CrossScalarPreMultiply(wA); // Compute tangent force float vt = Vector2.Dot(dv, tangent); float lambda = ccp.TangentMass * (-vt); // b2Clamp the accumulated force float maxFriction = friction * ccp.NormalImpulse; float newImpulse = Box2DNet.Common.Math.Clamp(ccp.TangentImpulse + lambda, -maxFriction, maxFriction); lambda = newImpulse - ccp.TangentImpulse; // Apply contact impulse Vector2 P = lambda * tangent; vA -= invMassA * P; wA -= invIA * ccp.RA.Cross(P); vB += invMassB * P; wB += invIB * ccp.RB.Cross(P); ccp.TangentImpulse = newImpulse; } // Solve normal constraints if (c.PointCount == 1) { ContactConstraintPoint ccp = c.Points[0]; // Relative velocity at contact Vector2 dv = vB + ccp.RB.CrossScalarPreMultiply(wB) - vA - ccp.RA.CrossScalarPreMultiply(wA); // Compute normal impulse float vn = Vector2.Dot(dv, normal); float lambda = -ccp.NormalMass * (vn - ccp.VelocityBias); // Clamp the accumulated impulse float newImpulse = Common.Math.Max(ccp.NormalImpulse + lambda, 0.0f); lambda = newImpulse - ccp.NormalImpulse; // Apply contact impulse Vector2 P = lambda * normal; vA -= invMassA * P; wA -= invIA * ccp.RA.Cross(P); vB += invMassB * P; wB += invIB * ccp.RB.Cross(P); ccp.NormalImpulse = newImpulse; } 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 = vn_0 - 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 = x' - a // // Plug into above equation: // // vn = A * x + b // = A * (x' - a) + b // = A * x' + b - A * a // = A * x' + b' // b' = b - A * a; ContactConstraintPoint cp1 = pointsPtr[0]; ContactConstraintPoint cp2 = pointsPtr[1]; Vector2 a = new Vector2(cp1.NormalImpulse, cp2.NormalImpulse); // Relative velocity at contact Vector2 dv1 = vB + cp1.RB.CrossScalarPreMultiply(wB) - vA - cp1.RA.CrossScalarPreMultiply(wA); Vector2 dv2 = vB + cp2.RB.CrossScalarPreMultiply(wB) - vA - cp2.RA.CrossScalarPreMultiply(wA); // Compute normal velocity float vn1 = Vector2.Dot(dv1, normal); float vn2 = Vector2.Dot(dv2, normal); Vector2 b = new Vector2(vn1 - cp1.VelocityBias, vn2 - cp2.VelocityBias); b -= c.K.Multiply(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 = -c.NormalMass.Multiply(b); if (x.X >= 0.0f && x.Y >= 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 -= invMassA * (P1 + P2); wA -= invIA * (cp1.RA.Cross(P1) + cp2.RA.Cross(P2)); vB += invMassB * (P1 + P2); wB += invIB * (cp1.RB.Cross(P1) + cp2.RB.Cross(P2)); // Accumulate cp1.NormalImpulse = x.X; cp2.NormalImpulse = x.Y; #if DEBUG_SOLVER // Postconditions dv1 = vB + Vec2.Cross(wB, cp1->RB) - vA - Vec2.Cross(wA, cp1->RA); dv2 = vB + Vec2.Cross(wB, cp2->RB) - vA - Vec2.Cross(wA, cp2->RA); // Compute normal velocity vn1 = Vec2.Dot(dv1, normal); vn2 = Vec2.Dot(dv2, normal); #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 = c.K.Col1.Y * x.X + b.Y; if (x.X >= 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 -= invMassA * (P1 + P2); wA -= invIA * (cp1.RA.Cross(P1) + cp2.RA.Cross(P2)); vB += invMassB * (P1 + P2); wB += invIB * (cp1.RB.Cross(P1) + cp2.RB.Cross(P2)); // Accumulate cp1.NormalImpulse = x.X; cp2.NormalImpulse = x.Y; #if DEBUG_SOLVER // Postconditions dv1 = vB + Vec2.Cross(wB, cp1->RB) - vA - Vec2.Cross(wA, cp1->RA); // Compute normal velocity vn1 = Vec2.Dot(dv1, normal); #endif break; } // // Case 3: w2 = 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 = c.K.Col2.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 -= invMassA * (P1 + P2); wA -= invIA * (cp1.RA.Cross(P1) + cp2.RA.Cross(P2)); vB += invMassB * (P1 + P2); wB += invIB * (cp1.RB.Cross(P1) + cp2.RB.Cross(P2)); // Accumulate cp1.NormalImpulse = x.X; cp2.NormalImpulse = x.Y; #if DEBUG_SOLVER // Postconditions dv2 = vB + Vec2.Cross(wB, cp2->RB) - vA - Vec2.Cross(wA, cp2->RA); // Compute normal velocity vn2 = Vec2.Dot(dv2, normal); #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 -= invMassA * (P1 + P2); wA -= invIA * (cp1.RA.Cross(P1) + cp2.RA.Cross(P2)); vB += invMassB * (P1 + P2); wB += invIB * (cp1.RB.Cross(P1) + cp2.RB.Cross(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; } } bodyA._linearVelocity = vA; bodyA._angularVelocity = wA; bodyB._linearVelocity = vB; bodyB._angularVelocity = wB; #endif // ALLOWUNSAFE } }
public void InitVelocityConstraints(TimeStep step) { #if ALLOWUNSAFE unsafe { // Warm start. for (int i = 0; i < _constraintCount; ++i) { ContactConstraint c = _constraints[i]; Body bodyA = c.BodyA; Body bodyB = c.BodyB; float invMassA = bodyA._invMass; float invIA = bodyA._invI; float invMassB = bodyB._invMass; float invIB = bodyB._invI; Vector2 normal = c.Normal; Vector2 tangent = normal.CrossScalarPostMultiply(1.0f); fixed(ContactConstraintPoint *pointsPtr = c.Points) { if (step.WarmStarting) { for (int j = 0; j < c.PointCount; ++j) { ContactConstraintPoint *ccp = &pointsPtr[j]; ccp->NormalImpulse *= step.DtRatio; ccp->TangentImpulse *= step.DtRatio; Vector2 P = ccp->NormalImpulse * normal + ccp->TangentImpulse * tangent; bodyA._angularVelocity -= invIA * ccp->RA.Cross(P); bodyA._linearVelocity -= invMassA * P; bodyB._angularVelocity += invIB * ccp->RB.Cross(P); bodyB._linearVelocity += invMassB * P; } } else { for (int j = 0; j < c.PointCount; ++j) { ContactConstraintPoint *ccp = &pointsPtr[j]; ccp->NormalImpulse = 0.0f; ccp->TangentImpulse = 0.0f; } } } } } #else // Warm start. for (int i = 0; i < _constraintCount; ++i) { ContactConstraint c = _constraints[i]; Body bodyA = c.BodyA; Body bodyB = c.BodyB; float invMassA = bodyA._invMass; float invIA = bodyA._invI; float invMassB = bodyB._invMass; float invIB = bodyB._invI; Vector2 normal = c.Normal; Vector2 tangent = normal.CrossScalarPostMultiply(1.0f); ContactConstraintPoint[] points = c.Points; if (step.WarmStarting) { for (int j = 0; j < c.PointCount; ++j) { ContactConstraintPoint ccp = points[j]; ccp.NormalImpulse *= step.DtRatio; ccp.TangentImpulse *= step.DtRatio; Vector2 P = ccp.NormalImpulse * normal + ccp.TangentImpulse * tangent; bodyA._angularVelocity -= invIA * ccp.RA.Cross(P); bodyA._linearVelocity -= invMassA * P; bodyB._angularVelocity += invIB * ccp.RB.Cross(P); bodyB._linearVelocity += invMassB * P; } } else { for (int j = 0; j < c.PointCount; ++j) { ContactConstraintPoint ccp = points[j]; ccp.NormalImpulse = 0.0f; ccp.TangentImpulse = 0.0f; } } } #endif }
internal unsafe void ContactSolverSetup(Manifold manifold, WorldManifold worldManifold, ContactConstraint cc) { // this is kind of yucky but we do know these were setup before entry to this method var bodyA = cc.BodyA; var bodyB = cc.BodyB; Vector2 vA = bodyA._linearVelocity; Vector2 vB = bodyB._linearVelocity; float wA = bodyA._angularVelocity; float wB = bodyB._angularVelocity; fixed(ContactConstraintPoint *ccPointsPtr = cc.Points) { for (int j = 0; j < cc.PointCount; ++j) { ManifoldPoint cp = manifold.Points[j]; ContactConstraintPoint *ccp = &ccPointsPtr[j]; ccp->NormalImpulse = cp.NormalImpulse; ccp->TangentImpulse = cp.TangentImpulse; ccp->LocalPoint = cp.LocalPoint; ccp->RA = worldManifold.Points[j] - bodyA._sweep.C; ccp->RB = worldManifold.Points[j] - bodyB._sweep.C; float rnA = ccp->RA.Cross(cc.Normal); float rnB = ccp->RB.Cross(cc.Normal); rnA *= rnA; rnB *= rnB; float kNormal = bodyA._invMass + bodyB._invMass + bodyA._invI * rnA + bodyB._invI * rnB; ccp->NormalMass = 1.0f / kNormal; float kEqualized = bodyA._mass * bodyA._invMass + bodyB._mass * bodyB._invMass; kEqualized += bodyA._mass * bodyA._invI * rnA + bodyB._mass * bodyB._invI * rnB; ccp->EqualizedMass = 1.0f / kEqualized; Vector2 tangent = cc.Normal.CrossScalarPostMultiply(1.0f); float rtA = ccp->RA.Cross(tangent); float rtB = ccp->RB.Cross(tangent); rtA *= rtA; rtB *= rtB; float kTangent = bodyA._invMass + bodyB._invMass + bodyA._invI * rtA + bodyB._invI * rtB; ccp->TangentMass = 1.0f / kTangent; // Setup a velocity bias for restitution. ccp->VelocityBias = 0.0f; float vRel = Vector2.Dot(cc.Normal, vB + ccp->RB.CrossScalarPreMultiply(wB) - vA - ccp->RA.CrossScalarPreMultiply(wA)); if (vRel < -Common.Settings.VelocityThreshold) { ccp->VelocityBias = -cc.Restitution * vRel; } } // If we have two points, then prepare the block solver. if (cc.PointCount == 2) { ContactConstraintPoint *ccp1 = &ccPointsPtr[0]; ContactConstraintPoint *ccp2 = &ccPointsPtr[1]; float invMassA = bodyA._invMass; float invIA = bodyA._invI; float invMassB = bodyB._invMass; float invIB = bodyB._invI; float rn1A = ccp1->RA.Cross(cc.Normal); float rn1B = ccp1->RB.Cross(cc.Normal); float rn2A = ccp2->RA.Cross(cc.Normal); float rn2B = ccp2->RB.Cross(cc.Normal); float k11 = invMassA + invMassB + invIA * rn1A * rn1A + invIB * rn1B * rn1B; float k22 = invMassA + invMassB + invIA * rn2A * rn2A + invIB * rn2B * rn2B; float k12 = invMassA + invMassB + invIA * rn1A * rn2A + invIB * rn1B * rn2B; // Ensure a reasonable condition number. const float k_maxConditionNumber = 100.0f; if (k11 * k11 < k_maxConditionNumber * (k11 * k22 - k12 * k12)) { // K is safe to invert. cc.K.Col1 = new Vector2(k11, k12); cc.K.Col2 = new Vector2(k12, k22); cc.NormalMass = cc.K.GetInverse(); } else { // The constraints are redundant, just use one. // TODO_ERIN use deepest? cc.PointCount = 1; } } } }
public ContactSolver(TimeStep step, Contact[] contacts, int contactCount) { _step = step; _constraintCount = contactCount; _constraints = new ContactConstraint[_constraintCount]; for (int i = 0; i < _constraintCount; i++) { _constraints[i] = new ContactConstraint(); } int count = 0; for (int i = 0; i < _constraintCount; ++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; float friction = Settings.MixFriction(fixtureA.Friction, fixtureB.Friction); float restitution = Settings.MixRestitution(fixtureA.Restitution, fixtureB.Restitution); Vec2 vA = bodyA._linearVelocity; Vec2 vB = bodyB._linearVelocity; float wA = bodyA._angularVelocity; float wB = bodyB._angularVelocity; Box2DXDebug.Assert(manifold.PointCount > 0); WorldManifold worldManifold = new WorldManifold(); worldManifold.Initialize(manifold, bodyA._xf, radiusA, bodyB._xf, radiusB); ContactConstraint cc = _constraints[i]; cc.BodyA = bodyA; cc.BodyB = bodyB; cc.Manifold = manifold; cc.Normal = worldManifold.Normal; cc.PointCount = manifold.PointCount; cc.Friction = friction; cc.Restitution = restitution; cc.LocalPlaneNormal = manifold.LocalPlaneNormal; cc.LocalPoint = manifold.LocalPoint; cc.Radius = radiusA + radiusB; cc.Type = manifold.Type; unsafe { fixed(ContactConstraintPoint *ccPointsPtr = cc.Points) { for (int j = 0; j < cc.PointCount; ++j) { ManifoldPoint cp = manifold.Points[j]; ContactConstraintPoint *ccp = &ccPointsPtr[j]; ccp->NormalImpulse = cp.NormalImpulse; ccp->TangentImpulse = cp.TangentImpulse; ccp->LocalPoint = cp.LocalPoint; ccp->RA = worldManifold.Points[j] - bodyA._sweep.C; ccp->RB = worldManifold.Points[j] - bodyB._sweep.C; float rnA = Vec2.Cross(ccp->RA, cc.Normal); float rnB = Vec2.Cross(ccp->RB, cc.Normal); rnA *= rnA; rnB *= rnB; float kNormal = bodyA._invMass + bodyB._invMass + bodyA._invI * rnA + bodyB._invI * rnB; Box2DXDebug.Assert(kNormal > Common.Settings.FLT_EPSILON); ccp->NormalMass = 1.0f / kNormal; float kEqualized = bodyA._mass * bodyA._invMass + bodyB._mass * bodyB._invMass; kEqualized += bodyA._mass * bodyA._invI * rnA + bodyB._mass * bodyB._invI * rnB; Box2DXDebug.Assert(kEqualized > Common.Settings.FLT_EPSILON); ccp->EqualizedMass = 1.0f / kEqualized; Vec2 tangent = Vec2.Cross(cc.Normal, 1.0f); float rtA = Vec2.Cross(ccp->RA, tangent); float rtB = Vec2.Cross(ccp->RB, tangent); rtA *= rtA; rtB *= rtB; float kTangent = bodyA._invMass + bodyB._invMass + bodyA._invI * rtA + bodyB._invI * rtB; Box2DXDebug.Assert(kTangent > Common.Settings.FLT_EPSILON); ccp->TangentMass = 1.0f / kTangent; // Setup a velocity bias for restitution. ccp->VelocityBias = 0.0f; float vRel = Vec2.Dot(cc.Normal, vB + Vec2.Cross(wB, ccp->RB) - vA - Vec2.Cross(wA, ccp->RA)); if (vRel < -Common.Settings.VelocityThreshold) { ccp->VelocityBias = -cc.Restitution * vRel; } } // If we have two points, then prepare the block solver. if (cc.PointCount == 2) { ContactConstraintPoint *ccp1 = &ccPointsPtr[0]; ContactConstraintPoint *ccp2 = &ccPointsPtr[1]; float invMassA = bodyA._invMass; float invIA = bodyA._invI; float invMassB = bodyB._invMass; float invIB = bodyB._invI; float rn1A = Vec2.Cross(ccp1->RA, cc.Normal); float rn1B = Vec2.Cross(ccp1->RB, cc.Normal); float rn2A = Vec2.Cross(ccp2->RA, cc.Normal); float rn2B = Vec2.Cross(ccp2->RB, cc.Normal); float k11 = invMassA + invMassB + invIA * rn1A * rn1A + invIB * rn1B * rn1B; float k22 = invMassA + invMassB + invIA * rn2A * rn2A + invIB * rn2B * rn2B; float k12 = invMassA + invMassB + invIA * rn1A * rn2A + invIB * rn1B * rn2B; // Ensure a reasonable condition number. const float k_maxConditionNumber = 100.0f; if (k11 * k11 < k_maxConditionNumber * (k11 * k22 - k12 * k12)) { // K is safe to invert. cc.K.Col1.Set(k11, k12); cc.K.Col2.Set(k12, k22); cc.NormalMass = cc.K.GetInverse(); } else { // The constraints are redundant, just use one. // TODO_ERIN use deepest? cc.PointCount = 1; } } } } } }