b2ContactSolver.cpp
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- /*
- * Copyright (c) 2006-2009 Erin Catto http://www.gphysics.com
- *
- * 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.
- */
- #include <Box2D/Dynamics/Contacts/b2ContactSolver.h>
- #include <Box2D/Dynamics/Contacts/b2Contact.h>
- #include <Box2D/Dynamics/b2Body.h>
- #include <Box2D/Dynamics/b2Fixture.h>
- #include <Box2D/Dynamics/b2World.h>
- #include <Box2D/Common/b2StackAllocator.h>
- #define B2_DEBUG_SOLVER 0
- b2ContactSolver::b2ContactSolver(b2Contact** contacts, int32 contactCount,
- b2StackAllocator* allocator, float32 impulseRatio)
- {
- m_allocator = allocator;
- m_constraintCount = contactCount;
- m_constraints = (b2ContactConstraint*)m_allocator->Allocate(m_constraintCount * sizeof(b2ContactConstraint));
- for (int32 i = 0; i < m_constraintCount; ++i)
- {
- b2Contact* contact = contacts[i];
- b2Fixture* fixtureA = contact->m_fixtureA;
- b2Fixture* fixtureB = contact->m_fixtureB;
- b2Shape* shapeA = fixtureA->GetShape();
- b2Shape* shapeB = fixtureB->GetShape();
- float32 radiusA = shapeA->m_radius;
- float32 radiusB = shapeB->m_radius;
- b2Body* bodyA = fixtureA->GetBody();
- b2Body* bodyB = fixtureB->GetBody();
- b2Manifold* manifold = contact->GetManifold();
- float32 friction = b2MixFriction(fixtureA->GetFriction(), fixtureB->GetFriction());
- float32 restitution = b2MixRestitution(fixtureA->GetRestitution(), fixtureB->GetRestitution());
- b2Vec2 vA = bodyA->m_linearVelocity;
- b2Vec2 vB = bodyB->m_linearVelocity;
- float32 wA = bodyA->m_angularVelocity;
- float32 wB = bodyB->m_angularVelocity;
- b2Assert(manifold->pointCount > 0);
- b2WorldManifold worldManifold;
- worldManifold.Initialize(manifold, bodyA->m_xf, radiusA, bodyB->m_xf, radiusB);
- b2ContactConstraint* cc = m_constraints + i;
- cc->bodyA = bodyA;
- cc->bodyB = bodyB;
- cc->manifold = manifold;
- cc->normal = worldManifold.normal;
- cc->pointCount = manifold->pointCount;
- cc->friction = friction;
- cc->localNormal = manifold->localNormal;
- cc->localPoint = manifold->localPoint;
- cc->radius = radiusA + radiusB;
- cc->type = manifold->type;
- for (int32 j = 0; j < cc->pointCount; ++j)
- {
- b2ManifoldPoint* cp = manifold->points + j;
- b2ContactConstraintPoint* ccp = cc->points + j;
- ccp->normalImpulse = impulseRatio * cp->normalImpulse;
- ccp->tangentImpulse = impulseRatio * cp->tangentImpulse;
- ccp->localPoint = cp->localPoint;
- ccp->rA = worldManifold.points[j] - bodyA->m_sweep.c;
- ccp->rB = worldManifold.points[j] - bodyB->m_sweep.c;
- float32 rnA = b2Cross(ccp->rA, cc->normal);
- float32 rnB = b2Cross(ccp->rB, cc->normal);
- rnA *= rnA;
- rnB *= rnB;
- float32 kNormal = bodyA->m_invMass + bodyB->m_invMass + bodyA->m_invI * rnA + bodyB->m_invI * rnB;
- b2Assert(kNormal > b2_epsilon);
- ccp->normalMass = 1.0f / kNormal;
- b2Vec2 tangent = b2Cross(cc->normal, 1.0f);
- float32 rtA = b2Cross(ccp->rA, tangent);
- float32 rtB = b2Cross(ccp->rB, tangent);
- rtA *= rtA;
- rtB *= rtB;
- float32 kTangent = bodyA->m_invMass + bodyB->m_invMass + bodyA->m_invI * rtA + bodyB->m_invI * rtB;
- b2Assert(kTangent > b2_epsilon);
- ccp->tangentMass = 1.0f / kTangent;
- // Setup a velocity bias for restitution.
- ccp->velocityBias = 0.0f;
- float32 vRel = b2Dot(cc->normal, vB + b2Cross(wB, ccp->rB) - vA - b2Cross(wA, ccp->rA));
- if (vRel < -b2_velocityThreshold)
- {
- ccp->velocityBias = -restitution * vRel;
- }
- }
- // If we have two points, then prepare the block solver.
- if (cc->pointCount == 2)
- {
- b2ContactConstraintPoint* ccp1 = cc->points + 0;
- b2ContactConstraintPoint* ccp2 = cc->points + 1;
-
- float32 invMassA = bodyA->m_invMass;
- float32 invIA = bodyA->m_invI;
- float32 invMassB = bodyB->m_invMass;
- float32 invIB = bodyB->m_invI;
- float32 rn1A = b2Cross(ccp1->rA, cc->normal);
- float32 rn1B = b2Cross(ccp1->rB, cc->normal);
- float32 rn2A = b2Cross(ccp2->rA, cc->normal);
- float32 rn2B = b2Cross(ccp2->rB, cc->normal);
- float32 k11 = invMassA + invMassB + invIA * rn1A * rn1A + invIB * rn1B * rn1B;
- float32 k22 = invMassA + invMassB + invIA * rn2A * rn2A + invIB * rn2B * rn2B;
- float32 k12 = invMassA + invMassB + invIA * rn1A * rn2A + invIB * rn1B * rn2B;
- // Ensure a reasonable condition number.
- const float32 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;
- }
- }
- }
- }
- b2ContactSolver::~b2ContactSolver()
- {
- m_allocator->Free(m_constraints);
- }
- void b2ContactSolver::WarmStart()
- {
- // Warm start.
- for (int32 i = 0; i < m_constraintCount; ++i)
- {
- b2ContactConstraint* c = m_constraints + i;
- b2Body* bodyA = c->bodyA;
- b2Body* bodyB = c->bodyB;
- float32 invMassA = bodyA->m_invMass;
- float32 invIA = bodyA->m_invI;
- float32 invMassB = bodyB->m_invMass;
- float32 invIB = bodyB->m_invI;
- b2Vec2 normal = c->normal;
- b2Vec2 tangent = b2Cross(normal, 1.0f);
- for (int32 j = 0; j < c->pointCount; ++j)
- {
- b2ContactConstraintPoint* ccp = c->points + j;
- b2Vec2 P = ccp->normalImpulse * normal + ccp->tangentImpulse * tangent;
- bodyA->m_angularVelocity -= invIA * b2Cross(ccp->rA, P);
- bodyA->m_linearVelocity -= invMassA * P;
- bodyB->m_angularVelocity += invIB * b2Cross(ccp->rB, P);
- bodyB->m_linearVelocity += invMassB * P;
- }
- }
- }
- void b2ContactSolver::SolveVelocityConstraints()
- {
- for (int32 i = 0; i < m_constraintCount; ++i)
- {
- b2ContactConstraint* c = m_constraints + i;
- b2Body* bodyA = c->bodyA;
- b2Body* bodyB = c->bodyB;
- float32 wA = bodyA->m_angularVelocity;
- float32 wB = bodyB->m_angularVelocity;
- b2Vec2 vA = bodyA->m_linearVelocity;
- b2Vec2 vB = bodyB->m_linearVelocity;
- float32 invMassA = bodyA->m_invMass;
- float32 invIA = bodyA->m_invI;
- float32 invMassB = bodyB->m_invMass;
- float32 invIB = bodyB->m_invI;
- b2Vec2 normal = c->normal;
- b2Vec2 tangent = b2Cross(normal, 1.0f);
- float32 friction = c->friction;
- b2Assert(c->pointCount == 1 || c->pointCount == 2);
- // Solve tangent constraints
- for (int32 j = 0; j < c->pointCount; ++j)
- {
- b2ContactConstraintPoint* ccp = c->points + j;
- // Relative velocity at contact
- b2Vec2 dv = vB + b2Cross(wB, ccp->rB) - vA - b2Cross(wA, ccp->rA);
- // Compute tangent force
- float32 vt = b2Dot(dv, tangent);
- float32 lambda = ccp->tangentMass * (-vt);
- // b2Clamp the accumulated force
- float32 maxFriction = friction * ccp->normalImpulse;
- float32 newImpulse = b2Clamp(ccp->tangentImpulse + lambda, -maxFriction, maxFriction);
- lambda = newImpulse - ccp->tangentImpulse;
- // Apply contact impulse
- b2Vec2 P = lambda * tangent;
- vA -= invMassA * P;
- wA -= invIA * b2Cross(ccp->rA, P);
- vB += invMassB * P;
- wB += invIB * b2Cross(ccp->rB, P);
- ccp->tangentImpulse = newImpulse;
- }
- // Solve normal constraints
- if (c->pointCount == 1)
- {
- b2ContactConstraintPoint* ccp = c->points + 0;
- // Relative velocity at contact
- b2Vec2 dv = vB + b2Cross(wB, ccp->rB) - vA - b2Cross(wA, ccp->rA);
- // Compute normal impulse
- float32 vn = b2Dot(dv, normal);
- float32 lambda = -ccp->normalMass * (vn - ccp->velocityBias);
- // b2Clamp the accumulated impulse
- float32 newImpulse = b2Max(ccp->normalImpulse + lambda, 0.0f);
- lambda = newImpulse - ccp->normalImpulse;
- // Apply contact impulse
- b2Vec2 P = lambda * normal;
- vA -= invMassA * P;
- wA -= invIA * b2Cross(ccp->rA, P);
- vB += invMassB * P;
- wB += invIB * b2Cross(ccp->rB, 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;
- b2ContactConstraintPoint* cp1 = c->points + 0;
- b2ContactConstraintPoint* cp2 = c->points + 1;
- b2Vec2 a(cp1->normalImpulse, cp2->normalImpulse);
- b2Assert(a.x >= 0.0f && a.y >= 0.0f);
- // Relative velocity at contact
- b2Vec2 dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
- b2Vec2 dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
- // Compute normal velocity
- float32 vn1 = b2Dot(dv1, normal);
- float32 vn2 = b2Dot(dv2, normal);
- b2Vec2 b;
- b.x = vn1 - cp1->velocityBias;
- b.y = vn2 - cp2->velocityBias;
- b -= b2Mul(c->K, a);
- const float32 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'
- //
- b2Vec2 x = - b2Mul(c->normalMass, b);
- if (x.x >= 0.0f && x.y >= 0.0f)
- {
- // Resubstitute for the incremental impulse
- b2Vec2 d = x - a;
- // Apply incremental impulse
- b2Vec2 P1 = d.x * normal;
- b2Vec2 P2 = d.y * normal;
- vA -= invMassA * (P1 + P2);
- wA -= invIA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
- vB += invMassB * (P1 + P2);
- wB += invIB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
- // Accumulate
- cp1->normalImpulse = x.x;
- cp2->normalImpulse = x.y;
- #if B2_DEBUG_SOLVER == 1
- // Postconditions
- dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
- dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
- // Compute normal velocity
- vn1 = b2Dot(dv1, normal);
- vn2 = b2Dot(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 = c->K.col1.y * x.x + b.y;
- if (x.x >= 0.0f && vn2 >= 0.0f)
- {
- // Resubstitute for the incremental impulse
- b2Vec2 d = x - a;
- // Apply incremental impulse
- b2Vec2 P1 = d.x * normal;
- b2Vec2 P2 = d.y * normal;
- vA -= invMassA * (P1 + P2);
- wA -= invIA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
- vB += invMassB * (P1 + P2);
- wB += invIB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
- // Accumulate
- cp1->normalImpulse = x.x;
- cp2->normalImpulse = x.y;
- #if B2_DEBUG_SOLVER == 1
- // Postconditions
- dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
- // Compute normal velocity
- vn1 = b2Dot(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 = c->K.col2.x * x.y + b.x;
- vn2 = 0.0f;
- if (x.y >= 0.0f && vn1 >= 0.0f)
- {
- // Resubstitute for the incremental impulse
- b2Vec2 d = x - a;
- // Apply incremental impulse
- b2Vec2 P1 = d.x * normal;
- b2Vec2 P2 = d.y * normal;
- vA -= invMassA * (P1 + P2);
- wA -= invIA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
- vB += invMassB * (P1 + P2);
- wB += invIB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
- // Accumulate
- cp1->normalImpulse = x.x;
- cp2->normalImpulse = x.y;
- #if B2_DEBUG_SOLVER == 1
- // Postconditions
- dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
- // Compute normal velocity
- vn2 = b2Dot(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
- b2Vec2 d = x - a;
- // Apply incremental impulse
- b2Vec2 P1 = d.x * normal;
- b2Vec2 P2 = d.y * normal;
- vA -= invMassA * (P1 + P2);
- wA -= invIA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
- vB += invMassB * (P1 + P2);
- wB += invIB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
- // Accumulate
- cp1->normalImpulse = x.x;
- cp2->normalImpulse = x.y;
- break;
- }
- // No solution, give up. This is hit sometimes, but it doesn't seem to matter.
- break;
- }
- }
- bodyA->m_linearVelocity = vA;
- bodyA->m_angularVelocity = wA;
- bodyB->m_linearVelocity = vB;
- bodyB->m_angularVelocity = wB;
- }
- }
- void b2ContactSolver::StoreImpulses()
- {
- for (int32 i = 0; i < m_constraintCount; ++i)
- {
- b2ContactConstraint* c = m_constraints + i;
- b2Manifold* m = c->manifold;
- for (int32 j = 0; j < c->pointCount; ++j)
- {
- m->points[j].normalImpulse = c->points[j].normalImpulse;
- m->points[j].tangentImpulse = c->points[j].tangentImpulse;
- }
- }
- }
- struct b2PositionSolverManifold
- {
- void Initialize(b2ContactConstraint* cc, int32 index)
- {
- b2Assert(cc->pointCount > 0);
- switch (cc->type)
- {
- case b2Manifold::e_circles:
- {
- b2Vec2 pointA = cc->bodyA->GetWorldPoint(cc->localPoint);
- b2Vec2 pointB = cc->bodyB->GetWorldPoint(cc->points[0].localPoint);
- if (b2DistanceSquared(pointA, pointB) > b2_epsilon * b2_epsilon)
- {
- normal = pointB - pointA;
- normal.Normalize();
- }
- else
- {
- normal.Set(1.0f, 0.0f);
- }
- point = 0.5f * (pointA + pointB);
- separation = b2Dot(pointB - pointA, normal) - cc->radius;
- }
- break;
- case b2Manifold::e_faceA:
- {
- normal = cc->bodyA->GetWorldVector(cc->localNormal);
- b2Vec2 planePoint = cc->bodyA->GetWorldPoint(cc->localPoint);
- b2Vec2 clipPoint = cc->bodyB->GetWorldPoint(cc->points[index].localPoint);
- separation = b2Dot(clipPoint - planePoint, normal) - cc->radius;
- point = clipPoint;
- }
- break;
- case b2Manifold::e_faceB:
- {
- normal = cc->bodyB->GetWorldVector(cc->localNormal);
- b2Vec2 planePoint = cc->bodyB->GetWorldPoint(cc->localPoint);
- b2Vec2 clipPoint = cc->bodyA->GetWorldPoint(cc->points[index].localPoint);
- separation = b2Dot(clipPoint - planePoint, normal) - cc->radius;
- point = clipPoint;
- // Ensure normal points from A to B
- normal = -normal;
- }
- break;
- }
- }
- b2Vec2 normal;
- b2Vec2 point;
- float32 separation;
- };
- // Sequential solver.
- bool b2ContactSolver::SolvePositionConstraints(float32 baumgarte)
- {
- float32 minSeparation = 0.0f;
- for (int32 i = 0; i < m_constraintCount; ++i)
- {
- b2ContactConstraint* c = m_constraints + i;
- b2Body* bodyA = c->bodyA;
- b2Body* bodyB = c->bodyB;
- float32 invMassA = bodyA->m_mass * bodyA->m_invMass;
- float32 invIA = bodyA->m_mass * bodyA->m_invI;
- float32 invMassB = bodyB->m_mass * bodyB->m_invMass;
- float32 invIB = bodyB->m_mass * bodyB->m_invI;
- // Solve normal constraints
- for (int32 j = 0; j < c->pointCount; ++j)
- {
- b2PositionSolverManifold psm;
- psm.Initialize(c, j);
- b2Vec2 normal = psm.normal;
- b2Vec2 point = psm.point;
- float32 separation = psm.separation;
- b2Vec2 rA = point - bodyA->m_sweep.c;
- b2Vec2 rB = point - bodyB->m_sweep.c;
- // Track max constraint error.
- minSeparation = b2Min(minSeparation, separation);
- // Prevent large corrections and allow slop.
- float32 C = b2Clamp(baumgarte * (separation + b2_linearSlop), -b2_maxLinearCorrection, 0.0f);
- // Compute the effective mass.
- float32 rnA = b2Cross(rA, normal);
- float32 rnB = b2Cross(rB, normal);
- float32 K = invMassA + invMassB + invIA * rnA * rnA + invIB * rnB * rnB;
- // Compute normal impulse
- float32 impulse = K > 0.0f ? - C / K : 0.0f;
- b2Vec2 P = impulse * normal;
- bodyA->m_sweep.c -= invMassA * P;
- bodyA->m_sweep.a -= invIA * b2Cross(rA, P);
- bodyA->SynchronizeTransform();
- bodyB->m_sweep.c += invMassB * P;
- bodyB->m_sweep.a += invIB * b2Cross(rB, P);
- bodyB->SynchronizeTransform();
- }
- }
- // We can't expect minSpeparation >= -b2_linearSlop because we don't
- // push the separation above -b2_linearSlop.
- return minSeparation >= -1.5f * b2_linearSlop;
- }