in Box2D/Dynamics/Contacts/b2ContactSolver.cpp [289:597]
void b2ContactSolver::SolveVelocityConstraints()
{
for (int32 i = 0; i < m_count; ++i)
{
b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
int32 indexA = vc->indexA;
int32 indexB = vc->indexB;
float32 mA = vc->invMassA;
float32 iA = vc->invIA;
float32 mB = vc->invMassB;
float32 iB = vc->invIB;
int32 pointCount = vc->pointCount;
b2Vec2 vA = m_velocities[indexA].v;
float32 wA = m_velocities[indexA].w;
b2Vec2 vB = m_velocities[indexB].v;
float32 wB = m_velocities[indexB].w;
b2Vec2 normal = vc->normal;
b2Vec2 tangent = b2Cross(normal, 1.0f);
float32 friction = vc->friction;
b2Assert(pointCount == 1 || pointCount == 2);
// Solve tangent constraints first because non-penetration is more important
// than friction.
for (int32 j = 0; j < pointCount; ++j)
{
b2VelocityConstraintPoint* vcp = vc->points + j;
// Relative velocity at contact
b2Vec2 dv = vB + b2Cross(wB, vcp->rB) - vA - b2Cross(wA, vcp->rA);
// Compute tangent force
float32 vt = b2Dot(dv, tangent) - vc->tangentSpeed;
float32 lambda = vcp->tangentMass * (-vt);
// b2Clamp the accumulated force
float32 maxFriction = friction * vcp->normalImpulse;
float32 newImpulse = b2Clamp(vcp->tangentImpulse + lambda, -maxFriction, maxFriction);
lambda = newImpulse - vcp->tangentImpulse;
vcp->tangentImpulse = newImpulse;
// Apply contact impulse
b2Vec2 P = lambda * tangent;
vA -= mA * P;
wA -= iA * b2Cross(vcp->rA, P);
vB += mB * P;
wB += iB * b2Cross(vcp->rB, P);
}
// Solve normal constraints
if (vc->pointCount == 1)
{
b2VelocityConstraintPoint* vcp = vc->points + 0;
// Relative velocity at contact
b2Vec2 dv = vB + b2Cross(wB, vcp->rB) - vA - b2Cross(wA, vcp->rA);
// Compute normal impulse
float32 vn = b2Dot(dv, normal);
float32 lambda = -vcp->normalMass * (vn - vcp->velocityBias);
// b2Clamp the accumulated impulse
float32 newImpulse = b2Max(vcp->normalImpulse + lambda, 0.0f);
lambda = newImpulse - vcp->normalImpulse;
vcp->normalImpulse = newImpulse;
// Apply contact impulse
b2Vec2 P = lambda * normal;
vA -= mA * P;
wA -= iA * b2Cross(vcp->rA, P);
vB += mB * P;
wB += iB * b2Cross(vcp->rB, 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;
b2VelocityConstraintPoint* cp1 = vc->points + 0;
b2VelocityConstraintPoint* cp2 = vc->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;
// Compute b'
b -= b2Mul(vc->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(vc->normalMass, b);
if (x.x >= 0.0f && x.y >= 0.0f)
{
// Get the incremental impulse
b2Vec2 d = x - a;
// Apply incremental impulse
b2Vec2 P1 = d.x * normal;
b2Vec2 P2 = d.y * normal;
vA -= mA * (P1 + P2);
wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += mB * (P1 + P2);
wB += iB * (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 = vc->K.ex.y * x.x + b.y;
if (x.x >= 0.0f && vn2 >= 0.0f)
{
// Get the incremental impulse
b2Vec2 d = x - a;
// Apply incremental impulse
b2Vec2 P1 = d.x * normal;
b2Vec2 P2 = d.y * normal;
vA -= mA * (P1 + P2);
wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += mB * (P1 + P2);
wB += iB * (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 = vc->K.ey.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 -= mA * (P1 + P2);
wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += mB * (P1 + P2);
wB += iB * (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 -= mA * (P1 + P2);
wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += mB * (P1 + P2);
wB += iB * (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;
}
}
m_velocities[indexA].v = vA;
m_velocities[indexA].w = wA;
m_velocities[indexB].v = vB;
m_velocities[indexB].w = wB;
}
}