public void WarmStart()
{
// Warm start.
for (int i = 0; i < m_count; ++i)
{
b2ContactVelocityConstraint vc = m_velocityConstraints[i];
int indexA = vc.indexA;
int indexB = vc.indexB;
float mA = vc.invMassA;
float iA = vc.invIA;
float mB = vc.invMassB;
float iB = vc.invIB;
int pointCount = vc.pointCount;
b2Vec2 vA = m_velocities[indexA].v;
float wA = m_velocities[indexA].w;
b2Vec2 vB = m_velocities[indexB].v;
float wB = m_velocities[indexB].w;
b2Vec2 normal = new b2Vec2(vc.normal);
b2Vec2 tangent = Utils.b2Cross(normal, 1.0f);
for (int j = 0; j < pointCount; ++j)
{
b2VelocityConstraintPoint vcp = vc.points[j];
b2Vec2 P = vcp.normalImpulse * normal + vcp.tangentImpulse * tangent;
wA -= iA * Utils.b2Cross(vcp.rA, P);
vA -= mA * P;
wB += iB * Utils.b2Cross(vcp.rB, P);
vB += mB * P;
}
m_velocities[indexA].v = vA;
m_velocities[indexA].w = wA;
m_velocities[indexB].v = vB;
m_velocities[indexB].w = wB;
}
}
public b2ContactSolver(b2ContactSolverDef def)
{
m_step = def.step;
m_count = def.count;
m_positionConstraints = Arrays.InitializeWithDefaultInstances <b2ContactPositionConstraint>(m_count);
m_velocityConstraints = Arrays.InitializeWithDefaultInstances <b2ContactVelocityConstraint>(m_count);
m_positions = def.positions;
m_velocities = def.velocities;
m_contacts = def.contacts;
// Initialize position independent portions of the constraints.
for (int i = 0; i < m_count; ++i)
{
b2Contact contact = m_contacts[i];
b2Fixture fixtureA = contact.m_fixtureA;
b2Fixture fixtureB = contact.m_fixtureB;
b2Shape shapeA = fixtureA.GetShape();
b2Shape shapeB = fixtureB.GetShape();
float radiusA = shapeA.m_radius;
float radiusB = shapeB.m_radius;
b2Body bodyA = fixtureA.GetBody();
b2Body bodyB = fixtureB.GetBody();
b2Manifold manifold = contact.GetManifold();
int pointCount = manifold.pointCount;
Debug.Assert(pointCount > 0);
b2ContactVelocityConstraint vc = m_velocityConstraints[i];
vc.friction = contact.m_friction;
vc.restitution = contact.m_restitution;
vc.tangentSpeed = contact.m_tangentSpeed;
vc.indexA = bodyA.m_islandIndex;
vc.indexB = bodyB.m_islandIndex;
vc.invMassA = bodyA.m_invMass;
vc.invMassB = bodyB.m_invMass;
vc.invIA = bodyA.m_invI;
vc.invIB = bodyB.m_invI;
vc.contactIndex = i;
vc.pointCount = pointCount;
vc.K.SetZero();
vc.normalMass.SetZero();
b2ContactPositionConstraint pc = m_positionConstraints[i];
pc.indexA = bodyA.m_islandIndex;
pc.indexB = bodyB.m_islandIndex;
pc.invMassA = bodyA.m_invMass;
pc.invMassB = bodyB.m_invMass;
pc.localCenterA = bodyA.m_sweep.localCenter;
pc.localCenterB = bodyB.m_sweep.localCenter;
pc.invIA = bodyA.m_invI;
pc.invIB = bodyB.m_invI;
pc.localNormal = manifold.localNormal;
pc.localPoint = manifold.localPoint;
pc.pointCount = pointCount;
pc.radiusA = radiusA;
pc.radiusB = radiusB;
pc.type = manifold.type;
for (int j = 0; j < pointCount; ++j)
{
b2ManifoldPoint cp = manifold.points[j];
b2VelocityConstraintPoint vcp = vc.points[j];
if (m_step.warmStarting)
{
vcp.normalImpulse = m_step.dtRatio * cp.normalImpulse;
vcp.tangentImpulse = m_step.dtRatio * cp.tangentImpulse;
}
else
{
vcp.normalImpulse = 0.0f;
vcp.tangentImpulse = 0.0f;
}
vcp.rA.SetZero();
vcp.rB.SetZero();
vcp.normalMass = 0.0f;
vcp.tangentMass = 0.0f;
vcp.velocityBias = 0.0f;
pc.localPoints[j] = cp.localPoint;
}
}
}
public void SolveVelocityConstraints()
{
for (int i = 0; i < m_count; ++i)
{
b2ContactVelocityConstraint vc = m_velocityConstraints[i];
int indexA = vc.indexA;
int indexB = vc.indexB;
float mA = vc.invMassA;
float iA = vc.invIA;
float mB = vc.invMassB;
float iB = vc.invIB;
int pointCount = vc.pointCount;
b2Vec2 vA = m_velocities[indexA].v;
float wA = m_velocities[indexA].w;
b2Vec2 vB = m_velocities[indexB].v;
float wB = m_velocities[indexB].w;
b2Vec2 normal = new b2Vec2(vc.normal);
b2Vec2 tangent = Utils.b2Cross(normal, 1.0f);
float friction = vc.friction;
Debug.Assert(pointCount == 1 || pointCount == 2);
// Solve tangent constraints first because non-penetration is more important
// than friction.
for (int j = 0; j < pointCount; ++j)
{
b2VelocityConstraintPoint vcp = vc.points[j];
// Relative velocity at contact
b2Vec2 dv = vB + Utils.b2Cross(wB, vcp.rB) - vA - Utils.b2Cross(wA, vcp.rA);
// Compute tangent force
float vt = Utils.b2Dot(dv, tangent) - vc.tangentSpeed;
float lambda = vcp.tangentMass * (-vt);
// b2Clamp the accumulated force
float maxFriction = friction * vcp.normalImpulse;
float newImpulse = Utils.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 * Utils.b2Cross(vcp.rA, P);
vB += mB * P;
wB += iB * Utils.b2Cross(vcp.rB, P);
}
// Solve normal constraints
if (pointCount == 1 || Utils.g_blockSolve == false)
{
for (int j = 0; j < pointCount; ++j)
{
b2VelocityConstraintPoint vcp = vc.points[j];
// Relative velocity at contact
b2Vec2 dv = vB + Utils.b2Cross(wB, vcp.rB) - vA - Utils.b2Cross(wA, vcp.rA);
// Compute normal impulse
float vn = Utils.b2Dot(dv, normal);
float lambda = -vcp.normalMass * (vn - vcp.velocityBias);
// b2Clamp the accumulated impulse
float newImpulse = Utils.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 * Utils.b2Cross(vcp.rA, P);
vB += mB * P;
wB += iB * Utils.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, 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 = new b2Vec2(cp1.normalImpulse, cp2.normalImpulse);
Debug.Assert(a.x >= 0.0f && a.y >= 0.0f);
// Relative velocity at contact
b2Vec2 dv1 = vB + Utils.b2Cross(wB, cp1.rB) - vA - Utils.b2Cross(wA, cp1.rA);
b2Vec2 dv2 = vB + Utils.b2Cross(wB, cp2.rB) - vA - Utils.b2Cross(wA, cp2.rA);
// Compute normal velocity
float vn1 = Utils.b2Dot(dv1, normal);
float vn2 = Utils.b2Dot(dv2, normal);
b2Vec2 b = new b2Vec2();
b.x = vn1 - cp1.velocityBias;
b.y = vn2 - cp2.velocityBias;
// Compute b'
b -= Utils.b2Mul(vc.K, a);
//const float k_errorTol = 1e-3f;
for (;;)
{
//
// Case 1: vn = 0
//
// 0 = A * x + b'
//
// Solve for x:
//
// x = - inv(A) * b'
//
b2Vec2 x = -Utils.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 * (Utils.b2Cross(cp1.rA, P1) + Utils.b2Cross(cp2.rA, P2));
vB += mB * (P1 + P2);
wB += iB * (Utils.b2Cross(cp1.rB, P1) + Utils.b2Cross(cp2.rB, P2));
// Accumulate
cp1.normalImpulse = x.x;
cp2.normalImpulse = x.y;
#if B2_DEBUG_SOLVER
// Postconditions
dv1 = vB + Utils.b2Cross(wB, cp1.rB) - vA - Utils.b2Cross(wA, cp1.rA);
dv2 = vB + Utils.b2Cross(wB, cp2.rB) - vA - Utils.b2Cross(wA, cp2.rA);
// Compute normal velocity
vn1 = Utils.b2Dot(dv1, normal);
vn2 = Utils.b2Dot(dv2, normal);
Debug.Assert(Utils.b2Abs(vn1 - cp1.velocityBias) < k_errorTol);
Debug.Assert(Utils.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 * (Utils.b2Cross(cp1.rA, P1) + Utils.b2Cross(cp2.rA, P2));
vB += mB * (P1 + P2);
wB += iB * (Utils.b2Cross(cp1.rB, P1) + Utils.b2Cross(cp2.rB, P2));
// Accumulate
cp1.normalImpulse = x.x;
cp2.normalImpulse = x.y;
#if B2_DEBUG_SOLVER
// Postconditions
dv1 = vB + Utils.b2Cross(wB, cp1.rB) - vA - Utils.b2Cross(wA, cp1.rA);
// Compute normal velocity
vn1 = Utils.b2Dot(dv1, normal);
Debug.Assert(Utils.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 * (Utils.b2Cross(cp1.rA, P1) + Utils.b2Cross(cp2.rA, P2));
vB += mB * (P1 + P2);
wB += iB * (Utils.b2Cross(cp1.rB, P1) + Utils.b2Cross(cp2.rB, P2));
// Accumulate
cp1.normalImpulse = x.x;
cp2.normalImpulse = x.y;
#if B2_DEBUG_SOLVER
// Postconditions
dv2 = vB + Utils.b2Cross(wB, cp2.rB) - vA - Utils.b2Cross(wA, cp2.rA);
// Compute normal velocity
vn2 = Utils.b2Dot(dv2, normal);
Debug.Assert(Utils.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 * (Utils.b2Cross(cp1.rA, P1) + Utils.b2Cross(cp2.rA, P2));
vB += mB * (P1 + P2);
wB += iB * (Utils.b2Cross(cp1.rB, P1) + Utils.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;
}
}
// Initialize position dependent portions of the velocity constraints.
public void InitializeVelocityConstraints()
{
for (int i = 0; i < m_count; ++i)
{
b2ContactVelocityConstraint vc = m_velocityConstraints[i];
b2ContactPositionConstraint pc = m_positionConstraints[i];
float radiusA = pc.radiusA;
float radiusB = pc.radiusB;
b2Manifold manifold = m_contacts[vc.contactIndex].GetManifold();
int indexA = vc.indexA;
int indexB = vc.indexB;
float mA = vc.invMassA;
float mB = vc.invMassB;
float iA = vc.invIA;
float iB = vc.invIB;
b2Vec2 localCenterA = new b2Vec2(pc.localCenterA);
b2Vec2 localCenterB = new b2Vec2(pc.localCenterB);
b2Vec2 cA = m_positions[indexA].c;
float aA = m_positions[indexA].a;
b2Vec2 vA = m_velocities[indexA].v;
float wA = m_velocities[indexA].w;
b2Vec2 cB = m_positions[indexB].c;
float aB = m_positions[indexB].a;
b2Vec2 vB = m_velocities[indexB].v;
float wB = m_velocities[indexB].w;
Debug.Assert(manifold.pointCount > 0);
b2Transform xfA = new b2Transform();
b2Transform xfB = new b2Transform();
xfA.q.Set(aA);
xfB.q.Set(aB);
xfA.p = cA - Utils.b2Mul(xfA.q, localCenterA);
xfB.p = cB - Utils.b2Mul(xfB.q, localCenterB);
b2WorldManifold worldManifold = new b2WorldManifold();
worldManifold.Initialize(manifold, xfA, radiusA, xfB, radiusB);
vc.normal = worldManifold.normal;
int pointCount = vc.pointCount;
for (int j = 0; j < pointCount; ++j)
{
b2VelocityConstraintPoint vcp = vc.points[j];
vcp.rA = worldManifold.points[j] - cA;
vcp.rB = worldManifold.points[j] - cB;
float rnA = Utils.b2Cross(vcp.rA, vc.normal);
float rnB = Utils.b2Cross(vcp.rB, vc.normal);
float kNormal = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
vcp.normalMass = kNormal > 0.0f ? 1.0f / kNormal : 0.0f;
b2Vec2 tangent = Utils.b2Cross(vc.normal, 1.0f);
float rtA = Utils.b2Cross(vcp.rA, tangent);
float rtB = Utils.b2Cross(vcp.rB, tangent);
float kTangent = mA + mB + iA * rtA * rtA + iB * rtB * rtB;
vcp.tangentMass = kTangent > 0.0f ? 1.0f / kTangent : 0.0f;
// Setup a velocity bias for restitution.
vcp.velocityBias = 0.0f;
float vRel = Utils.b2Dot(vc.normal, vB + Utils.b2Cross(wB, vcp.rB) - vA - Utils.b2Cross(wA, vcp.rA));
if (vRel < -Settings.b2_velocityThreshold)
{
vcp.velocityBias = -vc.restitution * vRel;
}
}
// If we have two points, then prepare the block solver.
if (vc.pointCount == 2 && Utils.g_blockSolve)
{
b2VelocityConstraintPoint vcp1 = vc.points[0];
b2VelocityConstraintPoint vcp2 = vc.points[1];
float rn1A = Utils.b2Cross(vcp1.rA, vc.normal);
float rn1B = Utils.b2Cross(vcp1.rB, vc.normal);
float rn2A = Utils.b2Cross(vcp2.rA, vc.normal);
float rn2B = Utils.b2Cross(vcp2.rB, vc.normal);
float k11 = mA + mB + iA * rn1A * rn1A + iB * rn1B * rn1B;
float k22 = mA + mB + iA * rn2A * rn2A + iB * rn2B * rn2B;
float k12 = mA + mB + iA * rn1A * rn2A + iB * 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.
vc.K.ex.Set(k11, k12);
vc.K.ey.Set(k12, k22);
vc.normalMass = vc.K.GetInverse();
}
else
{
// The constraints are redundant, just use one.
// TODO_ERIN use deepest?
vc.pointCount = 1;
}
}
}
}
