public void SolveVelocityConstraints()
{
for (int i = 0; i < _count; ++i)
{
ContactVelocityConstraint vc = _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;
Vector2 vA = _velocities[indexA].v;
float wA = _velocities[indexA].w;
Vector2 vB = _velocities[indexB].v;
float wB = _velocities[indexB].w;
Vector2 normal = vc.normal;
Vector2 tangent = Vectex.Cross(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)
{
VelocityConstraintPoint vcp = vc.points[j];
// Relative velocity at contact
Vector2 dv = vB + Vectex.Cross(wB, vcp.rB) - vA - Vectex.Cross(wA, vcp.rA);
// Compute tangent force
float vt = Vector2.Dot(dv, tangent) - vc.tangentSpeed;
float lambda = vcp.tangentMass * (-vt);
// b2Clamp the accumulated force
float maxFriction = friction * vcp.normalImpulse;
float newImpulse = Math.Clamp(vcp.tangentImpulse + lambda, -maxFriction, maxFriction);
lambda = newImpulse - vcp.tangentImpulse;
vcp.tangentImpulse = newImpulse;
// Apply contact impulse
Vector2 P = lambda * tangent;
vA -= mA * P;
wA -= iA * Vectex.Cross(vcp.rA, P);
vB += mB * P;
wB += iB * Vectex.Cross(vcp.rB, P);
}
// Solve normal constraints
if (pointCount == 1 || Settings.BlockSolve == false)
{
for (int j = 0; j < pointCount; ++j)
{
VelocityConstraintPoint vcp = vc.points[j];
// Relative velocity at contact
Vector2 dv = vB + Vectex.Cross(wB, vcp.rB) - vA - Vectex.Cross(wA, vcp.rA);
// Compute normal impulse
float vn = Vector2.Dot(dv, normal);
float lambda = -vcp.normalMass * (vn - vcp.velocityBias);
// b2Clamp the accumulated impulse
float newImpulse = MathF.Max(vcp.normalImpulse + lambda, 0.0f);
lambda = newImpulse - vcp.normalImpulse;
vcp.normalImpulse = newImpulse;
// Apply contact impulse
Vector2 P = lambda * normal;
vA -= mA * P;
wA -= iA * Vectex.Cross(vcp.rA, P);
vB += mB * P;
wB += iB * Vectex.Cross(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;
VelocityConstraintPoint cp1 = vc.points[0];
VelocityConstraintPoint cp2 = vc.points[1];
Vector2 a = new Vector2(cp1.normalImpulse, cp2.normalImpulse);
//Debug.Assert(a.X >= 0.0f && a.Y >= 0.0f);
// Relative velocity at contact
Vector2 dv1 = vB + Vectex.Cross(wB, cp1.rB) - vA - Vectex.Cross(wA, cp1.rA);
Vector2 dv2 = vB + Vectex.Cross(wB, cp2.rB) - vA - Vectex.Cross(wA, cp2.rA);
// Compute normal velocity
float vn1 = Vector2.Dot(dv1, normal);
float vn2 = Vector2.Dot(dv2, normal);
Vector2 b = new Vector2((float)(vn1 - cp1.velocityBias),
(float)(vn2 - cp2.velocityBias));
// Compute b'
b -= Vector2.Transform(a, vc.K); // Common.Math.Mul(vc.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 = -Vector2.Transform(b, vc.normalMass); //Common.Math.Mul(vc.normalMass, b);
if (x.X >= 0.0f && x.Y >= 0.0f)
{
// Get the incremental impulse
Vector2 d = x - a;
// Apply incremental impulse
Vector2 P1 = d.X * normal;
Vector2 P2 = d.Y * normal;
vA -= mA * (P1 + P2);
wA -= iA * (Vectex.Cross(cp1.rA, P1) + Vectex.Cross(cp2.rA, P2));
vB += mB * (P1 + P2);
wB += iB * (Vectex.Cross(cp1.rB, P1) + Vectex.Cross(cp2.rB, 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 = vc.K.M22 * 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 = d.X * normal;
Vector2 P2 = d.Y * normal;
vA -= mA * (P1 + P2);
wA -= iA * (Vectex.Cross(cp1.rA, P1) + Vectex.Cross(cp2.rA, P2));
vB += mB * (P1 + P2);
wB += iB * (Vectex.Cross(cp1.rB, P1) + Vectex.Cross(cp2.rB, 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 = vc.K.M12 * 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 -= mA * (P1 + P2);
wA -= iA * (Vectex.Cross(cp1.rA, P1) + Vectex.Cross(cp2.rA, P2));
vB += mB * (P1 + P2);
wB += iB * (Vectex.Cross(cp1.rB, P1) + Vectex.Cross(cp2.rB, 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 = d.X * normal;
Vector2 P2 = d.Y * normal;
vA -= mA * (P1 + P2);
wA -= iA * (Vectex.Cross(cp1.rA, P1) + Vectex.Cross(cp2.rA, P2));
vB += mB * (P1 + P2);
wB += iB * (Vectex.Cross(cp1.rB, P1) + Vectex.Cross(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;
}
}
_velocities[indexA].v = vA;
_velocities[indexA].w = wA;
_velocities[indexB].v = vB;
_velocities[indexB].w = wB;
}
}
public ContactSolver(ContactSolverDef def)
{
_step = def.step;
_count = def.count;
_positionConstraints = new ContactPositionConstraint[_count];
_velocityConstraints = new ContactVelocityConstraint[_count];
_positions = def.positions;
_velocities = def.velocities;
_contacts = def.contacts;
for (int i = 0; i < _count; ++i)
{
Contact contact = _contacts[i];
Fixture fixtureA = contact.m_fixtureA;
Fixture fixtureB = contact.m_fixtureB;
Shape shapeA = fixtureA.Shape;
Shape shapeB = fixtureB.Shape;
float radiusA = shapeA.m_radius;
float radiusB = shapeB.m_radius;
Body bodyA = fixtureA.Body;
Body bodyB = fixtureB.Body;
Manifold manifold = contact.Manifold;
int pointCount = manifold.pointCount;
//Debug.Assert(pointCount > 0);
_velocityConstraints[i] = new ContactVelocityConstraint();
ContactVelocityConstraint vc = _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 = new Matrix3x2(); // .SetZero();
vc.normalMass = new Matrix3x2(); // .SetZero();
_positionConstraints[i] = new ContactPositionConstraint();
ContactPositionConstraint pc = _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)
{
ManifoldPoint cp = manifold.points[j];
vc.points[j] = new VelocityConstraintPoint();
VelocityConstraintPoint vcp = vc.points[j];
if (_step.warmStarting)
{
vcp.normalImpulse = _step.dtRatio * cp.normalImpulse;
vcp.tangentImpulse = _step.dtRatio * cp.tangentImpulse;
}
else
{
vcp.normalImpulse = 0f;
vcp.tangentImpulse = 0f;
}
vcp.rA = Vector2.Zero;
vcp.rB = Vector2.Zero;
vcp.normalMass = 0f;
vcp.tangentMass = 0f;
vcp.velocityBias = 0f;
pc.localPoints[j] = cp.localPoint;
}
}
}
public void InitializeVelocityConstraints()
{
for (int i = 0; i < _count; ++i)
{
ContactVelocityConstraint vc = _velocityConstraints[i];
ContactPositionConstraint pc = _positionConstraints[i];
float radiusA = pc.radiusA;
float radiusB = pc.radiusB;
Manifold manifold = _contacts[vc.contactIndex].Manifold;
int indexA = vc.indexA;
int indexB = vc.indexB;
float mA = vc.invMassA;
float mB = vc.invMassB;
float iA = vc.invIA;
float iB = vc.invIB;
Vector2 localCenterA = pc.localCenterA;
Vector2 localCenterB = pc.localCenterB;
Vector2 cA = _positions[indexA].c;
float aA = _positions[indexA].a;
Vector2 vA = _velocities[indexA].v;
float wA = _velocities[indexA].w;
Vector2 cB = _positions[indexB].c;
float aB = _positions[indexB].a;
Vector2 vB = _velocities[indexB].v;
float wB = _velocities[indexB].w;
//Debug.Assert(manifold.pointCount > 0);
Transform xfA = new Transform();
Transform xfB = new Transform();
xfA.q = Matrex.CreateRotation(aA); // Actually about twice as fast to use our own function
xfB.q = Matrex.CreateRotation(aB); // Actually about twice as fast to use our own function
xfA.p = cA - Vector2.Transform(localCenterA, xfA.q); // Common.Math.Mul(xfA.q, localCenterA);
xfB.p = cB - Vector2.Transform(localCenterB, xfB.q); // Common.Math.Mul(xfB.q, localCenterB);
WorldManifold worldManifold = new WorldManifold();
worldManifold.Initialize(manifold, xfA, radiusA, xfB, radiusB);
vc.normal = worldManifold.normal;
int pointCount = vc.pointCount;
for (int j = 0; j < pointCount; ++j)
{
VelocityConstraintPoint vcp = vc.points[j];
vcp.rA = worldManifold.points[j] - cA;
vcp.rB = worldManifold.points[j] - cB;
float rnA = Vectex.Cross(vcp.rA, vc.normal);
float rnB = Vectex.Cross(vcp.rB, vc.normal);
float kNormal = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
vcp.normalMass = kNormal > 0f ? 1f / kNormal : 0f;
Vector2 tangent = Vectex.Cross(vc.normal, 1f);
float rtA = Vectex.Cross(vcp.rA, tangent);
float rtB = Vectex.Cross(vcp.rB, tangent);
float kTangent = mA + mB + iA * rtA * rtA + iB * rtB * rtB;
vcp.tangentMass = kTangent > 0f ? 1f / kTangent : 0f;
vcp.velocityBias = 0f;
float vRel = Vector2.Dot(vc.normal, vB + Vectex.Cross(wB, vcp.rB) - vA - Vectex.Cross(wA, vcp.rA));
if (vRel < -Settings.VelocityThreshold)
{
vcp.velocityBias = -vc.restitution * vRel;
}
}
// If we have two points, then prepare the block solver.
if (vc.pointCount == 2 && Settings.BlockSolve)
{
VelocityConstraintPoint vcp1 = vc.points[0];
VelocityConstraintPoint vcp2 = vc.points[1];
float rn1A = Vectex.Cross(vcp1.rA, vc.normal);
float rn1B = Vectex.Cross(vcp1.rB, vc.normal);
float rn2A = Vectex.Cross(vcp2.rA, vc.normal);
float rn2B = Vectex.Cross(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 = new Matrix3x2(k11, k12, k12, k22, 0, 0);
// vc.K.ex = new Vector2(k11, k12);
// vc.K.ey = new Vector2(k12, k22);
/*Matrix3x2*/
Matrex.Invert(vc.K, out Matrix3x2 KT);
vc.normalMass = KT;
}
else
{
// The constraints are redundant, just use one.
// TODO_ERIN use deepest?
vc.pointCount = 1;
}
}
}
}