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;
Box2DXDebug.Assert(c.PointCount == 1 || c.PointCount == 2);
#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);
Box2DXDebug.Assert(a.x >= 0.0f && a.y >= 0.0f);
// 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);
Box2DXDebug.Assert(Common.Math.Abs(vn1 - cp1.VelocityBias) < k_errorTol);
Box2DXDebug.Assert(Common.Math.Abs(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
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);
Box2DXDebug.Assert(Common.Math.Abs(vn1 - cp1.VelocityBias) < k_errorTol);
#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);
Box2DXDebug.Assert(Common.Math.Abs(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
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 = 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);
Box2DXDebug.Assert(a.x >= 0.0f && a.y >= 0.0f);
// 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);
Box2DXDebug.Assert(Common.Math.Abs(vn1 - cp1.VelocityBias) < k_errorTol);
Box2DXDebug.Assert(Common.Math.Abs(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
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);
Box2DXDebug.Assert(Common.Math.Abs(vn1 - cp1.VelocityBias) < k_errorTol);
#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);
Box2DXDebug.Assert(Common.Math.Abs(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
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
}
}
