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 = MathUtils.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 + MathUtils.cross( wB, vcp.rB ) - vA - MathUtils.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 = MathUtils.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 * MathUtils.cross( vcp.rA, P );
vB += mB * P;
wB += iB * MathUtils.cross( vcp.rB, P );
}
// Solve normal constraints
if( vc.pointCount == 1 )
{
VelocityConstraintPoint vcp = vc.points[0];
// Relative velocity at contact
Vector2 dv = vB + MathUtils.cross( wB, vcp.rB ) - vA - MathUtils.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 = Math.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 * MathUtils.cross( vcp.rA, P );
vB += mB * P;
wB += iB * MathUtils.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, , 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 + MathUtils.cross( wB, cp1.rB ) - vA - MathUtils.cross( wA, cp1.rA );
Vector2 dv2 = vB + MathUtils.cross( wB, cp2.rB ) - vA - MathUtils.cross( wA, cp2.rA );
// Compute normal velocity
float vn1 = Vector2.Dot( dv1, normal );
float vn2 = Vector2.Dot( dv2, normal );
Vector2 b = new Vector2();
b.X = vn1 - cp1.velocityBias;
b.Y = vn2 - cp2.velocityBias;
// Compute b'
b -= MathUtils.mul( ref 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 = -MathUtils.mul( ref 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 * ( MathUtils.cross( cp1.rA, P1 ) + MathUtils.cross( cp2.rA, P2 ) );
vB += mB * ( P1 + P2 );
wB += iB * ( MathUtils.cross( cp1.rB, P1 ) + MathUtils.cross( cp2.rB, P2 ) );
// Accumulate
cp1.normalImpulse = x.X;
cp2.normalImpulse = x.Y;
#if B2_DEBUG_SOLVER
// Postconditions
dv1 = vB + MathUtils.Cross(wB, cp1.rB) - vA - MathUtils.Cross(wA, cp1.rA);
dv2 = vB + MathUtils.Cross(wB, cp2.rB) - vA - MathUtils.Cross(wA, cp2.rA);
// Compute normal velocity
vn1 = Vector2.Dot(dv1, normal);
vn2 = Vector2.Dot(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
Vector2 d = x - a;
// Apply incremental impulse
Vector2 P1 = d.X * normal;
Vector2 P2 = d.Y * normal;
vA -= mA * ( P1 + P2 );
wA -= iA * ( MathUtils.cross( cp1.rA, P1 ) + MathUtils.cross( cp2.rA, P2 ) );
vB += mB * ( P1 + P2 );
wB += iB * ( MathUtils.cross( cp1.rB, P1 ) + MathUtils.cross( cp2.rB, P2 ) );
// Accumulate
cp1.normalImpulse = x.X;
cp2.normalImpulse = x.Y;
#if B2_DEBUG_SOLVER
// Postconditions
dv1 = vB + MathUtils.Cross(wB, cp1.rB) - vA - MathUtils.Cross(wA, cp1.rA);
// Compute normal velocity
vn1 = Vector2.Dot(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
Vector2 d = x - a;
// Apply incremental impulse
Vector2 P1 = d.X * normal;
Vector2 P2 = d.Y * normal;
vA -= mA * ( P1 + P2 );
wA -= iA * ( MathUtils.cross( cp1.rA, P1 ) + MathUtils.cross( cp2.rA, P2 ) );
vB += mB * ( P1 + P2 );
wB += iB * ( MathUtils.cross( cp1.rB, P1 ) + MathUtils.cross( cp2.rB, P2 ) );
// Accumulate
cp1.normalImpulse = x.X;
cp2.normalImpulse = x.Y;
#if B2_DEBUG_SOLVER
// Postconditions
dv2 = vB + MathUtils.Cross(wB, cp2.rB) - vA - MathUtils.Cross(wA, cp2.rA);
// Compute normal velocity
vn2 = Vector2.Dot(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
Vector2 d = x - a;
// Apply incremental impulse
Vector2 P1 = d.X * normal;
Vector2 P2 = d.Y * normal;
vA -= mA * ( P1 + P2 );
wA -= iA * ( MathUtils.cross( cp1.rA, P1 ) + MathUtils.cross( cp2.rA, P2 ) );
vB += mB * ( P1 + P2 );
wB += iB * ( MathUtils.cross( cp1.rB, P1 ) + MathUtils.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;
}
}