public override void SolveVelocityConstraints(SolverData data)
{
Vec2 vB = data.Velocities[IndexB].V;
float wB = data.Velocities[IndexB].W;
// Cdot = v + cross(w, r)
Vec2 Cdot = Pool.PopVec2();
Vec2.CrossToOutUnsafe(wB, RB, Cdot);
Cdot.AddLocal(vB);
Vec2 impulse = Pool.PopVec2();
Vec2 temp = Pool.PopVec2();
temp.Set(m_impulse).MulLocal(m_gamma).AddLocal(m_C).AddLocal(Cdot).NegateLocal();
Mat22.MulToOutUnsafe(m_mass, temp, impulse);
Vec2 oldImpulse = temp;
oldImpulse.Set(m_impulse);
m_impulse.AddLocal(impulse);
float maxImpulse = data.Step.Dt * m_maxForce;
if (m_impulse.LengthSquared() > maxImpulse * maxImpulse)
{
m_impulse.MulLocal(maxImpulse / m_impulse.Length());
}
impulse.Set(m_impulse).SubLocal(oldImpulse);
vB.X += InvMassB * m_impulse.X;
vB.Y += InvMassB * m_impulse.Y;
wB += InvIB * Vec2.Cross(RB, impulse);
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
Pool.PushVec2(3);
}
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 mB = vc.InvMassB;
float iA = vc.InvIA;
float iB = vc.InvIB;
int pointCount = vc.PointCount;
Vec2 vA = Velocities[indexA].V;
float wA = Velocities[indexA].W;
Vec2 vB = Velocities[indexB].V;
float wB = Velocities[indexB].W;
//Debug.Assert(wA == 0);
//Debug.Assert(wB == 0);
Vec2 normal = vc.Normal;
//Vec2.crossToOutUnsafe(normal, 1f, tangent);
tangent.X = 1.0f * vc.Normal.Y;
tangent.Y = (-1.0f) * vc.Normal.X;
float friction = vc.Friction;
Debug.Assert(pointCount == 1 || pointCount == 2);
// Solve tangent constraints
for (int j = 0; j < pointCount; ++j)
{
ContactVelocityConstraint.VelocityConstraintPoint vcp = vc.Points[j];
//Vec2.crossToOutUnsafe(wA, vcp.rA, temp);
//Vec2.crossToOutUnsafe(wB, vcp.rB, dv);
//dv.addLocal(vB).subLocal(vA).subLocal(temp);
Vec2 a = vcp.RA;
dv.X = (-wB) * vcp.RB.Y + vB.X - vA.X + wA * a.Y;
dv.Y = wB * vcp.RB.X + vB.Y - vA.Y - wA * a.X;
// Compute tangent force
float vt = dv.X * tangent.X + dv.Y * tangent.Y - vc.TangentSpeed;
float lambda = vcp.TangentMass * (-vt);
// Clamp 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
// Vec2 P = lambda * tangent;
float Px = tangent.X * lambda;
float Py = tangent.Y * lambda;
// vA -= invMassA * P;
vA.X -= Px * mA;
vA.Y -= Py * mA;
wA -= iA * (vcp.RA.X * Py - vcp.RA.Y * Px);
// vB += invMassB * P;
vB.X += Px * mB;
vB.Y += Py * mB;
wB += iB * (vcp.RB.X * Py - vcp.RB.Y * Px);
//Console.WriteLine("tangent solve velocity (point "+j+") for " + indexA + " is " + vA.x + "," + vA.y + " rot " + wA);
//Console.WriteLine("tangent solve velocity (point "+j+") for " + indexB + " is " + vB.x + "," + vB.y + " rot " + wB);
}
// Solve normal constraints
if (vc.PointCount == 1)
{
ContactVelocityConstraint.VelocityConstraintPoint vcp = vc.Points[0];
Vec2 a1 = vcp.RA;
// Relative velocity at contact
//Vec2 dv = vB + Cross(wB, vcp.rB) - vA - Cross(wA, vcp.rA);
//Vec2.crossToOut(wA, vcp.rA, temp1);
//Vec2.crossToOut(wB, vcp.rB, dv);
//dv.addLocal(vB).subLocal(vA).subLocal(temp1);
dv.X = (-wB) * vcp.RB.Y + vB.X - vA.X + wA * a1.Y;
dv.Y = wB * vcp.RB.X + vB.Y - vA.Y - wA * a1.X;
// Compute normal impulse
float vn = dv.X * normal.X + dv.Y * normal.Y;
float lambda = (-vcp.NormalMass) * (vn - vcp.VelocityBias);
// Clamp the accumulated impulse
float a = vcp.NormalImpulse + lambda;
float newImpulse = (a > 0.0f ? a : 0.0f);
lambda = newImpulse - vcp.NormalImpulse;
//Debug.Assert(newImpulse == 0);
vcp.NormalImpulse = newImpulse;
// Apply contact impulse
float Px = normal.X * lambda;
float Py = normal.Y * lambda;
// vA -= invMassA * P;
vA.X -= Px * mA;
vA.Y -= Py * mA;
wA -= iA * (vcp.RA.X * Py - vcp.RA.Y * Px);
//Debug.Assert(vA.x == 0);
// vB += invMassB * P;
vB.X += Px * mB;
vB.Y += Py * mB;
wB += iB * (vcp.RB.X * Py - vcp.RB.Y * Px);
//Debug.Assert(vB.x == 0);
}
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 = 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;
ContactVelocityConstraint.VelocityConstraintPoint cp1 = vc.Points[0];
ContactVelocityConstraint.VelocityConstraintPoint cp2 = vc.Points[1];
a.X = cp1.NormalImpulse;
a.Y = cp2.NormalImpulse;
Debug.Assert(a.X >= 0.0f && a.Y >= 0.0f);
// Relative velocity at contact
// Vec2 dv1 = vB + Cross(wB, cp1.rB) - vA - Cross(wA, cp1.rA);
dv1.X = (-wB) * cp1.RB.Y + vB.X - vA.X + wA * cp1.RA.Y;
dv1.Y = wB * cp1.RB.X + vB.Y - vA.Y - wA * cp1.RA.X;
// Vec2 dv2 = vB + Cross(wB, cp2.rB) - vA - Cross(wA, cp2.rA);
dv2.X = (-wB) * cp2.RB.Y + vB.X - vA.X + wA * cp2.RA.Y;
dv2.Y = wB * cp2.RB.X + vB.Y - vA.Y - wA * cp2.RA.X;
// Compute normal velocity
float vn1 = dv1.X * normal.X + dv1.Y * normal.Y;
float vn2 = dv2.X * normal.X + dv2.Y * normal.Y;
b.X = vn1 - cp1.VelocityBias;
b.Y = vn2 - cp2.VelocityBias;
//Console.WriteLine("b is " + b.x + "," + b.y);
// Compute b'
Mat22 R = vc.K;
b.X -= (R.Ex.X * a.X + R.Ey.X * a.Y);
b.Y -= (R.Ex.Y * a.X + R.Ey.Y * a.Y);
//Console.WriteLine("b' is " + b.x + "," + b.y);
// final 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'
//
// Vec2 x = - Mul(c.normalMass, b);
Mat22.MulToOutUnsafe(vc.NormalMass, b, x);
x.MulLocal(-1);
if (x.X >= 0.0f && x.Y >= 0.0f)
{
//Console.WriteLine("case 1");
// Get the incremental impulse
// Vec2 d = x - a;
d.Set(x).SubLocal(a);
// Apply incremental impulse
// Vec2 P1 = d.x * normal;
// Vec2 P2 = d.y * normal;
P1.Set(normal).MulLocal(d.X);
P2.Set(normal).MulLocal(d.Y);
/*
* vA -= invMassA * (P1 + P2); wA -= invIA * (Cross(cp1.rA, P1) + Cross(cp2.rA, P2));
*
* vB += invMassB * (P1 + P2); wB += invIB * (Cross(cp1.rB, P1) + Cross(cp2.rB, P2));
*/
temp1.Set(P1).AddLocal(P2);
temp2.Set(temp1).MulLocal(mA);
vA.SubLocal(temp2);
temp2.Set(temp1).MulLocal(mB);
vB.AddLocal(temp2);
//Debug.Assert(vA.x == 0);
//Debug.Assert(vB.x == 0);
wA -= iA * (Vec2.Cross(cp1.RA, P1) + Vec2.Cross(cp2.RA, P2));
wB += iB * (Vec2.Cross(cp1.RB, P1) + Vec2.Cross(cp2.RB, P2));
// Accumulate
cp1.NormalImpulse = x.X;
cp2.NormalImpulse = x.Y;
/*
* #if B2_DEBUG_SOLVER == 1 // Postconditions dv1 = vB + Cross(wB, cp1.rB) - vA -
* Cross(wA, cp1.rA); dv2 = vB + Cross(wB, cp2.rB) - vA - Cross(wA, cp2.rA);
*
* // Compute normal velocity vn1 = Dot(dv1, normal); vn2 = Dot(dv2, normal);
*
* Debug.Assert(Abs(vn1 - cp1.velocityBias) < k_errorTol); Debug.Assert(Abs(vn2 - cp2.velocityBias)
* < k_errorTol); #endif
*/
if (DEBUG_SOLVER)
{
// Postconditions
Vec2 _dv1 = vB.Add(Vec2.Cross(wB, cp1.RB).SubLocal(vA).SubLocal(Vec2.Cross(wA, cp1.RA)));
Vec2 _dv2 = vB.Add(Vec2.Cross(wB, cp2.RB).SubLocal(vA).SubLocal(Vec2.Cross(wA, cp2.RA)));
// Compute normal velocity
vn1 = Vec2.Dot(_dv1, normal);
vn2 = Vec2.Dot(_dv2, normal);
Debug.Assert(MathUtils.Abs(vn1 - cp1.VelocityBias) < ERROR_TO_I);
Debug.Assert(MathUtils.Abs(vn2 - cp2.VelocityBias) < ERROR_TO_I);
}
break;
}
//
// Case 2: vn1 = 0 and x2 = 0
//
// 0 = a11 * x1' + a12 * 0 + b1'
// vn2 = a21 * x1' + a22 * 0 + '
//
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)
{
//Console.WriteLine("case 2");
// Get the incremental impulse
d.Set(x).SubLocal(a);
// Apply incremental impulse
// Vec2 P1 = d.x * normal;
// Vec2 P2 = d.y * normal;
P1.Set(normal).MulLocal(d.X);
P2.Set(normal).MulLocal(d.Y);
/*
* Vec2 P1 = d.x * normal; Vec2 P2 = d.y * normal; vA -= invMassA * (P1 + P2); wA -=
* invIA * (Cross(cp1.rA, P1) + Cross(cp2.rA, P2));
*
* vB += invMassB * (P1 + P2); wB += invIB * (Cross(cp1.rB, P1) + Cross(cp2.rB, P2));
*/
temp1.Set(P1).AddLocal(P2);
temp2.Set(temp1).MulLocal(mA);
vA.SubLocal(temp2);
temp2.Set(temp1).MulLocal(mB);
vB.AddLocal(temp2);
//Debug.Assert(vA.x == 0);
//Debug.Assert(vB.x == 0);
wA -= iA * (Vec2.Cross(cp1.RA, P1) + Vec2.Cross(cp2.RA, P2));
wB += iB * (Vec2.Cross(cp1.RB, P1) + Vec2.Cross(cp2.RB, P2));
// Accumulate
//Debug.Assert(x.x == 0 && x.y == 0);
cp1.NormalImpulse = x.X;
cp2.NormalImpulse = x.Y;
/*
* #if B2_DEBUG_SOLVER == 1 // Postconditions dv1 = vB + Cross(wB, cp1.rB) - vA -
* Cross(wA, cp1.rA);
*
* // Compute normal velocity vn1 = Dot(dv1, normal);
*
* Debug.Assert(Abs(vn1 - cp1.velocityBias) < k_errorTol); #endif
*/
if (DEBUG_SOLVER)
{
// Postconditions
Vec2 _dv1 = vB.Add(Vec2.Cross(wB, cp1.RB).SubLocal(vA).SubLocal(Vec2.Cross(wA, cp1.RA)));
// Compute normal velocity
vn1 = Vec2.Dot(_dv1, normal);
Debug.Assert(MathUtils.Abs(vn1 - cp1.VelocityBias) < ERROR_TO_I);
}
break;
}
//
// Case 3: wB = 0 and x1 = 0
//
// vn1 = a11 * 0 + a12 * x2' + b1'
// 0 = a21 * 0 + a22 * x2' + '
//
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)
{
//Console.WriteLine("case 3");
// Resubstitute for the incremental impulse
d.Set(x).SubLocal(a);
// Apply incremental impulse
/*
* Vec2 P1 = d.x * normal; Vec2 P2 = d.y * normal; vA -= invMassA * (P1 + P2); wA -=
* invIA * (Cross(cp1.rA, P1) + Cross(cp2.rA, P2));
*
* vB += invMassB * (P1 + P2); wB += invIB * (Cross(cp1.rB, P1) + Cross(cp2.rB, P2));
*/
P1.Set(normal).MulLocal(d.X);
P2.Set(normal).MulLocal(d.Y);
temp1.Set(P1).AddLocal(P2);
temp2.Set(temp1).MulLocal(mA);
vA.SubLocal(temp2);
temp2.Set(temp1).MulLocal(mB);
vB.AddLocal(temp2);
//Debug.Assert(vA.x == 0);
//Debug.Assert(vB.x == 0);
wA -= iA * (Vec2.Cross(cp1.RA, P1) + Vec2.Cross(cp2.RA, P2));
wB += iB * (Vec2.Cross(cp1.RB, P1) + Vec2.Cross(cp2.RB, P2));
// Accumulate
//Debug.Assert(x.x == 0 && x.y == 0);
cp1.NormalImpulse = x.X;
cp2.NormalImpulse = x.Y;
/*
* #if B2_DEBUG_SOLVER == 1 // Postconditions dv2 = vB + Cross(wB, cp2.rB) - vA -
* Cross(wA, cp2.rA);
*
* // Compute normal velocity vn2 = Dot(dv2, normal);
*
* Debug.Assert(Abs(vn2 - cp2.velocityBias) < k_errorTol); #endif
*/
if (DEBUG_SOLVER)
{
// Postconditions
Vec2 _dv2 =
vB.Add(Vec2.Cross(wB, cp2.RB).SubLocal(vA).SubLocal(Vec2.Cross(wA, cp2.RA)));
// Compute normal velocity
vn2 = Vec2.Dot(_dv2, normal);
Debug.Assert(MathUtils.Abs(vn2 - cp2.VelocityBias) < ERROR_TO_I);
}
break;
}
//
// Case 4: x1 = 0 and x2 = 0
//
// vn1 = b1
// vn2 = ;
x.X = 0.0f;
x.Y = 0.0f;
vn1 = b.X;
vn2 = b.Y;
if (vn1 >= 0.0f && vn2 >= 0.0f)
{
//Console.WriteLine("case 4");
// Resubstitute for the incremental impulse
d.Set(x).SubLocal(a);
// Apply incremental impulse
/*
* Vec2 P1 = d.x * normal; Vec2 P2 = d.y * normal; vA -= invMassA * (P1 + P2); wA -=
* invIA * (Cross(cp1.rA, P1) + Cross(cp2.rA, P2));
*
* vB += invMassB * (P1 + P2); wB += invIB * (Cross(cp1.rB, P1) + Cross(cp2.rB, P2));
*/
P1.Set(normal).MulLocal(d.X);
P2.Set(normal).MulLocal(d.Y);
temp1.Set(P1).AddLocal(P2);
temp2.Set(temp1).MulLocal(mA);
vA.SubLocal(temp2);
temp2.Set(temp1).MulLocal(mB);
vB.AddLocal(temp2);
//Debug.Assert(vA.x == 0);
//Debug.Assert(vB.x == 0);
wA -= iA * (Vec2.Cross(cp1.RA, P1) + Vec2.Cross(cp2.RA, P2));
wB += iB * (Vec2.Cross(cp1.RB, P1) + Vec2.Cross(cp2.RB, P2));
// Accumulate
//Debug.Assert(x.x == 0 && x.y == 0);
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.Set(vA);
Velocities[indexA].W = wA;
Velocities[indexB].V.Set(vB);
Velocities[indexB].W = wB;
//Console.WriteLine("Ending velocity for " + indexA + " is " + vA.x + "," + vA.y + " rot " + wA);
//Console.WriteLine("Ending velocity for " + indexB + " is " + vB.x + "," + vB.y + " rot " + wB);
}
}
public override void SolveVelocityConstraints(SolverData data)
{
Vec2 vA = data.Velocities[IndexA].V;
float wA = data.Velocities[IndexA].W;
Vec2 vB = data.Velocities[IndexB].V;
float wB = data.Velocities[IndexB].W;
float mA = InvMassA, mB = InvMassB;
float iA = InvIA, iB = InvIB;
float h = data.Step.Dt;
// Solve angular friction
{
float Cdot = wB - wA;
float impulse = (-AngularMass) * Cdot;
float oldImpulse = m_angularImpulse;
float maxImpulse = h * m_maxTorque;
m_angularImpulse = MathUtils.Clamp(m_angularImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_angularImpulse - oldImpulse;
wA -= iA * impulse;
wB += iB * impulse;
}
// Solve linear friction
{
Vec2 Cdot = Pool.PopVec2();
Vec2 temp = Pool.PopVec2();
Vec2.CrossToOutUnsafe(wA, RA, temp);
Vec2.CrossToOutUnsafe(wB, RB, Cdot);
Cdot.AddLocal(vB).SubLocal(vA).SubLocal(temp);
Vec2 impulse = Pool.PopVec2();
Mat22.MulToOutUnsafe(LinearMass, Cdot, impulse);
impulse.NegateLocal();
Vec2 oldImpulse = Pool.PopVec2();
oldImpulse.Set(m_linearImpulse);
m_linearImpulse.AddLocal(impulse);
float maxImpulse = h * m_maxForce;
if (m_linearImpulse.LengthSquared() > maxImpulse * maxImpulse)
{
m_linearImpulse.Normalize();
m_linearImpulse.MulLocal(maxImpulse);
}
impulse.Set(m_linearImpulse).SubLocal(oldImpulse);
temp.Set(impulse).MulLocal(mA);
vA.SubLocal(temp);
wA -= iA * Vec2.Cross(RA, impulse);
temp.Set(impulse).MulLocal(mB);
vB.AddLocal(temp);
wB += iB * Vec2.Cross(RB, impulse);
}
data.Velocities[IndexA].V.Set(vA);
if (data.Velocities[IndexA].W != wA)
{
Debug.Assert(data.Velocities[IndexA].W != wA);
}
data.Velocities[IndexA].W = wA;
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
Pool.PushVec2(4);
}