public override void InitVelocityConstraints(SolverData data)
{
IndexA = BodyA.IslandIndex;
IndexB = BodyB.IslandIndex;
LocalCenterB.Set(BodyB.Sweep.LocalCenter);
InvMassB = BodyB.InvMass;
InvIB = BodyB.InvI;
Vec2 cB = data.Positions[IndexB].C;
float aB = data.Positions[IndexB].A;
Vec2 vB = data.Velocities[IndexB].V;
float wB = data.Velocities[IndexB].W;
Rot qB = Pool.PopRot();
qB.Set(aB);
float mass = BodyB.Mass;
// Frequency
float omega = 2.0f * MathUtils.PI * Frequency;
// Damping coefficient
float d = 2.0f * mass * DampingRatio * omega;
// Spring stiffness
float k = mass * (omega * omega);
// magic formulas
// gamma has units of inverse mass.
// beta has units of inverse time.
float h = data.Step.Dt;
Debug.Assert(d + h * k > Settings.EPSILON);
m_gamma = h * (d + h * k);
if (m_gamma != 0.0f)
{
m_gamma = 1.0f / m_gamma;
}
m_beta = h * k * m_gamma;
Vec2 temp = Pool.PopVec2();
// Compute the effective mass matrix.
Rot.MulToOutUnsafe(qB, temp.Set(m_localAnchorB).SubLocal(LocalCenterB), RB);
// K = [(1/m1 + 1/m2) * eye(2) - skew(r1) * invI1 * skew(r1) - skew(r2) * invI2 * skew(r2)]
// = [1/m1+1/m2 0 ] + invI1 * [r1.y*r1.y -r1.x*r1.y] + invI2 * [r1.y*r1.y -r1.x*r1.y]
// [ 0 1/m1+1/m2] [-r1.x*r1.y r1.x*r1.x] [-r1.x*r1.y r1.x*r1.x]
Mat22 K = Pool.PopMat22();
K.Ex.X = InvMassB + InvIB * RB.Y * RB.Y + m_gamma;
K.Ex.Y = (-InvIB) * RB.X * RB.Y;
K.Ey.X = K.Ex.Y;
K.Ey.Y = InvMassB + InvIB * RB.X * RB.X + m_gamma;
K.InvertToOut(m_mass);
m_C.Set(cB).AddLocal(RB).SubLocal(m_targetA);
m_C.MulLocal(m_beta);
// Cheat with some damping
wB *= 0.98f;
if (data.Step.WarmStarting)
{
m_impulse.MulLocal(data.Step.DtRatio);
vB.X += InvMassB * m_impulse.X;
vB.Y += InvMassB * m_impulse.Y;
wB += InvIB * Vec2.Cross(RB, m_impulse);
}
else
{
m_impulse.SetZero();
}
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
Pool.PushVec2(1);
Pool.PushMat22(1);
Pool.PushRot(1);
}
/// <seealso cref="Joint.initVelocityConstraints(TimeStep)"></seealso>
public override void InitVelocityConstraints(SolverData data)
{
IndexA = BodyA.IslandIndex;
IndexB = BodyB.IslandIndex;
LocalCenterA.Set(BodyA.Sweep.LocalCenter);
LocalCenterB.Set(BodyB.Sweep.LocalCenter);
InvMassA = BodyA.InvMass;
InvMassB = BodyB.InvMass;
InvIA = BodyA.InvI;
InvIB = BodyB.InvI;
float aA = data.Positions[IndexA].A;
Vec2 vA = data.Velocities[IndexA].V;
float wA = data.Velocities[IndexA].W;
float aB = data.Positions[IndexB].A;
Vec2 vB = data.Velocities[IndexB].V;
float wB = data.Velocities[IndexB].W;
Vec2 temp = Pool.PopVec2();
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
qA.Set(aA);
qB.Set(aB);
// Compute the effective mass matrix.
Rot.MulToOutUnsafe(qA, temp.Set(m_localAnchorA).SubLocal(LocalCenterA), RA);
Rot.MulToOutUnsafe(qB, temp.Set(m_localAnchorB).SubLocal(LocalCenterB), RB);
// J = [-I -r1_skew I r2_skew]
// [ 0 -1 0 1]
// r_skew = [-ry; rx]
// Matlab
// K = [ mA+r1y^2*iA+mB+r2y^2*iB, -r1y*iA*r1x-r2y*iB*r2x, -r1y*iA-r2y*iB]
// [ -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB, r1x*iA+r2x*iB]
// [ -r1y*iA-r2y*iB, r1x*iA+r2x*iB, iA+iB]
float mA = InvMassA, mB = InvMassB;
float iA = InvIA, iB = InvIB;
Mat22 K = Pool.PopMat22();
K.Ex.X = mA + mB + iA * RA.Y * RA.Y + iB * RB.Y * RB.Y;
K.Ex.Y = (-iA) * RA.X * RA.Y - iB * RB.X * RB.Y;
K.Ey.X = K.Ex.Y;
K.Ey.Y = mA + mB + iA * RA.X * RA.X + iB * RB.X * RB.X;
K.InvertToOut(LinearMass);
AngularMass = iA + iB;
if (AngularMass > 0.0f)
{
AngularMass = 1.0f / AngularMass;
}
if (data.Step.WarmStarting)
{
// Scale impulses to support a variable time step.
m_linearImpulse.MulLocal(data.Step.DtRatio);
m_angularImpulse *= data.Step.DtRatio;
Vec2 P = Pool.PopVec2();
P.Set(m_linearImpulse);
temp.Set(P).MulLocal(mA);
vA.SubLocal(temp);
wA -= iA * (Vec2.Cross(RA, P) + m_angularImpulse);
temp.Set(P).MulLocal(mB);
vB.AddLocal(temp);
wB += iB * (Vec2.Cross(RB, P) + m_angularImpulse);
Pool.PushVec2(1);
}
else
{
m_linearImpulse.SetZero();
m_angularImpulse = 0.0f;
}
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.PushRot(2);
Pool.PushVec2(1);
Pool.PushMat22(1);
}