public override bool SolvePositionConstraints(SolverData data)
{
if (FrequencyHz > 0.0f)
{
return(true);
}
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 rA = Pool.PopVec2();
Vec2 rB = Pool.PopVec2();
Vec2 u = Pool.PopVec2();
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 cB = data.Positions[IndexB].C;
float aB = data.Positions[IndexB].A;
qA.Set(aA);
qB.Set(aB);
Rot.MulToOutUnsafe(qA, u.Set(LocalAnchorA).SubLocal(LocalCenterA), rA);
Rot.MulToOutUnsafe(qB, u.Set(LocalAnchorB).SubLocal(LocalCenterB), rB);
u.Set(cB).AddLocal(rB).SubLocal(cA).SubLocal(rA);
float length = u.Normalize();
float C = length - Length;
C = MathUtils.Clamp(C, -Settings.MAX_LINEAR_CORRECTION, Settings.MAX_LINEAR_CORRECTION);
float impulse = (-Mass) * C;
float Px = impulse * u.X;
float Py = impulse * u.Y;
cA.X -= InvMassA * Px;
cA.Y -= InvMassA * Py;
aA -= InvIA * (rA.X * Py - rA.Y * Px);
cB.X += InvMassB * Px;
cB.Y += InvMassB * Py;
aB += InvIB * (rB.X * Py - rB.Y * Px);
data.Positions[IndexA].C.Set(cA);
data.Positions[IndexA].A = aA;
data.Positions[IndexB].C.Set(cB);
data.Positions[IndexB].A = aB;
Pool.PushVec2(3);
Pool.PushRot(2);
return(MathUtils.Abs(C) < Settings.LINEAR_SLOP);
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
Vector2 cA = data.Positions[_indexA].C;
float aA = data.Positions[_indexA].A;
Vector2 cB = data.Positions[_indexB].C;
float aB = data.Positions[_indexB].A;
Rot qA = new Rot(aA), qB = new Rot(aB);
float angularError = 0.0f;
float positionError;
bool fixedRotation = (_invIA + _invIB == 0.0f);
// Solve angular limit constraint.
if (_enableLimit && _limitState != LimitState.Inactive && fixedRotation == false)
{
float angle = aB - aA - ReferenceAngle;
float limitImpulse = 0.0f;
if (_limitState == LimitState.Equal)
{
// Prevent large angular corrections
float C = MathUtils.Clamp(angle - _lowerAngle, -Settings.MaxAngularCorrection, Settings.MaxAngularCorrection);
limitImpulse = -_motorMass * C;
angularError = Math.Abs(C);
}
else if (_limitState == LimitState.AtLower)
{
float C = angle - _lowerAngle;
angularError = -C;
// Prevent large angular corrections and allow some slop.
C = MathUtils.Clamp(C + Settings.AngularSlop, -Settings.MaxAngularCorrection, 0.0f);
limitImpulse = -_motorMass * C;
}
else if (_limitState == LimitState.AtUpper)
{
float C = angle - _upperAngle;
angularError = C;
// Prevent large angular corrections and allow some slop.
C = MathUtils.Clamp(C - Settings.AngularSlop, 0.0f, Settings.MaxAngularCorrection);
limitImpulse = -_motorMass * C;
}
aA -= _invIA * limitImpulse;
aB += _invIB * limitImpulse;
}
// Solve point-to-point constraint.
{
qA.Set(aA);
qB.Set(aB);
Vector2 rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
Vector2 rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
Vector2 C = cB + rB - cA - rA;
positionError = C.Length();
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
Mat22 K = new Mat22();
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;
Vector2 impulse = -K.Solve(C);
cA -= mA * impulse;
aA -= iA * MathUtils.Cross(rA, impulse);
cB += mB * impulse;
aB += iB * MathUtils.Cross(rB, impulse);
}
data.Positions[_indexA].C = cA;
data.Positions[_indexA].A = aA;
data.Positions[_indexB].C = cB;
data.Positions[_indexB].A = aB;
return(positionError <= Settings.LinearSlop && angularError <= Settings.AngularSlop);
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
FVector2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
FVector2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
Rot qA = new Rot(aA), qB = new Rot(aB);
float angularError = 0.0f;
float positionError;
bool fixedRotation = (m_invIA + m_invIB == 0.0f);
// Solve angular limit constraint.
if (_enableLimit && _limitState != LimitState.Inactive && fixedRotation == false)
{
float angle = aB - aA - ReferenceAngle;
float limitImpulse = 0.0f;
if (_limitState == LimitState.Equal)
{
// Prevent large angular corrections
float C = MathUtils.Clamp(angle - _lowerAngle, -Settings.MaxAngularCorrection, Settings.MaxAngularCorrection);
limitImpulse = -m_motorMass * C;
angularError = Math.Abs(C);
}
else if (_limitState == LimitState.AtLower)
{
float C = angle - _lowerAngle;
angularError = -C;
// Prevent large angular corrections and allow some slop.
C = MathUtils.Clamp(C + Settings.AngularSlop, -Settings.MaxAngularCorrection, 0.0f);
limitImpulse = -m_motorMass * C;
}
else if (_limitState == LimitState.AtUpper)
{
float C = angle - _upperAngle;
angularError = C;
// Prevent large angular corrections and allow some slop.
C = MathUtils.Clamp(C - Settings.AngularSlop, 0.0f, Settings.MaxAngularCorrection);
limitImpulse = -m_motorMass * C;
}
aA -= m_invIA * limitImpulse;
aB += m_invIB * limitImpulse;
}
// Solve point-to-point constraint.
{
qA.Set(aA);
qB.Set(aB);
FVector2 rA = MathUtils.Mul(qA, LocalAnchorA - m_localCenterA);
FVector2 rB = MathUtils.Mul(qB, LocalAnchorB - m_localCenterB);
FVector2 C = cB + rB - cA - rA;
positionError = C.Length();
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
Mat22 K = new Mat22();
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;
FVector2 impulse = -K.Solve(C);
cA -= mA * impulse;
aA -= iA * MathUtils.Cross(rA, impulse);
cB += mB * impulse;
aB += iB * MathUtils.Cross(rB, impulse);
}
data.positions[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
return positionError <= Settings.LinearSlop && angularError <= Settings.AngularSlop;
}
/// <seealso cref="Joint.solvePositionConstraints(float)"></seealso>
public override bool SolvePositionConstraints(SolverData data)
{
Vec2 cA = data.Positions[m_indexA].C;
float aA = data.Positions[m_indexA].A;
Vec2 cB = data.Positions[m_indexB].C;
float aB = data.Positions[m_indexB].A;
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 temp = Pool.PopVec2();
Vec2 rA = Pool.PopVec2();
Vec2 rB = Pool.PopVec2();
qA.Set(aA);
qB.Set(aB);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
Rot.MulToOutUnsafe(qA, temp.Set(LocalAnchorA).SubLocal(m_localCenterA), rA);
Rot.MulToOutUnsafe(qB, temp.Set(LocalAnchorB).SubLocal(m_localCenterB), rB);
float positionError, angularError;
Mat33 K = Pool.PopMat33();
Vec2 C1 = Pool.PopVec2();
Vec2 P = Pool.PopVec2();
K.Ex.X = mA + mB + rA.Y * rA.Y * iA + rB.Y * rB.Y * iB;
K.Ey.X = (-rA.Y) * rA.X * iA - rB.Y * rB.X * iB;
K.Ez.X = (-rA.Y) * iA - rB.Y * iB;
K.Ex.Y = K.Ey.X;
K.Ey.Y = mA + mB + rA.X * rA.X * iA + rB.X * rB.X * iB;
K.Ez.Y = rA.X * iA + rB.X * iB;
K.Ex.Z = K.Ez.X;
K.Ey.Z = K.Ez.Y;
K.Ez.Z = iA + iB;
if (Frequency > 0.0f)
{
C1.Set(cB).AddLocal(rB).SubLocal(cA).SubLocal(rA);
positionError = C1.Length();
angularError = 0.0f;
K.Solve22ToOut(C1, P);
P.NegateLocal();
cA.X -= mA * P.X;
cA.Y -= mA * P.Y;
aA -= iA * Vec2.Cross(rA, P);
cB.X += mB * P.X;
cB.Y += mB * P.Y;
aB += iB * Vec2.Cross(rB, P);
}
else
{
C1.Set(cB).AddLocal(rB).SubLocal(cA).SubLocal(rA);
float C2 = aB - aA - m_referenceAngle;
positionError = C1.Length();
angularError = MathUtils.Abs(C2);
Vec3 C = Pool.PopVec3();
Vec3 impulse = Pool.PopVec3();
C.Set(C1.X, C1.Y, C2);
K.Solve33ToOut(C, impulse);
impulse.NegateLocal();
P.Set(impulse.X, impulse.Y);
cA.X -= mA * P.X;
cA.Y -= mA * P.Y;
aA -= iA * (Vec2.Cross(rA, P) + impulse.Z);
cB.X += mB * P.X;
cB.Y += mB * P.Y;
aB += iB * (Vec2.Cross(rB, P) + impulse.Z);
}
data.Positions[m_indexA].C.Set(cA);
data.Positions[m_indexA].A = aA;
data.Positions[m_indexB].C.Set(cB);
data.Positions[m_indexB].A = aB;
Pool.PushVec2(5);
Pool.PushRot(2);
Pool.PushMat33(1);
return(positionError <= Settings.LINEAR_SLOP && angularError <= Settings.ANGULAR_SLOP);
}
/// <seealso cref="Joint.initVelocityConstraints(TimeStep)"></seealso>
public override void InitVelocityConstraints(SolverData data)
{
m_indexA = BodyA.IslandIndex;
m_indexB = BodyB.IslandIndex;
m_localCenterA.Set(BodyA.Sweep.LocalCenter);
m_localCenterB.Set(BodyB.Sweep.LocalCenter);
m_invMassA = BodyA.InvMass;
m_invMassB = BodyB.InvMass;
m_invIA = BodyA.InvI;
m_invIB = BodyB.InvI;
// Vec2 cA = data.positions[m_indexA].c;
float aA = data.Positions[m_indexA].A;
Vec2 vA = data.Velocities[m_indexA].V;
float wA = data.Velocities[m_indexA].W;
// Vec2 cB = data.positions[m_indexB].c;
float aB = data.Positions[m_indexB].A;
Vec2 vB = data.Velocities[m_indexB].V;
float wB = data.Velocities[m_indexB].W;
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 temp = Pool.PopVec2();
qA.Set(aA);
qB.Set(aB);
// Compute the effective masses.
Rot.MulToOutUnsafe(qA, temp.Set(LocalAnchorA).SubLocal(m_localCenterA), m_rA);
Rot.MulToOutUnsafe(qB, temp.Set(LocalAnchorB).SubLocal(m_localCenterB), m_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 = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
Mat33 K = Pool.PopMat33();
K.Ex.X = mA + mB + m_rA.Y * m_rA.Y * iA + m_rB.Y * m_rB.Y * iB;
K.Ey.X = (-m_rA.Y) * m_rA.X * iA - m_rB.Y * m_rB.X * iB;
K.Ez.X = (-m_rA.Y) * iA - m_rB.Y * iB;
K.Ex.Y = K.Ey.X;
K.Ey.Y = mA + mB + m_rA.X * m_rA.X * iA + m_rB.X * m_rB.X * iB;
K.Ez.Y = m_rA.X * iA + m_rB.X * iB;
K.Ex.Z = K.Ez.X;
K.Ey.Z = K.Ez.Y;
K.Ez.Z = iA + iB;
if (Frequency > 0.0f)
{
K.GetInverse22(m_mass);
float invM = iA + iB;
float m = invM > 0.0f ? 1.0f / invM : 0.0f;
float C = aB - aA - m_referenceAngle;
// Frequency
float omega = 2.0f * MathUtils.PI * Frequency;
// Damping coefficient
float d = 2.0f * m * DampingRatio * omega;
// Spring stiffness
float k = m * omega * omega;
// magic formulas
float h = data.Step.Dt;
m_gamma = h * (d + h * k);
m_gamma = m_gamma != 0.0f ? 1.0f / m_gamma : 0.0f;
m_bias = C * h * k * m_gamma;
invM += m_gamma;
m_mass.Ez.Z = invM != 0.0f ? 1.0f / invM : 0.0f;
}
else
{
K.GetSymInverse33(m_mass);
m_gamma = 0.0f;
m_bias = 0.0f;
}
if (data.Step.WarmStarting)
{
Vec2 P = Pool.PopVec2();
// Scale impulses to support a variable time step.
m_impulse.MulLocal(data.Step.DtRatio);
P.Set(m_impulse.X, m_impulse.Y);
vA.X -= mA * P.X;
vA.Y -= mA * P.Y;
wA -= iA * (Vec2.Cross(m_rA, P) + m_impulse.Z);
vB.X += mB * P.X;
vB.Y += mB * P.Y;
wB += iB * (Vec2.Cross(m_rB, P) + m_impulse.Z);
Pool.PushVec2(1);
}
else
{
m_impulse.SetZero();
}
data.Velocities[m_indexA].V.Set(vA);
data.Velocities[m_indexA].W = wA;
data.Velocities[m_indexB].V.Set(vB);
data.Velocities[m_indexB].W = wB;
Pool.PushVec2(1);
Pool.PushRot(2);
Pool.PushMat33(1);
}
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;
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 vA = data.Velocities[IndexA].V;
float wA = data.Velocities[IndexA].W;
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 qA = Pool.PopRot();
Rot qB = Pool.PopRot();
qA.Set(aA);
qB.Set(aB);
// use m_u as temporary variable
Rot.MulToOutUnsafe(qA, U.Set(LocalAnchorA).SubLocal(LocalCenterA), RA);
Rot.MulToOutUnsafe(qB, U.Set(LocalAnchorB).SubLocal(LocalCenterB), RB);
U.Set(cB).AddLocal(RB).SubLocal(cA).SubLocal(RA);
Pool.PushRot(2);
// Handle singularity.
float length = U.Length();
if (length > Settings.LINEAR_SLOP)
{
U.X *= 1.0f / length;
U.Y *= 1.0f / length;
}
else
{
U.Set(0.0f, 0.0f);
}
float crAu = Vec2.Cross(RA, U);
float crBu = Vec2.Cross(RB, U);
float invMass = InvMassA + InvIA * crAu * crAu + InvMassB + InvIB * crBu * crBu;
// Compute the effective mass matrix.
Mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
if (FrequencyHz > 0.0f)
{
float C = length - Length;
// Frequency
float omega = 2.0f * MathUtils.PI * FrequencyHz;
// Damping coefficient
float d = 2.0f * Mass * DampingRatio * omega;
// Spring stiffness
float k = Mass * omega * omega;
// magic formulas
float h = data.Step.Dt;
Gamma = h * (d + h * k);
Gamma = Gamma != 0.0f ? 1.0f / Gamma : 0.0f;
Bias = C * h * k * Gamma;
invMass += Gamma;
Mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
}
else
{
Gamma = 0.0f;
Bias = 0.0f;
}
if (data.Step.WarmStarting)
{
// Scale the impulse to support a variable time step.
Impulse *= data.Step.DtRatio;
Vec2 P = Pool.PopVec2();
P.Set(U).MulLocal(Impulse);
vA.X -= InvMassA * P.X;
vA.Y -= InvMassA * P.Y;
wA -= InvIA * Vec2.Cross(RA, P);
vB.X += InvMassB * P.X;
vB.Y += InvMassB * P.Y;
wB += InvIB * Vec2.Cross(RB, P);
Pool.PushVec2(1);
}
else
{
Impulse = 0.0f;
}
data.Velocities[IndexA].V.Set(vA);
data.Velocities[IndexA].W = wA;
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
}
public override void InitVelocityConstraints(SolverData data)
{
IndexA = BodyA.IslandIndex;
IndexB = BodyB.IslandIndex;
m_localCenterA.Set(BodyA.Sweep.LocalCenter);
m_localCenterB.Set(BodyB.Sweep.LocalCenter);
InvMassA = BodyA.InvMass;
InvMassB = BodyB.InvMass;
InvIA = BodyA.InvI;
InvIB = BodyB.InvI;
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 vA = data.Velocities[IndexA].V;
float wA = data.Velocities[IndexA].W;
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 qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 temp = Pool.PopVec2();
qA.Set(aA);
qB.Set(aB);
// Compute the effective masses.
Rot.MulToOutUnsafe(qA, temp.Set(LocalAnchorA).SubLocal(m_localCenterA), RA);
Rot.MulToOutUnsafe(qB, temp.Set(LocalAnchorB).SubLocal(m_localCenterB), RB);
m_uA.Set(cA).AddLocal(RA).SubLocal(m_groundAnchorA);
m_uB.Set(cB).AddLocal(RB).SubLocal(m_groundAnchorB);
float lengthA = m_uA.Length();
float lengthB = m_uB.Length();
if (lengthA > 10f * Settings.LINEAR_SLOP)
{
m_uA.MulLocal(1.0f / lengthA);
}
else
{
m_uA.SetZero();
}
if (lengthB > 10f * Settings.LINEAR_SLOP)
{
m_uB.MulLocal(1.0f / lengthB);
}
else
{
m_uB.SetZero();
}
// Compute effective mass.
float ruA = Vec2.Cross(RA, m_uA);
float ruB = Vec2.Cross(RB, m_uB);
float mA = InvMassA + InvIA * ruA * ruA;
float mB = InvMassB + InvIB * ruB * ruB;
m_mass = mA + m_ratio * m_ratio * mB;
if (m_mass > 0.0f)
{
m_mass = 1.0f / m_mass;
}
if (data.Step.WarmStarting)
{
// Scale impulses to support variable time steps.
m_impulse *= data.Step.DtRatio;
// Warm starting.
Vec2 PA = Pool.PopVec2();
Vec2 PB = Pool.PopVec2();
PA.Set(m_uA).MulLocal(-m_impulse);
PB.Set(m_uB).MulLocal((-m_ratio) * m_impulse);
vA.X += InvMassA * PA.X;
vA.Y += InvMassA * PA.Y;
wA += InvIA * Vec2.Cross(RA, PA);
vB.X += InvMassB * PB.X;
vB.Y += InvMassB * PB.Y;
wB += InvIB * Vec2.Cross(RB, PB);
Pool.PushVec2(2);
}
else
{
m_impulse = 0.0f;
}
data.Velocities[IndexA].V.Set(vA);
data.Velocities[IndexA].W = wA;
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
Pool.PushVec2(1);
Pool.PushRot(2);
}
public override bool SolvePositionConstraints(SolverData data)
{
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 rA = Pool.PopVec2();
Vec2 rB = Pool.PopVec2();
Vec2 uA = Pool.PopVec2();
Vec2 uB = Pool.PopVec2();
Vec2 temp = Pool.PopVec2();
Vec2 PA = Pool.PopVec2();
Vec2 PB = Pool.PopVec2();
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 cB = data.Positions[IndexB].C;
float aB = data.Positions[IndexB].A;
qA.Set(aA);
qB.Set(aB);
Rot.MulToOutUnsafe(qA, temp.Set(LocalAnchorA).SubLocal(m_localCenterA), rA);
Rot.MulToOutUnsafe(qB, temp.Set(LocalAnchorB).SubLocal(m_localCenterB), rB);
uA.Set(cA).AddLocal(rA).SubLocal(m_groundAnchorA);
uB.Set(cB).AddLocal(rB).SubLocal(m_groundAnchorB);
float lengthA = uA.Length();
float lengthB = uB.Length();
if (lengthA > 10.0f * Settings.LINEAR_SLOP)
{
uA.MulLocal(1.0f / lengthA);
}
else
{
uA.SetZero();
}
if (lengthB > 10.0f * Settings.LINEAR_SLOP)
{
uB.MulLocal(1.0f / lengthB);
}
else
{
uB.SetZero();
}
// Compute effective mass.
float ruA = Vec2.Cross(rA, uA);
float ruB = Vec2.Cross(rB, uB);
float mA = InvMassA + InvIA * ruA * ruA;
float mB = InvMassB + InvIB * ruB * ruB;
float mass = mA + m_ratio * m_ratio * mB;
if (mass > 0.0f)
{
mass = 1.0f / mass;
}
float C = m_constant - lengthA - m_ratio * lengthB;
float linearError = MathUtils.Abs(C);
float impulse = (-mass) * C;
PA.Set(uA).MulLocal(-impulse);
PB.Set(uB).MulLocal((-m_ratio) * impulse);
cA.X += InvMassA * PA.X;
cA.Y += InvMassA * PA.Y;
aA += InvIA * Vec2.Cross(rA, PA);
cB.X += InvMassB * PB.X;
cB.Y += InvMassB * PB.Y;
aB += InvIB * Vec2.Cross(rB, PB);
data.Positions[IndexA].C.Set(cA);
data.Positions[IndexA].A = aA;
data.Positions[IndexB].C.Set(cB);
data.Positions[IndexB].A = aB;
Pool.PushRot(2);
Pool.PushVec2(7);
return(linearError < Settings.LINEAR_SLOP);
}
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;
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 vA = data.Velocities[IndexA].V;
float wA = data.Velocities[IndexA].W;
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 qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 d = Pool.PopVec2();
Vec2 temp = Pool.PopVec2();
Vec2 rA = Pool.PopVec2();
Vec2 rB = Pool.PopVec2();
qA.Set(aA);
qB.Set(aB);
// Compute the effective masses.
Rot.MulToOutUnsafe(qA, d.Set(LocalAnchorA).SubLocal(LocalCenterA), rA);
Rot.MulToOutUnsafe(qB, d.Set(LocalAnchorB).SubLocal(LocalCenterB), rB);
d.Set(cB).SubLocal(cA).AddLocal(rB).SubLocal(rA);
float mA = InvMassA, mB = InvMassB;
float iA = InvIA, iB = InvIB;
// Compute motor Jacobian and effective mass.
{
Rot.MulToOutUnsafe(qA, LocalXAxisA, Axis);
temp.Set(d).AddLocal(rA);
A1 = Vec2.Cross(temp, Axis);
A2 = Vec2.Cross(rB, Axis);
MotorMass = mA + mB + iA * A1 * A1 + iB * A2 * A2;
if (MotorMass > 0.0f)
{
MotorMass = 1.0f / MotorMass;
}
}
// Prismatic constraint.
{
Rot.MulToOutUnsafe(qA, LocalYAxisA, Perp);
temp.Set(d).AddLocal(rA);
S1 = Vec2.Cross(temp, Perp);
S2 = Vec2.Cross(rB, Perp);
float k11 = mA + mB + iA * S1 * S1 + iB * S2 * S2;
float k12 = iA * S1 + iB * S2;
float k13 = iA * S1 * A1 + iB * S2 * A2;
float k22 = iA + iB;
if (k22 == 0.0f)
{
// For bodies with fixed rotation.
k22 = 1.0f;
}
float k23 = iA * A1 + iB * A2;
float k33 = mA + mB + iA * A1 * A1 + iB * A2 * A2;
K.Ex.Set(k11, k12, k13);
K.Ey.Set(k12, k22, k23);
K.Ez.Set(k13, k23, k33);
}
// Compute motor and limit terms.
if (m_limitEnabled)
{
float jointTranslation = Vec2.Dot(Axis, d);
if (MathUtils.Abs(UpperTranslation - LowerTranslation) < 2.0f * Settings.LINEAR_SLOP)
{
LimitState = LimitState.Equal;
}
else if (jointTranslation <= LowerTranslation)
{
if (LimitState != LimitState.AtLower)
{
LimitState = LimitState.AtLower;
Impulse.Z = 0.0f;
}
}
else if (jointTranslation >= UpperTranslation)
{
if (LimitState != LimitState.AtUpper)
{
LimitState = LimitState.AtUpper;
Impulse.Z = 0.0f;
}
}
else
{
LimitState = LimitState.Inactive;
Impulse.Z = 0.0f;
}
}
else
{
LimitState = LimitState.Inactive;
Impulse.Z = 0.0f;
}
if (m_motorEnabled == false)
{
MotorImpulse = 0.0f;
}
if (data.Step.WarmStarting)
{
// Account for variable time step.
Impulse.MulLocal(data.Step.DtRatio);
MotorImpulse *= data.Step.DtRatio;
Vec2 P = Pool.PopVec2();
temp.Set(Axis).MulLocal(MotorImpulse + Impulse.Z);
P.Set(Perp).MulLocal(Impulse.X).AddLocal(temp);
float LA = Impulse.X * S1 + Impulse.Y + (MotorImpulse + Impulse.Z) * A1;
float LB = Impulse.X * S2 + Impulse.Y + (MotorImpulse + Impulse.Z) * A2;
vA.X -= mA * P.X;
vA.Y -= mA * P.Y;
wA -= iA * LA;
vB.X += mB * P.X;
vB.Y += mB * P.Y;
wB += iB * LB;
Pool.PushVec2(1);
}
else
{
Impulse.SetZero();
MotorImpulse = 0.0f;
}
data.Velocities[IndexA].V.Set(vA);
data.Velocities[IndexA].W = wA;
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
Pool.PushRot(2);
Pool.PushVec2(4);
}
public override bool SolvePositionConstraints(SolverData data)
{
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 rA = Pool.PopVec2();
Vec2 rB = Pool.PopVec2();
Vec2 d = Pool.PopVec2();
Vec2 axis = Pool.PopVec2();
Vec2 perp = Pool.PopVec2();
Vec2 temp = Pool.PopVec2();
Vec2 C1 = Pool.PopVec2();
Vec3 impulse = Pool.PopVec3();
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 cB = data.Positions[IndexB].C;
float aB = data.Positions[IndexB].A;
qA.Set(aA);
qB.Set(aB);
float mA = InvMassA, mB = InvMassB;
float iA = InvIA, iB = InvIB;
// Compute fresh Jacobians
Rot.MulToOutUnsafe(qA, temp.Set(LocalAnchorA).SubLocal(LocalCenterA), rA);
Rot.MulToOutUnsafe(qB, temp.Set(LocalAnchorB).SubLocal(LocalCenterB), rB);
d.Set(cB).AddLocal(rB).SubLocal(cA).SubLocal(rA);
Rot.MulToOutUnsafe(qA, LocalXAxisA, axis);
float a1 = Vec2.Cross(temp.Set(d).AddLocal(rA), axis);
float a2 = Vec2.Cross(rB, axis);
Rot.MulToOutUnsafe(qA, LocalYAxisA, perp);
float s1 = Vec2.Cross(temp.Set(d).AddLocal(rA), perp);
float s2 = Vec2.Cross(rB, perp);
C1.X = Vec2.Dot(perp, d);
C1.Y = aB - aA - ReferenceAngle;
float linearError = MathUtils.Abs(C1.X);
float angularError = MathUtils.Abs(C1.Y);
bool active = false;
float C2 = 0.0f;
if (m_limitEnabled)
{
float translation = Vec2.Dot(axis, d);
if (MathUtils.Abs(UpperTranslation - LowerTranslation) < 2.0f * Settings.LINEAR_SLOP)
{
// Prevent large angular corrections
C2 = MathUtils.Clamp(translation, -Settings.MAX_LINEAR_CORRECTION, Settings.MAX_LINEAR_CORRECTION);
linearError = MathUtils.Max(linearError, MathUtils.Abs(translation));
active = true;
}
else if (translation <= LowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = MathUtils.Clamp(translation - LowerTranslation + Settings.LINEAR_SLOP, -Settings.MAX_LINEAR_CORRECTION, 0.0f);
linearError = MathUtils.Max(linearError, LowerTranslation - translation);
active = true;
}
else if (translation >= UpperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = MathUtils.Clamp(translation - UpperTranslation - Settings.LINEAR_SLOP, 0.0f, Settings.MAX_LINEAR_CORRECTION);
linearError = MathUtils.Max(linearError, translation - UpperTranslation);
active = true;
}
}
if (active)
{
float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
float k12 = iA * s1 + iB * s2;
float k13 = iA * s1 * a1 + iB * s2 * a2;
float k22 = iA + iB;
if (k22 == 0.0f)
{
// For fixed rotation
k22 = 1.0f;
}
float k23 = iA * a1 + iB * a2;
float k33 = mA + mB + iA * a1 * a1 + iB * a2 * a2;
Mat33 K = Pool.PopMat33();
K.Ex.Set(k11, k12, k13);
K.Ey.Set(k12, k22, k23);
K.Ez.Set(k13, k23, k33);
Vec3 C = Pool.PopVec3();
C.X = C1.X;
C.Y = C1.Y;
C.Z = C2;
K.Solve33ToOut(C.NegateLocal(), impulse);
Pool.PushVec3(1);
Pool.PushMat33(1);
}
else
{
float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
float k12 = iA * s1 + iB * s2;
float k22 = iA + iB;
if (k22 == 0.0f)
{
k22 = 1.0f;
}
Mat22 K = Pool.PopMat22();
K.Ex.Set(k11, k12);
K.Ey.Set(k12, k22);
// temp is impulse1
K.SolveToOut(C1.NegateLocal(), temp);
C1.NegateLocal();
impulse.X = temp.X;
impulse.Y = temp.Y;
impulse.Z = 0.0f;
Pool.PushMat22(1);
}
float Px = impulse.X * perp.X + impulse.Z * axis.X;
float Py = impulse.X * perp.Y + impulse.Z * axis.Y;
float LA = impulse.X * s1 + impulse.Y + impulse.Z * a1;
float LB = impulse.X * s2 + impulse.Y + impulse.Z * a2;
cA.X -= mA * Px;
cA.Y -= mA * Py;
aA -= iA * LA;
cB.X += mB * Px;
cB.Y += mB * Py;
aB += iB * LB;
data.Positions[IndexA].C.Set(cA);
data.Positions[IndexA].A = aA;
data.Positions[IndexB].C.Set(cB);
data.Positions[IndexB].A = aB;
Pool.PushVec2(7);
Pool.PushVec3(1);
Pool.PushRot(2);
return(linearError <= Settings.LINEAR_SLOP && angularError <= Settings.ANGULAR_SLOP);
}
internal override bool SolvePositionConstraints()
{
Vector2 cA = _bodyA.GetRelativePoint(m_LocalCenterA);
Vector2 cA0 = cA;
float aA = _bodyA.rotation * Mathf.Deg2Rad;
Vector2 cB = _bodyB.GetRelativePoint(m_LocalCenterB);
Vector2 cB0 = cB;
float aB = _bodyB.rotation * Mathf.Deg2Rad;
Rot qA = new Rot(aA), qB = new Rot(aB);
float angularError = 0.0f;
float positionError;
bool fixedRotation = (m_InvIA + m_InvIB == 0.0f);
// Solve angular limit constraint.
if (m_EnableLimit && limitState != JointLimitState2D.Inactive && fixedRotation == false)
{
float angle = aB - aA - referenceAngle;
float limitImpulse = 0.0f;
if (limitState == JointLimitState2D.EqualLimits)
{
// Prevent large angular corrections
float C = Mathf.Clamp(angle - m_LowerAngle, -Constants.maxAngularCorrection, Constants.maxAngularCorrection);
limitImpulse = -m_MotorMass * C;
angularError = Mathf.Abs(C);
}
else if (limitState == JointLimitState2D.LowerLimit)
{
float C = angle - m_LowerAngle;
angularError = -C;
// Prevent large angular corrections and allow some slop.
C = Mathf.Clamp(C + Constants.angularSlop, -Constants.maxAngularCorrection, 0.0f);
limitImpulse = -m_MotorMass * C;
}
else if (limitState == JointLimitState2D.UpperLimit)
{
float C = angle - m_UpperAngle;
angularError = C;
// Prevent large angular corrections and allow some slop.
C = Mathf.Clamp(C - Constants.angularSlop, 0.0f, Constants.maxAngularCorrection);
limitImpulse = -m_MotorMass * C;
}
aA -= m_InvIA * limitImpulse;
aB += m_InvIB * limitImpulse;
}
// Solve point-to-point constraint.
{
qA.Set(aA);
qB.Set(aB);
Vector2 rA = MathUtils.Mul(qA, _localAnchorA - m_LocalCenterA);
Vector2 rB = MathUtils.Mul(qB, _localAnchorB - m_LocalCenterB);
Vector2 C = cB + rB - cA - rA;
positionError = C.magnitude;
float mA = m_InvMassA, mB = m_InvMassB;
float iA = m_InvIA, iB = m_InvIB;
Mat22 K = new Mat22();
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;
Vector2 impulse = -K.Solve(C);
cA -= mA * impulse;
aA -= iA * MathUtils.Cross(rA, impulse);
cB += mB * impulse;
aB += iB * MathUtils.Cross(rB, impulse);
}
if (!_bodyA.isKinematic)
{
var dcA = cA0 - cA;
_bodyA.position -= dcA;
if (!_bodyA.fixedAngle)
{
_bodyA.rotation = aA * Mathf.Rad2Deg;
}
}
if (!_bodyB.isKinematic)
{
var dcB = cB0 - cB;
_bodyB.position -= dcB;
if (!_bodyB.fixedAngle)
{
_bodyB.rotation = aB * Mathf.Rad2Deg;
}
}
return(positionError <= Constants.linearSlop && angularError <= Constants.angularSlop);
}
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);
}
public override bool SolvePositionConstraints(SolverData data)
{
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 cB = data.Positions[IndexB].C;
float aB = data.Positions[IndexB].A;
qA.Set(aA);
qB.Set(aB);
float angularError = 0.0f;
float positionError = 0.0f;
bool fixedRotation = (InvIA + InvIB == 0.0f);
// Solve angular limit constraint.
if (m_limitEnabled && LimitState != LimitState.Inactive && fixedRotation == false)
{
float angle = aB - aA - ReferenceAngle;
float limitImpulse = 0.0f;
if (LimitState == LimitState.Equal)
{
// Prevent large angular corrections
float C = MathUtils.Clamp(angle - LowerAngle, -Settings.MAX_ANGULAR_CORRECTION, Settings.MAX_ANGULAR_CORRECTION);
limitImpulse = (-MotorMass) * C;
angularError = MathUtils.Abs(C);
}
else if (LimitState == LimitState.AtLower)
{
float C = angle - LowerAngle;
angularError = -C;
// Prevent large angular corrections and allow some slop.
C = MathUtils.Clamp(C + Settings.ANGULAR_SLOP, -Settings.MAX_ANGULAR_CORRECTION, 0.0f);
limitImpulse = (-MotorMass) * C;
}
else if (LimitState == LimitState.AtUpper)
{
float C = angle - UpperAngle;
angularError = C;
// Prevent large angular corrections and allow some slop.
C = MathUtils.Clamp(C - Settings.ANGULAR_SLOP, 0.0f, Settings.MAX_ANGULAR_CORRECTION);
limitImpulse = (-MotorMass) * C;
}
aA -= InvIA * limitImpulse;
aB += InvIB * limitImpulse;
}
// Solve point-to-point constraint.
{
qA.Set(aA);
qB.Set(aB);
Vec2 rA = Pool.PopVec2();
Vec2 rB = Pool.PopVec2();
Vec2 C = Pool.PopVec2();
Vec2 impulse = Pool.PopVec2();
Rot.MulToOutUnsafe(qA, C.Set(LocalAnchorA).SubLocal(LocalCenterA), rA);
Rot.MulToOutUnsafe(qB, C.Set(LocalAnchorB).SubLocal(LocalCenterB), rB);
C.Set(cB).AddLocal(rB).SubLocal(cA).SubLocal(rA);
positionError = C.Length();
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.SolveToOut(C, impulse);
impulse.NegateLocal();
cA.X -= mA * impulse.X;
cA.Y -= mA * impulse.Y;
aA -= iA * Vec2.Cross(rA, impulse);
cB.X += mB * impulse.X;
cB.Y += mB * impulse.Y;
aB += iB * Vec2.Cross(rB, impulse);
Pool.PushVec2(4);
Pool.PushMat22(1);
}
data.Positions[IndexA].C.Set(cA);
data.Positions[IndexA].A = aA;
data.Positions[IndexB].C.Set(cB);
data.Positions[IndexB].A = aB;
Pool.PushRot(2);
return(positionError <= Settings.LINEAR_SLOP && angularError <= Settings.ANGULAR_SLOP);
}
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;
// Vec2 cA = data.positions[m_indexA].c;
float aA = data.Positions[IndexA].A;
Vec2 vA = data.Velocities[IndexA].V;
float wA = data.Velocities[IndexA].W;
// Vec2 cB = data.positions[m_indexB].c;
float aB = data.Positions[IndexB].A;
Vec2 vB = data.Velocities[IndexB].V;
float wB = data.Velocities[IndexB].W;
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 temp = Pool.PopVec2();
qA.Set(aA);
qB.Set(aB);
// Compute the effective masses.
Rot.MulToOutUnsafe(qA, temp.Set(LocalAnchorA).SubLocal(LocalCenterA), RA);
Rot.MulToOutUnsafe(qB, temp.Set(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;
bool fixedRotation = (iA + iB == 0.0f);
Mass.Ex.X = mA + mB + RA.Y * RA.Y * iA + RB.Y * RB.Y * iB;
Mass.Ey.X = (-RA.Y) * RA.X * iA - RB.Y * RB.X * iB;
Mass.Ez.X = (-RA.Y) * iA - RB.Y * iB;
Mass.Ex.Y = Mass.Ey.X;
Mass.Ey.Y = mA + mB + RA.X * RA.X * iA + RB.X * RB.X * iB;
Mass.Ez.Y = RA.X * iA + RB.X * iB;
Mass.Ex.Z = Mass.Ez.X;
Mass.Ey.Z = Mass.Ez.Y;
Mass.Ez.Z = iA + iB;
MotorMass = iA + iB;
if (MotorMass > 0.0f)
{
MotorMass = 1.0f / MotorMass;
}
if (m_motorEnabled == false || fixedRotation)
{
MotorImpulse = 0.0f;
}
if (m_limitEnabled && fixedRotation == false)
{
float jointAngle = aB - aA - ReferenceAngle;
if (MathUtils.Abs(UpperAngle - LowerAngle) < 2.0f * Settings.ANGULAR_SLOP)
{
LimitState = LimitState.Equal;
}
else if (jointAngle <= LowerAngle)
{
if (LimitState != LimitState.AtLower)
{
Impulse.Z = 0.0f;
}
LimitState = LimitState.AtLower;
}
else if (jointAngle >= UpperAngle)
{
if (LimitState != LimitState.AtUpper)
{
Impulse.Z = 0.0f;
}
LimitState = LimitState.AtUpper;
}
else
{
LimitState = LimitState.Inactive;
Impulse.Z = 0.0f;
}
}
else
{
LimitState = LimitState.Inactive;
}
if (data.Step.WarmStarting)
{
Vec2 P = Pool.PopVec2();
// Scale impulses to support a variable time step.
Impulse.X *= data.Step.DtRatio;
Impulse.Y *= data.Step.DtRatio;
MotorImpulse *= data.Step.DtRatio;
P.X = Impulse.X;
P.Y = Impulse.Y;
vA.X -= mA * P.X;
vA.Y -= mA * P.Y;
wA -= iA * (Vec2.Cross(RA, P) + MotorImpulse + Impulse.Z);
vB.X += mB * P.X;
vB.Y += mB * P.Y;
wB += iB * (Vec2.Cross(RB, P) + MotorImpulse + Impulse.Z);
Pool.PushVec2(1);
}
else
{
Impulse.SetZero();
MotorImpulse = 0.0f;
}
data.Velocities[IndexA].V.Set(vA);
data.Velocities[IndexA].W = wA;
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
Pool.PushVec2(1);
Pool.PushRot(2);
}
/// <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);
}