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;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
Vector2 rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
Vector2 rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
Vector2 d = (cB - cA) + rB - rA;
Vector2 ay = Complex.Multiply(ref _localYAxis, ref qA);
float sAy = MathUtils.Cross(d + rA, ay);
float sBy = MathUtils.Cross(ref rB, ref ay);
float C = Vector2.Dot(d, ay);
float k = _invMassA + _invMassB + _invIA * _sAy * _sAy + _invIB * _sBy * _sBy;
float impulse;
if (k != 0.0f)
{
impulse = -C / k;
}
else
{
impulse = 0.0f;
}
Vector2 P = impulse * ay;
float LA = impulse * sAy;
float LB = impulse * sBy;
cA -= _invMassA * P;
aA -= _invIA * LA;
cB += _invMassB * P;
aB += _invIB * LB;
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
return(Math.Abs(C) <= Settings.LinearSlop);
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
if (Frequency > 0.0f)
{
// There is no position correction for soft distance constraints.
return(true);
}
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
Vector2 rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
Vector2 rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
Vector2 u = cB + rB - cA - rA;
float length = u.Length();
u = Vector2.Normalize(u);
float C = length - Length;
C = MathUtils.Clamp(C, -Settings.MaxLinearCorrection, Settings.MaxLinearCorrection);
float impulse = -_mass * C;
Vector2 P = impulse * u;
cA -= _invMassA * P;
aA -= _invIA * MathUtils.Cross(ref rA, ref P);
cB += _invMassB * P;
aB += _invIB * MathUtils.Cross(ref rB, ref P);
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
return(Math.Abs(C) < Settings.LinearSlop);
}
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;
Vector2 cC = data.positions[_indexC].c;
float aC = data.positions[_indexC].a;
Vector2 cD = data.positions[_indexD].c;
float aD = data.positions[_indexD].a;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
Complex qC = Complex.FromAngle(aC);
Complex qD = Complex.FromAngle(aD);
const float linearError = 0.0f;
float coordinateA, coordinateB;
Vector2 JvAC, JvBD;
float JwA, JwB, JwC, JwD;
float mass = 0.0f;
if (_typeA == JointType.Revolute)
{
JvAC = Vector2.Zero;
JwA = 1.0f;
JwC = 1.0f;
mass += _iA + _iC;
coordinateA = aA - aC - _referenceAngleA;
}
else
{
Vector2 u = Complex.Multiply(ref _localAxisC, ref qC);
Vector2 rC = Complex.Multiply(_localAnchorC - _lcC, ref qC);
Vector2 rA = Complex.Multiply(_localAnchorA - _lcA, ref qA);
JvAC = u;
JwC = MathUtils.Cross(ref rC, ref u);
JwA = MathUtils.Cross(ref rA, ref u);
mass += _mC + _mA + _iC * JwC * JwC + _iA * JwA * JwA;
Vector2 pC = _localAnchorC - _lcC;
Vector2 pA = Complex.Divide(rA + (cA - cC), ref qC);
coordinateA = Vector2.Dot(pA - pC, _localAxisC);
}
if (_typeB == JointType.Revolute)
{
JvBD = Vector2.Zero;
JwB = _ratio;
JwD = _ratio;
mass += _ratio * _ratio * (_iB + _iD);
coordinateB = aB - aD - _referenceAngleB;
}
else
{
Vector2 u = Complex.Multiply(ref _localAxisD, ref qD);
Vector2 rD = Complex.Multiply(_localAnchorD - _lcD, ref qD);
Vector2 rB = Complex.Multiply(_localAnchorB - _lcB, ref qB);
JvBD = _ratio * u;
JwD = _ratio * MathUtils.Cross(ref rD, ref u);
JwB = _ratio * MathUtils.Cross(ref rB, ref u);
mass += _ratio * _ratio * (_mD + _mB) + _iD * JwD * JwD + _iB * JwB * JwB;
Vector2 pD = _localAnchorD - _lcD;
Vector2 pB = Complex.Divide(rB + (cB - cD), ref qD);
coordinateB = Vector2.Dot(pB - pD, _localAxisD);
}
float C = (coordinateA + _ratio * coordinateB) - _constant;
float impulse = 0.0f;
if (mass > 0.0f)
{
impulse = -C / mass;
}
cA += _mA * impulse * JvAC;
aA += _iA * impulse * JwA;
cB += _mB * impulse * JvBD;
aB += _iB * impulse * JwB;
cC -= _mC * impulse * JvAC;
aC -= _iC * impulse * JwC;
cD -= _mD * impulse * JvBD;
aD -= _iD * impulse * JwD;
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
data.positions[_indexC].c = cC;
data.positions[_indexC].a = aC;
data.positions[_indexD].c = cD;
data.positions[_indexD].a = aD;
// TODO_ERIN not implemented
return(linearError < Settings.LinearSlop);
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = _bodyA.IslandIndex;
_indexB = _bodyB.IslandIndex;
_indexC = _bodyC.IslandIndex;
_indexD = _bodyD.IslandIndex;
_lcA = _bodyA._sweep.LocalCenter;
_lcB = _bodyB._sweep.LocalCenter;
_lcC = _bodyC._sweep.LocalCenter;
_lcD = _bodyD._sweep.LocalCenter;
_mA = _bodyA._invMass;
_mB = _bodyB._invMass;
_mC = _bodyC._invMass;
_mD = _bodyD._invMass;
_iA = _bodyA._invI;
_iB = _bodyB._invI;
_iC = _bodyC._invI;
_iD = _bodyD._invI;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
float aC = data.positions[_indexC].a;
Vector2 vC = data.velocities[_indexC].v;
float wC = data.velocities[_indexC].w;
float aD = data.positions[_indexD].a;
Vector2 vD = data.velocities[_indexD].v;
float wD = data.velocities[_indexD].w;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
Complex qC = Complex.FromAngle(aC);
Complex qD = Complex.FromAngle(aD);
_mass = 0.0f;
if (_typeA == JointType.Revolute)
{
_JvAC = Vector2.Zero;
_JwA = 1.0f;
_JwC = 1.0f;
_mass += _iA + _iC;
}
else
{
Vector2 u = Complex.Multiply(ref _localAxisC, ref qC);
Vector2 rC = Complex.Multiply(_localAnchorC - _lcC, ref qC);
Vector2 rA = Complex.Multiply(_localAnchorA - _lcA, ref qA);
_JvAC = u;
_JwC = MathUtils.Cross(ref rC, ref u);
_JwA = MathUtils.Cross(ref rA, ref u);
_mass += _mC + _mA + _iC * _JwC * _JwC + _iA * _JwA * _JwA;
}
if (_typeB == JointType.Revolute)
{
_JvBD = Vector2.Zero;
_JwB = _ratio;
_JwD = _ratio;
_mass += _ratio * _ratio * (_iB + _iD);
}
else
{
Vector2 u = Complex.Multiply(ref _localAxisD, ref qD);
Vector2 rD = Complex.Multiply(_localAnchorD - _lcD, ref qD);
Vector2 rB = Complex.Multiply(_localAnchorB - _lcB, ref qB);
_JvBD = _ratio * u;
_JwD = _ratio * MathUtils.Cross(ref rD, ref u);
_JwB = _ratio * MathUtils.Cross(ref rB, ref u);
_mass += _ratio * _ratio * (_mD + _mB) + _iD * _JwD * _JwD + _iB * _JwB * _JwB;
}
// Compute effective mass.
_mass = _mass > 0.0f ? 1.0f / _mass : 0.0f;
if (data.step.warmStarting)
{
vA += (_mA * _impulse) * _JvAC;
wA += _iA * _impulse * _JwA;
vB += (_mB * _impulse) * _JvBD;
wB += _iB * _impulse * _JwB;
vC -= (_mC * _impulse) * _JvAC;
wC -= _iC * _impulse * _JwC;
vD -= (_mD * _impulse) * _JvBD;
wD -= _iD * _impulse * _JwD;
}
else
{
_impulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
data.velocities[_indexC].v = vC;
data.velocities[_indexC].w = wC;
data.velocities[_indexD].v = vD;
data.velocities[_indexD].w = wD;
}
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;
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.
{
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
Vector2 rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
Vector2 rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
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(ref rA, ref impulse);
cB += mB * impulse;
aB += iB * MathUtils.Cross(ref rB, ref 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 void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
_rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
_rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
// 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 (_enableMotor == false || fixedRotation)
{
_motorImpulse = 0.0f;
}
if (_enableLimit && fixedRotation == false)
{
float jointAngle = aB - aA - ReferenceAngle;
if (Math.Abs(_upperAngle - _lowerAngle) < 2.0f * Settings.AngularSlop)
{
_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)
{
// Scale impulses to support a variable time step.
_impulse *= data.step.dtRatio;
_motorImpulse *= data.step.dtRatio;
Vector2 P = new Vector2(_impulse.X, _impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(ref _rA, ref P) + MotorImpulse + _impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(ref _rB, ref P) + MotorImpulse + _impulse.Z);
}
else
{
_impulse = Vector3.Zero;
_motorImpulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
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;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
Vector2 rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
Vector2 rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
// Get the pulley axes.
Vector2 uA = cA + rA - WorldAnchorA;
Vector2 uB = cB + rB - WorldAnchorB;
float lengthA = uA.Length();
float lengthB = uB.Length();
if (lengthA > 10.0f * Settings.LinearSlop)
{
uA *= 1.0f / lengthA;
}
else
{
uA = Vector2.Zero;
}
if (lengthB > 10.0f * Settings.LinearSlop)
{
uB *= 1.0f / lengthB;
}
else
{
uB = Vector2.Zero;
}
// Compute effective mass.
float ruA = MathUtils.Cross(ref rA, ref uA);
float ruB = MathUtils.Cross(ref rB, ref uB);
float mA = _invMassA + _invIA * ruA * ruA;
float mB = _invMassB + _invIB * ruB * ruB;
float mass = mA + Ratio * Ratio * mB;
if (mass > 0.0f)
{
mass = 1.0f / mass;
}
float C = Constant - lengthA - Ratio * lengthB;
float linearError = Math.Abs(C);
float impulse = -mass * C;
Vector2 PA = -impulse * uA;
Vector2 PB = -Ratio * impulse * uB;
cA += _invMassA * PA;
aA += _invIA * MathUtils.Cross(ref rA, ref PA);
cB += _invMassB * PB;
aB += _invIB * MathUtils.Cross(ref rB, ref PB);
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
return(linearError < Settings.LinearSlop);
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
_rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
_rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
// Get the pulley axes.
_uA = cA + _rA - WorldAnchorA;
_uB = cB + _rB - WorldAnchorB;
float lengthA = _uA.Length();
float lengthB = _uB.Length();
if (lengthA > 10.0f * Settings.LinearSlop)
{
_uA *= 1.0f / lengthA;
}
else
{
_uA = Vector2.Zero;
}
if (lengthB > 10.0f * Settings.LinearSlop)
{
_uB *= 1.0f / lengthB;
}
else
{
_uB = Vector2.Zero;
}
// Compute effective mass.
float ruA = MathUtils.Cross(ref _rA, ref _uA);
float ruB = MathUtils.Cross(ref _rB, ref _uB);
float mA = _invMassA + _invIA * ruA * ruA;
float mB = _invMassB + _invIB * ruB * ruB;
_mass = mA + Ratio * Ratio * mB;
if (_mass > 0.0f)
{
_mass = 1.0f / _mass;
}
if (data.step.warmStarting)
{
// Scale impulses to support variable time steps.
_impulse *= data.step.dtRatio;
// Warm starting.
Vector2 PA = -(_impulse) * _uA;
Vector2 PB = (-Ratio * _impulse) * _uB;
vA += _invMassA * PA;
wA += _invIA * MathUtils.Cross(ref _rA, ref PA);
vB += _invMassB * PB;
wB += _invIB * MathUtils.Cross(ref _rB, ref PB);
}
else
{
_impulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
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;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
// Compute fresh Jacobians
Vector2 rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
Vector2 rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
Vector2 d = cB + rB - cA - rA;
Vector2 axis = Complex.Multiply(ref _localXAxis, ref qA);
float a1 = MathUtils.Cross(d + rA, axis);
float a2 = MathUtils.Cross(ref rB, ref axis);
Vector2 perp = Complex.Multiply(ref _localYAxisA, ref qA);
float s1 = MathUtils.Cross(d + rA, perp);
float s2 = MathUtils.Cross(ref rB, ref perp);
Vector3 impulse;
Vector2 C1 = new Vector2();
C1.X = Vector2.Dot(perp, d);
C1.Y = aB - aA - ReferenceAngle;
float linearError = Math.Abs(C1.X);
float angularError = Math.Abs(C1.Y);
bool active = false;
float C2 = 0.0f;
if (_enableLimit)
{
float translation = Vector2.Dot(axis, d);
if (Math.Abs(_upperTranslation - _lowerTranslation) < 2.0f * Settings.LinearSlop)
{
// Prevent large angular corrections
C2 = MathUtils.Clamp(translation, -Settings.MaxLinearCorrection, Settings.MaxLinearCorrection);
linearError = Math.Max(linearError, Math.Abs(translation));
active = true;
}
else if (translation <= _lowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = MathUtils.Clamp(translation - _lowerTranslation + Settings.LinearSlop, -Settings.MaxLinearCorrection, 0.0f);
linearError = Math.Max(linearError, _lowerTranslation - translation);
active = true;
}
else if (translation >= _upperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = MathUtils.Clamp(translation - _upperTranslation - Settings.LinearSlop, 0.0f, Settings.MaxLinearCorrection);
linearError = Math.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 = new Mat33();
K.ex = new Vector3(k11, k12, k13);
K.ey = new Vector3(k12, k22, k23);
K.ez = new Vector3(k13, k23, k33);
Vector3 C = new Vector3();
C.X = C1.X;
C.Y = C1.Y;
C.Z = C2;
impulse = K.Solve33(-C);
}
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 = new Mat22();
K.ex = new Vector2(k11, k12);
K.ey = new Vector2(k12, k22);
Vector2 impulse1 = K.Solve(-C1);
impulse = new Vector3();
impulse.X = impulse1.X;
impulse.Y = impulse1.Y;
impulse.Z = 0.0f;
}
Vector2 P = impulse.X * perp + impulse.Z * axis;
float LA = impulse.X * s1 + impulse.Y + impulse.Z * a1;
float LB = impulse.X * s2 + impulse.Y + impulse.Z * a2;
cA -= mA * P;
aA -= iA * LA;
cB += mB * P;
aB += iB * LB;
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
return(linearError <= Settings.LinearSlop && angularError <= Settings.AngularSlop);
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
_rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
_rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
_u = cB + _rB - cA - _rA;
// Handle singularity.
float length = _u.Length();
if (length > Settings.LinearSlop)
{
_u *= 1.0f / length;
}
else
{
_u = Vector2.Zero;
}
float crAu = MathUtils.Cross(ref _rA, ref _u);
float crBu = MathUtils.Cross(ref _rB, ref _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 (Frequency > 0.0f)
{
float C = length - Length;
// Frequency
float omega = Constant.Tau * Frequency;
// 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;
Vector2 P = _impulse * _u;
vA -= _invMassA * P;
wA -= _invIA * MathUtils.Cross(ref _rA, ref P);
vB += _invMassB * P;
wB += _invIB * MathUtils.Cross(ref _rB, ref P);
}
else
{
_impulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invIA = BodyA._invI;
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Complex qA = Complex.FromAngle(aA);
float mass = BodyA.Mass;
// Frequency
float omega = Constant.Tau * 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);
_gamma = h * (d + h * k);
if (_gamma != 0.0f)
{
_gamma = 1.0f / _gamma;
}
_beta = h * k * _gamma;
// Compute the effective mass matrix.
_rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
// 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 = new Mat22();
K.ex.X = _invMassA + _invIA * _rA.Y * _rA.Y + _gamma;
K.ex.Y = -_invIA * _rA.X * _rA.Y;
K.ey.X = K.ex.Y;
K.ey.Y = _invMassA + _invIA * _rA.X * _rA.X + _gamma;
_mass = K.Inverse;
_C = cA + _rA - _worldAnchor;
_C *= _beta;
// Cheat with some damping
wA *= 0.98f;
if (data.step.warmStarting)
{
_impulse *= data.step.dtRatio;
vA += _invMassA * _impulse;
wA += _invIA * MathUtils.Cross(ref _rA, ref _impulse);
}
else
{
_impulse = Vector2.Zero;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
}
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;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
Vector2 rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
Vector2 rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
float positionError, angularError;
Mat33 K = new Mat33();
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 (FrequencyHz > 0.0f)
{
Vector2 C1 = cB + rB - cA - rA;
positionError = C1.Length();
angularError = 0.0f;
Vector2 P = -K.Solve22(C1);
cA -= mA * P;
aA -= iA * MathUtils.Cross(ref rA, ref P);
cB += mB * P;
aB += iB * MathUtils.Cross(ref rB, ref P);
}
else
{
Vector2 C1 = cB + rB - cA - rA;
float C2 = aB - aA - ReferenceAngle;
positionError = C1.Length();
angularError = Math.Abs(C2);
Vector3 C = new Vector3(C1.X, C1.Y, C2);
Vector3 impulse;
if (K.ez.Z <= 0.0f)
{
Vector2 impulse2 = -K.Solve22(C1);
impulse = new Vector3(impulse2.X, impulse2.Y, 0.0f);
}
else
{
impulse = -K.Solve33(C);
}
Vector2 P = new Vector2(impulse.X, impulse.Y);
cA -= mA * P;
aA -= iA * (MathUtils.Cross(ref rA, ref P) + impulse.Z);
cB += mB * P;
aB += iB * (MathUtils.Cross(ref rB, ref P) + impulse.Z);
}
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 void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
_rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
_rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
// 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;
Mat33 K = new Mat33();
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 (FrequencyHz > 0.0f)
{
K.GetInverse22(ref _mass);
float invM = iA + iB;
float m = invM > 0.0f ? 1.0f / invM : 0.0f;
float C = aB - aA - ReferenceAngle;
// Frequency
float omega = Constant.Tau * FrequencyHz;
// Damping coefficient
float d = 2.0f * m * DampingRatio * omega;
// Spring stiffness
float k = m * 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;
invM += _gamma;
_mass.ez.Z = invM != 0.0f ? 1.0f / invM : 0.0f;
}
else if (K.ez.Z == 0.0f)
{
K.GetInverse22(ref _mass);
_gamma = 0.0f;
_bias = 0.0f;
}
else
{
K.GetSymInverse33(ref _mass);
_gamma = 0.0f;
_bias = 0.0f;
}
if (data.step.warmStarting)
{
// Scale impulses to support a variable time step.
_impulse *= data.step.dtRatio;
Vector2 P = new Vector2(_impulse.X, _impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(ref _rA, ref P) + _impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(ref _rB, ref P) + _impulse.Z);
}
else
{
_impulse = Vector3.Zero;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
// Compute the effective masses.
Vector2 rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
Vector2 rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
Vector2 d1 = cB + rB - cA - rA;
// Point to line constraint
{
_ay = Complex.Multiply(ref _localYAxis, ref qA);
_sAy = MathUtils.Cross(d1 + rA, _ay);
_sBy = MathUtils.Cross(ref rB, ref _ay);
_mass = mA + mB + iA * _sAy * _sAy + iB * _sBy * _sBy;
if (_mass > 0.0f)
{
_mass = 1.0f / _mass;
}
}
// Spring constraint
_springMass = 0.0f;
_bias = 0.0f;
_gamma = 0.0f;
if (Frequency > 0.0f)
{
_ax = Complex.Multiply(ref _localXAxis, ref qA);
_sAx = MathUtils.Cross(d1 + rA, _ax);
_sBx = MathUtils.Cross(ref rB, ref _ax);
float invMass = mA + mB + iA * _sAx * _sAx + iB * _sBx * _sBx;
if (invMass > 0.0f)
{
_springMass = 1.0f / invMass;
float C = Vector2.Dot(d1, _ax);
// Frequency
float omega = Constant.Tau * Frequency;
// Damping coefficient
float d = 2.0f * _springMass * DampingRatio * omega;
// Spring stiffness
float k = _springMass * omega * omega;
// magic formulas
float h = data.step.dt;
_gamma = h * (d + h * k);
if (_gamma > 0.0f)
{
_gamma = 1.0f / _gamma;
}
_bias = C * h * k * _gamma;
_springMass = invMass + _gamma;
if (_springMass > 0.0f)
{
_springMass = 1.0f / _springMass;
}
}
}
else
{
_springImpulse = 0.0f;
}
// Rotational motor
if (_enableMotor)
{
_motorMass = iA + iB;
if (_motorMass > 0.0f)
{
_motorMass = 1.0f / _motorMass;
}
}
else
{
_motorMass = 0.0f;
_motorImpulse = 0.0f;
}
if (data.step.warmStarting)
{
// Account for variable time step.
_impulse *= data.step.dtRatio;
_springImpulse *= data.step.dtRatio;
_motorImpulse *= data.step.dtRatio;
Vector2 P = _impulse * _ay + _springImpulse * _ax;
float LA = _impulse * _sAy + _springImpulse * _sAx + _motorImpulse;
float LB = _impulse * _sBy + _springImpulse * _sBx + _motorImpulse;
vA -= _invMassA * P;
wA -= _invIA * LA;
vB += _invMassB * P;
wB += _invIB * LB;
}
else
{
_impulse = 0.0f;
_springImpulse = 0.0f;
_motorImpulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
// Compute the effective mass matrix.
_rA = -Complex.Multiply(ref _localCenterA, ref qA);
_rB = -Complex.Multiply(ref _localCenterB, ref qB);
// 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 = 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;
_linearMass = K.Inverse;
_angularMass = iA + iB;
if (_angularMass > 0.0f)
{
_angularMass = 1.0f / _angularMass;
}
_linearError = cB + _rB - cA - _rA - Complex.Multiply(ref _linearOffset, ref qA);
_angularError = aB - aA - _angularOffset;
if (data.step.warmStarting)
{
// Scale impulses to support a variable time step.
_linearImpulse *= data.step.dtRatio;
_angularImpulse *= data.step.dtRatio;
Vector2 P = new Vector2(_linearImpulse.X, _linearImpulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(ref _rA, ref P) + _angularImpulse);
vB += mB * P;
wB += iB * (MathUtils.Cross(ref _rB, ref P) + _angularImpulse);
}
else
{
_linearImpulse = Vector2.Zero;
_angularImpulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
_rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
_rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
_u = cB + _rB - cA - _rA;
_length = _u.Length();
float C = _length - MaxLength;
if (C > 0.0f)
{
State = LimitState.AtUpper;
}
else
{
State = LimitState.Inactive;
}
if (_length > Settings.LinearSlop)
{
_u *= 1.0f / _length;
}
else
{
_u = Vector2.Zero;
_mass = 0.0f;
_impulse = 0.0f;
return;
}
// Compute effective mass.
float crA = MathUtils.Cross(ref _rA, ref _u);
float crB = MathUtils.Cross(ref _rB, ref _u);
float invMass = _invMassA + _invIA * crA * crA + _invMassB + _invIB * crB * crB;
_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
if (data.step.warmStarting)
{
// Scale the impulse to support a variable time step.
_impulse *= data.step.dtRatio;
Vector2 P = _impulse * _u;
vA -= _invMassA * P;
wA -= _invIA * MathUtils.Cross(ref _rA, ref P);
vB += _invMassB * P;
wB += _invIB * MathUtils.Cross(ref _rB, ref P);
}
else
{
_impulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
// Compute the effective masses.
Vector2 rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
Vector2 rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
Vector2 d = (cB - cA) + rB - rA;
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
// Compute motor Jacobian and effective mass.
{
_axis = Complex.Multiply(ref _localXAxis, ref qA);
_a1 = MathUtils.Cross(d + rA, _axis);
_a2 = MathUtils.Cross(ref rB, ref _axis);
_motorMass = mA + mB + iA * _a1 * _a1 + iB * _a2 * _a2;
if (_motorMass > 0.0f)
{
_motorMass = 1.0f / _motorMass;
}
}
// Prismatic constraint.
{
_perp = Complex.Multiply(ref _localYAxisA, ref qA);
_s1 = MathUtils.Cross(d + rA, _perp);
_s2 = MathUtils.Cross(ref rB, ref _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 = new Vector3(k11, k12, k13);
_K.ey = new Vector3(k12, k22, k23);
_K.ez = new Vector3(k13, k23, k33);
}
// Compute motor and limit terms.
if (_enableLimit)
{
float jointTranslation = Vector2.Dot(_axis, d);
if (Math.Abs(_upperTranslation - _lowerTranslation) < 2.0f * Settings.LinearSlop)
{
_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 (_enableMotor == false)
{
MotorImpulse = 0.0f;
}
if (data.step.warmStarting)
{
// Account for variable time step.
_impulse *= data.step.dtRatio;
MotorImpulse *= data.step.dtRatio;
Vector2 P = _impulse.X * _perp + (MotorImpulse + _impulse.Z) * _axis;
float LA = _impulse.X * _s1 + _impulse.Y + (MotorImpulse + _impulse.Z) * _a1;
float LB = _impulse.X * _s2 + _impulse.Y + (MotorImpulse + _impulse.Z) * _a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
_impulse = Vector3.Zero;
MotorImpulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}