internal override void SolveVelocityConstraints(SolverData data){
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
// Cdot = dot(u, v + cross(w, r))
Vec2 vpA = vA + Utilities.Cross(wA, m_rA);
Vec2 vpB = vB + Utilities.Cross(wB, m_rB);
float C = m_length - m_maxLength;
float Cdot = Utilities.Dot(m_u, vpB - vpA);
// Predictive constraint.
if (C < 0.0f)
{
Cdot += data.step.inv_dt * C;
}
float impulse = -m_mass * Cdot;
float oldImpulse = m_impulse;
m_impulse = Math.Min(0.0f, m_impulse + impulse);
impulse = m_impulse - oldImpulse;
Vec2 P = impulse * m_u;
vA -= m_invMassA * P;
wA -= m_invIA * Utilities.Cross(m_rA, P);
vB += m_invMassB * P;
wB += m_invIB * Utilities.Cross(m_rB, P);
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
// This returns true if the position errors are within tolerance. internal abstract bool SolvePositionConstraints(SolverData data);
internal override void SolveVelocityConstraints(SolverData data) {
throw new NotImplementedException();
//Vec2 vB = data.velocities[m_indexB].v;
//float wB = data.velocities[m_indexB].w;
//// Cdot = v + cross(w, r)
//Vec2 Cdot = vB + Utilities.Cross(wB, m_rB);
//Vec2 impulse = Utilities.Mul(m_mass, -(Cdot + m_C + m_gamma * m_impulse));
//Vec2 oldImpulse = m_impulse;
//m_impulse += impulse;
//float maxImpulse = data.step.dt * m_maxForce;
//if (m_impulse.LengthSquared() > maxImpulse * maxImpulse)
//{
// m_impulse *= maxImpulse / m_impulse.Length();
//}
//impulse = m_impulse - oldImpulse;
//vB += m_invMassB * impulse;
//wB += m_invIB * Utilities.Cross(m_rB, impulse);
//data.velocities[m_indexB].v = vB;
//data.velocities[m_indexB].w = wB;
}
internal 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 = new Rot(aA);
Rot qB = new Rot(aB);
float angularError = 0.0f;
float positionError = 0.0f;
bool fixedRotation = (m_invIA + m_invIB == 0.0f);
// Solve angular limit constraint.
if (m_enableLimit && m_limitState != LimitState.e_inactiveLimit && fixedRotation == false)
{
float angle = aB - aA - m_referenceAngle;
float limitImpulse = 0.0f;
if (m_limitState ==LimitState.e_equalLimits)
{
// Prevent large angular corrections
float C = Utilities.Clamp(angle - m_lowerAngle, -Settings._maxAngularCorrection, Settings._maxAngularCorrection);
limitImpulse = -m_motorMass * C;
angularError = Math.Abs(C);
}
else if (m_limitState == LimitState.e_atLowerLimit)
{
float C = angle - m_lowerAngle;
angularError = -C;
// Prevent large angular corrections and allow some slop.
C = Utilities.Clamp(C + Settings._angularSlop, -Settings._maxAngularCorrection, 0.0f);
limitImpulse = -m_motorMass * C;
}
else if (m_limitState == LimitState.e_atUpperLimit)
{
float C = angle - m_upperAngle;
angularError = C;
// Prevent large angular corrections and allow some slop.
C = Utilities.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);
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
Vec2 C = cB + rB - cA - rA;
positionError = C.Length();
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
Mat22 K;
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;
Vec2 impulse = -K.Solve(C);
cA -= mA * impulse;
aA -= iA * Utilities.Cross(rA, impulse);
cB += mB * impulse;
aB += iB * Utilities.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;
}
internal override void SolveVelocityConstraints(SolverData data){
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
float h = data.step.dt;
float inv_h = data.step.inv_dt;
// Solve angular friction
{
float Cdot = wB - wA + inv_h * m_correctionFactor * m_angularError;
float impulse = -m_angularMass * Cdot;
float oldImpulse = m_angularImpulse;
float maxImpulse = h * m_maxTorque;
m_angularImpulse = Utilities.Clamp(m_angularImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_angularImpulse - oldImpulse;
wA -= iA * impulse;
wB += iB * impulse;
}
// Solve linear friction
{
Vec2 Cdot = vB + Utilities.Cross(wB, m_rB) - vA - Utilities.Cross(wA, m_rA) + inv_h * m_correctionFactor * m_linearError;
Vec2 impulse = -Utilities.Mul(m_linearMass, Cdot);
Vec2 oldImpulse = m_linearImpulse;
m_linearImpulse += impulse;
float maxImpulse = h * m_maxForce;
if (m_linearImpulse.LengthSquared() > maxImpulse * maxImpulse)
{
m_linearImpulse.Normalize();
m_linearImpulse *= maxImpulse;
}
impulse = m_linearImpulse - oldImpulse;
vA -= mA * impulse;
wA -= iA * Utilities.Cross(m_rA, impulse);
vB += mB * impulse;
wB += iB * Utilities.Cross(m_rB, impulse);
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void InitVelocityConstraints(SolverData data){
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA = m_bodyA.m_sweep.localCenter;
m_localCenterB = m_bodyB.m_sweep.localCenter;
m_invMassA = m_bodyA.m_invMass;
m_invMassB = m_bodyB.m_invMass;
m_invIA = m_bodyA.m_invI;
m_invIB = m_bodyB.m_invI;
float aA = data.positions[m_indexA].a;
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
float aB = data.positions[m_indexB].a;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
Rot qA = new Rot(aA); Rot qB = new Rot(aB);
m_rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
m_rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
// 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;
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 (m_frequencyHz > 0.0f)
{
K.GetInverse22(out 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 * (float)Math.PI * m_frequencyHz;
// Damping coefficient
float d = 2.0f * m * 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(out m_mass);
m_gamma = 0.0f;
m_bias = 0.0f;
}
if (data.step.warmStarting)
{
// Scale impulses to support a variable time step.
m_impulse *= data.step.dtRatio;
Vec2 P = new Vec2(m_impulse.X, m_impulse.Y);
vA -= mA * P;
wA -= iA * (Utilities.Cross(m_rA, P) + m_impulse.Z);
vB += mB * P;
wB += iB * (Utilities.Cross(m_rB, P) + m_impulse.Z);
}
else
{
m_impulse.SetZero();
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void InitVelocityConstraints(SolverData data){
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA = m_bodyA.m_sweep.localCenter;
m_localCenterB = m_bodyB.m_sweep.localCenter;
m_invMassA = m_bodyA.m_invMass;
m_invMassB = m_bodyB.m_invMass;
m_invIA = m_bodyA.m_invI;
m_invIB = m_bodyB.m_invI;
float aA = data.positions[m_indexA].a;
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
float aB = data.positions[m_indexB].a;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
Rot qA = new Rot(aA); Rot qB = new Rot(aB);
m_rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
m_rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
// 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;
bool fixedRotation = (iA + iB == 0.0f);
m_mass.ex.X = mA + mB + m_rA.Y * m_rA.Y * iA + m_rB.Y * m_rB.Y * iB;
m_mass.ey.X = -m_rA.Y * m_rA.X * iA - m_rB.Y * m_rB.X * iB;
m_mass.ez.X = -m_rA.Y * iA - m_rB.Y * iB;
m_mass.ex.Y = m_mass.ey.X;
m_mass.ey.Y = mA + mB + m_rA.X * m_rA.X * iA + m_rB.X * m_rB.X * iB;
m_mass.ez.Y = m_rA.X * iA + m_rB.X * iB;
m_mass.ex.Z = m_mass.ez.X;
m_mass.ey.Z = m_mass.ez.Y;
m_mass.ez.Z = iA + iB;
m_motorMass = iA + iB;
if (m_motorMass > 0.0f)
{
m_motorMass = 1.0f / m_motorMass;
}
if (m_enableMotor == false || fixedRotation)
{
m_motorImpulse = 0.0f;
}
if (m_enableLimit && fixedRotation == false)
{
float jointAngle = aB - aA - m_referenceAngle;
if (Math.Abs(m_upperAngle - m_lowerAngle) < 2.0f * Settings._angularSlop)
{
m_limitState = LimitState.e_equalLimits;
}
else if (jointAngle <= m_lowerAngle)
{
if (m_limitState != LimitState.e_atLowerLimit)
{
m_impulse.Z = 0.0f;
}
m_limitState = LimitState.e_atLowerLimit;
}
else if (jointAngle >= m_upperAngle)
{
if (m_limitState != LimitState.e_atUpperLimit)
{
m_impulse.Z = 0.0f;
}
m_limitState = LimitState.e_atUpperLimit;
}
else
{
m_limitState = LimitState.e_inactiveLimit;
m_impulse.Z = 0.0f;
}
}
else
{
m_limitState = LimitState.e_inactiveLimit;
}
if (data.step.warmStarting)
{
// Scale impulses to support a variable time step.
m_impulse *= data.step.dtRatio;
m_motorImpulse *= data.step.dtRatio;
Vec2 P = new Vec2(m_impulse.X, m_impulse.Y);
vA -= mA * P;
wA -= iA * (Utilities.Cross(m_rA, P) + m_motorImpulse + m_impulse.Z);
vB += mB * P;
wB += iB * (Utilities.Cross(m_rB, P) + m_motorImpulse + m_impulse.Z);
}
else
{
m_impulse.SetZero();
m_motorImpulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal 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;
Vec2 cC = data.positions[m_indexC].c;
float aC = data.positions[m_indexC].a;
Vec2 cD = data.positions[m_indexD].c;
float aD = data.positions[m_indexD].a;
Rot qA = new Rot(aA);
Rot qB = new Rot(aB);
Rot qC = new Rot(aC);
Rot qD = new Rot(aD);
float linearError = 0.0f;
float coordinateA, coordinateB;
Vec2 JvAC = new Vec2();
Vec2 JvBD = new Vec2();
float JwA, JwB, JwC, JwD;
float mass = 0.0f;
if (m_typeA == JointType.e_revoluteJoint)
{
JvAC.SetZero();
JwA = 1.0f;
JwC = 1.0f;
mass += m_iA + m_iC;
coordinateA = aA - aC - m_referenceAngleA;
}
else
{
Vec2 u = Utilities.Mul(qC, m_localAxisC);
Vec2 rC = Utilities.Mul(qC, m_localAnchorC - m_lcC);
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_lcA);
JvAC = u;
JwC = Utilities.Cross(rC, u);
JwA = Utilities.Cross(rA, u);
mass += m_mC + m_mA + m_iC * JwC * JwC + m_iA * JwA * JwA;
Vec2 pC = m_localAnchorC - m_lcC;
Vec2 pA = Utilities.MulT(qC, rA + (cA - cC));
coordinateA = Utilities.Dot(pA - pC, m_localAxisC);
}
if (m_typeB == JointType.e_revoluteJoint)
{
JvBD.SetZero();
JwB = m_ratio;
JwD = m_ratio;
mass += m_ratio * m_ratio * (m_iB + m_iD);
coordinateB = aB - aD - m_referenceAngleB;
}
else
{
Vec2 u = Utilities.Mul(qD, m_localAxisD);
Vec2 rD = Utilities.Mul(qD, m_localAnchorD - m_lcD);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_lcB);
JvBD = m_ratio * u;
JwD = m_ratio * Utilities.Cross(rD, u);
JwB = m_ratio * Utilities.Cross(rB, u);
mass += m_ratio * m_ratio * (m_mD + m_mB) + m_iD * JwD * JwD + m_iB * JwB * JwB;
Vec2 pD = m_localAnchorD - m_lcD;
Vec2 pB = Utilities.MulT(qD, rB + (cB - cD));
coordinateB = Utilities.Dot(pB - pD, m_localAxisD);
}
float C = (coordinateA + m_ratio * coordinateB) - m_constant;
float impulse = 0.0f;
if (mass > 0.0f)
{
impulse = -C / mass;
}
cA += m_mA * impulse * JvAC;
aA += m_iA * impulse * JwA;
cB += m_mB * impulse * JvBD;
aB += m_iB * impulse * JwB;
cC -= m_mC * impulse * JvAC;
aC -= m_iC * impulse * JwC;
cD -= m_mD * impulse * JvBD;
aD -= m_iD * impulse * JwD;
data.positions[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
data.positions[m_indexC].c = cC;
data.positions[m_indexC].a = aC;
data.positions[m_indexD].c = cD;
data.positions[m_indexD].a = aD;
// TODO_ERIN not implemented
return(linearError < Settings._linearSlop);
}
internal override void InitVelocityConstraints(SolverData data) {
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA = m_bodyA.m_sweep.localCenter;
m_localCenterB = m_bodyB.m_sweep.localCenter;
m_invMassA = m_bodyA.m_invMass;
m_invMassB = m_bodyB.m_invMass;
m_invIA = m_bodyA.m_invI;
m_invIB = m_bodyB.m_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 = new Rot(aA);
Rot qB = new Rot(aB);
// Compute the effective masses.
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
Vec2 d = (cB - cA) + rB - rA;
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Compute motor Jacobian and effective mass.
{
m_axis = Utilities.Mul(qA, m_localXAxisA);
m_a1 = Utilities.Cross(d + rA, m_axis);
m_a2 = Utilities.Cross(rB, m_axis);
m_motorMass = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
if (m_motorMass > 0.0f)
{
m_motorMass = 1.0f / m_motorMass;
}
}
// Prismatic constraint.
{
m_perp = Utilities.Mul(qA, m_localYAxisA);
m_s1 = Utilities.Cross(d + rA, m_perp);
m_s2 = Utilities.Cross(rB, m_perp);
float k11 = mA + mB + iA * m_s1 * m_s1 + iB * m_s2 * m_s2;
float k12 = iA * m_s1 + iB * m_s2;
float k13 = iA * m_s1 * m_a1 + iB * m_s2 * m_a2;
float k22 = iA + iB;
if (k22 == 0.0f)
{
// For bodies with fixed rotation.
k22 = 1.0f;
}
float k23 = iA * m_a1 + iB * m_a2;
float k33 = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
m_K.ex.Set(k11, k12, k13);
m_K.ey.Set(k12, k22, k23);
m_K.ez.Set(k13, k23, k33);
}
// Compute motor and limit terms.
if (m_enableLimit)
{
float jointTranslation = Utilities.Dot(m_axis, d);
if (Math.Abs(m_upperTranslation - m_lowerTranslation) < 2.0f *Settings._linearSlop)
{
m_limitState = LimitState.e_equalLimits;
}
else if (jointTranslation <= m_lowerTranslation)
{
if (m_limitState != LimitState.e_atLowerLimit)
{
m_limitState = LimitState.e_atLowerLimit;
m_impulse.Z = 0.0f;
}
}
else if (jointTranslation >= m_upperTranslation)
{
if (m_limitState != LimitState.e_atUpperLimit)
{
m_limitState = LimitState.e_atUpperLimit;
m_impulse.Z = 0.0f;
}
}
else
{
m_limitState = LimitState.e_inactiveLimit;
m_impulse.Z = 0.0f;
}
}
else
{
m_limitState = LimitState.e_inactiveLimit;
m_impulse.Z = 0.0f;
}
if (m_enableMotor == false)
{
m_motorImpulse = 0.0f;
}
if (data.step.warmStarting)
{
// Account for variable time step.
m_impulse *= data.step.dtRatio;
m_motorImpulse *= data.step.dtRatio;
Vec2 P = m_impulse.X * m_perp + (m_motorImpulse + m_impulse.Z) * m_axis;
float LA = m_impulse.X * m_s1 + m_impulse.Y + (m_motorImpulse + m_impulse.Z) * m_a1;
float LB = m_impulse.X * m_s2 + m_impulse.Y + (m_motorImpulse + m_impulse.Z) * m_a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
m_impulse.SetZero();
m_motorImpulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void InitVelocityConstraints(SolverData data)
{
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA = m_bodyA.m_sweep.localCenter;
m_localCenterB = m_bodyB.m_sweep.localCenter;
m_invMassA = m_bodyA.m_invMass;
m_invMassB = m_bodyB.m_invMass;
m_invIA = m_bodyA.m_invI;
m_invIB = m_bodyB.m_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 = new Rot(aA);
Rot qB = new Rot(aB);
m_rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
m_rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
m_u = cB + m_rB - cA - m_rA;
// Handle singularity.
float length = m_u.Length();
if (length > Settings._linearSlop)
{
m_u *= 1.0f / length;
}
else
{
m_u.Set(0.0f, 0.0f);
}
float crAu = Utilities.Cross(m_rA, m_u);
float crBu = Utilities.Cross(m_rB, m_u);
float invMass = m_invMassA + m_invIA * crAu * crAu + m_invMassB + m_invIB * crBu * crBu;
// Compute the effective mass matrix.
m_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
if (m_frequencyHz > 0.0f)
{
float C = length - m_length;
// Frequency
float omega = 2.0f * (float)Math.PI * m_frequencyHz;
// Damping coefficient
float d = 2.0f * m_mass * m_dampingRatio * omega;
// Spring stiffness
float k = m_mass * 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;
invMass += m_gamma;
m_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
}
else
{
m_gamma = 0.0f;
m_bias = 0.0f;
}
if (data.step.warmStarting)
{
// Scale the impulse to support a variable time step.
m_impulse *= data.step.dtRatio;
Vec2 P = m_impulse * m_u;
vA -= m_invMassA * P;
wA -= m_invIA * Utilities.Cross(m_rA, P);
vB += m_invMassB * P;
wB += m_invIB * Utilities.Cross(m_rB, P);
}
else
{
m_impulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void InitVelocityConstraints(SolverData data)
{
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_indexC = m_bodyC.m_islandIndex;
m_indexD = m_bodyD.m_islandIndex;
m_lcA = m_bodyA.m_sweep.localCenter;
m_lcB = m_bodyB.m_sweep.localCenter;
m_lcC = m_bodyC.m_sweep.localCenter;
m_lcD = m_bodyD.m_sweep.localCenter;
m_mA = m_bodyA.m_invMass;
m_mB = m_bodyB.m_invMass;
m_mC = m_bodyC.m_invMass;
m_mD = m_bodyD.m_invMass;
m_iA = m_bodyA.m_invI;
m_iB = m_bodyB.m_invI;
m_iC = m_bodyC.m_invI;
m_iD = m_bodyD.m_invI;
float aA = data.positions[m_indexA].a;
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
float aB = data.positions[m_indexB].a;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
float aC = data.positions[m_indexC].a;
Vec2 vC = data.velocities[m_indexC].v;
float wC = data.velocities[m_indexC].w;
float aD = data.positions[m_indexD].a;
Vec2 vD = data.velocities[m_indexD].v;
float wD = data.velocities[m_indexD].w;
Rot qA = new Rot(aA);
Rot qB = new Rot(aB);
Rot qC = new Rot(aC);
Rot qD = new Rot(aD);
m_mass = 0.0f;
if (m_typeA == JointType.e_revoluteJoint)
{
m_JvAC.SetZero();
m_JwA = 1.0f;
m_JwC = 1.0f;
m_mass += m_iA + m_iC;
}
else
{
Vec2 u = Utilities.Mul(qC, m_localAxisC);
Vec2 rC = Utilities.Mul(qC, m_localAnchorC - m_lcC);
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_lcA);
m_JvAC = u;
m_JwC = Utilities.Cross(rC, u);
m_JwA = Utilities.Cross(rA, u);
m_mass += m_mC + m_mA + m_iC * m_JwC * m_JwC + m_iA * m_JwA * m_JwA;
}
if (m_typeB == JointType.e_revoluteJoint)
{
m_JvBD.SetZero();
m_JwB = m_ratio;
m_JwD = m_ratio;
m_mass += m_ratio * m_ratio * (m_iB + m_iD);
}
else
{
Vec2 u = Utilities.Mul(qD, m_localAxisD);
Vec2 rD = Utilities.Mul(qD, m_localAnchorD - m_lcD);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_lcB);
m_JvBD = m_ratio * u;
m_JwD = m_ratio * Utilities.Cross(rD, u);
m_JwB = m_ratio * Utilities.Cross(rB, u);
m_mass += m_ratio * m_ratio * (m_mD + m_mB) + m_iD * m_JwD * m_JwD + m_iB * m_JwB * m_JwB;
}
// Compute effective mass.
m_mass = m_mass > 0.0f ? 1.0f / m_mass : 0.0f;
if (data.step.warmStarting)
{
vA += (m_mA * m_impulse) * m_JvAC;
wA += m_iA * m_impulse * m_JwA;
vB += (m_mB * m_impulse) * m_JvBD;
wB += m_iB * m_impulse * m_JwB;
vC -= (m_mC * m_impulse) * m_JvAC;
wC -= m_iC * m_impulse * m_JwC;
vD -= (m_mD * m_impulse) * m_JvBD;
wD -= m_iD * m_impulse * m_JwD;
}
else
{
m_impulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
data.velocities[m_indexC].v = vC;
data.velocities[m_indexC].w = wC;
data.velocities[m_indexD].v = vD;
data.velocities[m_indexD].w = wD;
}
internal 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 = new Rot(aA);
Rot qB = new Rot(aB);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Compute fresh Jacobians
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
Vec2 d = cB + rB - cA - rA;
Vec2 axis = Utilities.Mul(qA, m_localXAxisA);
float a1 = Utilities.Cross(d + rA, axis);
float a2 = Utilities.Cross(rB, axis);
Vec2 perp = Utilities.Mul(qA, m_localYAxisA);
float s1 = Utilities.Cross(d + rA, perp);
float s2 = Utilities.Cross(rB, perp);
Vec3 impulse;
Vec2 C1;
C1.X = Utilities.Dot(perp, d);
C1.Y = aB - aA - m_referenceAngle;
float linearError = Math.Abs(C1.X);
float angularError = Math.Abs(C1.Y);
bool active = false;
float C2 = 0.0f;
if (m_enableLimit)
{
float translation = Utilities.Dot(axis, d);
if (Math.Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * Settings._linearSlop)
{
// Prevent large angular corrections
C2 = Utilities.Clamp(translation, -Settings._maxLinearCorrection, Settings._maxLinearCorrection);
linearError = Math.Max(linearError, Math.Abs(translation));
active = true;
}
else if (translation <= m_lowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = Utilities.Clamp(translation - m_lowerTranslation + Settings._linearSlop, -Settings._maxLinearCorrection, 0.0f);
linearError = Math.Max(linearError, m_lowerTranslation - translation);
active = true;
}
else if (translation >= m_upperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = Utilities.Clamp(translation - m_upperTranslation - Settings._linearSlop, 0.0f, Settings._maxLinearCorrection);
linearError = Math.Max(linearError, translation - m_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.Set(k11, k12, k13);
K.ey.Set(k12, k22, k23);
K.ez.Set(k13, k23, k33);
Vec3 C = new Vec3();
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.Set(k11, k12);
K.ey.Set(k12, k22);
Vec2 impulse1 = K.Solve(-C1);
impulse.X = impulse1.X;
impulse.Y = impulse1.Y;
impulse.Z = 0.0f;
}
Vec2 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[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
return(linearError <= Settings._linearSlop && angularError <= Settings._angularSlop);
}
internal override void SolveVelocityConstraints(SolverData data)
{
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Solve linear motor constraint.
if (m_enableMotor && m_limitState != LimitState.e_equalLimits)
{
float Cdot = Utilities.Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
float impulse = m_motorMass * (m_motorSpeed - Cdot);
float oldImpulse = m_motorImpulse;
float maxImpulse = data.step.dt * m_maxMotorForce;
m_motorImpulse = Utilities.Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_motorImpulse - oldImpulse;
Vec2 P = impulse * m_axis;
float LA = impulse * m_a1;
float LB = impulse * m_a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
Vec2 Cdot1;
Cdot1.X = Utilities.Dot(m_perp, vB - vA) + m_s2 * wB - m_s1 * wA;
Cdot1.Y = wB - wA;
if (m_enableLimit && m_limitState != LimitState.e_inactiveLimit)
{
// Solve prismatic and limit constraint in block form.
float Cdot2;
Cdot2 = Utilities.Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
Vec3 Cdot = new Vec3(Cdot1.X, Cdot1.Y, Cdot2);
Vec3 f1 = m_impulse;
Vec3 df = m_K.Solve33(-Cdot);
m_impulse += df;
if (m_limitState == LimitState.e_atLowerLimit)
{
m_impulse.Z = Math.Max(m_impulse.Z, 0.0f);
}
else if (m_limitState == LimitState.e_atUpperLimit)
{
m_impulse.Z = Math.Min(m_impulse.Z, 0.0f);
}
// f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) + f1(1:2)
Vec2 b = -Cdot1 - (m_impulse.Z - f1.Z) * new Vec2(m_K.ez.X, m_K.ez.Y);
Vec2 f2r = m_K.Solve22(b) + new Vec2(f1.X, f1.Y);
m_impulse.X = f2r.X;
m_impulse.Y = f2r.Y;
df = m_impulse - f1;
Vec2 P = df.X * m_perp + df.Z * m_axis;
float LA = df.X * m_s1 + df.Y + df.Z * m_a1;
float LB = df.X * m_s2 + df.Y + df.Z * m_a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
// Limit is inactive, just solve the prismatic constraint in block form.
Vec2 df = m_K.Solve22(-Cdot1);
m_impulse.X += df.X;
m_impulse.Y += df.Y;
Vec2 P = df.X * m_perp;
float LA = df.X * m_s1 + df.Y;
float LB = df.X * m_s2 + df.Y;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void InitVelocityConstraints(SolverData data)
{
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA = m_bodyA.m_sweep.localCenter;
m_localCenterB = m_bodyB.m_sweep.localCenter;
m_invMassA = m_bodyA.m_invMass;
m_invMassB = m_bodyB.m_invMass;
m_invIA = m_bodyA.m_invI;
m_invIB = m_bodyB.m_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 = new Rot(aA);
Rot qB = new Rot(aB);
// Compute the effective masses.
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
Vec2 d = (cB - cA) + rB - rA;
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Compute motor Jacobian and effective mass.
{
m_axis = Utilities.Mul(qA, m_localXAxisA);
m_a1 = Utilities.Cross(d + rA, m_axis);
m_a2 = Utilities.Cross(rB, m_axis);
m_motorMass = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
if (m_motorMass > 0.0f)
{
m_motorMass = 1.0f / m_motorMass;
}
}
// Prismatic constraint.
{
m_perp = Utilities.Mul(qA, m_localYAxisA);
m_s1 = Utilities.Cross(d + rA, m_perp);
m_s2 = Utilities.Cross(rB, m_perp);
float k11 = mA + mB + iA * m_s1 * m_s1 + iB * m_s2 * m_s2;
float k12 = iA * m_s1 + iB * m_s2;
float k13 = iA * m_s1 * m_a1 + iB * m_s2 * m_a2;
float k22 = iA + iB;
if (k22 == 0.0f)
{
// For bodies with fixed rotation.
k22 = 1.0f;
}
float k23 = iA * m_a1 + iB * m_a2;
float k33 = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
m_K.ex.Set(k11, k12, k13);
m_K.ey.Set(k12, k22, k23);
m_K.ez.Set(k13, k23, k33);
}
// Compute motor and limit terms.
if (m_enableLimit)
{
float jointTranslation = Utilities.Dot(m_axis, d);
if (Math.Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * Settings._linearSlop)
{
m_limitState = LimitState.e_equalLimits;
}
else if (jointTranslation <= m_lowerTranslation)
{
if (m_limitState != LimitState.e_atLowerLimit)
{
m_limitState = LimitState.e_atLowerLimit;
m_impulse.Z = 0.0f;
}
}
else if (jointTranslation >= m_upperTranslation)
{
if (m_limitState != LimitState.e_atUpperLimit)
{
m_limitState = LimitState.e_atUpperLimit;
m_impulse.Z = 0.0f;
}
}
else
{
m_limitState = LimitState.e_inactiveLimit;
m_impulse.Z = 0.0f;
}
}
else
{
m_limitState = LimitState.e_inactiveLimit;
m_impulse.Z = 0.0f;
}
if (m_enableMotor == false)
{
m_motorImpulse = 0.0f;
}
if (data.step.warmStarting)
{
// Account for variable time step.
m_impulse *= data.step.dtRatio;
m_motorImpulse *= data.step.dtRatio;
Vec2 P = m_impulse.X * m_perp + (m_motorImpulse + m_impulse.Z) * m_axis;
float LA = m_impulse.X * m_s1 + m_impulse.Y + (m_motorImpulse + m_impulse.Z) * m_a1;
float LB = m_impulse.X * m_s2 + m_impulse.Y + (m_motorImpulse + m_impulse.Z) * m_a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
m_impulse.SetZero();
m_motorImpulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void InitVelocityConstraints(SolverData data){
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA = m_bodyA.m_sweep.localCenter;
m_localCenterB = m_bodyB.m_sweep.localCenter;
m_invMassA = m_bodyA.m_invMass;
m_invMassB = m_bodyB.m_invMass;
m_invIA = m_bodyA.m_invI;
m_invIB = m_bodyB.m_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 = new Rot(aA); Rot qB = new Rot(aB);
m_rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
m_rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
m_u = cB + m_rB - cA - m_rA;
m_length = m_u.Length();
float C = m_length - m_maxLength;
if (C > 0.0f)
{
m_state = LimitState.e_atUpperLimit;
}
else
{
m_state = LimitState.e_inactiveLimit;
}
if (m_length >Settings._linearSlop)
{
m_u *= 1.0f / m_length;
}
else
{
m_u.SetZero();
m_mass = 0.0f;
m_impulse = 0.0f;
return;
}
// Compute effective mass.
float crA = Utilities.Cross(m_rA, m_u);
float crB = Utilities.Cross(m_rB, m_u);
float invMass = m_invMassA + m_invIA * crA * crA + m_invMassB + m_invIB * crB * crB;
m_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
if (data.step.warmStarting)
{
// Scale the impulse to support a variable time step.
m_impulse *= data.step.dtRatio;
Vec2 P = m_impulse * m_u;
vA -= m_invMassA * P;
wA -= m_invIA * Utilities.Cross(m_rA, P);
vB += m_invMassB * P;
wB += m_invIB * Utilities.Cross(m_rB, P);
}
else
{
m_impulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void SolveVelocityConstraints(SolverData data) {
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Solve linear motor constraint.
if (m_enableMotor && m_limitState != LimitState.e_equalLimits)
{
float Cdot = Utilities.Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
float impulse = m_motorMass * (m_motorSpeed - Cdot);
float oldImpulse = m_motorImpulse;
float maxImpulse = data.step.dt * m_maxMotorForce;
m_motorImpulse = Utilities.Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_motorImpulse - oldImpulse;
Vec2 P = impulse * m_axis;
float LA = impulse * m_a1;
float LB = impulse * m_a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
Vec2 Cdot1;
Cdot1.X = Utilities.Dot(m_perp, vB - vA) + m_s2 * wB - m_s1 * wA;
Cdot1.Y = wB - wA;
if (m_enableLimit && m_limitState != LimitState.e_inactiveLimit)
{
// Solve prismatic and limit constraint in block form.
float Cdot2;
Cdot2 = Utilities.Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
Vec3 Cdot = new Vec3(Cdot1.X, Cdot1.Y, Cdot2);
Vec3 f1 = m_impulse;
Vec3 df = m_K.Solve33(-Cdot);
m_impulse += df;
if (m_limitState == LimitState.e_atLowerLimit)
{
m_impulse.Z = Math.Max(m_impulse.Z, 0.0f);
}
else if (m_limitState == LimitState.e_atUpperLimit)
{
m_impulse.Z = Math.Min(m_impulse.Z, 0.0f);
}
// f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) + f1(1:2)
Vec2 b = -Cdot1 - (m_impulse.Z - f1.Z) * new Vec2(m_K.ez.X, m_K.ez.Y);
Vec2 f2r = m_K.Solve22(b) + new Vec2(f1.X, f1.Y);
m_impulse.X = f2r.X;
m_impulse.Y = f2r.Y;
df = m_impulse - f1;
Vec2 P = df.X * m_perp + df.Z * m_axis;
float LA = df.X * m_s1 + df.Y + df.Z * m_a1;
float LB = df.X * m_s2 + df.Y + df.Z * m_a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
// Limit is inactive, just solve the prismatic constraint in block form.
Vec2 df = m_K.Solve22(-Cdot1);
m_impulse.X += df.X;
m_impulse.Y += df.Y;
Vec2 P = df.X * m_perp;
float LA = df.X * m_s1 + df.Y;
float LB = df.X * m_s2 + df.Y;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void SolveVelocityConstraints(SolverData data){
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
// Solve spring constraint
{
float Cdot = Utilities.Dot(m_ax, vB - vA) + m_sBx * wB - m_sAx * wA;
float impulse = -m_springMass * (Cdot + m_bias + m_gamma * m_springImpulse);
m_springImpulse += impulse;
Vec2 P = impulse * m_ax;
float LA = impulse * m_sAx;
float LB = impulse * m_sBx;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
// Solve rotational motor constraint
{
float Cdot = wB - wA - m_motorSpeed;
float impulse = -m_motorMass * Cdot;
float oldImpulse = m_motorImpulse;
float maxImpulse = data.step.dt * m_maxMotorTorque;
m_motorImpulse = Utilities.Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_motorImpulse - oldImpulse;
wA -= iA * impulse;
wB += iB * impulse;
}
// Solve point to line constraint
{
float Cdot = Utilities.Dot(m_ay, vB - vA) + m_sBy * wB - m_sAy * wA;
float impulse = -m_mass * Cdot;
m_impulse += impulse;
Vec2 P = impulse * m_ay;
float LA = impulse * m_sAy;
float LB = impulse * m_sBy;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal 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 = new Rot(aA);
Rot qB = new Rot(aB);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Compute fresh Jacobians
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
Vec2 d = cB + rB - cA - rA;
Vec2 axis = Utilities.Mul(qA, m_localXAxisA);
float a1 = Utilities.Cross(d + rA, axis);
float a2 = Utilities.Cross(rB, axis);
Vec2 perp = Utilities.Mul(qA, m_localYAxisA);
float s1 = Utilities.Cross(d + rA, perp);
float s2 = Utilities.Cross(rB, perp);
Vec3 impulse;
Vec2 C1;
C1.X = Utilities.Dot(perp, d);
C1.Y = aB - aA - m_referenceAngle;
float linearError = Math.Abs(C1.X);
float angularError = Math.Abs(C1.Y);
bool active = false;
float C2 = 0.0f;
if (m_enableLimit)
{
float translation = Utilities.Dot(axis, d);
if (Math.Abs(m_upperTranslation - m_lowerTranslation) < 2.0f *Settings._linearSlop)
{
// Prevent large angular corrections
C2 = Utilities.Clamp(translation, -Settings._maxLinearCorrection, Settings._maxLinearCorrection);
linearError = Math.Max(linearError, Math.Abs(translation));
active = true;
}
else if (translation <= m_lowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = Utilities.Clamp(translation - m_lowerTranslation + Settings._linearSlop, -Settings._maxLinearCorrection, 0.0f);
linearError = Math.Max(linearError, m_lowerTranslation - translation);
active = true;
}
else if (translation >= m_upperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = Utilities.Clamp(translation - m_upperTranslation - Settings._linearSlop, 0.0f, Settings._maxLinearCorrection);
linearError = Math.Max(linearError, translation - m_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.Set(k11, k12, k13);
K.ey.Set(k12, k22, k23);
K.ez.Set(k13, k23, k33);
Vec3 C = new Vec3();
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.Set(k11, k12);
K.ey.Set(k12, k22);
Vec2 impulse1 = K.Solve(-C1);
impulse.X = impulse1.X;
impulse.Y = impulse1.Y;
impulse.Z = 0.0f;
}
Vec2 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[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
return linearError <= Settings._linearSlop && angularError <= Settings._angularSlop;
}
internal override void InitVelocityConstraints(SolverData data){
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA = m_bodyA.m_sweep.localCenter;
m_localCenterB = m_bodyB.m_sweep.localCenter;
m_invMassA = m_bodyA.m_invMass;
m_invMassB = m_bodyB.m_invMass;
m_invIA = m_bodyA.m_invI;
m_invIB = m_bodyB.m_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 = new Rot(aA);
Rot qB = new Rot(aB);
m_rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
m_rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
m_u = cB + m_rB - cA - m_rA;
// Handle singularity.
float length = m_u.Length();
if (length >Settings._linearSlop)
{
m_u *= 1.0f / length;
}
else
{
m_u.Set(0.0f, 0.0f);
}
float crAu = Utilities.Cross(m_rA, m_u);
float crBu = Utilities.Cross(m_rB, m_u);
float invMass = m_invMassA + m_invIA * crAu * crAu + m_invMassB + m_invIB * crBu * crBu;
// Compute the effective mass matrix.
m_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
if (m_frequencyHz > 0.0f)
{
float C = length - m_length;
// Frequency
float omega = 2.0f * (float)Math.PI * m_frequencyHz;
// Damping coefficient
float d = 2.0f * m_mass * m_dampingRatio * omega;
// Spring stiffness
float k = m_mass * 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;
invMass += m_gamma;
m_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
}
else
{
m_gamma = 0.0f;
m_bias = 0.0f;
}
if (data.step.warmStarting)
{
// Scale the impulse to support a variable time step.
m_impulse *= data.step.dtRatio;
Vec2 P = m_impulse * m_u;
vA -= m_invMassA * P;
wA -= m_invIA * Utilities.Cross(m_rA, P);
vB += m_invMassB * P;
wB += m_invIB * Utilities.Cross(m_rB, P);
}
else
{
m_impulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void InitVelocityConstraints(SolverData data){
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA = m_bodyA.m_sweep.localCenter;
m_localCenterB = m_bodyB.m_sweep.localCenter;
m_invMassA = m_bodyA.m_invMass;
m_invMassB = m_bodyB.m_invMass;
m_invIA = m_bodyA.m_invI;
m_invIB = m_bodyB.m_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 = new Rot(aA); Rot qB = new Rot(aB);
m_rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
m_rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
// Get the pulley axes.
m_uA = cA + m_rA - m_groundAnchorA;
m_uB = cB + m_rB - m_groundAnchorB;
float lengthA = m_uA.Length();
float lengthB = m_uB.Length();
if (lengthA > 10.0f *Settings._linearSlop)
{
m_uA *= 1.0f / lengthA;
}
else
{
m_uA.SetZero();
}
if (lengthB > 10.0f *Settings._linearSlop)
{
m_uB *= 1.0f / lengthB;
}
else
{
m_uB.SetZero();
}
// Compute effective mass.
float ruA = Utilities.Cross(m_rA, m_uA);
float ruB = Utilities.Cross(m_rB, m_uB);
float mA = m_invMassA + m_invIA * ruA * ruA;
float mB = m_invMassB + m_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 = -(m_impulse) * m_uA;
Vec2 PB = (-m_ratio * m_impulse) * m_uB;
vA += m_invMassA * PA;
wA += m_invIA * Utilities.Cross(m_rA, PA);
vB += m_invMassB * PB;
wB += m_invIB * Utilities.Cross(m_rB, PB);
}
else
{
m_impulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void SolveVelocityConstraints(SolverData data){
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
bool fixedRotation = (iA + iB == 0.0f);
// Solve motor constraint.
if (m_enableMotor && m_limitState !=LimitState.e_equalLimits && fixedRotation == false)
{
float Cdot = wB - wA - m_motorSpeed;
float impulse = -m_motorMass * Cdot;
float oldImpulse = m_motorImpulse;
float maxImpulse = data.step.dt * m_maxMotorTorque;
m_motorImpulse = Utilities.Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_motorImpulse - oldImpulse;
wA -= iA * impulse;
wB += iB * impulse;
}
// Solve limit constraint.
if (m_enableLimit && m_limitState != LimitState.e_inactiveLimit && fixedRotation == false)
{
Vec2 Cdot1 = vB + Utilities.Cross(wB, m_rB) - vA - Utilities.Cross(wA, m_rA);
float Cdot2 = wB - wA;
Vec3 Cdot = new Vec3(Cdot1.X, Cdot1.Y, Cdot2);
Vec3 impulse = -m_mass.Solve33(Cdot);
if (m_limitState ==LimitState.e_equalLimits)
{
m_impulse += impulse;
}
else if (m_limitState == LimitState.e_atLowerLimit)
{
float newImpulse = m_impulse.Z + impulse.Z;
if (newImpulse < 0.0f)
{
Vec2 rhs = -Cdot1 + m_impulse.Z * new Vec2(m_mass.ez.X, m_mass.ez.Y);
Vec2 reduced = m_mass.Solve22(rhs);
impulse.X = reduced.X;
impulse.Y = reduced.Y;
impulse.Z = -m_impulse.Z;
m_impulse.X += reduced.X;
m_impulse.Y += reduced.Y;
m_impulse.Z = 0.0f;
}
else
{
m_impulse += impulse;
}
}
else if (m_limitState == LimitState.e_atUpperLimit)
{
float newImpulse = m_impulse.Z + impulse.Z;
if (newImpulse > 0.0f)
{
Vec2 rhs = -Cdot1 + m_impulse.Z * new Vec2(m_mass.ez.X, m_mass.ez.Y);
Vec2 reduced = m_mass.Solve22(rhs);
impulse.X = reduced.X;
impulse.Y = reduced.Y;
impulse.Z = -m_impulse.Z;
m_impulse.X += reduced.X;
m_impulse.Y += reduced.Y;
m_impulse.Z = 0.0f;
}
else
{
m_impulse += impulse;
}
}
Vec2 P = new Vec2(impulse.X, impulse.Y);
vA -= mA * P;
wA -= iA * (Utilities.Cross(m_rA, P) + impulse.Z);
vB += mB * P;
wB += iB * (Utilities.Cross(m_rB, P) + impulse.Z);
}
else
{
// Solve point-to-point constraint
Vec2 Cdot = vB + Utilities.Cross(wB, m_rB) - vA - Utilities.Cross(wA, m_rA);
Vec2 impulse = m_mass.Solve22(-Cdot);
m_impulse.X += impulse.X;
m_impulse.Y += impulse.Y;
vA -= mA * impulse;
wA -= iA * Utilities.Cross(m_rA, impulse);
vB += mB * impulse;
wB += iB * Utilities.Cross(m_rB, impulse);
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void SolveVelocityConstraints(SolverData data){
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
Vec2 vpA = vA + Utilities.Cross(wA, m_rA);
Vec2 vpB = vB + Utilities.Cross(wB, m_rB);
float Cdot = -Utilities.Dot(m_uA, vpA) - m_ratio * Utilities.Dot(m_uB, vpB);
float impulse = -m_mass * Cdot;
m_impulse += impulse;
Vec2 PA = -impulse * m_uA;
Vec2 PB = -m_ratio * impulse * m_uB;
vA += m_invMassA * PA;
wA += m_invIA * Utilities.Cross(m_rA, PA);
vB += m_invMassB * PB;
wB += m_invIB * Utilities.Cross(m_rB, PB);
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void InitVelocityConstraints(SolverData data){
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA = m_bodyA.m_sweep.localCenter;
m_localCenterB = m_bodyB.m_sweep.localCenter;
m_invMassA = m_bodyA.m_invMass;
m_invMassB = m_bodyB.m_invMass;
m_invIA = m_bodyA.m_invI;
m_invIB = m_bodyB.m_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 = new Rot(aA); Rot qB = new Rot(aB);
// Compute the effective mass matrix.
m_rA = Utilities.Mul(qA, -m_localCenterA);
m_rB = Utilities.Mul(qB, -m_localCenterB);
// 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;
Mat22 K;
K.ex.X = mA + mB + iA * m_rA.Y * m_rA.Y + iB * m_rB.Y * m_rB.Y;
K.ex.Y = -iA * m_rA.X * m_rA.Y - iB * m_rB.X * m_rB.Y;
K.ey.X = K.ex.Y;
K.ey.Y = mA + mB + iA * m_rA.X * m_rA.X + iB * m_rB.X * m_rB.X;
m_linearMass = K.GetInverse();
m_angularMass = iA + iB;
if (m_angularMass > 0.0f)
{
m_angularMass = 1.0f / m_angularMass;
}
m_linearError = cB + m_rB - cA - m_rA - Utilities.Mul(qA, m_linearOffset);
m_angularError = aB - aA - m_angularOffset;
if (data.step.warmStarting)
{
// Scale impulses to support a variable time step.
m_linearImpulse *= data.step.dtRatio;
m_angularImpulse *= data.step.dtRatio;
Vec2 P = new Vec2(m_linearImpulse.X, m_linearImpulse.Y);
vA -= mA * P;
wA -= iA * (Utilities.Cross(m_rA, P) + m_angularImpulse);
vB += mB * P;
wB += iB * (Utilities.Cross(m_rB, P) + m_angularImpulse);
}
else
{
m_linearImpulse.SetZero();
m_angularImpulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal 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 = new Rot(aA); Rot qB = new Rot(aB);
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
// Get the pulley axes.
Vec2 uA = cA + rA - m_groundAnchorA;
Vec2 uB = cB + rB - m_groundAnchorB;
float lengthA = uA.Length();
float lengthB = uB.Length();
if (lengthA > 10.0f *Settings._linearSlop)
{
uA *= 1.0f / lengthA;
}
else
{
uA.SetZero();
}
if (lengthB > 10.0f *Settings._linearSlop)
{
uB *= 1.0f / lengthB;
}
else
{
uB.SetZero();
}
// Compute effective mass.
float ruA = Utilities.Cross(rA, uA);
float ruB = Utilities.Cross(rB, uB);
float mA = m_invMassA + m_invIA * ruA * ruA;
float mB = m_invMassB + m_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 = Math.Abs(C);
float impulse = -mass * C;
Vec2 PA = -impulse * uA;
Vec2 PB = -m_ratio * impulse * uB;
cA += m_invMassA * PA;
aA += m_invIA * Utilities.Cross(rA, PA);
cB += m_invMassB * PB;
aB += m_invIB * Utilities.Cross(rB, PB);
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 linearError <Settings._linearSlop;
}
internal abstract void SolveVelocityConstraints(SolverData data);
internal override void InitVelocityConstraints(SolverData data){
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_indexC = m_bodyC.m_islandIndex;
m_indexD = m_bodyD.m_islandIndex;
m_lcA = m_bodyA.m_sweep.localCenter;
m_lcB = m_bodyB.m_sweep.localCenter;
m_lcC = m_bodyC.m_sweep.localCenter;
m_lcD = m_bodyD.m_sweep.localCenter;
m_mA = m_bodyA.m_invMass;
m_mB = m_bodyB.m_invMass;
m_mC = m_bodyC.m_invMass;
m_mD = m_bodyD.m_invMass;
m_iA = m_bodyA.m_invI;
m_iB = m_bodyB.m_invI;
m_iC = m_bodyC.m_invI;
m_iD = m_bodyD.m_invI;
float aA = data.positions[m_indexA].a;
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
float aB = data.positions[m_indexB].a;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
float aC = data.positions[m_indexC].a;
Vec2 vC = data.velocities[m_indexC].v;
float wC = data.velocities[m_indexC].w;
float aD = data.positions[m_indexD].a;
Vec2 vD = data.velocities[m_indexD].v;
float wD = data.velocities[m_indexD].w;
Rot qA = new Rot(aA);
Rot qB = new Rot(aB);
Rot qC= new Rot(aC);
Rot qD= new Rot(aD);
m_mass = 0.0f;
if (m_typeA == JointType.e_revoluteJoint)
{
m_JvAC.SetZero();
m_JwA = 1.0f;
m_JwC = 1.0f;
m_mass += m_iA + m_iC;
}
else
{
Vec2 u = Utilities.Mul(qC, m_localAxisC);
Vec2 rC = Utilities.Mul(qC, m_localAnchorC - m_lcC);
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_lcA);
m_JvAC = u;
m_JwC = Utilities.Cross(rC, u);
m_JwA = Utilities.Cross(rA, u);
m_mass += m_mC + m_mA + m_iC * m_JwC * m_JwC + m_iA * m_JwA * m_JwA;
}
if (m_typeB == JointType.e_revoluteJoint)
{
m_JvBD.SetZero();
m_JwB = m_ratio;
m_JwD = m_ratio;
m_mass += m_ratio * m_ratio * (m_iB + m_iD);
}
else
{
Vec2 u = Utilities.Mul(qD, m_localAxisD);
Vec2 rD = Utilities.Mul(qD, m_localAnchorD - m_lcD);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_lcB);
m_JvBD = m_ratio * u;
m_JwD = m_ratio * Utilities.Cross(rD, u);
m_JwB = m_ratio * Utilities.Cross(rB, u);
m_mass += m_ratio * m_ratio * (m_mD + m_mB) + m_iD * m_JwD * m_JwD + m_iB * m_JwB * m_JwB;
}
// Compute effective mass.
m_mass = m_mass > 0.0f ? 1.0f / m_mass : 0.0f;
if (data.step.warmStarting)
{
vA += (m_mA * m_impulse) * m_JvAC;
wA += m_iA * m_impulse * m_JwA;
vB += (m_mB * m_impulse) * m_JvBD;
wB += m_iB * m_impulse * m_JwB;
vC -= (m_mC * m_impulse) * m_JvAC;
wC -= m_iC * m_impulse * m_JwC;
vD -= (m_mD * m_impulse) * m_JvBD;
wD -= m_iD * m_impulse * m_JwD;
}
else
{
m_impulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
data.velocities[m_indexC].v = vC;
data.velocities[m_indexC].w = wC;
data.velocities[m_indexD].v = vD;
data.velocities[m_indexD].w = wD;
}
internal override void InitVelocityConstraints(SolverData data) {
throw new NotImplementedException();
//m_indexB = m_bodyB.m_islandIndex;
//m_localCenterB = m_bodyB.m_sweep.localCenter;
//m_invMassB = m_bodyB.m_invMass;
//m_invIB = m_bodyB.m_invI;
//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 qB(aB);
//float mass = m_bodyB.GetMass();
//// Frequency
//float omega = 2.0f * (float)Math.PI * m_frequencyHz;
//// Damping coefficient
//float d = 2.0f * mass * m_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;
//Utilities.Assert(d + h * k > Single.Epsilon);
//m_gamma = h * (d + h * k);
//if (m_gamma != 0.0f)
//{
// m_gamma = 1.0f / m_gamma;
//}
//m_beta = h * k * m_gamma;
//// Compute the effective mass matrix.
//m_rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
//// 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;
//K.ex.X = m_invMassB + m_invIB * m_rB.Y * m_rB.Y + m_gamma;
//K.ex.Y = -m_invIB * m_rB.X * m_rB.Y;
//K.ey.X = K.ex.Y;
//K.ey.Y = m_invMassB + m_invIB * m_rB.X * m_rB.X + m_gamma;
//m_mass = K.GetInverse();
//m_C = cB + m_rB - m_targetA;
//m_C *= m_beta;
//// Cheat with some damping
//wB *= 0.98f;
//if (data.step.warmStarting)
//{
// m_impulse *= data.step.dtRatio;
// vB += m_invMassB * m_impulse;
// wB += m_invIB * Utilities.Cross(m_rB, m_impulse);
//}
//else
//{
// m_impulse.SetZero();
//}
//data.velocities[m_indexB].v = vB;
//data.velocities[m_indexB].w = wB;
}
internal override void SolveVelocityConstraints(SolverData data){
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
Vec2 vC = data.velocities[m_indexC].v;
float wC = data.velocities[m_indexC].w;
Vec2 vD = data.velocities[m_indexD].v;
float wD = data.velocities[m_indexD].w;
float Cdot = Utilities.Dot(m_JvAC, vA - vC) + Utilities.Dot(m_JvBD, vB - vD);
Cdot += (m_JwA * wA - m_JwC * wC) + (m_JwB * wB - m_JwD * wD);
float impulse = -m_mass * Cdot;
m_impulse += impulse;
vA += (m_mA * impulse) * m_JvAC;
wA += m_iA * impulse * m_JwA;
vB += (m_mB * impulse) * m_JvBD;
wB += m_iB * impulse * m_JwB;
vC -= (m_mC * impulse) * m_JvAC;
wC -= m_iC * impulse * m_JwC;
vD -= (m_mD * impulse) * m_JvBD;
wD -= m_iD * impulse * m_JwD;
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
data.velocities[m_indexC].v = vC;
data.velocities[m_indexC].w = wC;
data.velocities[m_indexD].v = vD;
data.velocities[m_indexD].w = wD;
}
internal override bool SolvePositionConstraints(SolverData data) {
return true;
}
internal 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;
Vec2 cC = data.positions[m_indexC].c;
float aC = data.positions[m_indexC].a;
Vec2 cD = data.positions[m_indexD].c;
float aD = data.positions[m_indexD].a;
Rot qA = new Rot(aA);
Rot qB = new Rot(aB);
Rot qC= new Rot(aC);
Rot qD = new Rot(aD);
float linearError = 0.0f;
float coordinateA, coordinateB;
Vec2 JvAC = new Vec2();
Vec2 JvBD = new Vec2();
float JwA, JwB, JwC, JwD;
float mass = 0.0f;
if (m_typeA == JointType.e_revoluteJoint)
{
JvAC.SetZero();
JwA = 1.0f;
JwC = 1.0f;
mass += m_iA + m_iC;
coordinateA = aA - aC - m_referenceAngleA;
}
else
{
Vec2 u = Utilities.Mul(qC, m_localAxisC);
Vec2 rC = Utilities.Mul(qC, m_localAnchorC - m_lcC);
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_lcA);
JvAC = u;
JwC = Utilities.Cross(rC, u);
JwA = Utilities.Cross(rA, u);
mass += m_mC + m_mA + m_iC * JwC * JwC + m_iA * JwA * JwA;
Vec2 pC = m_localAnchorC - m_lcC;
Vec2 pA = Utilities.MulT(qC, rA + (cA - cC));
coordinateA = Utilities.Dot(pA - pC, m_localAxisC);
}
if (m_typeB == JointType.e_revoluteJoint)
{
JvBD.SetZero();
JwB = m_ratio;
JwD = m_ratio;
mass += m_ratio * m_ratio * (m_iB + m_iD);
coordinateB = aB - aD - m_referenceAngleB;
}
else
{
Vec2 u = Utilities.Mul(qD, m_localAxisD);
Vec2 rD = Utilities.Mul(qD, m_localAnchorD - m_lcD);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_lcB);
JvBD = m_ratio * u;
JwD = m_ratio * Utilities.Cross(rD, u);
JwB = m_ratio * Utilities.Cross(rB, u);
mass += m_ratio * m_ratio * (m_mD + m_mB) + m_iD * JwD * JwD + m_iB * JwB * JwB;
Vec2 pD = m_localAnchorD - m_lcD;
Vec2 pB = Utilities.MulT(qD, rB + (cB - cD));
coordinateB = Utilities.Dot(pB - pD, m_localAxisD);
}
float C = (coordinateA + m_ratio * coordinateB) - m_constant;
float impulse = 0.0f;
if (mass > 0.0f)
{
impulse = -C / mass;
}
cA += m_mA * impulse * JvAC;
aA += m_iA * impulse * JwA;
cB += m_mB * impulse * JvBD;
aB += m_iB * impulse * JwB;
cC -= m_mC * impulse * JvAC;
aC -= m_iC * impulse * JwC;
cD -= m_mD * impulse * JvBD;
aD -= m_iD * impulse * JwD;
data.positions[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
data.positions[m_indexC].c = cC;
data.positions[m_indexC].a = aC;
data.positions[m_indexD].c = cD;
data.positions[m_indexD].a = aD;
// TODO_ERIN not implemented
return linearError <Settings._linearSlop;
}
internal 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 = new Rot(aA);
Rot qB = new Rot(aB);
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
Vec2 u = cB + rB - cA - rA;
float length = u.Normalize();
float C = length - m_maxLength;
C = Utilities.Clamp(C, 0.0f, Settings._maxLinearCorrection);
float impulse = -m_mass * C;
Vec2 P = impulse * u;
cA -= m_invMassA * P;
aA -= m_invIA * Utilities.Cross(rA, P);
cB += m_invMassB * P;
aB += m_invIB * Utilities.Cross(rB, P);
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 length - m_maxLength <Settings._linearSlop;
}
internal override void SolveVelocityConstraints(SolverData data){
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
// Cdot = dot(u, v + cross(w, r))
Vec2 vpA = vA + Utilities.Cross(wA, m_rA);
Vec2 vpB = vB + Utilities.Cross(wB, m_rB);
float Cdot = Utilities.Dot(m_u, vpB - vpA);
float impulse = -m_mass * (Cdot + m_bias + m_gamma * m_impulse);
m_impulse += impulse;
Vec2 P = impulse * m_u;
vA -= m_invMassA * P;
wA -= m_invIA * Utilities.Cross(m_rA, P);
vB += m_invMassB * P;
wB += m_invIB * Utilities.Cross(m_rB, P);
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void InitVelocityConstraints(SolverData data){
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA = m_bodyA.m_sweep.localCenter;
m_localCenterB = m_bodyB.m_sweep.localCenter;
m_invMassA = m_bodyA.m_invMass;
m_invMassB = m_bodyB.m_invMass;
m_invIA = m_bodyA.m_invI;
m_invIB = m_bodyB.m_invI;
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
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 = new Rot(aA); Rot qB = new Rot(aB);
// Compute the effective masses.
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
Vec2 d = cB + rB - cA - rA;
// Point to line constraint
{
m_ay = Utilities.Mul(qA, m_localYAxisA);
m_sAy = Utilities.Cross(d + rA, m_ay);
m_sBy = Utilities.Cross(rB, m_ay);
m_mass = mA + mB + iA * m_sAy * m_sAy + iB * m_sBy * m_sBy;
if (m_mass > 0.0f)
{
m_mass = 1.0f / m_mass;
}
}
// Spring constraint
m_springMass = 0.0f;
m_bias = 0.0f;
m_gamma = 0.0f;
if (m_frequencyHz > 0.0f)
{
m_ax = Utilities.Mul(qA, m_localXAxisA);
m_sAx = Utilities.Cross(d + rA, m_ax);
m_sBx = Utilities.Cross(rB, m_ax);
float invMass = mA + mB + iA * m_sAx * m_sAx + iB * m_sBx * m_sBx;
if (invMass > 0.0f)
{
m_springMass = 1.0f / invMass;
float C = Utilities.Dot(d, m_ax);
// Frequency
float omega = 2.0f * (float)Math.PI * m_frequencyHz;
// Damping coefficient
float df = 2.0f * m_springMass * m_dampingRatio * omega;
// Spring stiffness
float k = m_springMass * omega * omega;
// magic formulas
float h = data.step.dt;
m_gamma = h * (df + h * k);
if (m_gamma > 0.0f)
{
m_gamma = 1.0f / m_gamma;
}
m_bias = C * h * k * m_gamma;
m_springMass = invMass + m_gamma;
if (m_springMass > 0.0f)
{
m_springMass = 1.0f / m_springMass;
}
}
}
else
{
m_springImpulse = 0.0f;
}
// Rotational motor
if (m_enableMotor)
{
m_motorMass = iA + iB;
if (m_motorMass > 0.0f)
{
m_motorMass = 1.0f / m_motorMass;
}
}
else
{
m_motorMass = 0.0f;
m_motorImpulse = 0.0f;
}
if (data.step.warmStarting)
{
// Account for variable time step.
m_impulse *= data.step.dtRatio;
m_springImpulse *= data.step.dtRatio;
m_motorImpulse *= data.step.dtRatio;
Vec2 P = m_impulse * m_ay + m_springImpulse * m_ax;
float LA = m_impulse * m_sAy + m_springImpulse * m_sAx + m_motorImpulse;
float LB = m_impulse * m_sBy + m_springImpulse * m_sBx + m_motorImpulse;
vA -= m_invMassA * P;
wA -= m_invIA * LA;
vB += m_invMassB * P;
wB += m_invIB * LB;
}
else
{
m_impulse = 0.0f;
m_springImpulse = 0.0f;
m_motorImpulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override bool SolvePositionConstraints(SolverData data){
if (m_frequencyHz > 0.0f)
{
// There is no position correction for soft distance constraints.
return true;
}
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 = new Rot(aA); Rot qB = new Rot(aB);
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
Vec2 u = cB + rB - cA - rA;
float length = u.Normalize();
float C = length - m_length;
C = Utilities.Clamp(C, -Settings._maxLinearCorrection, Settings._maxLinearCorrection);
float impulse = -m_mass * C;
Vec2 P = impulse * u;
cA -= m_invMassA * P;
aA -= m_invIA * Utilities.Cross(rA, P);
cB += m_invMassB * P;
aB += m_invIB * Utilities.Cross(rB, P);
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 Math.Abs(C) <Settings._linearSlop;
}
internal 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 = new Rot(aA);
Rot qB = new Rot(aB);
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
Vec2 d = (cB - cA) + rB - rA;
Vec2 ay = Utilities.Mul(qA, m_localYAxisA);
float sAy = Utilities.Cross(d + rA, ay);
float sBy = Utilities.Cross(rB, ay);
float C = Utilities.Dot(d, ay);
float k = m_invMassA + m_invMassB + m_invIA * m_sAy * m_sAy + m_invIB * m_sBy * m_sBy;
float impulse;
if (k != 0.0f)
{
impulse = - C / k;
}
else
{
impulse = 0.0f;
}
Vec2 P = impulse * ay;
float LA = impulse * sAy;
float LB = impulse * sBy;
cA -= m_invMassA * P;
aA -= m_invIA * LA;
cB += m_invMassB * P;
aB += m_invIB * LB;
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 Math.Abs(C) <=Settings._linearSlop;
}
internal 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 = new Rot(aA);
Rot qB = new Rot(aB);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
float positionError, angularError;
Mat33 K;
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 (m_frequencyHz > 0.0f)
{
Vec2 C1 = cB + rB - cA - rA;
positionError = C1.Length();
angularError = 0.0f;
Vec2 P = -K.Solve22(C1);
cA -= mA * P;
aA -= iA * Utilities.Cross(rA, P);
cB += mB * P;
aB += iB * Utilities.Cross(rB, P);
}
else
{
Vec2 C1 = cB + rB - cA - rA;
float C2 = aB - aA - m_referenceAngle;
positionError = C1.Length();
angularError = Math.Abs(C2);
Vec3 C = new Vec3(C1.X, C1.Y, C2);
Vec3 impulse = -K.Solve33(C);
Vec2 P = new Vec2(impulse.X, impulse.Y);
cA -= mA * P;
aA -= iA * (Utilities.Cross(rA, P) + impulse.Z);
cB += mB * P;
aB += iB * (Utilities.Cross(rB, P) + impulse.Z);
}
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;
}