/// Solve A * x = b, where b is a column vector. This is more efficient
/// than computing the inverse in one-shot cases.
public Vec3 Solve33(Vec3 b) {
float det = Utilities.Dot(ex, Utilities.Cross(ey, ez));
if (det != 0.0f) {
det = 1.0f / det;
}
Vec3 x;
x.X = det * Utilities.Dot(b, Utilities.Cross(ey, ez));
x.Y = det * Utilities.Dot(ex, Utilities.Cross(b, ez));
x.Z = det * Utilities.Dot(ex, Utilities.Cross(ey, b));
return x;
}
/// Negate this vector.
public static Vec3 operator -(Vec3 other) {
Vec3 v = new Vec3();
v.Set(-other.X, -other.Y, -other.Z);
return v;
}
/// Construct this matrix using columns.
public Mat33(Vec3 c1, Vec3 c2, Vec3 c3)
{
ex = c1;
ey = c2;
ez = c3;
}
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;
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;
}
/// Perform the dot product on two vectors.
public static float Dot(Vec3 a, Vec3 b)
{
return a.X * b.X + a.Y * b.Y + a.Z * b.Z;
}
/// Perform the cross product on two vectors.
public static Vec3 Cross(Vec3 a, Vec3 b)
{
return new Vec3(a.Y * b.Z - a.Z * b.Y, a.Z * b.X - a.X * b.Z, a.X * b.Y - a.Y * b.X);
}
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;
}
/// Multiply a matrix times a vector.
public static Vec3 Mul(Mat33 A, Vec3 v)
{
return v.X * A.ex + v.Y * A.ey + v.Z * A.ez;
}
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 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 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;
}
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;
if (m_frequencyHz > 0.0f)
{
float Cdot2 = wB - wA;
float impulse2 = -m_mass.ez.Z * (Cdot2 + m_bias + m_gamma * m_impulse.Z);
m_impulse.Z += impulse2;
wA -= iA * impulse2;
wB += iB * impulse2;
Vec2 Cdot1 = vB + Utilities.Cross(wB, m_rB) - vA - Utilities.Cross(wA, m_rA);
Vec2 impulse1 = -Utilities.Mul22(m_mass, Cdot1);
m_impulse.X += impulse1.X;
m_impulse.Y += impulse1.Y;
Vec2 P = impulse1;
vA -= mA * P;
wA -= iA * Utilities.Cross(m_rA, P);
vB += mB * P;
wB += iB * Utilities.Cross(m_rB, P);
}
else
{
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 = -Utilities.Mul(m_mass, Cdot);
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);
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}