in Box2D/Dynamics/Joints/b2WheelJoint.cpp [77:214]
void b2WheelJoint::InitVelocityConstraints(const b2SolverData& 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;
float32 mA = m_invMassA, mB = m_invMassB;
float32 iA = m_invIA, iB = m_invIB;
b2Vec2 cA = data.positions[m_indexA].c;
float32 aA = data.positions[m_indexA].a;
b2Vec2 vA = data.velocities[m_indexA].v;
float32 wA = data.velocities[m_indexA].w;
b2Vec2 cB = data.positions[m_indexB].c;
float32 aB = data.positions[m_indexB].a;
b2Vec2 vB = data.velocities[m_indexB].v;
float32 wB = data.velocities[m_indexB].w;
b2Rot qA(aA), qB(aB);
// Compute the effective masses.
b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
b2Vec2 d = cB + rB - cA - rA;
// Point to line constraint
{
m_ay = b2Mul(qA, m_localYAxisA);
m_sAy = b2Cross(d + rA, m_ay);
m_sBy = b2Cross(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 = b2Mul(qA, m_localXAxisA);
m_sAx = b2Cross(d + rA, m_ax);
m_sBx = b2Cross(rB, m_ax);
float32 invMass = mA + mB + iA * m_sAx * m_sAx + iB * m_sBx * m_sBx;
if (invMass > 0.0f)
{
m_springMass = 1.0f / invMass;
float32 C = b2Dot(d, m_ax);
// Frequency
float32 omega = 2.0f * b2_pi * m_frequencyHz;
// Damping coefficient
float32 d = 2.0f * m_springMass * m_dampingRatio * omega;
// Spring stiffness
float32 k = m_springMass * omega * omega;
// magic formulas
float32 h = data.step.dt;
m_gamma = h * (d + 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;
b2Vec2 P = m_impulse * m_ay + m_springImpulse * m_ax;
float32 LA = m_impulse * m_sAy + m_springImpulse * m_sAx + m_motorImpulse;
float32 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;
}