in Box2D/Dynamics/Joints/b2PulleyJoint.cpp [190:260]
bool b2PulleyJoint::SolvePositionConstraints(const b2SolverData& data)
{
b2Vec2 cA = data.positions[m_indexA].c;
float32 aA = data.positions[m_indexA].a;
b2Vec2 cB = data.positions[m_indexB].c;
float32 aB = data.positions[m_indexB].a;
b2Rot qA(aA), qB(aB);
b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
// Get the pulley axes.
b2Vec2 uA = cA + rA - m_groundAnchorA;
b2Vec2 uB = cB + rB - m_groundAnchorB;
float32 lengthA = uA.Length();
float32 lengthB = uB.Length();
if (lengthA > 10.0f * b2_linearSlop)
{
uA *= 1.0f / lengthA;
}
else
{
uA.SetZero();
}
if (lengthB > 10.0f * b2_linearSlop)
{
uB *= 1.0f / lengthB;
}
else
{
uB.SetZero();
}
// Compute effective mass.
float32 ruA = b2Cross(rA, uA);
float32 ruB = b2Cross(rB, uB);
float32 mA = m_invMassA + m_invIA * ruA * ruA;
float32 mB = m_invMassB + m_invIB * ruB * ruB;
float32 mass = mA + m_ratio * m_ratio * mB;
if (mass > 0.0f)
{
mass = 1.0f / mass;
}
float32 C = m_constant - lengthA - m_ratio * lengthB;
float32 linearError = b2Abs(C);
float32 impulse = -mass * C;
b2Vec2 PA = -impulse * uA;
b2Vec2 PB = -m_ratio * impulse * uB;
cA += m_invMassA * PA;
aA += m_invIA * b2Cross(rA, PA);
cB += m_invMassB * PB;
aB += m_invIB * b2Cross(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 < b2_linearSlop;
}