in Box2D/Dynamics/Joints/b2WeldJoint.cpp [221:290]
bool b2WeldJoint::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);
float32 mA = m_invMassA, mB = m_invMassB;
float32 iA = m_invIA, iB = m_invIB;
b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
float32 positionError, angularError;
b2Mat33 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)
{
b2Vec2 C1 = cB + rB - cA - rA;
positionError = C1.Length();
angularError = 0.0f;
b2Vec2 P = -K.Solve22(C1);
cA -= mA * P;
aA -= iA * b2Cross(rA, P);
cB += mB * P;
aB += iB * b2Cross(rB, P);
}
else
{
b2Vec2 C1 = cB + rB - cA - rA;
float32 C2 = aB - aA - m_referenceAngle;
positionError = C1.Length();
angularError = b2Abs(C2);
b2Vec3 C(C1.x, C1.y, C2);
b2Vec3 impulse = -K.Solve33(C);
b2Vec2 P(impulse.x, impulse.y);
cA -= mA * P;
aA -= iA * (b2Cross(rA, P) + impulse.z);
cB += mB * P;
aB += iB * (b2Cross(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 <= b2_linearSlop && angularError <= b2_angularSlop;
}