btVector3 btRigidBody::computeGyroscopicImpulseImplicit_World(btScalar step) const
{
// use full newton-euler equations. common practice to drop the wxIw term. want it for better tumbling behavior.
// calculate using implicit euler step so it's stable.
const btVector3 inertiaLocal = getLocalInertia();
const btVector3 w0 = getAngularVelocity();
btMatrix3x3 I;
I = m_worldTransform.getBasis().scaled(inertiaLocal) *
m_worldTransform.getBasis().transpose();
// use newtons method to find implicit solution for new angular velocity (w')
// f(w') = -(T*step + Iw) + Iw' + w' + w'xIw'*step = 0
// df/dw' = I + 1xIw'*step + w'xI*step
btVector3 w1 = w0;
// one step of newton's method
{
const btVector3 fw = evalEulerEqn(w1, w0, btVector3(0, 0, 0), step, I);
const btMatrix3x3 dfw = evalEulerEqnDeriv(w1, w0, step, I);
btVector3 dw;
dw = dfw.solve33(fw);
//const btMatrix3x3 dfw_inv = dfw.inverse();
//dw = dfw_inv*fw;
w1 -= dw;
}
btVector3 gf = (w1 - w0);
return gf;
}
btVector3 btRigidBody::computeGyroscopicForceExplicit(btScalar maxGyroscopicForce) const
{
btVector3 inertiaLocal = getLocalInertia();
btMatrix3x3 inertiaTensorWorld = getWorldTransform().getBasis().scaled(inertiaLocal) * getWorldTransform().getBasis().transpose();
btVector3 tmp = inertiaTensorWorld*getAngularVelocity();
btVector3 gf = getAngularVelocity().cross(tmp);
btScalar l2 = gf.length2();
if (l2>maxGyroscopicForce*maxGyroscopicForce)
{
gf *= btScalar(1.)/btSqrt(l2)*maxGyroscopicForce;
}
return gf;
}
btVector3 btRigidBody::computeGyroscopicImpulseImplicit_Body(btScalar step) const
{
btVector3 idl = getLocalInertia();
btVector3 omega1 = getAngularVelocity();
btQuaternion q = getWorldTransform().getRotation();
// Convert to body coordinates
btVector3 omegab = quatRotate(q.inverse(), omega1);
btMatrix3x3 Ib;
Ib.setValue(idl.x(),0,0,
0,idl.y(),0,
0,0,idl.z());
btVector3 ibo = Ib*omegab;
// Residual vector
btVector3 f = step * omegab.cross(ibo);
btMatrix3x3 skew0;
omegab.getSkewSymmetricMatrix(&skew0[0], &skew0[1], &skew0[2]);
btVector3 om = Ib*omegab;
btMatrix3x3 skew1;
om.getSkewSymmetricMatrix(&skew1[0],&skew1[1],&skew1[2]);
// Jacobian
btMatrix3x3 J = Ib + (skew0*Ib - skew1)*step;
// btMatrix3x3 Jinv = J.inverse();
// btVector3 omega_div = Jinv*f;
btVector3 omega_div = J.solve33(f);
// Single Newton-Raphson update
omegab = omegab - omega_div;//Solve33(J, f);
// Back to world coordinates
btVector3 omega2 = quatRotate(q,omegab);
btVector3 gf = omega2-omega1;
return gf;
}
btVector3 btRigidBody::computeGyroscopicImpulseImplicit_Cooper(btScalar step) const
{
#if 0
dReal h = callContext->m_stepperCallContext->m_stepSize; // Step size
dVector3 L; // Compute angular momentum
dMultiply0_331(L, I, b->avel);
#endif
btVector3 inertiaLocal = getLocalInertia();
btMatrix3x3 inertiaTensorWorld = getWorldTransform().getBasis().scaled(inertiaLocal) * getWorldTransform().getBasis().transpose();
btVector3 L = inertiaTensorWorld*getAngularVelocity();
btMatrix3x3 Itild(0, 0, 0, 0, 0, 0, 0, 0, 0);
#if 0
for (int ii = 0; ii<12; ++ii) {
Itild[ii] = Itild[ii] * h + I[ii];
}
#endif
btSetCrossMatrixMinus(Itild, L*step);
Itild += inertiaTensorWorld;
#if 0
// Compute a new effective 'inertia tensor'
// for the implicit step: the cross-product
// matrix of the angular momentum plus the
// old tensor scaled by the timestep.
// Itild may not be symmetric pos-definite,
// but we can still use it to compute implicit
// gyroscopic torques.
dMatrix3 Itild = { 0 };
dSetCrossMatrixMinus(Itild, L, 4);
for (int ii = 0; ii<12; ++ii) {
Itild[ii] = Itild[ii] * h + I[ii];
}
#endif
L *= step;
//Itild may not be symmetric pos-definite
btMatrix3x3 itInv = Itild.inverse();
Itild = inertiaTensorWorld * itInv;
btMatrix3x3 ident(1,0,0,0,1,0,0,0,1);
Itild -= ident;
#if 0
// Scale momentum by inverse time to get
// a sort of "torque"
dScaleVector3(L, dRecip(h));
// Invert the pseudo-tensor
dMatrix3 itInv;
// This is a closed-form inversion.
// It's probably not numerically stable
// when dealing with small masses with
// a large asymmetry.
// An LU decomposition might be better.
if (dInvertMatrix3(itInv, Itild) != 0) {
// "Divide" the original tensor
// by the pseudo-tensor (on the right)
dMultiply0_333(Itild, I, itInv);
// Subtract an identity matrix
Itild[0] -= 1; Itild[5] -= 1; Itild[10] -= 1;
// This new inertia matrix rotates the
// momentum to get a new set of torques
// that will work correctly when applied
// to the old inertia matrix as explicit
// torques with a semi-implicit update
// step.
dVector3 tau0;
dMultiply0_331(tau0, Itild, L);
// Add the gyro torques to the torque
// accumulator
for (int ii = 0; ii<3; ++ii) {
b->tacc[ii] += tau0[ii];
}
#endif
btVector3 tau0 = Itild * L;
// printf("tau0 = %f,%f,%f\n",tau0.x(),tau0.y(),tau0.z());
return tau0;
}
btVector3 btRigidBody::computeGyroscopicImpulseImplicit_Ewert(btScalar step) const
{
// use full newton-euler equations. common practice to drop the wxIw term. want it for better tumbling behavior.
// calculate using implicit euler step so it's stable.
const btVector3 inertiaLocal = getLocalInertia();
const btVector3 w0 = getAngularVelocity();
btMatrix3x3 I;
I = m_worldTransform.getBasis().scaled(inertiaLocal) *
m_worldTransform.getBasis().transpose();
// use newtons method to find implicit solution for new angular velocity (w')
// f(w') = -(T*step + Iw) + Iw' + w' + w'xIw'*step = 0
// df/dw' = I + 1xIw'*step + w'xI*step
btVector3 w1 = w0;
// one step of newton's method
{
const btVector3 fw = evalEulerEqn(w1, w0, btVector3(0, 0, 0), step, I);
const btMatrix3x3 dfw = evalEulerEqnDeriv(w1, w0, step, I);
const btMatrix3x3 dfw_inv = dfw.inverse();
btVector3 dw;
dw = dfw_inv*fw;
w1 -= dw;
}
btVector3 gf = (w1 - w0);
return gf;
}
void btRigidBody::integrateVelocities(btScalar step)
{
if (isStaticOrKinematicObject())
return;
m_linearVelocity += m_totalForce * (m_inverseMass * step);
m_angularVelocity += m_invInertiaTensorWorld * m_totalTorque * step;
#define MAX_ANGVEL SIMD_HALF_PI
/// clamp angular velocity. collision calculations will fail on higher angular velocities
btScalar angvel = m_angularVelocity.length();
if (angvel*step > MAX_ANGVEL)
{
m_angularVelocity *= (MAX_ANGVEL/step) /angvel;
}
}
btQuaternion btRigidBody::getOrientation() const
{
btQuaternion orn;
m_worldTransform.getBasis().getRotation(orn);
return orn;
}