///bilateral constraint between two dynamic objects
///positive distance = separation, negative distance = penetration
public static void ResolveSingleBilateral(RigidBody body1, ref Vector3 pos1,
RigidBody body2, ref Vector3 pos2,
float distance, ref Vector3 normal, ref float impulse, float timeStep)
{
float normalLenSqr = normal.LengthSquared();
Debug.Assert(System.Math.Abs(normalLenSqr) < 1.1f);
if (normalLenSqr > 1.1f)
{
impulse = 0f;
return;
}
Vector3 rel_pos1 = pos1 - body1.GetCenterOfMassPosition();
Vector3 rel_pos2 = pos2 - body2.GetCenterOfMassPosition();
//this jacobian entry could be re-used for all iterations
Vector3 vel1 = body1.GetVelocityInLocalPoint(ref rel_pos1);
Vector3 vel2 = body2.GetVelocityInLocalPoint(ref rel_pos2);
Vector3 vel = vel1 - vel2;
Matrix m1 = MathUtil.TransposeBasis(body1.GetCenterOfMassTransform());
Matrix m2 = MathUtil.TransposeBasis(body2.GetCenterOfMassTransform());
JacobianEntry jac = new JacobianEntry(m1,m2,rel_pos1,rel_pos2,normal,
body1.GetInvInertiaDiagLocal(),body1.GetInvMass(),
body2.GetInvInertiaDiagLocal(),body2.GetInvMass());
float jacDiagAB = jac.GetDiagonal();
float jacDiagABInv = 1f / jacDiagAB;
float rel_vel = jac.GetRelativeVelocity(
body1.GetLinearVelocity(),Vector3.TransformNormal(body1.GetAngularVelocity(),m1),
body2.GetLinearVelocity(),Vector3.TransformNormal(body2.GetAngularVelocity(),m2));
float a = jacDiagABInv;
rel_vel = Vector3.Dot(normal,vel);
//todo: move this into proper structure
float contactDamping = 0.2f;
if(ONLY_USE_LINEAR_MASS)
{
float massTerm = 1f / (body1.GetInvMass() + body2.GetInvMass());
impulse = - contactDamping * rel_vel * massTerm;
}
else
{
float velocityImpulse = -contactDamping * rel_vel * jacDiagABInv;
impulse = velocityImpulse;
}
}
protected virtual void BuildAngularJacobian(ref JacobianEntry jacAngular, ref Vector3 jointAxisW)
{
jacAngular = new JacobianEntry(jointAxisW,
MathUtil.TransposeBasis(m_rbA.GetCenterOfMassTransform()),
MathUtil.TransposeBasis(m_rbB.GetCenterOfMassTransform()),
m_rbA.GetInvInertiaDiagLocal(),
m_rbB.GetInvInertiaDiagLocal());
}
protected virtual void BuildLinearJacobian(
ref JacobianEntry jacLinear, ref Vector3 normalWorld,
ref Vector3 pivotAInW, ref Vector3 pivotBInW)
{
jacLinear = new JacobianEntry(
MathUtil.TransposeBasis(m_rbA.GetCenterOfMassTransform()),
MathUtil.TransposeBasis(m_rbB.GetCenterOfMassTransform()),
pivotAInW - m_rbA.GetCenterOfMassPosition(),
pivotBInW - m_rbB.GetCenterOfMassPosition(),
normalWorld,
m_rbA.GetInvInertiaDiagLocal(),
m_rbA.GetInvMass(),
m_rbB.GetInvInertiaDiagLocal(),
m_rbB.GetInvMass());
}
//
// solve unilateral raint (equality, direct method)
//
public void ResolveUnilateralPairConstraint(RigidBody body0, RigidBody body1, ref Matrix world2A,
ref Matrix world2B,
ref Vector3 invInertiaADiag,
float invMassA,
ref Vector3 linvelA, ref Vector3 angvelA,
ref Vector3 rel_posA1,
ref Vector3 invInertiaBDiag,
float invMassB,
ref Vector3 linvelB, ref Vector3 angvelB,
ref Vector3 rel_posA2,
float depthA, ref Vector3 normalA,
ref Vector3 rel_posB1, ref Vector3 rel_posB2,
float depthB, ref Vector3 normalB,
ref float imp0, ref float imp1)
{
//(void)linvelA;
//(void)linvelB;
//(void)angvelB;
//(void)angvelA;
imp0 = 0f;
imp1 = 0f;
float len = System.Math.Abs(normalA.Length()) - 1f;
if (System.Math.Abs(len) >= MathUtil.SIMD_EPSILON)
return;
Debug.Assert(len < MathUtil.SIMD_EPSILON);
//this jacobian entry could be re-used for all iterations
JacobianEntry jacA = new JacobianEntry(ref world2A,ref world2B,ref rel_posA1,ref rel_posA2,ref normalA,ref invInertiaADiag,invMassA,
ref invInertiaBDiag,invMassB);
JacobianEntry jacB = new JacobianEntry(ref world2A,ref world2B,ref rel_posB1,ref rel_posB2,ref normalB,ref invInertiaADiag,invMassA,
ref invInertiaBDiag,invMassB);
// float vel0 = jacA.getRelativeVelocity(linvelA,angvelA,linvelB,angvelB);
// float vel1 = jacB.getRelativeVelocity(linvelA,angvelA,linvelB,angvelB);
float vel0 = Vector3.Dot(normalA,(body0.GetVelocityInLocalPoint(ref rel_posA1)-body1.GetVelocityInLocalPoint(ref rel_posA1)));
float vel1 = Vector3.Dot(normalB,(body0.GetVelocityInLocalPoint(ref rel_posB1)-body1.GetVelocityInLocalPoint(ref rel_posB1)));
// float penetrationImpulse = (depth*contactTau*timeCorrection) * massTerm;//jacDiagABInv
float massTerm = 1f / (invMassA + invMassB);
// calculate rhs (or error) terms
float dv0 = depthA * m_tau * massTerm - vel0 * m_damping;
float dv1 = depthB * m_tau * massTerm - vel1 * m_damping;
// dC/dv * dv = -C
// jacobian * impulse = -error
//
//impulse = jacobianInverse * -error
// inverting 2x2 symmetric system (offdiagonal are equal!)
//
float nonDiag = jacA.GetNonDiagonal(jacB,invMassA,invMassB);
float invDet = 1f / (jacA.GetDiagonal() * jacB.GetDiagonal() - nonDiag * nonDiag );
//imp0 = dv0 * jacA.getDiagonal() * invDet + dv1 * -nonDiag * invDet;
//imp1 = dv1 * jacB.getDiagonal() * invDet + dv0 * - nonDiag * invDet;
imp0 = dv0 * jacA.GetDiagonal() * invDet + dv1 * -nonDiag * invDet;
imp1 = dv1 * jacB.GetDiagonal() * invDet + dv0 * - nonDiag * invDet;
//[a b] [d -c]
//[c d] inverse = (1 / determinant) * [-b a] where determinant is (ad - bc)
//[jA nD] * [imp0] = [dv0]
//[nD jB] [imp1] [dv1]
}
// for two constraints on sharing two same rigidbodies (for example two contact points between two rigidbodies)
public float GetNonDiagonal(JacobianEntry jacB,float massInvA,float massInvB)
{
JacobianEntry jacA = this;
Vector3 lin = jacA.m_linearJointAxis * jacB.m_linearJointAxis;
Vector3 ang0 = jacA.m_0MinvJt * jacB.m_aJ;
Vector3 ang1 = jacA.m_1MinvJt * jacB.m_bJ;
Vector3 lin0 = massInvA * lin ;
Vector3 lin1 = massInvB * lin;
Vector3 sum = ang0+ang1+lin0+lin1;
return sum.X+sum.Y+sum.Z;
}
// for two constraints on the same rigidbody (for example vehicle friction)
public float GetNonDiagonal(JacobianEntry jacB, float massInvA)
{
JacobianEntry jacA = this;
float lin = massInvA * Vector3.Dot(jacA.m_linearJointAxis,jacB.m_linearJointAxis);
float ang = Vector3.Dot(jacA.m_0MinvJt,jacB.m_aJ);
return lin + ang;
}