bullet3

/*
 Written by Xuchen Han <xuchenhan2015@u.northwestern.edu>
 
 Bullet Continuous Collision Detection and Physics Library
 Copyright (c) 2019 Google Inc. http://bulletphysics.org
 This software is provided 'as-is', without any express or implied warranty.
 In no event will the authors be held liable for any damages arising from the use of this software.
 Permission is granted to anyone to use this software for any purpose,
 including commercial applications, and to alter it and redistribute it freely,
 subject to the following restrictions:
 1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
 2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
 3. This notice may not be removed or altered from any source distribution.
 */

#include "btDeformableContactConstraint.h"
/* ================   Deformable Node Anchor   =================== */
btDeformableNodeAnchorConstraint::btDeformableNodeAnchorConstraint(const btSoftBody::DeformableNodeRigidAnchor& a, const btContactSolverInfo& infoGlobal)
	: m_anchor(&a), btDeformableContactConstraint(a.m_cti.m_normal, infoGlobal)
{
}

btDeformableNodeAnchorConstraint::btDeformableNodeAnchorConstraint(const btDeformableNodeAnchorConstraint& other)
	: m_anchor(other.m_anchor), btDeformableContactConstraint(other)
{
}

btVector3 btDeformableNodeAnchorConstraint::getVa() const
{
	const btSoftBody::sCti& cti = m_anchor->m_cti;
	btVector3 va(0, 0, 0);
	if (cti.m_colObj->hasContactResponse())
	{
		btRigidBody* rigidCol = 0;
		btMultiBodyLinkCollider* multibodyLinkCol = 0;

		// grab the velocity of the rigid body
		if (cti.m_colObj->getInternalType() == btCollisionObject::CO_RIGID_BODY)
		{
			rigidCol = (btRigidBody*)btRigidBody::upcast(cti.m_colObj);
			va = rigidCol ? (rigidCol->getVelocityInLocalPoint(m_anchor->m_c1)) : btVector3(0, 0, 0);
		}
		else if (cti.m_colObj->getInternalType() == btCollisionObject::CO_FEATHERSTONE_LINK)
		{
			multibodyLinkCol = (btMultiBodyLinkCollider*)btMultiBodyLinkCollider::upcast(cti.m_colObj);
			if (multibodyLinkCol)
			{
				const int ndof = multibodyLinkCol->m_multiBody->getNumDofs() + 6;
				const btScalar* J_n = &m_anchor->jacobianData_normal.m_jacobians[0];
				const btScalar* J_t1 = &m_anchor->jacobianData_t1.m_jacobians[0];
				const btScalar* J_t2 = &m_anchor->jacobianData_t2.m_jacobians[0];
				const btScalar* local_v = multibodyLinkCol->m_multiBody->getVelocityVector();
				const btScalar* local_dv = multibodyLinkCol->m_multiBody->getDeltaVelocityVector();
				// add in the normal component of the va
				btScalar vel = 0.0;
				for (int k = 0; k < ndof; ++k)
				{
					vel += (local_v[k] + local_dv[k]) * J_n[k];
				}
				va = cti.m_normal * vel;
				// add in the tangential components of the va
				vel = 0.0;
				for (int k = 0; k < ndof; ++k)
				{
					vel += (local_v[k] + local_dv[k]) * J_t1[k];
				}
				va += m_anchor->t1 * vel;
				vel = 0.0;
				for (int k = 0; k < ndof; ++k)
				{
					vel += (local_v[k] + local_dv[k]) * J_t2[k];
				}
				va += m_anchor->t2 * vel;
			}
		}
	}
	return va;
}

btScalar btDeformableNodeAnchorConstraint::solveConstraint(const btContactSolverInfo& infoGlobal)
{
	const btSoftBody::sCti& cti = m_anchor->m_cti;
	btVector3 va = getVa();
	btVector3 vb = getVb();
	btVector3 vr = (vb - va);
	// + (m_anchor->m_node->m_x - cti.m_colObj->getWorldTransform() * m_anchor->m_local) * 10.0
	const btScalar dn = btDot(vr, vr);
	// dn is the normal component of velocity diffrerence. Approximates the residual. // todo xuchenhan@: this prob needs to be scaled by dt
	btScalar residualSquare = dn * dn;
	btVector3 impulse = m_anchor->m_c0 * vr;
	// apply impulse to deformable nodes involved and change their velocities
	applyImpulse(impulse);

	// apply impulse to the rigid/multibodies involved and change their velocities
	if (cti.m_colObj->getInternalType() == btCollisionObject::CO_RIGID_BODY)
	{
		btRigidBody* rigidCol = 0;
		rigidCol = (btRigidBody*)btRigidBody::upcast(cti.m_colObj);
		if (rigidCol)
		{
			rigidCol->applyImpulse(impulse, m_anchor->m_c1);
		}
	}
	else if (cti.m_colObj->getInternalType() == btCollisionObject::CO_FEATHERSTONE_LINK)
	{
		btMultiBodyLinkCollider* multibodyLinkCol = 0;
		multibodyLinkCol = (btMultiBodyLinkCollider*)btMultiBodyLinkCollider::upcast(cti.m_colObj);
		if (multibodyLinkCol)
		{
			const btScalar* deltaV_normal = &m_anchor->jacobianData_normal.m_deltaVelocitiesUnitImpulse[0];
			// apply normal component of the impulse
			multibodyLinkCol->m_multiBody->applyDeltaVeeMultiDof2(deltaV_normal, impulse.dot(cti.m_normal));
			// apply tangential component of the impulse
			const btScalar* deltaV_t1 = &m_anchor->jacobianData_t1.m_deltaVelocitiesUnitImpulse[0];
			multibodyLinkCol->m_multiBody->applyDeltaVeeMultiDof2(deltaV_t1, impulse.dot(m_anchor->t1));
			const btScalar* deltaV_t2 = &m_anchor->jacobianData_t2.m_deltaVelocitiesUnitImpulse[0];
			multibodyLinkCol->m_multiBody->applyDeltaVeeMultiDof2(deltaV_t2, impulse.dot(m_anchor->t2));
		}
	}
	return residualSquare;
}

btVector3 btDeformableNodeAnchorConstraint::getVb() const
{
	return m_anchor->m_node->m_v;
}

void btDeformableNodeAnchorConstraint::applyImpulse(const btVector3& impulse)
{
	btVector3 dv = impulse * m_anchor->m_c2;
	m_anchor->m_node->m_v -= dv;
}

/* ================   Deformable vs. Rigid   =================== */
btDeformableRigidContactConstraint::btDeformableRigidContactConstraint(const btSoftBody::DeformableRigidContact& c, const btContactSolverInfo& infoGlobal)
	: m_contact(&c), btDeformableContactConstraint(c.m_cti.m_normal, infoGlobal)
{
	m_total_normal_dv.setZero();
	m_total_tangent_dv.setZero();
	// The magnitude of penetration is the depth of penetration.
	m_penetration = c.m_cti.m_offset;
	m_total_split_impulse = 0;
	m_binding = false;
}

btDeformableRigidContactConstraint::btDeformableRigidContactConstraint(const btDeformableRigidContactConstraint& other)
	: m_contact(other.m_contact), btDeformableContactConstraint(other), m_penetration(other.m_penetration), m_total_split_impulse(other.m_total_split_impulse), m_binding(other.m_binding)
{
	m_total_normal_dv = other.m_total_normal_dv;
	m_total_tangent_dv = other.m_total_tangent_dv;
}

btVector3 btDeformableRigidContactConstraint::getVa() const
{
	const btSoftBody::sCti& cti = m_contact->m_cti;
	btVector3 va(0, 0, 0);
	if (cti.m_colObj->hasContactResponse())
	{
		btRigidBody* rigidCol = 0;
		btMultiBodyLinkCollider* multibodyLinkCol = 0;

		// grab the velocity of the rigid body
		if (cti.m_colObj->getInternalType() == btCollisionObject::CO_RIGID_BODY)
		{
			rigidCol = (btRigidBody*)btRigidBody::upcast(cti.m_colObj);
			va = rigidCol ? (rigidCol->getVelocityInLocalPoint(m_contact->m_c1)) : btVector3(0, 0, 0);
		}
		else if (cti.m_colObj->getInternalType() == btCollisionObject::CO_FEATHERSTONE_LINK)
		{
			multibodyLinkCol = (btMultiBodyLinkCollider*)btMultiBodyLinkCollider::upcast(cti.m_colObj);
			if (multibodyLinkCol)
			{
				const int ndof = multibodyLinkCol->m_multiBody->getNumDofs() + 6;
				const btScalar* J_n = &m_contact->jacobianData_normal.m_jacobians[0];
				const btScalar* J_t1 = &m_contact->jacobianData_t1.m_jacobians[0];
				const btScalar* J_t2 = &m_contact->jacobianData_t2.m_jacobians[0];
				const btScalar* local_v = multibodyLinkCol->m_multiBody->getVelocityVector();
				const btScalar* local_dv = multibodyLinkCol->m_multiBody->getDeltaVelocityVector();
				// add in the normal component of the va
				btScalar vel = 0.0;
				for (int k = 0; k < ndof; ++k)
				{
					vel += (local_v[k] + local_dv[k]) * J_n[k];
				}
				va = cti.m_normal * vel;
				// add in the tangential components of the va
				vel = 0.0;
				for (int k = 0; k < ndof; ++k)
				{
					vel += (local_v[k] + local_dv[k]) * J_t1[k];
				}
				va += m_contact->t1 * vel;
				vel = 0.0;
				for (int k = 0; k < ndof; ++k)
				{
					vel += (local_v[k] + local_dv[k]) * J_t2[k];
				}
				va += m_contact->t2 * vel;
			}
		}
	}
	return va;
}

btVector3 btDeformableRigidContactConstraint::getSplitVa() const
{
	const btSoftBody::sCti& cti = m_contact->m_cti;
	btVector3 va(0, 0, 0);
	if (cti.m_colObj->hasContactResponse())
	{
		btRigidBody* rigidCol = 0;
		btMultiBodyLinkCollider* multibodyLinkCol = 0;

		// grab the velocity of the rigid body
		if (cti.m_colObj->getInternalType() == btCollisionObject::CO_RIGID_BODY)
		{
			rigidCol = (btRigidBody*)btRigidBody::upcast(cti.m_colObj);
			va = rigidCol ? (rigidCol->getPushVelocityInLocalPoint(m_contact->m_c1)) : btVector3(0, 0, 0);
		}
		else if (cti.m_colObj->getInternalType() == btCollisionObject::CO_FEATHERSTONE_LINK)
		{
			multibodyLinkCol = (btMultiBodyLinkCollider*)btMultiBodyLinkCollider::upcast(cti.m_colObj);
			if (multibodyLinkCol)
			{
				const int ndof = multibodyLinkCol->m_multiBody->getNumDofs() + 6;
				const btScalar* J_n = &m_contact->jacobianData_normal.m_jacobians[0];
				const btScalar* J_t1 = &m_contact->jacobianData_t1.m_jacobians[0];
				const btScalar* J_t2 = &m_contact->jacobianData_t2.m_jacobians[0];
				const btScalar* local_split_v = multibodyLinkCol->m_multiBody->getSplitVelocityVector();
				// add in the normal component of the va
				btScalar vel = 0.0;
				for (int k = 0; k < ndof; ++k)
				{
					vel += local_split_v[k] * J_n[k];
				}
				va = cti.m_normal * vel;
				// add in the tangential components of the va
				vel = 0.0;
				for (int k = 0; k < ndof; ++k)
				{
					vel += local_split_v[k] * J_t1[k];
				}
				va += m_contact->t1 * vel;
				vel = 0.0;
				for (int k = 0; k < ndof; ++k)
				{
					vel += local_split_v[k] * J_t2[k];
				}
				va += m_contact->t2 * vel;
			}
		}
	}
	return va;
}

btScalar btDeformableRigidContactConstraint::solveConstraint(const btContactSolverInfo& infoGlobal)
{
	const btSoftBody::sCti& cti = m_contact->m_cti;
	btVector3 va = getVa();
	btVector3 vb = getVb();
	btVector3 vr = vb - va;
	btScalar dn = btDot(vr, cti.m_normal) + m_total_normal_dv.dot(cti.m_normal) * infoGlobal.m_deformable_cfm;
	if (m_penetration > 0)
	{
		dn += m_penetration / infoGlobal.m_timeStep;
	}
	if (!infoGlobal.m_splitImpulse)
	{
		dn += m_penetration * infoGlobal.m_deformable_erp / infoGlobal.m_timeStep;
	}
	// dn is the normal component of velocity difference. Approximates the residual. // todo xuchenhan@: this prob needs to be scaled by dt
	btVector3 impulse = m_contact->m_c0 * (vr + m_total_normal_dv * infoGlobal.m_deformable_cfm + ((m_penetration > 0) ? m_penetration / infoGlobal.m_timeStep * cti.m_normal : btVector3(0, 0, 0)));
	if (!infoGlobal.m_splitImpulse)
	{
		impulse += m_contact->m_c0 * (m_penetration * infoGlobal.m_deformable_erp / infoGlobal.m_timeStep * cti.m_normal);
	}
	btVector3 impulse_normal = m_contact->m_c0 * (cti.m_normal * dn);
	btVector3 impulse_tangent = impulse - impulse_normal;
	if (dn > 0)
	{
		return 0;
	}
	m_binding = true;
	btScalar residualSquare = dn * dn;
	btVector3 old_total_tangent_dv = m_total_tangent_dv;
	// m_c5 is the inverse mass of the deformable node/face
	m_total_normal_dv -= m_contact->m_c5 * impulse_normal;
	m_total_tangent_dv -= m_contact->m_c5 * impulse_tangent;

	if (m_total_normal_dv.dot(cti.m_normal) < 0)
	{
		// separating in the normal direction
		m_binding = false;
		m_static = false;
		impulse_tangent.setZero();
	}
	else
	{
		if (m_total_normal_dv.norm() * m_contact->m_c3 < m_total_tangent_dv.norm())
		{
			// dynamic friction
			// with dynamic friction, the impulse are still applied to the two objects colliding, however, it does not pose a constraint in the cg solve, hence the change to dv merely serves to update velocity in the contact iterations.
			m_static = false;
			if (m_total_tangent_dv.safeNorm() < SIMD_EPSILON)
			{
				m_total_tangent_dv = btVector3(0, 0, 0);
			}
			else
			{
				m_total_tangent_dv = m_total_tangent_dv.normalized() * m_total_normal_dv.safeNorm() * m_contact->m_c3;
			}
			//            impulse_tangent = -btScalar(1)/m_contact->m_c2 * (m_total_tangent_dv - old_total_tangent_dv);
			impulse_tangent = m_contact->m_c5.inverse() * (old_total_tangent_dv - m_total_tangent_dv);
		}
		else
		{
			// static friction
			m_static = true;
		}
	}
	impulse = impulse_normal + impulse_tangent;
	// apply impulse to deformable nodes involved and change their velocities
	applyImpulse(impulse);
	// apply impulse to the rigid/multibodies involved and change their velocities
	if (cti.m_colObj->getInternalType() == btCollisionObject::CO_RIGID_BODY)
	{
		btRigidBody* rigidCol = 0;
		rigidCol = (btRigidBody*)btRigidBody::upcast(cti.m_colObj);
		if (rigidCol)
		{
			rigidCol->applyImpulse(impulse, m_contact->m_c1);
		}
	}
	else if (cti.m_colObj->getInternalType() == btCollisionObject::CO_FEATHERSTONE_LINK)
	{
		btMultiBodyLinkCollider* multibodyLinkCol = 0;
		multibodyLinkCol = (btMultiBodyLinkCollider*)btMultiBodyLinkCollider::upcast(cti.m_colObj);
		if (multibodyLinkCol)
		{
			const btScalar* deltaV_normal = &m_contact->jacobianData_normal.m_deltaVelocitiesUnitImpulse[0];
			// apply normal component of the impulse
			multibodyLinkCol->m_multiBody->applyDeltaVeeMultiDof2(deltaV_normal, impulse.dot(cti.m_normal));
			if (impulse_tangent.norm() > SIMD_EPSILON)
			{
				// apply tangential component of the impulse
				const btScalar* deltaV_t1 = &m_contact->jacobianData_t1.m_deltaVelocitiesUnitImpulse[0];
				multibodyLinkCol->m_multiBody->applyDeltaVeeMultiDof2(deltaV_t1, impulse.dot(m_contact->t1));
				const btScalar* deltaV_t2 = &m_contact->jacobianData_t2.m_deltaVelocitiesUnitImpulse[0];
				multibodyLinkCol->m_multiBody->applyDeltaVeeMultiDof2(deltaV_t2, impulse.dot(m_contact->t2));
			}
		}
	}
	return residualSquare;
}

btScalar btDeformableRigidContactConstraint::solveSplitImpulse(const btContactSolverInfo& infoGlobal)
{
	btScalar MAX_PENETRATION_CORRECTION = infoGlobal.m_deformable_maxErrorReduction;
	const btSoftBody::sCti& cti = m_contact->m_cti;
	btVector3 vb = getSplitVb();
	btVector3 va = getSplitVa();
	btScalar p = m_penetration;
	if (p > 0)
	{
		return 0;
	}
	btVector3 vr = vb - va;
	btScalar dn = btDot(vr, cti.m_normal) + p * infoGlobal.m_deformable_erp / infoGlobal.m_timeStep;
	if (dn > 0)
	{
		return 0;
	}
	if (m_total_split_impulse + dn > MAX_PENETRATION_CORRECTION)
	{
		dn = MAX_PENETRATION_CORRECTION - m_total_split_impulse;
	}
	if (m_total_split_impulse + dn < -MAX_PENETRATION_CORRECTION)
	{
		dn = -MAX_PENETRATION_CORRECTION - m_total_split_impulse;
	}
	m_total_split_impulse += dn;

	btScalar residualSquare = dn * dn;
	const btVector3 impulse = m_contact->m_c0 * (cti.m_normal * dn);
	applySplitImpulse(impulse);

	// apply split impulse to the rigid/multibodies involved and change their velocities
	if (cti.m_colObj->getInternalType() == btCollisionObject::CO_RIGID_BODY)
	{
		btRigidBody* rigidCol = 0;
		rigidCol = (btRigidBody*)btRigidBody::upcast(cti.m_colObj);
		if (rigidCol)
		{
			rigidCol->applyPushImpulse(impulse, m_contact->m_c1);
		}
	}
	else if (cti.m_colObj->getInternalType() == btCollisionObject::CO_FEATHERSTONE_LINK)
	{
		btMultiBodyLinkCollider* multibodyLinkCol = 0;
		multibodyLinkCol = (btMultiBodyLinkCollider*)btMultiBodyLinkCollider::upcast(cti.m_colObj);
		if (multibodyLinkCol)
		{
			const btScalar* deltaV_normal = &m_contact->jacobianData_normal.m_deltaVelocitiesUnitImpulse[0];
			// apply normal component of the impulse
			multibodyLinkCol->m_multiBody->applyDeltaSplitVeeMultiDof(deltaV_normal, impulse.dot(cti.m_normal));
		}
	}
	return residualSquare;
}
/* ================   Node vs. Rigid   =================== */
btDeformableNodeRigidContactConstraint::btDeformableNodeRigidContactConstraint(const btSoftBody::DeformableNodeRigidContact& contact, const btContactSolverInfo& infoGlobal)
	: m_node(contact.m_node), btDeformableRigidContactConstraint(contact, infoGlobal)
{
}

btDeformableNodeRigidContactConstraint::btDeformableNodeRigidContactConstraint(const btDeformableNodeRigidContactConstraint& other)
	: m_node(other.m_node), btDeformableRigidContactConstraint(other)
{
}

btVector3 btDeformableNodeRigidContactConstraint::getVb() const
{
	return m_node->m_v;
}

btVector3 btDeformableNodeRigidContactConstraint::getSplitVb() const
{
	return m_node->m_splitv;
}

btVector3 btDeformableNodeRigidContactConstraint::getDv(const btSoftBody::Node* node) const
{
	return m_total_normal_dv + m_total_tangent_dv;
}

void btDeformableNodeRigidContactConstraint::applyImpulse(const btVector3& impulse)
{
	const btSoftBody::DeformableNodeRigidContact* contact = getContact();
	btVector3 dv = contact->m_c5 * impulse;
	contact->m_node->m_v -= dv;
}

void btDeformableNodeRigidContactConstraint::applySplitImpulse(const btVector3& impulse)
{
	const btSoftBody::DeformableNodeRigidContact* contact = getContact();
	btVector3 dv = contact->m_c5 * impulse;
	contact->m_node->m_splitv -= dv;
}

/* ================   Face vs. Rigid   =================== */
btDeformableFaceRigidContactConstraint::btDeformableFaceRigidContactConstraint(const btSoftBody::DeformableFaceRigidContact& contact, const btContactSolverInfo& infoGlobal, bool useStrainLimiting)
	: m_face(contact.m_face), m_useStrainLimiting(useStrainLimiting), btDeformableRigidContactConstraint(contact, infoGlobal)
{
}

btDeformableFaceRigidContactConstraint::btDeformableFaceRigidContactConstraint(const btDeformableFaceRigidContactConstraint& other)
	: m_face(other.m_face), m_useStrainLimiting(other.m_useStrainLimiting), btDeformableRigidContactConstraint(other)
{
}

btVector3 btDeformableFaceRigidContactConstraint::getVb() const
{
	const btSoftBody::DeformableFaceRigidContact* contact = getContact();
	btVector3 vb = m_face->m_n[0]->m_v * contact->m_bary[0] + m_face->m_n[1]->m_v * contact->m_bary[1] + m_face->m_n[2]->m_v * contact->m_bary[2];
	return vb;
}

btVector3 btDeformableFaceRigidContactConstraint::getDv(const btSoftBody::Node* node) const
{
	btVector3 face_dv = m_total_normal_dv + m_total_tangent_dv;
	const btSoftBody::DeformableFaceRigidContact* contact = getContact();
	if (m_face->m_n[0] == node)
	{
		return face_dv * contact->m_weights[0];
	}
	if (m_face->m_n[1] == node)
	{
		return face_dv * contact->m_weights[1];
	}
	btAssert(node == m_face->m_n[2]);
	return face_dv * contact->m_weights[2];
}

void btDeformableFaceRigidContactConstraint::applyImpulse(const btVector3& impulse)
{
	const btSoftBody::DeformableFaceRigidContact* contact = getContact();
	btVector3 dv = impulse * contact->m_c2;
	btSoftBody::Face* face = contact->m_face;

	// save applied impulse
	contact->m_cti.m_impulse = impulse;

	btVector3& v0 = face->m_n[0]->m_v;
	btVector3& v1 = face->m_n[1]->m_v;
	btVector3& v2 = face->m_n[2]->m_v;
	const btScalar& im0 = face->m_n[0]->m_im;
	const btScalar& im1 = face->m_n[1]->m_im;
	const btScalar& im2 = face->m_n[2]->m_im;
	if (im0 > 0)
		v0 -= dv * contact->m_weights[0];
	if (im1 > 0)
		v1 -= dv * contact->m_weights[1];
	if (im2 > 0)
		v2 -= dv * contact->m_weights[2];
	if (m_useStrainLimiting)
	{
		btScalar relaxation = 1. / btScalar(m_infoGlobal->m_numIterations);
		btScalar m01 = (relaxation / (im0 + im1));
		btScalar m02 = (relaxation / (im0 + im2));
		btScalar m12 = (relaxation / (im1 + im2));
#ifdef USE_STRAIN_RATE_LIMITING
		// apply strain limiting to prevent the new velocity to change the current length of the edge by more than 1%.
		btScalar p = 0.01;
		btVector3& x0 = face->m_n[0]->m_x;
		btVector3& x1 = face->m_n[1]->m_x;
		btVector3& x2 = face->m_n[2]->m_x;
		const btVector3 x_diff[3] = {x1 - x0, x2 - x0, x2 - x1};
		const btVector3 v_diff[3] = {v1 - v0, v2 - v0, v2 - v1};
		btVector3 u[3];
		btScalar x_diff_dot_u, dn[3];
		btScalar dt = m_infoGlobal->m_timeStep;
		for (int i = 0; i < 3; ++i)
		{
			btScalar x_diff_norm = x_diff[i].safeNorm();
			btScalar x_diff_norm_new = (x_diff[i] + v_diff[i] * dt).safeNorm();
			btScalar strainRate = x_diff_norm_new / x_diff_norm;
			u[i] = v_diff[i];
			u[i].safeNormalize();
			if (x_diff_norm == 0 || (1 - p <= strainRate && strainRate <= 1 + p))
			{
				dn[i] = 0;
				continue;
			}
			x_diff_dot_u = btDot(x_diff[i], u[i]);
			btScalar s;
			if (1 - p > strainRate)
			{
				s = 1 / dt * (-x_diff_dot_u - btSqrt(x_diff_dot_u * x_diff_dot_u + (p * p - 2 * p) * x_diff_norm * x_diff_norm));
			}
			else
			{
				s = 1 / dt * (-x_diff_dot_u + btSqrt(x_diff_dot_u * x_diff_dot_u + (p * p + 2 * p) * x_diff_norm * x_diff_norm));
			}
			//		x_diff_norm_new = (x_diff[i] + s * u[i] * dt).safeNorm();
			//		strainRate = x_diff_norm_new/x_diff_norm;
			dn[i] = s - v_diff[i].safeNorm();
		}
		btVector3 dv0 = im0 * (m01 * u[0] * (-dn[0]) + m02 * u[1] * -(dn[1]));
		btVector3 dv1 = im1 * (m01 * u[0] * (dn[0]) + m12 * u[2] * (-dn[2]));
		btVector3 dv2 = im2 * (m12 * u[2] * (dn[2]) + m02 * u[1] * (dn[1]));
#else
		// apply strain limiting to prevent undamped modes
		btVector3 dv0 = im0 * (m01 * (v1 - v0) + m02 * (v2 - v0));
		btVector3 dv1 = im1 * (m01 * (v0 - v1) + m12 * (v2 - v1));
		btVector3 dv2 = im2 * (m12 * (v1 - v2) + m02 * (v0 - v2));
#endif
		v0 += dv0;
		v1 += dv1;
		v2 += dv2;
	}
}

btVector3 btDeformableFaceRigidContactConstraint::getSplitVb() const
{
	const btSoftBody::DeformableFaceRigidContact* contact = getContact();
	btVector3 vb = (m_face->m_n[0]->m_splitv) * contact->m_bary[0] + (m_face->m_n[1]->m_splitv) * contact->m_bary[1] + (m_face->m_n[2]->m_splitv) * contact->m_bary[2];
	return vb;
}

void btDeformableFaceRigidContactConstraint::applySplitImpulse(const btVector3& impulse)
{
	const btSoftBody::DeformableFaceRigidContact* contact = getContact();
	btVector3 dv = impulse * contact->m_c2;
	btSoftBody::Face* face = contact->m_face;
	btVector3& v0 = face->m_n[0]->m_splitv;
	btVector3& v1 = face->m_n[1]->m_splitv;
	btVector3& v2 = face->m_n[2]->m_splitv;
	const btScalar& im0 = face->m_n[0]->m_im;
	const btScalar& im1 = face->m_n[1]->m_im;
	const btScalar& im2 = face->m_n[2]->m_im;
	if (im0 > 0)
	{
		v0 -= dv * contact->m_weights[0];
	}
	if (im1 > 0)
	{
		v1 -= dv * contact->m_weights[1];
	}
	if (im2 > 0)
	{
		v2 -= dv * contact->m_weights[2];
	}
}

/* ================   Face vs. Node   =================== */
btDeformableFaceNodeContactConstraint::btDeformableFaceNodeContactConstraint(const btSoftBody::DeformableFaceNodeContact& contact, const btContactSolverInfo& infoGlobal)
	: m_node(contact.m_node), m_face(contact.m_face), m_contact(&contact), btDeformableContactConstraint(contact.m_normal, infoGlobal)
{
	m_total_normal_dv.setZero();
	m_total_tangent_dv.setZero();
}

btVector3 btDeformableFaceNodeContactConstraint::getVa() const
{
	return m_node->m_v;
}

btVector3 btDeformableFaceNodeContactConstraint::getVb() const
{
	const btSoftBody::DeformableFaceNodeContact* contact = getContact();
	btVector3 vb = m_face->m_n[0]->m_v * contact->m_bary[0] + m_face->m_n[1]->m_v * contact->m_bary[1] + m_face->m_n[2]->m_v * contact->m_bary[2];
	return vb;
}

btVector3 btDeformableFaceNodeContactConstraint::getDv(const btSoftBody::Node* n) const
{
	btVector3 dv = m_total_normal_dv + m_total_tangent_dv;
	if (n == m_node)
		return dv;
	const btSoftBody::DeformableFaceNodeContact* contact = getContact();
	if (m_face->m_n[0] == n)
	{
		return dv * contact->m_weights[0];
	}
	if (m_face->m_n[1] == n)
	{
		return dv * contact->m_weights[1];
	}
	btAssert(n == m_face->m_n[2]);
	return dv * contact->m_weights[2];
}

btScalar btDeformableFaceNodeContactConstraint::solveConstraint(const btContactSolverInfo& infoGlobal)
{
	btVector3 va = getVa();
	btVector3 vb = getVb();
	btVector3 vr = vb - va;
	const btScalar dn = btDot(vr, m_contact->m_normal);
	// dn is the normal component of velocity diffrerence. Approximates the residual. // todo xuchenhan@: this prob needs to be scaled by dt
	btScalar residualSquare = dn * dn;
	btVector3 impulse = m_contact->m_c0 * vr;
	const btVector3 impulse_normal = m_contact->m_c0 * (m_contact->m_normal * dn);
	btVector3 impulse_tangent = impulse - impulse_normal;

	btVector3 old_total_tangent_dv = m_total_tangent_dv;
	// m_c2 is the inverse mass of the deformable node/face
	if (m_node->m_im > 0)
	{
		m_total_normal_dv -= impulse_normal * m_node->m_im;
		m_total_tangent_dv -= impulse_tangent * m_node->m_im;
	}
	else
	{
		m_total_normal_dv -= impulse_normal * m_contact->m_imf;
		m_total_tangent_dv -= impulse_tangent * m_contact->m_imf;
	}

	if (m_total_normal_dv.dot(m_contact->m_normal) > 0)
	{
		// separating in the normal direction
		m_static = false;
		m_total_tangent_dv = btVector3(0, 0, 0);
		impulse_tangent.setZero();
	}
	else
	{
		if (m_total_normal_dv.norm() * m_contact->m_friction < m_total_tangent_dv.norm())
		{
			// dynamic friction
			// with dynamic friction, the impulse are still applied to the two objects colliding, however, it does not pose a constraint in the cg solve, hence the change to dv merely serves to update velocity in the contact iterations.
			m_static = false;
			if (m_total_tangent_dv.safeNorm() < SIMD_EPSILON)
			{
				m_total_tangent_dv = btVector3(0, 0, 0);
			}
			else
			{
				m_total_tangent_dv = m_total_tangent_dv.normalized() * m_total_normal_dv.safeNorm() * m_contact->m_friction;
			}
			impulse_tangent = -btScalar(1) / m_node->m_im * (m_total_tangent_dv - old_total_tangent_dv);
		}
		else
		{
			// static friction
			m_static = true;
		}
	}
	impulse = impulse_normal + impulse_tangent;
	// apply impulse to deformable nodes involved and change their velocities
	applyImpulse(impulse);
	return residualSquare;
}

void btDeformableFaceNodeContactConstraint::applyImpulse(const btVector3& impulse)
{
	const btSoftBody::DeformableFaceNodeContact* contact = getContact();
	btVector3 dva = impulse * contact->m_node->m_im;
	btVector3 dvb = impulse * contact->m_imf;
	if (contact->m_node->m_im > 0)
	{
		contact->m_node->m_v += dva;
	}

	btSoftBody::Face* face = contact->m_face;
	btVector3& v0 = face->m_n[0]->m_v;
	btVector3& v1 = face->m_n[1]->m_v;
	btVector3& v2 = face->m_n[2]->m_v;
	const btScalar& im0 = face->m_n[0]->m_im;
	const btScalar& im1 = face->m_n[1]->m_im;
	const btScalar& im2 = face->m_n[2]->m_im;
	if (im0 > 0)
	{
		v0 -= dvb * contact->m_weights[0];
	}
	if (im1 > 0)
	{
		v1 -= dvb * contact->m_weights[1];
	}
	if (im2 > 0)
	{
		v2 -= dvb * contact->m_weights[2];
	}
}