422 lines
17 KiB
C++
422 lines
17 KiB
C++
/*
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Written by Xuchen Han <xuchenhan2015@u.northwestern.edu>
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Bullet Continuous Collision Detection and Physics Library
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Copyright (c) 2019 Google Inc. http://bulletphysics.org
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This software is provided 'as-is', without any express or implied warranty.
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In no event will the authors be held liable for any damages arising from the use of this software.
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Permission is granted to anyone to use this software for any purpose,
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including commercial applications, and to alter it and redistribute it freely,
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subject to the following restrictions:
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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.
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2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
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3. This notice may not be removed or altered from any source distribution.
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*/
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#ifndef BT_NEOHOOKEAN_H
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#define BT_NEOHOOKEAN_H
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#include "btDeformableLagrangianForce.h"
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#include "LinearMath/btQuickprof.h"
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#include "LinearMath/btImplicitQRSVD.h"
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// This energy is as described in https://graphics.pixar.com/library/StableElasticity/paper.pdf
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class btDeformableNeoHookeanForce : public btDeformableLagrangianForce
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{
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public:
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typedef btAlignedObjectArray<btVector3> TVStack;
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btScalar m_mu, m_lambda; // Lame Parameters
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btScalar m_E, m_nu; // Young's modulus and Poisson ratio
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btScalar m_mu_damp, m_lambda_damp;
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btDeformableNeoHookeanForce(): m_mu(1), m_lambda(1)
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{
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btScalar damping = 0.05;
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m_mu_damp = damping * m_mu;
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m_lambda_damp = damping * m_lambda;
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updateYoungsModulusAndPoissonRatio();
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}
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btDeformableNeoHookeanForce(btScalar mu, btScalar lambda, btScalar damping = 0.05): m_mu(mu), m_lambda(lambda)
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{
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m_mu_damp = damping * m_mu;
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m_lambda_damp = damping * m_lambda;
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updateYoungsModulusAndPoissonRatio();
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}
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void updateYoungsModulusAndPoissonRatio()
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{
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// conversion from Lame Parameters to Young's modulus and Poisson ratio
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// https://en.wikipedia.org/wiki/Lam%C3%A9_parameters
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m_E = m_mu * (3*m_lambda + 2*m_mu)/(m_lambda + m_mu);
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m_nu = m_lambda * 0.5 / (m_mu + m_lambda);
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}
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void updateLameParameters()
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{
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// conversion from Young's modulus and Poisson ratio to Lame Parameters
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// https://en.wikipedia.org/wiki/Lam%C3%A9_parameters
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m_mu = m_E * 0.5 / (1 + m_nu);
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m_lambda = m_E * m_nu / ((1 + m_nu) * (1- 2*m_nu));
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}
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void setYoungsModulus(btScalar E)
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{
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m_E = E;
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updateLameParameters();
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}
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void setPoissonRatio(btScalar nu)
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{
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m_nu = nu;
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updateLameParameters();
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}
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void setDamping(btScalar damping)
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{
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m_mu_damp = damping * m_mu;
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m_lambda_damp = damping * m_lambda;
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}
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void setLameParameters(btScalar mu, btScalar lambda)
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{
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m_mu = mu;
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m_lambda = lambda;
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updateYoungsModulusAndPoissonRatio();
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}
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virtual void addScaledForces(btScalar scale, TVStack& force)
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{
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addScaledDampingForce(scale, force);
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addScaledElasticForce(scale, force);
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}
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virtual void addScaledExplicitForce(btScalar scale, TVStack& force)
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{
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addScaledElasticForce(scale, force);
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}
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// The damping matrix is calculated using the time n state as described in https://www.math.ucla.edu/~jteran/papers/GSSJT15.pdf to allow line search
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virtual void addScaledDampingForce(btScalar scale, TVStack& force)
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{
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if (m_mu_damp == 0 && m_lambda_damp == 0)
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return;
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int numNodes = getNumNodes();
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btAssert(numNodes <= force.size());
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btVector3 grad_N_hat_1st_col = btVector3(-1,-1,-1);
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for (int i = 0; i < m_softBodies.size(); ++i)
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{
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btSoftBody* psb = m_softBodies[i];
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if (!psb->isActive())
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{
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continue;
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}
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for (int j = 0; j < psb->m_tetras.size(); ++j)
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{
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btSoftBody::Tetra& tetra = psb->m_tetras[j];
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btSoftBody::Node* node0 = tetra.m_n[0];
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btSoftBody::Node* node1 = tetra.m_n[1];
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btSoftBody::Node* node2 = tetra.m_n[2];
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btSoftBody::Node* node3 = tetra.m_n[3];
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size_t id0 = node0->index;
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size_t id1 = node1->index;
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size_t id2 = node2->index;
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size_t id3 = node3->index;
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btMatrix3x3 dF = DsFromVelocity(node0, node1, node2, node3) * tetra.m_Dm_inverse;
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btMatrix3x3 I;
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I.setIdentity();
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btMatrix3x3 dP = (dF + dF.transpose()) * m_mu_damp + I * (dF[0][0]+dF[1][1]+dF[2][2]) * m_lambda_damp;
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// firstPiolaDampingDifferential(psb->m_tetraScratchesTn[j], dF, dP);
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btVector3 df_on_node0 = dP * (tetra.m_Dm_inverse.transpose()*grad_N_hat_1st_col);
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btMatrix3x3 df_on_node123 = dP * tetra.m_Dm_inverse.transpose();
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// damping force differential
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btScalar scale1 = scale * tetra.m_element_measure;
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force[id0] -= scale1 * df_on_node0;
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force[id1] -= scale1 * df_on_node123.getColumn(0);
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force[id2] -= scale1 * df_on_node123.getColumn(1);
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force[id3] -= scale1 * df_on_node123.getColumn(2);
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}
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}
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}
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virtual double totalElasticEnergy(btScalar dt)
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{
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double energy = 0;
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for (int i = 0; i < m_softBodies.size(); ++i)
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{
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btSoftBody* psb = m_softBodies[i];
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if (!psb->isActive())
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{
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continue;
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}
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for (int j = 0; j < psb->m_tetraScratches.size(); ++j)
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{
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btSoftBody::Tetra& tetra = psb->m_tetras[j];
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btSoftBody::TetraScratch& s = psb->m_tetraScratches[j];
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energy += tetra.m_element_measure * elasticEnergyDensity(s);
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}
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}
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return energy;
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}
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// The damping energy is formulated as in https://www.math.ucla.edu/~jteran/papers/GSSJT15.pdf to allow line search
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virtual double totalDampingEnergy(btScalar dt)
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{
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double energy = 0;
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int sz = 0;
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for (int i = 0; i < m_softBodies.size(); ++i)
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{
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btSoftBody* psb = m_softBodies[i];
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if (!psb->isActive())
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{
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continue;
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}
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for (int j = 0; j < psb->m_nodes.size(); ++j)
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{
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sz = btMax(sz, psb->m_nodes[j].index);
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}
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}
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TVStack dampingForce;
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dampingForce.resize(sz+1);
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for (int i = 0; i < dampingForce.size(); ++i)
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dampingForce[i].setZero();
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addScaledDampingForce(0.5, dampingForce);
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for (int i = 0; i < m_softBodies.size(); ++i)
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{
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btSoftBody* psb = m_softBodies[i];
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for (int j = 0; j < psb->m_nodes.size(); ++j)
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{
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const btSoftBody::Node& node = psb->m_nodes[j];
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energy -= dampingForce[node.index].dot(node.m_v) / dt;
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}
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}
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return energy;
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}
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double elasticEnergyDensity(const btSoftBody::TetraScratch& s)
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{
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double density = 0;
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density += m_mu * 0.5 * (s.m_trace - 3.);
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density += m_lambda * 0.5 * (s.m_J - 1. - 0.75 * m_mu / m_lambda)* (s.m_J - 1. - 0.75 * m_mu / m_lambda);
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density -= m_mu * 0.5 * log(s.m_trace+1);
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return density;
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}
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virtual void addScaledElasticForce(btScalar scale, TVStack& force)
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{
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int numNodes = getNumNodes();
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btAssert(numNodes <= force.size());
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btVector3 grad_N_hat_1st_col = btVector3(-1,-1,-1);
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for (int i = 0; i < m_softBodies.size(); ++i)
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{
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btSoftBody* psb = m_softBodies[i];
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if (!psb->isActive())
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{
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continue;
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}
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btScalar max_p = psb->m_cfg.m_maxStress;
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for (int j = 0; j < psb->m_tetras.size(); ++j)
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{
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btSoftBody::Tetra& tetra = psb->m_tetras[j];
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btMatrix3x3 P;
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firstPiola(psb->m_tetraScratches[j],P);
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#ifdef USE_SVD
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if (max_p > 0)
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{
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// since we want to clamp the principal stress to max_p, we only need to
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// calculate SVD when sigma_0^2 + sigma_1^2 + sigma_2^2 > max_p * max_p
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btScalar trPTP = (P[0].length2() + P[1].length2() + P[2].length2());
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if (trPTP > max_p * max_p)
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{
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btMatrix3x3 U, V;
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btVector3 sigma;
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singularValueDecomposition(P, U, sigma, V);
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sigma[0] = btMin(sigma[0], max_p);
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sigma[1] = btMin(sigma[1], max_p);
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sigma[2] = btMin(sigma[2], max_p);
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sigma[0] = btMax(sigma[0], -max_p);
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sigma[1] = btMax(sigma[1], -max_p);
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sigma[2] = btMax(sigma[2], -max_p);
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btMatrix3x3 Sigma;
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Sigma.setIdentity();
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Sigma[0][0] = sigma[0];
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Sigma[1][1] = sigma[1];
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Sigma[2][2] = sigma[2];
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P = U * Sigma * V.transpose();
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}
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}
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#endif
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// btVector3 force_on_node0 = P * (tetra.m_Dm_inverse.transpose()*grad_N_hat_1st_col);
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btMatrix3x3 force_on_node123 = P * tetra.m_Dm_inverse.transpose();
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btVector3 force_on_node0 = force_on_node123 * grad_N_hat_1st_col;
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btSoftBody::Node* node0 = tetra.m_n[0];
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btSoftBody::Node* node1 = tetra.m_n[1];
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btSoftBody::Node* node2 = tetra.m_n[2];
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btSoftBody::Node* node3 = tetra.m_n[3];
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size_t id0 = node0->index;
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size_t id1 = node1->index;
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size_t id2 = node2->index;
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size_t id3 = node3->index;
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// elastic force
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btScalar scale1 = scale * tetra.m_element_measure;
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force[id0] -= scale1 * force_on_node0;
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force[id1] -= scale1 * force_on_node123.getColumn(0);
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force[id2] -= scale1 * force_on_node123.getColumn(1);
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force[id3] -= scale1 * force_on_node123.getColumn(2);
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}
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}
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}
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// The damping matrix is calculated using the time n state as described in https://www.math.ucla.edu/~jteran/papers/GSSJT15.pdf to allow line search
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virtual void addScaledDampingForceDifferential(btScalar scale, const TVStack& dv, TVStack& df)
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{
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if (m_mu_damp == 0 && m_lambda_damp == 0)
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return;
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int numNodes = getNumNodes();
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btAssert(numNodes <= df.size());
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btVector3 grad_N_hat_1st_col = btVector3(-1,-1,-1);
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for (int i = 0; i < m_softBodies.size(); ++i)
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{
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btSoftBody* psb = m_softBodies[i];
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if (!psb->isActive())
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{
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continue;
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}
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for (int j = 0; j < psb->m_tetras.size(); ++j)
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{
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btSoftBody::Tetra& tetra = psb->m_tetras[j];
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btSoftBody::Node* node0 = tetra.m_n[0];
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btSoftBody::Node* node1 = tetra.m_n[1];
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btSoftBody::Node* node2 = tetra.m_n[2];
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btSoftBody::Node* node3 = tetra.m_n[3];
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size_t id0 = node0->index;
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size_t id1 = node1->index;
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size_t id2 = node2->index;
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size_t id3 = node3->index;
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btMatrix3x3 dF = Ds(id0, id1, id2, id3, dv) * tetra.m_Dm_inverse;
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btMatrix3x3 I;
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I.setIdentity();
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btMatrix3x3 dP = (dF + dF.transpose()) * m_mu_damp + I * (dF[0][0]+dF[1][1]+dF[2][2]) * m_lambda_damp;
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// firstPiolaDampingDifferential(psb->m_tetraScratchesTn[j], dF, dP);
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// btVector3 df_on_node0 = dP * (tetra.m_Dm_inverse.transpose()*grad_N_hat_1st_col);
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btMatrix3x3 df_on_node123 = dP * tetra.m_Dm_inverse.transpose();
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btVector3 df_on_node0 = df_on_node123 * grad_N_hat_1st_col;
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// damping force differential
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btScalar scale1 = scale * tetra.m_element_measure;
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df[id0] -= scale1 * df_on_node0;
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df[id1] -= scale1 * df_on_node123.getColumn(0);
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df[id2] -= scale1 * df_on_node123.getColumn(1);
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df[id3] -= scale1 * df_on_node123.getColumn(2);
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}
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}
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}
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virtual void buildDampingForceDifferentialDiagonal(btScalar scale, TVStack& diagA){}
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virtual void addScaledElasticForceDifferential(btScalar scale, const TVStack& dx, TVStack& df)
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{
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int numNodes = getNumNodes();
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btAssert(numNodes <= df.size());
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btVector3 grad_N_hat_1st_col = btVector3(-1,-1,-1);
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for (int i = 0; i < m_softBodies.size(); ++i)
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{
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btSoftBody* psb = m_softBodies[i];
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if (!psb->isActive())
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{
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continue;
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}
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for (int j = 0; j < psb->m_tetras.size(); ++j)
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{
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btSoftBody::Tetra& tetra = psb->m_tetras[j];
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btSoftBody::Node* node0 = tetra.m_n[0];
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btSoftBody::Node* node1 = tetra.m_n[1];
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btSoftBody::Node* node2 = tetra.m_n[2];
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btSoftBody::Node* node3 = tetra.m_n[3];
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size_t id0 = node0->index;
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size_t id1 = node1->index;
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size_t id2 = node2->index;
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size_t id3 = node3->index;
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btMatrix3x3 dF = Ds(id0, id1, id2, id3, dx) * tetra.m_Dm_inverse;
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btMatrix3x3 dP;
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firstPiolaDifferential(psb->m_tetraScratches[j], dF, dP);
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// btVector3 df_on_node0 = dP * (tetra.m_Dm_inverse.transpose()*grad_N_hat_1st_col);
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btMatrix3x3 df_on_node123 = dP * tetra.m_Dm_inverse.transpose();
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btVector3 df_on_node0 = df_on_node123 * grad_N_hat_1st_col;
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// elastic force differential
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btScalar scale1 = scale * tetra.m_element_measure;
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df[id0] -= scale1 * df_on_node0;
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df[id1] -= scale1 * df_on_node123.getColumn(0);
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df[id2] -= scale1 * df_on_node123.getColumn(1);
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df[id3] -= scale1 * df_on_node123.getColumn(2);
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}
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}
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}
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void firstPiola(const btSoftBody::TetraScratch& s, btMatrix3x3& P)
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{
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btScalar c1 = (m_mu * ( 1. - 1. / (s.m_trace + 1.)));
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btScalar c2 = (m_lambda * (s.m_J - 1.) - 0.75 * m_mu);
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P = s.m_F * c1 + s.m_cofF * c2;
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}
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// Let P be the first piola stress.
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// This function calculates the dP = dP/dF * dF
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void firstPiolaDifferential(const btSoftBody::TetraScratch& s, const btMatrix3x3& dF, btMatrix3x3& dP)
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{
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btScalar c1 = m_mu * ( 1. - 1. / (s.m_trace + 1.));
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btScalar c2 = (2.*m_mu) * DotProduct(s.m_F, dF) * (1./((1.+s.m_trace)*(1.+s.m_trace)));
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btScalar c3 = (m_lambda * DotProduct(s.m_cofF, dF));
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dP = dF * c1 + s.m_F * c2;
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addScaledCofactorMatrixDifferential(s.m_F, dF, m_lambda*(s.m_J-1.) - 0.75*m_mu, dP);
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dP += s.m_cofF * c3;
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}
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// Let Q be the damping stress.
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// This function calculates the dP = dQ/dF * dF
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void firstPiolaDampingDifferential(const btSoftBody::TetraScratch& s, const btMatrix3x3& dF, btMatrix3x3& dP)
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{
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btScalar c1 = (m_mu_damp * ( 1. - 1. / (s.m_trace + 1.)));
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btScalar c2 = ((2.*m_mu_damp) * DotProduct(s.m_F, dF) *(1./((1.+s.m_trace)*(1.+s.m_trace))));
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btScalar c3 = (m_lambda_damp * DotProduct(s.m_cofF, dF));
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dP = dF * c1 + s.m_F * c2;
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addScaledCofactorMatrixDifferential(s.m_F, dF, m_lambda_damp*(s.m_J-1.) - 0.75*m_mu_damp, dP);
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dP += s.m_cofF * c3;
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}
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btScalar DotProduct(const btMatrix3x3& A, const btMatrix3x3& B)
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{
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btScalar ans = 0;
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for (int i = 0; i < 3; ++i)
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{
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ans += A[i].dot(B[i]);
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}
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return ans;
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}
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// Let C(A) be the cofactor of the matrix A
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// Let H = the derivative of C(A) with respect to A evaluated at F = A
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// This function calculates H*dF
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void addScaledCofactorMatrixDifferential(const btMatrix3x3& F, const btMatrix3x3& dF, btScalar scale, btMatrix3x3& M)
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{
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M[0][0] += scale * (dF[1][1] * F[2][2] + F[1][1] * dF[2][2] - dF[2][1] * F[1][2] - F[2][1] * dF[1][2]);
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M[1][0] += scale * (dF[2][1] * F[0][2] + F[2][1] * dF[0][2] - dF[0][1] * F[2][2] - F[0][1] * dF[2][2]);
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M[2][0] += scale * (dF[0][1] * F[1][2] + F[0][1] * dF[1][2] - dF[1][1] * F[0][2] - F[1][1] * dF[0][2]);
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M[0][1] += scale * (dF[2][0] * F[1][2] + F[2][0] * dF[1][2] - dF[1][0] * F[2][2] - F[1][0] * dF[2][2]);
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M[1][1] += scale * (dF[0][0] * F[2][2] + F[0][0] * dF[2][2] - dF[2][0] * F[0][2] - F[2][0] * dF[0][2]);
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M[2][1] += scale * (dF[1][0] * F[0][2] + F[1][0] * dF[0][2] - dF[0][0] * F[1][2] - F[0][0] * dF[1][2]);
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M[0][2] += scale * (dF[1][0] * F[2][1] + F[1][0] * dF[2][1] - dF[2][0] * F[1][1] - F[2][0] * dF[1][1]);
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M[1][2] += scale * (dF[2][0] * F[0][1] + F[2][0] * dF[0][1] - dF[0][0] * F[2][1] - F[0][0] * dF[2][1]);
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M[2][2] += scale * (dF[0][0] * F[1][1] + F[0][0] * dF[1][1] - dF[1][0] * F[0][1] - F[1][0] * dF[0][1]);
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}
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virtual btDeformableLagrangianForceType getForceType()
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{
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return BT_NEOHOOKEAN_FORCE;
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}
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};
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#endif /* BT_NEOHOOKEAN_H */
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