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+/*
+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.
+*/
+
+#ifndef BT_NEOHOOKEAN_H
+#define BT_NEOHOOKEAN_H
+
+#include "btDeformableLagrangianForce.h"
+#include "LinearMath/btQuickprof.h"
+#include "LinearMath/btImplicitQRSVD.h"
+// This energy is as described in https://graphics.pixar.com/library/StableElasticity/paper.pdf
+class btDeformableNeoHookeanForce : public btDeformableLagrangianForce
+{
+public:
+ typedef btAlignedObjectArray<btVector3> TVStack;
+ btScalar m_mu, m_lambda;
+ btScalar m_mu_damp, m_lambda_damp;
+ btDeformableNeoHookeanForce(): m_mu(1), m_lambda(1)
+ {
+ btScalar damping = 0.05;
+ m_mu_damp = damping * m_mu;
+ m_lambda_damp = damping * m_lambda;
+ }
+
+ btDeformableNeoHookeanForce(btScalar mu, btScalar lambda, btScalar damping = 0.05): m_mu(mu), m_lambda(lambda)
+ {
+ m_mu_damp = damping * m_mu;
+ m_lambda_damp = damping * m_lambda;
+ }
+
+ virtual void addScaledForces(btScalar scale, TVStack& force)
+ {
+ addScaledDampingForce(scale, force);
+ addScaledElasticForce(scale, force);
+ }
+
+ virtual void addScaledExplicitForce(btScalar scale, TVStack& force)
+ {
+ addScaledElasticForce(scale, force);
+ }
+
+ // 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
+ virtual void addScaledDampingForce(btScalar scale, TVStack& force)
+ {
+ if (m_mu_damp == 0 && m_lambda_damp == 0)
+ return;
+ int numNodes = getNumNodes();
+ btAssert(numNodes <= force.size());
+ btVector3 grad_N_hat_1st_col = btVector3(-1,-1,-1);
+ for (int i = 0; i < m_softBodies.size(); ++i)
+ {
+ btSoftBody* psb = m_softBodies[i];
+ if (!psb->isActive())
+ {
+ continue;
+ }
+ for (int j = 0; j < psb->m_tetras.size(); ++j)
+ {
+ btSoftBody::Tetra& tetra = psb->m_tetras[j];
+ btSoftBody::Node* node0 = tetra.m_n[0];
+ btSoftBody::Node* node1 = tetra.m_n[1];
+ btSoftBody::Node* node2 = tetra.m_n[2];
+ btSoftBody::Node* node3 = tetra.m_n[3];
+ size_t id0 = node0->index;
+ size_t id1 = node1->index;
+ size_t id2 = node2->index;
+ size_t id3 = node3->index;
+ btMatrix3x3 dF = DsFromVelocity(node0, node1, node2, node3) * tetra.m_Dm_inverse;
+ btMatrix3x3 I;
+ I.setIdentity();
+ btMatrix3x3 dP = (dF + dF.transpose()) * m_mu_damp + I * (dF[0][0]+dF[1][1]+dF[2][2]) * m_lambda_damp;
+// firstPiolaDampingDifferential(psb->m_tetraScratchesTn[j], dF, dP);
+ btVector3 df_on_node0 = dP * (tetra.m_Dm_inverse.transpose()*grad_N_hat_1st_col);
+ btMatrix3x3 df_on_node123 = dP * tetra.m_Dm_inverse.transpose();
+
+ // damping force differential
+ btScalar scale1 = scale * tetra.m_element_measure;
+ force[id0] -= scale1 * df_on_node0;
+ force[id1] -= scale1 * df_on_node123.getColumn(0);
+ force[id2] -= scale1 * df_on_node123.getColumn(1);
+ force[id3] -= scale1 * df_on_node123.getColumn(2);
+ }
+ }
+ }
+
+ virtual double totalElasticEnergy(btScalar dt)
+ {
+ double energy = 0;
+ for (int i = 0; i < m_softBodies.size(); ++i)
+ {
+ btSoftBody* psb = m_softBodies[i];
+ if (!psb->isActive())
+ {
+ continue;
+ }
+ for (int j = 0; j < psb->m_tetraScratches.size(); ++j)
+ {
+ btSoftBody::Tetra& tetra = psb->m_tetras[j];
+ btSoftBody::TetraScratch& s = psb->m_tetraScratches[j];
+ energy += tetra.m_element_measure * elasticEnergyDensity(s);
+ }
+ }
+ return energy;
+ }
+
+ // The damping energy is formulated as in https://www.math.ucla.edu/~jteran/papers/GSSJT15.pdf to allow line search
+ virtual double totalDampingEnergy(btScalar dt)
+ {
+ double energy = 0;
+ int sz = 0;
+ for (int i = 0; i < m_softBodies.size(); ++i)
+ {
+ btSoftBody* psb = m_softBodies[i];
+ if (!psb->isActive())
+ {
+ continue;
+ }
+ for (int j = 0; j < psb->m_nodes.size(); ++j)
+ {
+ sz = btMax(sz, psb->m_nodes[j].index);
+ }
+ }
+ TVStack dampingForce;
+ dampingForce.resize(sz+1);
+ for (int i = 0; i < dampingForce.size(); ++i)
+ dampingForce[i].setZero();
+ addScaledDampingForce(0.5, dampingForce);
+ for (int i = 0; i < m_softBodies.size(); ++i)
+ {
+ btSoftBody* psb = m_softBodies[i];
+ for (int j = 0; j < psb->m_nodes.size(); ++j)
+ {
+ const btSoftBody::Node& node = psb->m_nodes[j];
+ energy -= dampingForce[node.index].dot(node.m_v) / dt;
+ }
+ }
+ return energy;
+ }
+
+ double elasticEnergyDensity(const btSoftBody::TetraScratch& s)
+ {
+ double density = 0;
+ density += m_mu * 0.5 * (s.m_trace - 3.);
+ 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);
+ density -= m_mu * 0.5 * log(s.m_trace+1);
+ return density;
+ }
+
+ virtual void addScaledElasticForce(btScalar scale, TVStack& force)
+ {
+ int numNodes = getNumNodes();
+ btAssert(numNodes <= force.size());
+ btVector3 grad_N_hat_1st_col = btVector3(-1,-1,-1);
+ for (int i = 0; i < m_softBodies.size(); ++i)
+ {
+ btSoftBody* psb = m_softBodies[i];
+ if (!psb->isActive())
+ {
+ continue;
+ }
+ btScalar max_p = psb->m_cfg.m_maxStress;
+ for (int j = 0; j < psb->m_tetras.size(); ++j)
+ {
+ btSoftBody::Tetra& tetra = psb->m_tetras[j];
+ btMatrix3x3 P;
+ firstPiola(psb->m_tetraScratches[j],P);
+#ifdef USE_SVD
+ if (max_p > 0)
+ {
+ // since we want to clamp the principal stress to max_p, we only need to
+ // calculate SVD when sigma_0^2 + sigma_1^2 + sigma_2^2 > max_p * max_p
+ btScalar trPTP = (P[0].length2() + P[1].length2() + P[2].length2());
+ if (trPTP > max_p * max_p)
+ {
+ btMatrix3x3 U, V;
+ btVector3 sigma;
+ singularValueDecomposition(P, U, sigma, V);
+ sigma[0] = btMin(sigma[0], max_p);
+ sigma[1] = btMin(sigma[1], max_p);
+ sigma[2] = btMin(sigma[2], max_p);
+ sigma[0] = btMax(sigma[0], -max_p);
+ sigma[1] = btMax(sigma[1], -max_p);
+ sigma[2] = btMax(sigma[2], -max_p);
+ btMatrix3x3 Sigma;
+ Sigma.setIdentity();
+ Sigma[0][0] = sigma[0];
+ Sigma[1][1] = sigma[1];
+ Sigma[2][2] = sigma[2];
+ P = U * Sigma * V.transpose();
+ }
+ }
+#endif
+// btVector3 force_on_node0 = P * (tetra.m_Dm_inverse.transpose()*grad_N_hat_1st_col);
+ btMatrix3x3 force_on_node123 = P * tetra.m_Dm_inverse.transpose();
+ btVector3 force_on_node0 = force_on_node123 * grad_N_hat_1st_col;
+
+ btSoftBody::Node* node0 = tetra.m_n[0];
+ btSoftBody::Node* node1 = tetra.m_n[1];
+ btSoftBody::Node* node2 = tetra.m_n[2];
+ btSoftBody::Node* node3 = tetra.m_n[3];
+ size_t id0 = node0->index;
+ size_t id1 = node1->index;
+ size_t id2 = node2->index;
+ size_t id3 = node3->index;
+
+ // elastic force
+ btScalar scale1 = scale * tetra.m_element_measure;
+ force[id0] -= scale1 * force_on_node0;
+ force[id1] -= scale1 * force_on_node123.getColumn(0);
+ force[id2] -= scale1 * force_on_node123.getColumn(1);
+ force[id3] -= scale1 * force_on_node123.getColumn(2);
+ }
+ }
+ }
+
+ // 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
+ virtual void addScaledDampingForceDifferential(btScalar scale, const TVStack& dv, TVStack& df)
+ {
+ if (m_mu_damp == 0 && m_lambda_damp == 0)
+ return;
+ int numNodes = getNumNodes();
+ btAssert(numNodes <= df.size());
+ btVector3 grad_N_hat_1st_col = btVector3(-1,-1,-1);
+ for (int i = 0; i < m_softBodies.size(); ++i)
+ {
+ btSoftBody* psb = m_softBodies[i];
+ if (!psb->isActive())
+ {
+ continue;
+ }
+ for (int j = 0; j < psb->m_tetras.size(); ++j)
+ {
+ btSoftBody::Tetra& tetra = psb->m_tetras[j];
+ btSoftBody::Node* node0 = tetra.m_n[0];
+ btSoftBody::Node* node1 = tetra.m_n[1];
+ btSoftBody::Node* node2 = tetra.m_n[2];
+ btSoftBody::Node* node3 = tetra.m_n[3];
+ size_t id0 = node0->index;
+ size_t id1 = node1->index;
+ size_t id2 = node2->index;
+ size_t id3 = node3->index;
+ btMatrix3x3 dF = Ds(id0, id1, id2, id3, dv) * tetra.m_Dm_inverse;
+ btMatrix3x3 I;
+ I.setIdentity();
+ btMatrix3x3 dP = (dF + dF.transpose()) * m_mu_damp + I * (dF[0][0]+dF[1][1]+dF[2][2]) * m_lambda_damp;
+// firstPiolaDampingDifferential(psb->m_tetraScratchesTn[j], dF, dP);
+// btVector3 df_on_node0 = dP * (tetra.m_Dm_inverse.transpose()*grad_N_hat_1st_col);
+ btMatrix3x3 df_on_node123 = dP * tetra.m_Dm_inverse.transpose();
+ btVector3 df_on_node0 = df_on_node123 * grad_N_hat_1st_col;
+
+ // damping force differential
+ btScalar scale1 = scale * tetra.m_element_measure;
+ df[id0] -= scale1 * df_on_node0;
+ df[id1] -= scale1 * df_on_node123.getColumn(0);
+ df[id2] -= scale1 * df_on_node123.getColumn(1);
+ df[id3] -= scale1 * df_on_node123.getColumn(2);
+ }
+ }
+ }
+
+ virtual void addScaledElasticForceDifferential(btScalar scale, const TVStack& dx, TVStack& df)
+ {
+ int numNodes = getNumNodes();
+ btAssert(numNodes <= df.size());
+ btVector3 grad_N_hat_1st_col = btVector3(-1,-1,-1);
+ for (int i = 0; i < m_softBodies.size(); ++i)
+ {
+ btSoftBody* psb = m_softBodies[i];
+ if (!psb->isActive())
+ {
+ continue;
+ }
+ for (int j = 0; j < psb->m_tetras.size(); ++j)
+ {
+ btSoftBody::Tetra& tetra = psb->m_tetras[j];
+ btSoftBody::Node* node0 = tetra.m_n[0];
+ btSoftBody::Node* node1 = tetra.m_n[1];
+ btSoftBody::Node* node2 = tetra.m_n[2];
+ btSoftBody::Node* node3 = tetra.m_n[3];
+ size_t id0 = node0->index;
+ size_t id1 = node1->index;
+ size_t id2 = node2->index;
+ size_t id3 = node3->index;
+ btMatrix3x3 dF = Ds(id0, id1, id2, id3, dx) * tetra.m_Dm_inverse;
+ btMatrix3x3 dP;
+ firstPiolaDifferential(psb->m_tetraScratches[j], dF, dP);
+// btVector3 df_on_node0 = dP * (tetra.m_Dm_inverse.transpose()*grad_N_hat_1st_col);
+ btMatrix3x3 df_on_node123 = dP * tetra.m_Dm_inverse.transpose();
+ btVector3 df_on_node0 = df_on_node123 * grad_N_hat_1st_col;
+
+ // elastic force differential
+ btScalar scale1 = scale * tetra.m_element_measure;
+ df[id0] -= scale1 * df_on_node0;
+ df[id1] -= scale1 * df_on_node123.getColumn(0);
+ df[id2] -= scale1 * df_on_node123.getColumn(1);
+ df[id3] -= scale1 * df_on_node123.getColumn(2);
+ }
+ }
+ }
+
+ void firstPiola(const btSoftBody::TetraScratch& s, btMatrix3x3& P)
+ {
+ btScalar c1 = (m_mu * ( 1. - 1. / (s.m_trace + 1.)));
+ btScalar c2 = (m_lambda * (s.m_J - 1.) - 0.75 * m_mu);
+ P = s.m_F * c1 + s.m_cofF * c2;
+ }
+
+ // Let P be the first piola stress.
+ // This function calculates the dP = dP/dF * dF
+ void firstPiolaDifferential(const btSoftBody::TetraScratch& s, const btMatrix3x3& dF, btMatrix3x3& dP)
+ {
+ btScalar c1 = m_mu * ( 1. - 1. / (s.m_trace + 1.));
+ btScalar c2 = (2.*m_mu) * DotProduct(s.m_F, dF) * (1./((1.+s.m_trace)*(1.+s.m_trace)));
+ btScalar c3 = (m_lambda * DotProduct(s.m_cofF, dF));
+ dP = dF * c1 + s.m_F * c2;
+ addScaledCofactorMatrixDifferential(s.m_F, dF, m_lambda*(s.m_J-1.) - 0.75*m_mu, dP);
+ dP += s.m_cofF * c3;
+ }
+
+ // Let Q be the damping stress.
+ // This function calculates the dP = dQ/dF * dF
+ void firstPiolaDampingDifferential(const btSoftBody::TetraScratch& s, const btMatrix3x3& dF, btMatrix3x3& dP)
+ {
+ btScalar c1 = (m_mu_damp * ( 1. - 1. / (s.m_trace + 1.)));
+ btScalar c2 = ((2.*m_mu_damp) * DotProduct(s.m_F, dF) *(1./((1.+s.m_trace)*(1.+s.m_trace))));
+ btScalar c3 = (m_lambda_damp * DotProduct(s.m_cofF, dF));
+ dP = dF * c1 + s.m_F * c2;
+ addScaledCofactorMatrixDifferential(s.m_F, dF, m_lambda_damp*(s.m_J-1.) - 0.75*m_mu_damp, dP);
+ dP += s.m_cofF * c3;
+ }
+
+ btScalar DotProduct(const btMatrix3x3& A, const btMatrix3x3& B)
+ {
+ btScalar ans = 0;
+ for (int i = 0; i < 3; ++i)
+ {
+ ans += A[i].dot(B[i]);
+ }
+ return ans;
+ }
+
+ // Let C(A) be the cofactor of the matrix A
+ // Let H = the derivative of C(A) with respect to A evaluated at F = A
+ // This function calculates H*dF
+ void addScaledCofactorMatrixDifferential(const btMatrix3x3& F, const btMatrix3x3& dF, btScalar scale, btMatrix3x3& M)
+ {
+ 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]);
+ 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]);
+ 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]);
+ 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]);
+ 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]);
+ 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]);
+ 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]);
+ 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]);
+ 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]);
+ }
+
+ virtual btDeformableLagrangianForceType getForceType()
+ {
+ return BT_NEOHOOKEAN_FORCE;
+ }
+
+};
+#endif /* BT_NEOHOOKEAN_H */
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