diff options
Diffstat (limited to 'extern/bullet2/src/BulletSoftBody/btDeformableNeoHookeanForce.h')
| -rw-r--r-- | extern/bullet2/src/BulletSoftBody/btDeformableNeoHookeanForce.h | 420 |
1 files changed, 420 insertions, 0 deletions
diff --git a/extern/bullet2/src/BulletSoftBody/btDeformableNeoHookeanForce.h b/extern/bullet2/src/BulletSoftBody/btDeformableNeoHookeanForce.h new file mode 100644 index 00000000000..60798c5bcd3 --- /dev/null +++ b/extern/bullet2/src/BulletSoftBody/btDeformableNeoHookeanForce.h @@ -0,0 +1,420 @@ +/* +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; // Lame Parameters + btScalar m_E, m_nu; // Young's modulus and Poisson ratio + 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; + updateYoungsModulusAndPoissonRatio(); + } + + 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; + updateYoungsModulusAndPoissonRatio(); + } + + void updateYoungsModulusAndPoissonRatio() + { + // conversion from Lame Parameters to Young's modulus and Poisson ratio + // https://en.wikipedia.org/wiki/Lam%C3%A9_parameters + m_E = m_mu * (3 * m_lambda + 2 * m_mu) / (m_lambda + m_mu); + m_nu = m_lambda * 0.5 / (m_mu + m_lambda); + } + + void updateLameParameters() + { + // conversion from Young's modulus and Poisson ratio to Lame Parameters + // https://en.wikipedia.org/wiki/Lam%C3%A9_parameters + m_mu = m_E * 0.5 / (1 + m_nu); + m_lambda = m_E * m_nu / ((1 + m_nu) * (1 - 2 * m_nu)); + } + + void setYoungsModulus(btScalar E) + { + m_E = E; + updateLameParameters(); + } + + void setPoissonRatio(btScalar nu) + { + m_nu = nu; + updateLameParameters(); + } + + void setDamping(btScalar damping) + { + m_mu_damp = damping * m_mu; + m_lambda_damp = damping * m_lambda; + } + + void setLameParameters(btScalar mu, btScalar lambda) + { + m_mu = mu; + m_lambda = lambda; + updateYoungsModulusAndPoissonRatio(); + } + + 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 buildDampingForceDifferentialDiagonal(btScalar scale, TVStack& diagA) {} + + 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 */ |