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Diffstat (limited to 'source/blender/simulation/intern/implicit_eigen.cpp')
| -rw-r--r-- | source/blender/simulation/intern/implicit_eigen.cpp | 1509 |
1 files changed, 1509 insertions, 0 deletions
diff --git a/source/blender/simulation/intern/implicit_eigen.cpp b/source/blender/simulation/intern/implicit_eigen.cpp new file mode 100644 index 00000000000..15b9e30e32a --- /dev/null +++ b/source/blender/simulation/intern/implicit_eigen.cpp @@ -0,0 +1,1509 @@ +/* + * This program is free software; you can redistribute it and/or + * modify it under the terms of the GNU General Public License + * as published by the Free Software Foundation; either version 2 + * of the License, or (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software Foundation, + * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. + * + * The Original Code is Copyright (C) Blender Foundation + * All rights reserved. + */ + +/** \file + * \ingroup bph + */ + +#include "implicit.h" + +#ifdef IMPLICIT_SOLVER_EIGEN + +//#define USE_EIGEN_CORE +# define USE_EIGEN_CONSTRAINED_CG + +# ifdef __GNUC__ +# pragma GCC diagnostic push +/* XXX suppress verbose warnings in eigen */ +//# pragma GCC diagnostic ignored "-Wlogical-op" +# endif + +# ifndef IMPLICIT_ENABLE_EIGEN_DEBUG +# ifdef NDEBUG +# define IMPLICIT_NDEBUG +# endif +# define NDEBUG +# endif + +# include <Eigen/Sparse> +# include <Eigen/src/Core/util/DisableStupidWarnings.h> + +# ifdef USE_EIGEN_CONSTRAINED_CG +# include <intern/ConstrainedConjugateGradient.h> +# endif + +# ifndef IMPLICIT_ENABLE_EIGEN_DEBUG +# ifndef IMPLICIT_NDEBUG +# undef NDEBUG +# else +# undef IMPLICIT_NDEBUG +# endif +# endif + +# ifdef __GNUC__ +# pragma GCC diagnostic pop +# endif + +# include "MEM_guardedalloc.h" + +extern "C" { +# include "DNA_meshdata_types.h" +# include "DNA_object_force_types.h" +# include "DNA_object_types.h" +# include "DNA_scene_types.h" +# include "DNA_texture_types.h" + +# include "BLI_linklist.h" +# include "BLI_math.h" +# include "BLI_utildefines.h" + +# include "BKE_cloth.h" +# include "BKE_collision.h" +# include "BKE_effect.h" +# include "BKE_global.h" + +# include "SIM_mass_spring.h" +} + +typedef float Scalar; + +static float I[3][3] = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}; + +/* slightly extended Eigen vector class + * with conversion to/from plain C float array + */ +class fVector : public Eigen::Vector3f { + public: + typedef float *ctype; + + fVector() + { + } + + fVector(const ctype &v) + { + for (int k = 0; k < 3; k++) { + coeffRef(k) = v[k]; + } + } + + fVector &operator=(const ctype &v) + { + for (int k = 0; k < 3; k++) { + coeffRef(k) = v[k]; + } + return *this; + } + + operator ctype() + { + return data(); + } +}; + +/* slightly extended Eigen matrix class + * with conversion to/from plain C float array + */ +class fMatrix : public Eigen::Matrix3f { + public: + typedef float (*ctype)[3]; + + fMatrix() + { + } + + fMatrix(const ctype &v) + { + for (int k = 0; k < 3; k++) { + for (int l = 0; l < 3; l++) { + coeffRef(l, k) = v[k][l]; + } + } + } + + fMatrix &operator=(const ctype &v) + { + for (int k = 0; k < 3; k++) { + for (int l = 0; l < 3; l++) { + coeffRef(l, k) = v[k][l]; + } + } + return *this; + } + + operator ctype() + { + return (ctype)data(); + } +}; + +/* Extension of dense Eigen vectors, + * providing 3-float block access for blenlib math functions + */ +class lVector : public Eigen::VectorXf { + public: + typedef Eigen::VectorXf base_t; + + lVector() + { + } + + template<typename T> lVector &operator=(T rhs) + { + base_t::operator=(rhs); + return *this; + } + + float *v3(int vertex) + { + return &coeffRef(3 * vertex); + } + + const float *v3(int vertex) const + { + return &coeffRef(3 * vertex); + } +}; + +typedef Eigen::Triplet<Scalar> Triplet; +typedef std::vector<Triplet> TripletList; + +typedef Eigen::SparseMatrix<Scalar> lMatrix; + +/* Constructor type that provides more convenient handling of Eigen triplets + * for efficient construction of sparse 3x3 block matrices. + * This should be used for building lMatrix instead of writing to such lMatrix directly (which is + * very inefficient). After all elements have been defined using the set() method, the actual + * matrix can be filled using construct(). + */ +struct lMatrixCtor { + lMatrixCtor() + { + } + + void reset() + { + m_trips.clear(); + } + + void reserve(int numverts) + { + /* reserve for diagonal entries */ + m_trips.reserve(numverts * 9); + } + + void add(int i, int j, const fMatrix &m) + { + i *= 3; + j *= 3; + for (int k = 0; k < 3; k++) { + for (int l = 0; l < 3; l++) { + m_trips.push_back(Triplet(i + k, j + l, m.coeff(l, k))); + } + } + } + + void sub(int i, int j, const fMatrix &m) + { + i *= 3; + j *= 3; + for (int k = 0; k < 3; k++) { + for (int l = 0; l < 3; l++) { + m_trips.push_back(Triplet(i + k, j + l, -m.coeff(l, k))); + } + } + } + + inline void construct(lMatrix &m) + { + m.setFromTriplets(m_trips.begin(), m_trips.end()); + m_trips.clear(); + } + + private: + TripletList m_trips; +}; + +# ifdef USE_EIGEN_CORE +typedef Eigen::ConjugateGradient<lMatrix, Eigen::Lower, Eigen::DiagonalPreconditioner<Scalar>> + ConjugateGradient; +# endif +# ifdef USE_EIGEN_CONSTRAINED_CG +typedef Eigen::ConstrainedConjugateGradient<lMatrix, + Eigen::Lower, + lMatrix, + Eigen::DiagonalPreconditioner<Scalar>> + ConstraintConjGrad; +# endif +using Eigen::ComputationInfo; + +static void print_lvector(const lVector &v) +{ + for (int i = 0; i < v.rows(); i++) { + if (i > 0 && i % 3 == 0) { + printf("\n"); + } + + printf("%f,\n", v[i]); + } +} + +static void print_lmatrix(const lMatrix &m) +{ + for (int j = 0; j < m.rows(); j++) { + if (j > 0 && j % 3 == 0) { + printf("\n"); + } + + for (int i = 0; i < m.cols(); i++) { + if (i > 0 && i % 3 == 0) { + printf(" "); + } + + implicit_print_matrix_elem(m.coeff(j, i)); + } + printf("\n"); + } +} + +BLI_INLINE void lMatrix_reserve_elems(lMatrix &m, int num) +{ + m.reserve(Eigen::VectorXi::Constant(m.cols(), num)); +} + +BLI_INLINE float *lVector_v3(lVector &v, int vertex) +{ + return v.data() + 3 * vertex; +} + +BLI_INLINE const float *lVector_v3(const lVector &v, int vertex) +{ + return v.data() + 3 * vertex; +} + +# if 0 +BLI_INLINE void triplets_m3(TripletList &tlist, float m[3][3], int i, int j) +{ + i *= 3; + j *= 3; + for (int l = 0; l < 3; l++) { + for (int k = 0; k < 3; k++) { + tlist.push_back(Triplet(i + k, j + l, m[k][l])); + } + } +} + +BLI_INLINE void triplets_m3fl(TripletList &tlist, float m[3][3], int i, int j, float factor) +{ + i *= 3; + j *= 3; + for (int l = 0; l < 3; l++) { + for (int k = 0; k < 3; k++) { + tlist.push_back(Triplet(i + k, j + l, m[k][l] * factor)); + } + } +} + +BLI_INLINE void lMatrix_add_triplets(lMatrix &r, const TripletList &tlist) +{ + lMatrix t(r.rows(), r.cols()); + t.setFromTriplets(tlist.begin(), tlist.end()); + r += t; +} + +BLI_INLINE void lMatrix_madd_triplets(lMatrix &r, const TripletList &tlist, float f) +{ + lMatrix t(r.rows(), r.cols()); + t.setFromTriplets(tlist.begin(), tlist.end()); + r += f * t; +} + +BLI_INLINE void lMatrix_sub_triplets(lMatrix &r, const TripletList &tlist) +{ + lMatrix t(r.rows(), r.cols()); + t.setFromTriplets(tlist.begin(), tlist.end()); + r -= t; +} +# endif + +BLI_INLINE void outerproduct(float r[3][3], const float a[3], const float b[3]) +{ + mul_v3_v3fl(r[0], a, b[0]); + mul_v3_v3fl(r[1], a, b[1]); + mul_v3_v3fl(r[2], a, b[2]); +} + +BLI_INLINE void cross_m3_v3m3(float r[3][3], const float v[3], float m[3][3]) +{ + cross_v3_v3v3(r[0], v, m[0]); + cross_v3_v3v3(r[1], v, m[1]); + cross_v3_v3v3(r[2], v, m[2]); +} + +BLI_INLINE void cross_v3_identity(float r[3][3], const float v[3]) +{ + r[0][0] = 0.0f; + r[1][0] = v[2]; + r[2][0] = -v[1]; + r[0][1] = -v[2]; + r[1][1] = 0.0f; + r[2][1] = v[0]; + r[0][2] = v[1]; + r[1][2] = -v[0]; + r[2][2] = 0.0f; +} + +BLI_INLINE void madd_m3_m3fl(float r[3][3], float m[3][3], float f) +{ + r[0][0] += m[0][0] * f; + r[0][1] += m[0][1] * f; + r[0][2] += m[0][2] * f; + r[1][0] += m[1][0] * f; + r[1][1] += m[1][1] * f; + r[1][2] += m[1][2] * f; + r[2][0] += m[2][0] * f; + r[2][1] += m[2][1] * f; + r[2][2] += m[2][2] * f; +} + +BLI_INLINE void madd_m3_m3m3fl(float r[3][3], float a[3][3], float b[3][3], float f) +{ + r[0][0] = a[0][0] + b[0][0] * f; + r[0][1] = a[0][1] + b[0][1] * f; + r[0][2] = a[0][2] + b[0][2] * f; + r[1][0] = a[1][0] + b[1][0] * f; + r[1][1] = a[1][1] + b[1][1] * f; + r[1][2] = a[1][2] + b[1][2] * f; + r[2][0] = a[2][0] + b[2][0] * f; + r[2][1] = a[2][1] + b[2][1] * f; + r[2][2] = a[2][2] + b[2][2] * f; +} + +struct Implicit_Data { + typedef std::vector<fMatrix> fMatrixVector; + + Implicit_Data(int numverts) + { + resize(numverts); + } + + void resize(int numverts) + { + this->numverts = numverts; + int tot = 3 * numverts; + + M.resize(tot, tot); + F.resize(tot); + dFdX.resize(tot, tot); + dFdV.resize(tot, tot); + + tfm.resize(numverts, I); + + X.resize(tot); + Xnew.resize(tot); + V.resize(tot); + Vnew.resize(tot); + + A.resize(tot, tot); + B.resize(tot); + + dV.resize(tot); + z.resize(tot); + S.resize(tot, tot); + + iM.reserve(numverts); + idFdX.reserve(numverts); + idFdV.reserve(numverts); + iS.reserve(numverts); + } + + int numverts; + + /* inputs */ + lMatrix M; /* masses */ + lVector F; /* forces */ + lMatrix dFdX, dFdV; /* force jacobians */ + + fMatrixVector tfm; /* local coordinate transform */ + + /* motion state data */ + lVector X, Xnew; /* positions */ + lVector V, Vnew; /* velocities */ + + /* internal solver data */ + lVector B; /* B for A*dV = B */ + lMatrix A; /* A for A*dV = B */ + + lVector dV; /* velocity change (solution of A*dV = B) */ + lVector z; /* target velocity in constrained directions */ + lMatrix S; /* filtering matrix for constraints */ + + /* temporary constructors */ + lMatrixCtor iM; /* masses */ + lMatrixCtor idFdX, idFdV; /* force jacobians */ + lMatrixCtor iS; /* filtering matrix for constraints */ +}; + +Implicit_Data *SIM_mass_spring_solver_create(int numverts, int numsprings) +{ + Implicit_Data *id = new Implicit_Data(numverts); + return id; +} + +void SIM_mass_spring_solver_free(Implicit_Data *id) +{ + if (id) { + delete id; + } +} + +int SIM_mass_spring_solver_numvert(Implicit_Data *id) +{ + if (id) { + return id->numverts; + } + else { + return 0; + } +} + +/* ==== Transformation from/to root reference frames ==== */ + +BLI_INLINE void world_to_root_v3(Implicit_Data *data, int index, float r[3], const float v[3]) +{ + copy_v3_v3(r, v); + mul_transposed_m3_v3(data->tfm[index], r); +} + +BLI_INLINE void root_to_world_v3(Implicit_Data *data, int index, float r[3], const float v[3]) +{ + mul_v3_m3v3(r, data->tfm[index], v); +} + +BLI_INLINE void world_to_root_m3(Implicit_Data *data, int index, float r[3][3], float m[3][3]) +{ + float trot[3][3]; + copy_m3_m3(trot, data->tfm[index]); + transpose_m3(trot); + mul_m3_m3m3(r, trot, m); +} + +BLI_INLINE void root_to_world_m3(Implicit_Data *data, int index, float r[3][3], float m[3][3]) +{ + mul_m3_m3m3(r, data->tfm[index], m); +} + +/* ================================ */ + +bool SIM_mass_spring_solve_velocities(Implicit_Data *data, float dt, ImplicitSolverResult *result) +{ +# ifdef USE_EIGEN_CORE + typedef ConjugateGradient solver_t; +# endif +# ifdef USE_EIGEN_CONSTRAINED_CG + typedef ConstraintConjGrad solver_t; +# endif + + data->iM.construct(data->M); + data->idFdX.construct(data->dFdX); + data->idFdV.construct(data->dFdV); + data->iS.construct(data->S); + + solver_t cg; + cg.setMaxIterations(100); + cg.setTolerance(0.01f); + +# ifdef USE_EIGEN_CONSTRAINED_CG + cg.filter() = data->S; +# endif + + data->A = data->M - dt * data->dFdV - dt * dt * data->dFdX; + cg.compute(data->A); + + data->B = dt * data->F + dt * dt * data->dFdX * data->V; + +# ifdef IMPLICIT_PRINT_SOLVER_INPUT_OUTPUT + printf("==== A ====\n"); + print_lmatrix(id->A); + printf("==== z ====\n"); + print_lvector(id->z); + printf("==== B ====\n"); + print_lvector(id->B); + printf("==== S ====\n"); + print_lmatrix(id->S); +# endif + +# ifdef USE_EIGEN_CORE + data->dV = cg.solve(data->B); +# endif +# ifdef USE_EIGEN_CONSTRAINED_CG + data->dV = cg.solveWithGuess(data->B, data->z); +# endif + +# ifdef IMPLICIT_PRINT_SOLVER_INPUT_OUTPUT + printf("==== dV ====\n"); + print_lvector(id->dV); + printf("========\n"); +# endif + + data->Vnew = data->V + data->dV; + + switch (cg.info()) { + case Eigen::Success: + result->status = SIM_SOLVER_SUCCESS; + break; + case Eigen::NoConvergence: + result->status = SIM_SOLVER_NO_CONVERGENCE; + break; + case Eigen::InvalidInput: + result->status = SIM_SOLVER_INVALID_INPUT; + break; + case Eigen::NumericalIssue: + result->status = SIM_SOLVER_NUMERICAL_ISSUE; + break; + } + + result->iterations = cg.iterations(); + result->error = cg.error(); + + return cg.info() == Eigen::Success; +} + +bool SIM_mass_spring_solve_positions(Implicit_Data *data, float dt) +{ + data->Xnew = data->X + data->Vnew * dt; + return true; +} + +/* ================================ */ + +void SIM_mass_spring_apply_result(Implicit_Data *data) +{ + data->X = data->Xnew; + data->V = data->Vnew; +} + +void SIM_mass_spring_set_vertex_mass(Implicit_Data *data, int index, float mass) +{ + float m[3][3]; + copy_m3_m3(m, I); + mul_m3_fl(m, mass); + data->iM.add(index, index, m); +} + +void SIM_mass_spring_set_rest_transform(Implicit_Data *data, int index, float tfm[3][3]) +{ +# ifdef CLOTH_ROOT_FRAME + copy_m3_m3(data->tfm[index], tfm); +# else + unit_m3(data->tfm[index]); + (void)tfm; +# endif +} + +void SIM_mass_spring_set_motion_state(Implicit_Data *data, + int index, + const float x[3], + const float v[3]) +{ + world_to_root_v3(data, index, data->X.v3(index), x); + world_to_root_v3(data, index, data->V.v3(index), v); +} + +void SIM_mass_spring_set_position(Implicit_Data *data, int index, const float x[3]) +{ + world_to_root_v3(data, index, data->X.v3(index), x); +} + +void SIM_mass_spring_set_velocity(Implicit_Data *data, int index, const float v[3]) +{ + world_to_root_v3(data, index, data->V.v3(index), v); +} + +void SIM_mass_spring_get_motion_state(struct Implicit_Data *data, + int index, + float x[3], + float v[3]) +{ + if (x) { + root_to_world_v3(data, index, x, data->X.v3(index)); + } + if (v) { + root_to_world_v3(data, index, v, data->V.v3(index)); + } +} + +void SIM_mass_spring_get_position(struct Implicit_Data *data, int index, float x[3]) +{ + root_to_world_v3(data, index, x, data->X.v3(index)); +} + +void SIM_mass_spring_get_new_velocity(Implicit_Data *data, int index, float v[3]) +{ + root_to_world_v3(data, index, v, data->V.v3(index)); +} + +void SIM_mass_spring_set_new_velocity(Implicit_Data *data, int index, const float v[3]) +{ + world_to_root_v3(data, index, data->V.v3(index), v); +} + +void SIM_mass_spring_clear_constraints(Implicit_Data *data) +{ + int numverts = data->numverts; + for (int i = 0; i < numverts; i++) { + data->iS.add(i, i, I); + zero_v3(data->z.v3(i)); + } +} + +void SIM_mass_spring_add_constraint_ndof0(Implicit_Data *data, int index, const float dV[3]) +{ + data->iS.sub(index, index, I); + + world_to_root_v3(data, index, data->z.v3(index), dV); +} + +void SIM_mass_spring_add_constraint_ndof1( + Implicit_Data *data, int index, const float c1[3], const float c2[3], const float dV[3]) +{ + float m[3][3], p[3], q[3], u[3], cmat[3][3]; + + world_to_root_v3(data, index, p, c1); + outerproduct(cmat, p, p); + copy_m3_m3(m, cmat); + + world_to_root_v3(data, index, q, c2); + outerproduct(cmat, q, q); + add_m3_m3m3(m, m, cmat); + + /* XXX not sure but multiplication should work here */ + data->iS.sub(index, index, m); + // mul_m3_m3m3(data->S[index].m, data->S[index].m, m); + + world_to_root_v3(data, index, u, dV); + add_v3_v3(data->z.v3(index), u); +} + +void SIM_mass_spring_add_constraint_ndof2(Implicit_Data *data, + int index, + const float c1[3], + const float dV[3]) +{ + float m[3][3], p[3], u[3], cmat[3][3]; + + world_to_root_v3(data, index, p, c1); + outerproduct(cmat, p, p); + copy_m3_m3(m, cmat); + + data->iS.sub(index, index, m); + // mul_m3_m3m3(data->S[index].m, data->S[index].m, m); + + world_to_root_v3(data, index, u, dV); + add_v3_v3(data->z.v3(index), u); +} + +void SIM_mass_spring_clear_forces(Implicit_Data *data) +{ + data->F.setZero(); + data->dFdX.setZero(); + data->dFdV.setZero(); +} + +void SIM_mass_spring_force_reference_frame(Implicit_Data *data, + int index, + const float acceleration[3], + const float omega[3], + const float domega_dt[3], + float mass) +{ +# ifdef CLOTH_ROOT_FRAME + float acc[3], w[3], dwdt[3]; + float f[3], dfdx[3][3], dfdv[3][3]; + float euler[3], coriolis[3], centrifugal[3], rotvel[3]; + float deuler[3][3], dcoriolis[3][3], dcentrifugal[3][3], drotvel[3][3]; + + world_to_root_v3(data, index, acc, acceleration); + world_to_root_v3(data, index, w, omega); + world_to_root_v3(data, index, dwdt, domega_dt); + + cross_v3_v3v3(euler, dwdt, data->X.v3(index)); + cross_v3_v3v3(coriolis, w, data->V.v3(index)); + mul_v3_fl(coriolis, 2.0f); + cross_v3_v3v3(rotvel, w, data->X.v3(index)); + cross_v3_v3v3(centrifugal, w, rotvel); + + sub_v3_v3v3(f, acc, euler); + sub_v3_v3(f, coriolis); + sub_v3_v3(f, centrifugal); + + mul_v3_fl(f, mass); /* F = m * a */ + + cross_v3_identity(deuler, dwdt); + cross_v3_identity(dcoriolis, w); + mul_m3_fl(dcoriolis, 2.0f); + cross_v3_identity(drotvel, w); + cross_m3_v3m3(dcentrifugal, w, drotvel); + + add_m3_m3m3(dfdx, deuler, dcentrifugal); + negate_m3(dfdx); + mul_m3_fl(dfdx, mass); + + copy_m3_m3(dfdv, dcoriolis); + negate_m3(dfdv); + mul_m3_fl(dfdv, mass); + + add_v3_v3(data->F.v3(index), f); + data->idFdX.add(index, index, dfdx); + data->idFdV.add(index, index, dfdv); +# else + (void)data; + (void)index; + (void)acceleration; + (void)omega; + (void)domega_dt; +# endif +} + +void SIM_mass_spring_force_gravity(Implicit_Data *data, int index, float mass, const float g[3]) +{ + /* force = mass * acceleration (in this case: gravity) */ + float f[3]; + world_to_root_v3(data, index, f, g); + mul_v3_fl(f, mass); + + add_v3_v3(data->F.v3(index), f); +} + +void SIM_mass_spring_force_drag(Implicit_Data *data, float drag) +{ + int numverts = data->numverts; + for (int i = 0; i < numverts; i++) { + float tmp[3][3]; + + /* NB: uses root space velocity, no need to transform */ + madd_v3_v3fl(data->F.v3(i), data->V.v3(i), -drag); + + copy_m3_m3(tmp, I); + mul_m3_fl(tmp, -drag); + data->idFdV.add(i, i, tmp); + } +} + +void SIM_mass_spring_force_extern( + struct Implicit_Data *data, int i, const float f[3], float dfdx[3][3], float dfdv[3][3]) +{ + float tf[3], tdfdx[3][3], tdfdv[3][3]; + world_to_root_v3(data, i, tf, f); + world_to_root_m3(data, i, tdfdx, dfdx); + world_to_root_m3(data, i, tdfdv, dfdv); + + add_v3_v3(data->F.v3(i), tf); + data->idFdX.add(i, i, tdfdx); + data->idFdV.add(i, i, tdfdv); +} + +static float calc_nor_area_tri(float nor[3], + const float v1[3], + const float v2[3], + const float v3[3]) +{ + float n1[3], n2[3]; + + sub_v3_v3v3(n1, v1, v2); + sub_v3_v3v3(n2, v2, v3); + + cross_v3_v3v3(nor, n1, n2); + return normalize_v3(nor) / 2.0f; +} + +/* XXX does not support force jacobians yet, + * since the effector system does not provide them either. */ +void SIM_mass_spring_force_face_wind( + Implicit_Data *data, int v1, int v2, int v3, const float (*winvec)[3]) +{ + const float effector_scale = 0.02f; + float win[3], nor[3], area; + float factor; + + // calculate face normal and area + area = calc_nor_area_tri(nor, data->X.v3(v1), data->X.v3(v2), data->X.v3(v3)); + factor = effector_scale * area / 3.0f; + + world_to_root_v3(data, v1, win, winvec[v1]); + madd_v3_v3fl(data->F.v3(v1), nor, factor * dot_v3v3(win, nor)); + + world_to_root_v3(data, v2, win, winvec[v2]); + madd_v3_v3fl(data->F.v3(v2), nor, factor * dot_v3v3(win, nor)); + + world_to_root_v3(data, v3, win, winvec[v3]); + madd_v3_v3fl(data->F.v3(v3), nor, factor * dot_v3v3(win, nor)); +} + +void SIM_mass_spring_force_edge_wind(Implicit_Data *data, int v1, int v2, const float (*winvec)[3]) +{ + const float effector_scale = 0.01; + float win[3], dir[3], nor[3], length; + + sub_v3_v3v3(dir, data->X.v3(v1), data->X.v3(v2)); + length = normalize_v3(dir); + + world_to_root_v3(data, v1, win, winvec[v1]); + madd_v3_v3v3fl(nor, win, dir, -dot_v3v3(win, dir)); + madd_v3_v3fl(data->F.v3(v1), nor, effector_scale * length); + + world_to_root_v3(data, v2, win, winvec[v2]); + madd_v3_v3v3fl(nor, win, dir, -dot_v3v3(win, dir)); + madd_v3_v3fl(data->F.v3(v2), nor, effector_scale * length); +} + +BLI_INLINE void dfdx_spring(float to[3][3], const float dir[3], float length, float L, float k) +{ + /* dir is unit length direction, rest is spring's restlength, k is spring constant. */ + // return ((I - outerprod(dir, dir)) * Min(1.0f, rest / length) - I) * -k; + outerproduct(to, dir, dir); + sub_m3_m3m3(to, I, to); + + mul_m3_fl(to, (L / length)); + sub_m3_m3m3(to, to, I); + mul_m3_fl(to, k); +} + +/* unused */ +# if 0 +BLI_INLINE void dfdx_damp(float to[3][3], + const float dir[3], + float length, + const float vel[3], + float rest, + float damping) +{ + // inner spring damping vel is the relative velocity of the endpoints. + // return (I-outerprod(dir, dir)) * (-damping * -(dot(dir, vel)/Max(length, rest))); + mul_fvectorT_fvector(to, dir, dir); + sub_fmatrix_fmatrix(to, I, to); + mul_fmatrix_S(to, (-damping * -(dot_v3v3(dir, vel) / MAX2(length, rest)))); +} +# endif + +BLI_INLINE void dfdv_damp(float to[3][3], const float dir[3], float damping) +{ + // derivative of force wrt velocity + outerproduct(to, dir, dir); + mul_m3_fl(to, -damping); +} + +BLI_INLINE float fb(float length, float L) +{ + float x = length / L; + return (-11.541f * powf(x, 4) + 34.193f * powf(x, 3) - 39.083f * powf(x, 2) + 23.116f * x - + 9.713f); +} + +BLI_INLINE float fbderiv(float length, float L) +{ + float x = length / L; + + return (-46.164f * powf(x, 3) + 102.579f * powf(x, 2) - 78.166f * x + 23.116f); +} + +BLI_INLINE float fbstar(float length, float L, float kb, float cb) +{ + float tempfb_fl = kb * fb(length, L); + float fbstar_fl = cb * (length - L); + + if (tempfb_fl < fbstar_fl) { + return fbstar_fl; + } + else { + return tempfb_fl; + } +} + +// function to calculae bending spring force (taken from Choi & Co) +BLI_INLINE float fbstar_jacobi(float length, float L, float kb, float cb) +{ + float tempfb_fl = kb * fb(length, L); + float fbstar_fl = cb * (length - L); + + if (tempfb_fl < fbstar_fl) { + return -cb; + } + else { + return -kb * fbderiv(length, L); + } +} + +/* calculate elonglation */ +BLI_INLINE bool spring_length(Implicit_Data *data, + int i, + int j, + float r_extent[3], + float r_dir[3], + float *r_length, + float r_vel[3]) +{ + sub_v3_v3v3(r_extent, data->X.v3(j), data->X.v3(i)); + sub_v3_v3v3(r_vel, data->V.v3(j), data->V.v3(i)); + *r_length = len_v3(r_extent); + + if (*r_length > ALMOST_ZERO) { +# if 0 + if (length > L) { + if ((clmd->sim_parms->flags & CSIMSETT_FLAG_TEARING_ENABLED) && + (((length - L) * 100.0f / L) > clmd->sim_parms->maxspringlen)) { + // cut spring! + s->flags |= CSPRING_FLAG_DEACTIVATE; + return false; + } + } +# endif + mul_v3_v3fl(r_dir, r_extent, 1.0f / (*r_length)); + } + else { + zero_v3(r_dir); + } + + return true; +} + +BLI_INLINE void apply_spring( + Implicit_Data *data, int i, int j, const float f[3], float dfdx[3][3], float dfdv[3][3]) +{ + add_v3_v3(data->F.v3(i), f); + sub_v3_v3(data->F.v3(j), f); + + data->idFdX.add(i, i, dfdx); + data->idFdX.add(j, j, dfdx); + data->idFdX.sub(i, j, dfdx); + data->idFdX.sub(j, i, dfdx); + + data->idFdV.add(i, i, dfdv); + data->idFdV.add(j, j, dfdv); + data->idFdV.sub(i, j, dfdv); + data->idFdV.sub(j, i, dfdv); +} + +bool SIM_mass_spring_force_spring_linear(Implicit_Data *data, + int i, + int j, + float restlen, + float stiffness, + float damping, + bool no_compress, + float clamp_force, + float r_f[3], + float r_dfdx[3][3], + float r_dfdv[3][3]) +{ + float extent[3], length, dir[3], vel[3]; + + // calculate elonglation + spring_length(data, i, j, extent, dir, &length, vel); + + if (length > restlen || no_compress) { + float stretch_force, f[3], dfdx[3][3], dfdv[3][3]; + + stretch_force = stiffness * (length - restlen); + if (clamp_force > 0.0f && stretch_force > clamp_force) { + stretch_force = clamp_force; + } + mul_v3_v3fl(f, dir, stretch_force); + + // Ascher & Boxman, p.21: Damping only during elonglation + // something wrong with it... + madd_v3_v3fl(f, dir, damping * dot_v3v3(vel, dir)); + + dfdx_spring(dfdx, dir, length, restlen, stiffness); + dfdv_damp(dfdv, dir, damping); + + apply_spring(data, i, j, f, dfdx, dfdv); + + if (r_f) { + copy_v3_v3(r_f, f); + } + if (r_dfdx) { + copy_m3_m3(r_dfdx, dfdx); + } + if (r_dfdv) { + copy_m3_m3(r_dfdv, dfdv); + } + + return true; + } + else { + if (r_f) { + zero_v3(r_f); + } + if (r_dfdx) { + zero_m3(r_dfdx); + } + if (r_dfdv) { + zero_m3(r_dfdv); + } + + return false; + } +} + +/* See "Stable but Responsive Cloth" (Choi, Ko 2005) */ +bool SIM_mass_spring_force_spring_bending(Implicit_Data *data, + int i, + int j, + float restlen, + float kb, + float cb, + float r_f[3], + float r_dfdx[3][3], + float r_dfdv[3][3]) +{ + float extent[3], length, dir[3], vel[3]; + + // calculate elonglation + spring_length(data, i, j, extent, dir, &length, vel); + + if (length < restlen) { + float f[3], dfdx[3][3], dfdv[3][3]; + + mul_v3_v3fl(f, dir, fbstar(length, restlen, kb, cb)); + + outerproduct(dfdx, dir, dir); + mul_m3_fl(dfdx, fbstar_jacobi(length, restlen, kb, cb)); + + /* XXX damping not supported */ + zero_m3(dfdv); + + apply_spring(data, i, j, f, dfdx, dfdv); + + if (r_f) { + copy_v3_v3(r_f, f); + } + if (r_dfdx) { + copy_m3_m3(r_dfdx, dfdx); + } + if (r_dfdv) { + copy_m3_m3(r_dfdv, dfdv); + } + + return true; + } + else { + if (r_f) { + zero_v3(r_f); + } + if (r_dfdx) { + zero_m3(r_dfdx); + } + if (r_dfdv) { + zero_m3(r_dfdv); + } + + return false; + } +} + +/* Jacobian of a direction vector. + * Basically the part of the differential orthogonal to the direction, + * inversely proportional to the length of the edge. + * + * dD_ij/dx_i = -dD_ij/dx_j = (D_ij * D_ij^T - I) / len_ij + */ +BLI_INLINE void spring_grad_dir( + Implicit_Data *data, int i, int j, float edge[3], float dir[3], float grad_dir[3][3]) +{ + float length; + + sub_v3_v3v3(edge, data->X.v3(j), data->X.v3(i)); + length = normalize_v3_v3(dir, edge); + + if (length > ALMOST_ZERO) { + outerproduct(grad_dir, dir, dir); + sub_m3_m3m3(grad_dir, I, grad_dir); + mul_m3_fl(grad_dir, 1.0f / length); + } + else { + zero_m3(grad_dir); + } +} + +BLI_INLINE void spring_angbend_forces(Implicit_Data *data, + int i, + int j, + int k, + const float goal[3], + float stiffness, + float damping, + int q, + const float dx[3], + const float dv[3], + float r_f[3]) +{ + float edge_ij[3], dir_ij[3]; + float edge_jk[3], dir_jk[3]; + float vel_ij[3], vel_jk[3], vel_ortho[3]; + float f_bend[3], f_damp[3]; + float fk[3]; + float dist[3]; + + zero_v3(fk); + + sub_v3_v3v3(edge_ij, data->X.v3(j), data->X.v3(i)); + if (q == i) { + sub_v3_v3(edge_ij, dx); + } + if (q == j) { + add_v3_v3(edge_ij, dx); + } + normalize_v3_v3(dir_ij, edge_ij); + + sub_v3_v3v3(edge_jk, data->X.v3(k), data->X.v3(j)); + if (q == j) { + sub_v3_v3(edge_jk, dx); + } + if (q == k) { + add_v3_v3(edge_jk, dx); + } + normalize_v3_v3(dir_jk, edge_jk); + + sub_v3_v3v3(vel_ij, data->V.v3(j), data->V.v3(i)); + if (q == i) { + sub_v3_v3(vel_ij, dv); + } + if (q == j) { + add_v3_v3(vel_ij, dv); + } + + sub_v3_v3v3(vel_jk, data->V.v3(k), data->V.v3(j)); + if (q == j) { + sub_v3_v3(vel_jk, dv); + } + if (q == k) { + add_v3_v3(vel_jk, dv); + } + + /* bending force */ + sub_v3_v3v3(dist, goal, edge_jk); + mul_v3_v3fl(f_bend, dist, stiffness); + + add_v3_v3(fk, f_bend); + + /* damping force */ + madd_v3_v3v3fl(vel_ortho, vel_jk, dir_jk, -dot_v3v3(vel_jk, dir_jk)); + mul_v3_v3fl(f_damp, vel_ortho, damping); + + sub_v3_v3(fk, f_damp); + + copy_v3_v3(r_f, fk); +} + +/* Finite Differences method for estimating the jacobian of the force */ +BLI_INLINE void spring_angbend_estimate_dfdx(Implicit_Data *data, + int i, + int j, + int k, + const float goal[3], + float stiffness, + float damping, + int q, + float dfdx[3][3]) +{ + const float delta = 0.00001f; // TODO find a good heuristic for this + float dvec_null[3][3], dvec_pos[3][3], dvec_neg[3][3]; + float f[3]; + int a, b; + + zero_m3(dvec_null); + unit_m3(dvec_pos); + mul_m3_fl(dvec_pos, delta * 0.5f); + copy_m3_m3(dvec_neg, dvec_pos); + negate_m3(dvec_neg); + + /* XXX TODO offset targets to account for position dependency */ + + for (a = 0; a < 3; a++) { + spring_angbend_forces( + data, i, j, k, goal, stiffness, damping, q, dvec_pos[a], dvec_null[a], f); + copy_v3_v3(dfdx[a], f); + + spring_angbend_forces( + data, i, j, k, goal, stiffness, damping, q, dvec_neg[a], dvec_null[a], f); + sub_v3_v3(dfdx[a], f); + + for (b = 0; b < 3; b++) { + dfdx[a][b] /= delta; + } + } +} + +/* Finite Differences method for estimating the jacobian of the force */ +BLI_INLINE void spring_angbend_estimate_dfdv(Implicit_Data *data, + int i, + int j, + int k, + const float goal[3], + float stiffness, + float damping, + int q, + float dfdv[3][3]) +{ + const float delta = 0.00001f; // TODO find a good heuristic for this + float dvec_null[3][3], dvec_pos[3][3], dvec_neg[3][3]; + float f[3]; + int a, b; + + zero_m3(dvec_null); + unit_m3(dvec_pos); + mul_m3_fl(dvec_pos, delta * 0.5f); + copy_m3_m3(dvec_neg, dvec_pos); + negate_m3(dvec_neg); + + /* XXX TODO offset targets to account for position dependency */ + + for (a = 0; a < 3; a++) { + spring_angbend_forces( + data, i, j, k, goal, stiffness, damping, q, dvec_null[a], dvec_pos[a], f); + copy_v3_v3(dfdv[a], f); + + spring_angbend_forces( + data, i, j, k, goal, stiffness, damping, q, dvec_null[a], dvec_neg[a], f); + sub_v3_v3(dfdv[a], f); + + for (b = 0; b < 3; b++) { + dfdv[a][b] /= delta; + } + } +} + +/* Angular spring that pulls the vertex toward the local target + * See "Artistic Simulation of Curly Hair" (Pixar technical memo #12-03a) + */ +bool SIM_mass_spring_force_spring_bending_angular(Implicit_Data *data, + int i, + int j, + int k, + const float target[3], + float stiffness, + float damping) +{ + float goal[3]; + float fj[3], fk[3]; + float dfj_dxi[3][3], dfj_dxj[3][3], dfk_dxi[3][3], dfk_dxj[3][3], dfk_dxk[3][3]; + float dfj_dvi[3][3], dfj_dvj[3][3], dfk_dvi[3][3], dfk_dvj[3][3], dfk_dvk[3][3]; + + const float vecnull[3] = {0.0f, 0.0f, 0.0f}; + + world_to_root_v3(data, j, goal, target); + + spring_angbend_forces(data, i, j, k, goal, stiffness, damping, k, vecnull, vecnull, fk); + negate_v3_v3(fj, fk); /* counterforce */ + + spring_angbend_estimate_dfdx(data, i, j, k, goal, stiffness, damping, i, dfk_dxi); + spring_angbend_estimate_dfdx(data, i, j, k, goal, stiffness, damping, j, dfk_dxj); + spring_angbend_estimate_dfdx(data, i, j, k, goal, stiffness, damping, k, dfk_dxk); + copy_m3_m3(dfj_dxi, dfk_dxi); + negate_m3(dfj_dxi); + copy_m3_m3(dfj_dxj, dfk_dxj); + negate_m3(dfj_dxj); + + spring_angbend_estimate_dfdv(data, i, j, k, goal, stiffness, damping, i, dfk_dvi); + spring_angbend_estimate_dfdv(data, i, j, k, goal, stiffness, damping, j, dfk_dvj); + spring_angbend_estimate_dfdv(data, i, j, k, goal, stiffness, damping, k, dfk_dvk); + copy_m3_m3(dfj_dvi, dfk_dvi); + negate_m3(dfj_dvi); + copy_m3_m3(dfj_dvj, dfk_dvj); + negate_m3(dfj_dvj); + + /* add forces and jacobians to the solver data */ + + add_v3_v3(data->F.v3(j), fj); + add_v3_v3(data->F.v3(k), fk); + + data->idFdX.add(j, j, dfj_dxj); + data->idFdX.add(k, k, dfk_dxk); + + data->idFdX.add(i, j, dfj_dxi); + data->idFdX.add(j, i, dfj_dxi); + data->idFdX.add(j, k, dfk_dxj); + data->idFdX.add(k, j, dfk_dxj); + data->idFdX.add(i, k, dfk_dxi); + data->idFdX.add(k, i, dfk_dxi); + + data->idFdV.add(j, j, dfj_dvj); + data->idFdV.add(k, k, dfk_dvk); + + data->idFdV.add(i, j, dfj_dvi); + data->idFdV.add(j, i, dfj_dvi); + data->idFdV.add(j, k, dfk_dvj); + data->idFdV.add(k, j, dfk_dvj); + data->idFdV.add(i, k, dfk_dvi); + data->idFdV.add(k, i, dfk_dvi); + + /* XXX analytical calculation of derivatives below is incorrect. + * This proved to be difficult, but for now just using the finite difference method for + * estimating the jacobians should be sufficient. + */ +# if 0 + float edge_ij[3], dir_ij[3], grad_dir_ij[3][3]; + float edge_jk[3], dir_jk[3], grad_dir_jk[3][3]; + float dist[3], vel_jk[3], vel_jk_ortho[3], projvel[3]; + float target[3]; + float tmp[3][3]; + float fi[3], fj[3], fk[3]; + float dfi_dxi[3][3], dfj_dxi[3][3], dfj_dxj[3][3], dfk_dxi[3][3], dfk_dxj[3][3], dfk_dxk[3][3]; + float dfdvi[3][3]; + + // TESTING + damping = 0.0f; + + zero_v3(fi); + zero_v3(fj); + zero_v3(fk); + zero_m3(dfi_dxi); + zero_m3(dfj_dxi); + zero_m3(dfk_dxi); + zero_m3(dfk_dxj); + zero_m3(dfk_dxk); + + /* jacobian of direction vectors */ + spring_grad_dir(data, i, j, edge_ij, dir_ij, grad_dir_ij); + spring_grad_dir(data, j, k, edge_jk, dir_jk, grad_dir_jk); + + sub_v3_v3v3(vel_jk, data->V[k], data->V[j]); + + /* bending force */ + mul_v3_v3fl(target, dir_ij, restlen); + sub_v3_v3v3(dist, target, edge_jk); + mul_v3_v3fl(fk, dist, stiffness); + + /* damping force */ + madd_v3_v3v3fl(vel_jk_ortho, vel_jk, dir_jk, -dot_v3v3(vel_jk, dir_jk)); + madd_v3_v3fl(fk, vel_jk_ortho, damping); + + /* XXX this only holds true as long as we assume straight rest shape! + * eventually will become a bit more involved since the opposite segment + * gets its own target, under condition of having equal torque on both sides. + */ + copy_v3_v3(fi, fk); + + /* counterforce on the middle point */ + sub_v3_v3(fj, fi); + sub_v3_v3(fj, fk); + + /* === derivatives === */ + + madd_m3_m3fl(dfk_dxi, grad_dir_ij, stiffness * restlen); + + madd_m3_m3fl(dfk_dxj, grad_dir_ij, -stiffness * restlen); + madd_m3_m3fl(dfk_dxj, I, stiffness); + + madd_m3_m3fl(dfk_dxk, I, -stiffness); + + copy_m3_m3(dfi_dxi, dfk_dxk); + negate_m3(dfi_dxi); + + /* dfj_dfi == dfi_dfj due to symmetry, + * dfi_dfj == dfk_dfj due to fi == fk + * XXX see comment above on future bent rest shapes + */ + copy_m3_m3(dfj_dxi, dfk_dxj); + + /* dfj_dxj == -(dfi_dxj + dfk_dxj) due to fj == -(fi + fk) */ + sub_m3_m3m3(dfj_dxj, dfj_dxj, dfj_dxi); + sub_m3_m3m3(dfj_dxj, dfj_dxj, dfk_dxj); + + /* add forces and jacobians to the solver data */ + add_v3_v3(data->F[i], fi); + add_v3_v3(data->F[j], fj); + add_v3_v3(data->F[k], fk); + + add_m3_m3m3(data->dFdX[i].m, data->dFdX[i].m, dfi_dxi); + add_m3_m3m3(data->dFdX[j].m, data->dFdX[j].m, dfj_dxj); + add_m3_m3m3(data->dFdX[k].m, data->dFdX[k].m, dfk_dxk); + + add_m3_m3m3(data->dFdX[block_ij].m, data->dFdX[block_ij].m, dfj_dxi); + add_m3_m3m3(data->dFdX[block_jk].m, data->dFdX[block_jk].m, dfk_dxj); + add_m3_m3m3(data->dFdX[block_ik].m, data->dFdX[block_ik].m, dfk_dxi); +# endif + + return true; +} + +bool SIM_mass_spring_force_spring_goal(Implicit_Data *data, + int i, + const float goal_x[3], + const float goal_v[3], + float stiffness, + float damping, + float r_f[3], + float r_dfdx[3][3], + float r_dfdv[3][3]) +{ + float root_goal_x[3], root_goal_v[3], extent[3], length, dir[3], vel[3]; + float f[3], dfdx[3][3], dfdv[3][3]; + + /* goal is in world space */ + world_to_root_v3(data, i, root_goal_x, goal_x); + world_to_root_v3(data, i, root_goal_v, goal_v); + + sub_v3_v3v3(extent, root_goal_x, data->X.v3(i)); + sub_v3_v3v3(vel, root_goal_v, data->V.v3(i)); + length = normalize_v3_v3(dir, extent); + + if (length > ALMOST_ZERO) { + mul_v3_v3fl(f, dir, stiffness * length); + + // Ascher & Boxman, p.21: Damping only during elonglation + // something wrong with it... + madd_v3_v3fl(f, dir, damping * dot_v3v3(vel, dir)); + + dfdx_spring(dfdx, dir, length, 0.0f, stiffness); + dfdv_damp(dfdv, dir, damping); + + add_v3_v3(data->F.v3(i), f); + data->idFdX.add(i, i, dfdx); + data->idFdV.add(i, i, dfdv); + + if (r_f) { + copy_v3_v3(r_f, f); + } + if (r_dfdx) { + copy_m3_m3(r_dfdx, dfdx); + } + if (r_dfdv) { + copy_m3_m3(r_dfdv, dfdv); + } + + return true; + } + else { + if (r_f) { + zero_v3(r_f); + } + if (r_dfdx) { + zero_m3(r_dfdx); + } + if (r_dfdv) { + zero_m3(r_dfdv); + } + + return false; + } +} + +#endif /* IMPLICIT_SOLVER_EIGEN */ |