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BambuStudio/libigl/igl/slim.cpp

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// This file is part of libigl, a simple c++ geometry processing library.
//
// Copyright (C) 2016 Michael Rabinovich
//
// This Source Code Form is subject to the terms of the Mozilla Public License
// v. 2.0. If a copy of the MPL was not distributed with this file, You can
// obtain one at http://mozilla.org/MPL/2.0/.
#include "slim.h"
#include "boundary_loop.h"
#include "cotmatrix.h"
#include "edge_lengths.h"
#include "grad.h"
#include "local_basis.h"
#include "repdiag.h"
#include "vector_area_matrix.h"
#include "arap.h"
#include "cat.h"
#include "doublearea.h"
#include "grad.h"
#include "local_basis.h"
#include "per_face_normals.h"
#include "slice_into.h"
#include "volume.h"
#include "polar_svd.h"
#include "flip_avoiding_line_search.h"
#include <iostream>
#include <map>
#include <set>
#include <vector>
#include <Eigen/IterativeLinearSolvers>
#include <Eigen/SparseCholesky>
#include <Eigen/IterativeLinearSolvers>
#include "Timer.h"
#include "sparse_cached.h"
#include "AtA_cached.h"
#ifdef CHOLMOD
#include <Eigen/CholmodSupport>
#endif
namespace igl
{
namespace slim
{
// Definitions of internal functions
IGL_INLINE void compute_surface_gradient_matrix(const Eigen::MatrixXd &V, const Eigen::MatrixXi &F,
const Eigen::MatrixXd &F1, const Eigen::MatrixXd &F2,
Eigen::SparseMatrix<double> &D1, Eigen::SparseMatrix<double> &D2);
IGL_INLINE void buildA(igl::SLIMData& s, std::vector<Eigen::Triplet<double> > & IJV);
IGL_INLINE void buildRhs(igl::SLIMData& s, const Eigen::SparseMatrix<double> &A);
IGL_INLINE void add_soft_constraints(igl::SLIMData& s, Eigen::SparseMatrix<double> &L);
IGL_INLINE double compute_energy(igl::SLIMData& s, Eigen::MatrixXd &V_new);
IGL_INLINE double compute_soft_const_energy(igl::SLIMData& s,
const Eigen::MatrixXd &V,
const Eigen::MatrixXi &F,
Eigen::MatrixXd &V_o);
IGL_INLINE double compute_energy_with_jacobians(igl::SLIMData& s,
const Eigen::MatrixXd &V,
const Eigen::MatrixXi &F, const Eigen::MatrixXd &Ji,
Eigen::MatrixXd &uv, Eigen::VectorXd &areas);
IGL_INLINE void solve_weighted_arap(igl::SLIMData& s,
const Eigen::MatrixXd &V,
const Eigen::MatrixXi &F,
Eigen::MatrixXd &uv,
Eigen::VectorXi &soft_b_p,
Eigen::MatrixXd &soft_bc_p);
IGL_INLINE void update_weights_and_closest_rotations( igl::SLIMData& s,
const Eigen::MatrixXd &V,
const Eigen::MatrixXi &F,
Eigen::MatrixXd &uv);
IGL_INLINE void compute_jacobians(igl::SLIMData& s, const Eigen::MatrixXd &uv);
IGL_INLINE void build_linear_system(igl::SLIMData& s, Eigen::SparseMatrix<double> &L);
IGL_INLINE void pre_calc(igl::SLIMData& s);
// Implementation
IGL_INLINE void compute_surface_gradient_matrix(const Eigen::MatrixXd &V, const Eigen::MatrixXi &F,
const Eigen::MatrixXd &F1, const Eigen::MatrixXd &F2,
Eigen::SparseMatrix<double> &D1, Eigen::SparseMatrix<double> &D2)
{
Eigen::SparseMatrix<double> G;
igl::grad(V, F, G);
Eigen::SparseMatrix<double> Dx = G.block(0, 0, F.rows(), V.rows());
Eigen::SparseMatrix<double> Dy = G.block(F.rows(), 0, F.rows(), V.rows());
Eigen::SparseMatrix<double> Dz = G.block(2 * F.rows(), 0, F.rows(), V.rows());
D1 = F1.col(0).asDiagonal() * Dx + F1.col(1).asDiagonal() * Dy + F1.col(2).asDiagonal() * Dz;
D2 = F2.col(0).asDiagonal() * Dx + F2.col(1).asDiagonal() * Dy + F2.col(2).asDiagonal() * Dz;
}
IGL_INLINE void compute_jacobians(igl::SLIMData& s, const Eigen::MatrixXd &uv)
{
if (s.F.cols() == 3)
{
// Ji=[D1*u,D2*u,D1*v,D2*v];
s.Ji.col(0) = s.Dx * uv.col(0);
s.Ji.col(1) = s.Dy * uv.col(0);
s.Ji.col(2) = s.Dx * uv.col(1);
s.Ji.col(3) = s.Dy * uv.col(1);
}
else /*tet mesh*/{
// Ji=[D1*u,D2*u,D3*u, D1*v,D2*v, D3*v, D1*w,D2*w,D3*w];
s.Ji.col(0) = s.Dx * uv.col(0);
s.Ji.col(1) = s.Dy * uv.col(0);
s.Ji.col(2) = s.Dz * uv.col(0);
s.Ji.col(3) = s.Dx * uv.col(1);
s.Ji.col(4) = s.Dy * uv.col(1);
s.Ji.col(5) = s.Dz * uv.col(1);
s.Ji.col(6) = s.Dx * uv.col(2);
s.Ji.col(7) = s.Dy * uv.col(2);
s.Ji.col(8) = s.Dz * uv.col(2);
}
}
IGL_INLINE void update_weights_and_closest_rotations(igl::SLIMData& s,
const Eigen::MatrixXd &V,
const Eigen::MatrixXi &F,
Eigen::MatrixXd &uv)
{
compute_jacobians(s, uv);
const double eps = 1e-8;
double exp_f = s.exp_factor;
if (s.dim == 2)
{
for (int i = 0; i < s.Ji.rows(); ++i)
{
typedef Eigen::Matrix<double, 2, 2> Mat2;
typedef Eigen::Matrix<double, 2, 1> Vec2;
Mat2 ji, ri, ti, ui, vi;
Vec2 sing;
Vec2 closest_sing_vec;
Mat2 mat_W;
Vec2 m_sing_new;
double s1, s2;
ji(0, 0) = s.Ji(i, 0);
ji(0, 1) = s.Ji(i, 1);
ji(1, 0) = s.Ji(i, 2);
ji(1, 1) = s.Ji(i, 3);
igl::polar_svd(ji, ri, ti, ui, sing, vi);
s1 = sing(0);
s2 = sing(1);
// Update Weights according to energy
switch (s.slim_energy)
{
case igl::SLIMData::ARAP:
{
m_sing_new << 1, 1;
break;
}
case igl::SLIMData::SYMMETRIC_DIRICHLET:
{
double s1_g = 2 * (s1 - pow(s1, -3));
double s2_g = 2 * (s2 - pow(s2, -3));
m_sing_new << sqrt(s1_g / (2 * (s1 - 1))), sqrt(s2_g / (2 * (s2 - 1)));
break;
}
case igl::SLIMData::LOG_ARAP:
{
double s1_g = 2 * (log(s1) / s1);
double s2_g = 2 * (log(s2) / s2);
m_sing_new << sqrt(s1_g / (2 * (s1 - 1))), sqrt(s2_g / (2 * (s2 - 1)));
break;
}
case igl::SLIMData::CONFORMAL:
{
double s1_g = 1 / (2 * s2) - s2 / (2 * pow(s1, 2));
double s2_g = 1 / (2 * s1) - s1 / (2 * pow(s2, 2));
double geo_avg = sqrt(s1 * s2);
double s1_min = geo_avg;
double s2_min = geo_avg;
m_sing_new << sqrt(s1_g / (2 * (s1 - s1_min))), sqrt(s2_g / (2 * (s2 - s2_min)));
// change local step
closest_sing_vec << s1_min, s2_min;
ri = ui * closest_sing_vec.asDiagonal() * vi.transpose();
break;
}
case igl::SLIMData::EXP_CONFORMAL:
{
double s1_g = 2 * (s1 - pow(s1, -3));
double s2_g = 2 * (s2 - pow(s2, -3));
double geo_avg = sqrt(s1 * s2);
double s1_min = geo_avg;
double s2_min = geo_avg;
double in_exp = exp_f * ((pow(s1, 2) + pow(s2, 2)) / (2 * s1 * s2));
double exp_thing = exp(in_exp);
s1_g *= exp_thing * exp_f;
s2_g *= exp_thing * exp_f;
m_sing_new << sqrt(s1_g / (2 * (s1 - 1))), sqrt(s2_g / (2 * (s2 - 1)));
break;
}
case igl::SLIMData::EXP_SYMMETRIC_DIRICHLET:
{
double s1_g = 2 * (s1 - pow(s1, -3));
double s2_g = 2 * (s2 - pow(s2, -3));
double in_exp = exp_f * (pow(s1, 2) + pow(s1, -2) + pow(s2, 2) + pow(s2, -2));
double exp_thing = exp(in_exp);
s1_g *= exp_thing * exp_f;
s2_g *= exp_thing * exp_f;
m_sing_new << sqrt(s1_g / (2 * (s1 - 1))), sqrt(s2_g / (2 * (s2 - 1)));
break;
}
}
if (std::abs(s1 - 1) < eps) m_sing_new(0) = 1;
if (std::abs(s2 - 1) < eps) m_sing_new(1) = 1;
mat_W = ui * m_sing_new.asDiagonal() * ui.transpose();
s.W_11(i) = mat_W(0, 0);
s.W_12(i) = mat_W(0, 1);
s.W_21(i) = mat_W(1, 0);
s.W_22(i) = mat_W(1, 1);
// 2) Update local step (doesn't have to be a rotation, for instance in case of conformal energy)
s.Ri(i, 0) = ri(0, 0);
s.Ri(i, 1) = ri(1, 0);
s.Ri(i, 2) = ri(0, 1);
s.Ri(i, 3) = ri(1, 1);
}
}
else
{
typedef Eigen::Matrix<double, 3, 1> Vec3;
typedef Eigen::Matrix<double, 3, 3> Mat3;
Mat3 ji;
Vec3 m_sing_new;
Vec3 closest_sing_vec;
const double sqrt_2 = sqrt(2);
for (int i = 0; i < s.Ji.rows(); ++i)
{
ji(0, 0) = s.Ji(i, 0);
ji(0, 1) = s.Ji(i, 1);
ji(0, 2) = s.Ji(i, 2);
ji(1, 0) = s.Ji(i, 3);
ji(1, 1) = s.Ji(i, 4);
ji(1, 2) = s.Ji(i, 5);
ji(2, 0) = s.Ji(i, 6);
ji(2, 1) = s.Ji(i, 7);
ji(2, 2) = s.Ji(i, 8);
Mat3 ri, ti, ui, vi;
Vec3 sing;
igl::polar_svd(ji, ri, ti, ui, sing, vi);
double s1 = sing(0);
double s2 = sing(1);
double s3 = sing(2);
// 1) Update Weights
switch (s.slim_energy)
{
case igl::SLIMData::ARAP:
{
m_sing_new << 1, 1, 1;
break;
}
case igl::SLIMData::LOG_ARAP:
{
double s1_g = 2 * (log(s1) / s1);
double s2_g = 2 * (log(s2) / s2);
double s3_g = 2 * (log(s3) / s3);
m_sing_new << sqrt(s1_g / (2 * (s1 - 1))), sqrt(s2_g / (2 * (s2 - 1))), sqrt(s3_g / (2 * (s3 - 1)));
break;
}
case igl::SLIMData::SYMMETRIC_DIRICHLET:
{
double s1_g = 2 * (s1 - pow(s1, -3));
double s2_g = 2 * (s2 - pow(s2, -3));
double s3_g = 2 * (s3 - pow(s3, -3));
m_sing_new << sqrt(s1_g / (2 * (s1 - 1))), sqrt(s2_g / (2 * (s2 - 1))), sqrt(s3_g / (2 * (s3 - 1)));
break;
}
case igl::SLIMData::EXP_SYMMETRIC_DIRICHLET:
{
double s1_g = 2 * (s1 - pow(s1, -3));
double s2_g = 2 * (s2 - pow(s2, -3));
double s3_g = 2 * (s3 - pow(s3, -3));
m_sing_new << sqrt(s1_g / (2 * (s1 - 1))), sqrt(s2_g / (2 * (s2 - 1))), sqrt(s3_g / (2 * (s3 - 1)));
double in_exp = exp_f * (pow(s1, 2) + pow(s1, -2) + pow(s2, 2) + pow(s2, -2) + pow(s3, 2) + pow(s3, -2));
double exp_thing = exp(in_exp);
s1_g *= exp_thing * exp_f;
s2_g *= exp_thing * exp_f;
s3_g *= exp_thing * exp_f;
m_sing_new << sqrt(s1_g / (2 * (s1 - 1))), sqrt(s2_g / (2 * (s2 - 1))), sqrt(s3_g / (2 * (s3 - 1)));
break;
}
case igl::SLIMData::CONFORMAL:
{
double common_div = 9 * (pow(s1 * s2 * s3, 5. / 3.));
double s1_g = (-2 * s2 * s3 * (pow(s2, 2) + pow(s3, 2) - 2 * pow(s1, 2))) / common_div;
double s2_g = (-2 * s1 * s3 * (pow(s1, 2) + pow(s3, 2) - 2 * pow(s2, 2))) / common_div;
double s3_g = (-2 * s1 * s2 * (pow(s1, 2) + pow(s2, 2) - 2 * pow(s3, 2))) / common_div;
double closest_s = sqrt(pow(s1, 2) + pow(s3, 2)) / sqrt_2;
double s1_min = closest_s;
double s2_min = closest_s;
double s3_min = closest_s;
m_sing_new << sqrt(s1_g / (2 * (s1 - s1_min))), sqrt(s2_g / (2 * (s2 - s2_min))), sqrt(
s3_g / (2 * (s3 - s3_min)));
// change local step
closest_sing_vec << s1_min, s2_min, s3_min;
ri = ui * closest_sing_vec.asDiagonal() * vi.transpose();
break;
}
case igl::SLIMData::EXP_CONFORMAL:
{
// E_conf = (s1^2 + s2^2 + s3^2)/(3*(s1*s2*s3)^(2/3) )
// dE_conf/ds1 = (-2*(s2*s3)*(s2^2+s3^2 -2*s1^2) ) / (9*(s1*s2*s3)^(5/3))
// Argmin E_conf(s1): s1 = sqrt(s1^2+s2^2)/sqrt(2)
double common_div = 9 * (pow(s1 * s2 * s3, 5. / 3.));
double s1_g = (-2 * s2 * s3 * (pow(s2, 2) + pow(s3, 2) - 2 * pow(s1, 2))) / common_div;
double s2_g = (-2 * s1 * s3 * (pow(s1, 2) + pow(s3, 2) - 2 * pow(s2, 2))) / common_div;
double s3_g = (-2 * s1 * s2 * (pow(s1, 2) + pow(s2, 2) - 2 * pow(s3, 2))) / common_div;
double in_exp = exp_f * ((pow(s1, 2) + pow(s2, 2) + pow(s3, 2)) / (3 * pow((s1 * s2 * s3), 2. / 3)));;
double exp_thing = exp(in_exp);
double closest_s = sqrt(pow(s1, 2) + pow(s3, 2)) / sqrt_2;
double s1_min = closest_s;
double s2_min = closest_s;
double s3_min = closest_s;
s1_g *= exp_thing * exp_f;
s2_g *= exp_thing * exp_f;
s3_g *= exp_thing * exp_f;
m_sing_new << sqrt(s1_g / (2 * (s1 - s1_min))), sqrt(s2_g / (2 * (s2 - s2_min))), sqrt(
s3_g / (2 * (s3 - s3_min)));
// change local step
closest_sing_vec << s1_min, s2_min, s3_min;
ri = ui * closest_sing_vec.asDiagonal() * vi.transpose();
}
}
if (std::abs(s1 - 1) < eps) m_sing_new(0) = 1;
if (std::abs(s2 - 1) < eps) m_sing_new(1) = 1;
if (std::abs(s3 - 1) < eps) m_sing_new(2) = 1;
Mat3 mat_W;
mat_W = ui * m_sing_new.asDiagonal() * ui.transpose();
s.W_11(i) = mat_W(0, 0);
s.W_12(i) = mat_W(0, 1);
s.W_13(i) = mat_W(0, 2);
s.W_21(i) = mat_W(1, 0);
s.W_22(i) = mat_W(1, 1);
s.W_23(i) = mat_W(1, 2);
s.W_31(i) = mat_W(2, 0);
s.W_32(i) = mat_W(2, 1);
s.W_33(i) = mat_W(2, 2);
// 2) Update closest rotations (not rotations in case of conformal energy)
s.Ri(i, 0) = ri(0, 0);
s.Ri(i, 1) = ri(1, 0);
s.Ri(i, 2) = ri(2, 0);
s.Ri(i, 3) = ri(0, 1);
s.Ri(i, 4) = ri(1, 1);
s.Ri(i, 5) = ri(2, 1);
s.Ri(i, 6) = ri(0, 2);
s.Ri(i, 7) = ri(1, 2);
s.Ri(i, 8) = ri(2, 2);
} // for loop end
} // if dim end
}
IGL_INLINE void solve_weighted_arap(igl::SLIMData& s,
const Eigen::MatrixXd &V,
const Eigen::MatrixXi &F,
Eigen::MatrixXd &uv,
Eigen::VectorXi &soft_b_p,
Eigen::MatrixXd &soft_bc_p)
{
using namespace Eigen;
Eigen::SparseMatrix<double> L;
build_linear_system(s,L);
igl::Timer t;
//t.start();
// solve
Eigen::VectorXd Uc;
#ifndef CHOLMOD
if (s.dim == 2)
{
SimplicialLDLT<Eigen::SparseMatrix<double> > solver;
Uc = solver.compute(L).solve(s.rhs);
}
else
{ // seems like CG performs much worse for 2D and way better for 3D
Eigen::VectorXd guess(uv.rows() * s.dim);
for (int i = 0; i < s.v_num; i++) for (int j = 0; j < s.dim; j++) guess(uv.rows() * j + i) = uv(i, j); // flatten vector
ConjugateGradient<Eigen::SparseMatrix<double>, Lower | Upper> cg;
cg.setTolerance(1e-8);
cg.compute(L);
Uc = cg.solveWithGuess(s.rhs, guess);
}
#else
CholmodSimplicialLDLT<Eigen::SparseMatrix<double> > solver;
Uc = solver.compute(L).solve(s.rhs);
#endif
for (int i = 0; i < s.dim; i++)
uv.col(i) = Uc.block(i * s.v_n, 0, s.v_n, 1);
// t.stop();
// std::cerr << "solve: " << t.getElapsedTime() << std::endl;
}
IGL_INLINE void pre_calc(igl::SLIMData& s)
{
if (!s.has_pre_calc)
{
s.v_n = s.v_num;
s.f_n = s.f_num;
if (s.F.cols() == 3)
{
s.dim = 2;
Eigen::MatrixXd F1, F2, F3;
igl::local_basis(s.V, s.F, F1, F2, F3);
compute_surface_gradient_matrix(s.V, s.F, F1, F2, s.Dx, s.Dy);
s.W_11.resize(s.f_n);
s.W_12.resize(s.f_n);
s.W_21.resize(s.f_n);
s.W_22.resize(s.f_n);
}
else
{
s.dim = 3;
Eigen::SparseMatrix<double> G;
igl::grad(s.V, s.F, G,
s.mesh_improvement_3d /*use normal gradient, or one from a "regular" tet*/);
s.Dx = G.block(0, 0, s.F.rows(), s.V.rows());
s.Dy = G.block(s.F.rows(), 0, s.F.rows(), s.V.rows());
s.Dz = G.block(2 * s.F.rows(), 0, s.F.rows(), s.V.rows());
s.W_11.resize(s.f_n);
s.W_12.resize(s.f_n);
s.W_13.resize(s.f_n);
s.W_21.resize(s.f_n);
s.W_22.resize(s.f_n);
s.W_23.resize(s.f_n);
s.W_31.resize(s.f_n);
s.W_32.resize(s.f_n);
s.W_33.resize(s.f_n);
}
s.Dx.makeCompressed();
s.Dy.makeCompressed();
s.Dz.makeCompressed();
s.Ri.resize(s.f_n, s.dim * s.dim);
s.Ji.resize(s.f_n, s.dim * s.dim);
s.rhs.resize(s.dim * s.v_num);
// flattened weight matrix
s.WGL_M.resize(s.dim * s.dim * s.f_n);
for (int i = 0; i < s.dim * s.dim; i++)
for (int j = 0; j < s.f_n; j++)
s.WGL_M(i * s.f_n + j) = s.M(j);
s.first_solve = true;
s.has_pre_calc = true;
}
}
IGL_INLINE void build_linear_system(igl::SLIMData& s, Eigen::SparseMatrix<double> &L)
{
// formula (35) in paper
std::vector<Eigen::Triplet<double> > IJV;
#ifdef SLIM_CACHED
buildA(s,IJV);
if (s.A.rows() == 0)
{
s.A = Eigen::SparseMatrix<double>(s.dim * s.dim * s.f_n, s.dim * s.v_n);
igl::sparse_cached_precompute(IJV,s.A_data,s.A);
}
else
igl::sparse_cached(IJV,s.A_data,s.A);
#else
Eigen::SparseMatrix<double> A(s.dim * s.dim * s.f_n, s.dim * s.v_n);
buildA(s,IJV);
A.setFromTriplets(IJV.begin(),IJV.end());
A.makeCompressed();
#endif
#ifdef SLIM_CACHED
#else
Eigen::SparseMatrix<double> At = A.transpose();
At.makeCompressed();
#endif
#ifdef SLIM_CACHED
Eigen::SparseMatrix<double> id_m(s.A.cols(), s.A.cols());
#else
Eigen::SparseMatrix<double> id_m(A.cols(), A.cols());
#endif
id_m.setIdentity();
// add proximal penalty
#ifdef SLIM_CACHED
s.AtA_data.W = s.WGL_M;
if (s.AtA.rows() == 0)
igl::AtA_cached_precompute(s.A,s.AtA_data,s.AtA);
else
igl::AtA_cached(s.A,s.AtA_data,s.AtA);
L = s.AtA + s.proximal_p * id_m; //add also a proximal
L.makeCompressed();
#else
L = At * s.WGL_M.asDiagonal() * A + s.proximal_p * id_m; //add also a proximal term
L.makeCompressed();
#endif
#ifdef SLIM_CACHED
buildRhs(s, s.A);
#else
buildRhs(s, A);
#endif
Eigen::SparseMatrix<double> OldL = L;
add_soft_constraints(s,L);
L.makeCompressed();
}
IGL_INLINE void add_soft_constraints(igl::SLIMData& s, Eigen::SparseMatrix<double> &L)
{
int v_n = s.v_num;
for (int d = 0; d < s.dim; d++)
{
for (int i = 0; i < s.b.rows(); i++)
{
int v_idx = s.b(i);
s.rhs(d * v_n + v_idx) += s.soft_const_p * s.bc(i, d); // rhs
L.coeffRef(d * v_n + v_idx, d * v_n + v_idx) += s.soft_const_p; // diagonal of matrix
}
}
}
IGL_INLINE double compute_energy(igl::SLIMData& s, Eigen::MatrixXd &V_new)
{
compute_jacobians(s,V_new);
return compute_energy_with_jacobians(s, s.V, s.F, s.Ji, V_new, s.M) +
compute_soft_const_energy(s, s.V, s.F, V_new);
}
IGL_INLINE double compute_soft_const_energy(igl::SLIMData& s,
const Eigen::MatrixXd &V,
const Eigen::MatrixXi &F,
Eigen::MatrixXd &V_o)
{
double e = 0;
for (int i = 0; i < s.b.rows(); i++)
{
e += s.soft_const_p * (s.bc.row(i) - V_o.row(s.b(i))).squaredNorm();
}
return e;
}
IGL_INLINE double compute_energy_with_jacobians(igl::SLIMData& s,
const Eigen::MatrixXd &V,
const Eigen::MatrixXi &F, const Eigen::MatrixXd &Ji,
Eigen::MatrixXd &uv, Eigen::VectorXd &areas)
{
double energy = 0;
if (s.dim == 2)
{
Eigen::Matrix<double, 2, 2> ji;
for (int i = 0; i < s.f_n; i++)
{
ji(0, 0) = Ji(i, 0);
ji(0, 1) = Ji(i, 1);
ji(1, 0) = Ji(i, 2);
ji(1, 1) = Ji(i, 3);
typedef Eigen::Matrix<double, 2, 2> Mat2;
typedef Eigen::Matrix<double, 2, 1> Vec2;
Mat2 ri, ti, ui, vi;
Vec2 sing;
igl::polar_svd(ji, ri, ti, ui, sing, vi);
double s1 = sing(0);
double s2 = sing(1);
switch (s.slim_energy)
{
case igl::SLIMData::ARAP:
{
energy += areas(i) * (pow(s1 - 1, 2) + pow(s2 - 1, 2));
break;
}
case igl::SLIMData::SYMMETRIC_DIRICHLET:
{
energy += areas(i) * (pow(s1, 2) + pow(s1, -2) + pow(s2, 2) + pow(s2, -2));
break;
}
case igl::SLIMData::EXP_SYMMETRIC_DIRICHLET:
{
energy += areas(i) * exp(s.exp_factor * (pow(s1, 2) + pow(s1, -2) + pow(s2, 2) + pow(s2, -2)));
break;
}
case igl::SLIMData::LOG_ARAP:
{
energy += areas(i) * (pow(log(s1), 2) + pow(log(s2), 2));
break;
}
case igl::SLIMData::CONFORMAL:
{
energy += areas(i) * ((pow(s1, 2) + pow(s2, 2)) / (2 * s1 * s2));
break;
}
case igl::SLIMData::EXP_CONFORMAL:
{
energy += areas(i) * exp(s.exp_factor * ((pow(s1, 2) + pow(s2, 2)) / (2 * s1 * s2)));
break;
}
}
}
}
else
{
Eigen::Matrix<double, 3, 3> ji;
for (int i = 0; i < s.f_n; i++)
{
ji(0, 0) = Ji(i, 0);
ji(0, 1) = Ji(i, 1);
ji(0, 2) = Ji(i, 2);
ji(1, 0) = Ji(i, 3);
ji(1, 1) = Ji(i, 4);
ji(1, 2) = Ji(i, 5);
ji(2, 0) = Ji(i, 6);
ji(2, 1) = Ji(i, 7);
ji(2, 2) = Ji(i, 8);
typedef Eigen::Matrix<double, 3, 3> Mat3;
typedef Eigen::Matrix<double, 3, 1> Vec3;
Mat3 ri, ti, ui, vi;
Vec3 sing;
igl::polar_svd(ji, ri, ti, ui, sing, vi);
double s1 = sing(0);
double s2 = sing(1);
double s3 = sing(2);
switch (s.slim_energy)
{
case igl::SLIMData::ARAP:
{
energy += areas(i) * (pow(s1 - 1, 2) + pow(s2 - 1, 2) + pow(s3 - 1, 2));
break;
}
case igl::SLIMData::SYMMETRIC_DIRICHLET:
{
energy += areas(i) * (pow(s1, 2) + pow(s1, -2) + pow(s2, 2) + pow(s2, -2) + pow(s3, 2) + pow(s3, -2));
break;
}
case igl::SLIMData::EXP_SYMMETRIC_DIRICHLET:
{
energy += areas(i) * exp(s.exp_factor *
(pow(s1, 2) + pow(s1, -2) + pow(s2, 2) + pow(s2, -2) + pow(s3, 2) + pow(s3, -2)));
break;
}
case igl::SLIMData::LOG_ARAP:
{
energy += areas(i) * (pow(log(s1), 2) + pow(log(std::abs(s2)), 2) + pow(log(std::abs(s3)), 2));
break;
}
case igl::SLIMData::CONFORMAL:
{
energy += areas(i) * ((pow(s1, 2) + pow(s2, 2) + pow(s3, 2)) / (3 * pow(s1 * s2 * s3, 2. / 3.)));
break;
}
case igl::SLIMData::EXP_CONFORMAL:
{
energy += areas(i) * exp((pow(s1, 2) + pow(s2, 2) + pow(s3, 2)) / (3 * pow(s1 * s2 * s3, 2. / 3.)));
break;
}
}
}
}
return energy;
}
IGL_INLINE void buildA(igl::SLIMData& s, std::vector<Eigen::Triplet<double> > & IJV)
{
// formula (35) in paper
if (s.dim == 2)
{
IJV.reserve(4 * (s.Dx.outerSize() + s.Dy.outerSize()));
/*A = [W11*Dx, W12*Dx;
W11*Dy, W12*Dy;
W21*Dx, W22*Dx;
W21*Dy, W22*Dy];*/
for (int k = 0; k < s.Dx.outerSize(); ++k)
{
for (Eigen::SparseMatrix<double>::InnerIterator it(s.Dx, k); it; ++it)
{
int dx_r = it.row();
int dx_c = it.col();
double val = it.value();
IJV.push_back(Eigen::Triplet<double>(dx_r, dx_c, val * s.W_11(dx_r)));
IJV.push_back(Eigen::Triplet<double>(dx_r, s.v_n + dx_c, val * s.W_12(dx_r)));
IJV.push_back(Eigen::Triplet<double>(2 * s.f_n + dx_r, dx_c, val * s.W_21(dx_r)));
IJV.push_back(Eigen::Triplet<double>(2 * s.f_n + dx_r, s.v_n + dx_c, val * s.W_22(dx_r)));
}
}
for (int k = 0; k < s.Dy.outerSize(); ++k)
{
for (Eigen::SparseMatrix<double>::InnerIterator it(s.Dy, k); it; ++it)
{
int dy_r = it.row();
int dy_c = it.col();
double val = it.value();
IJV.push_back(Eigen::Triplet<double>(s.f_n + dy_r, dy_c, val * s.W_11(dy_r)));
IJV.push_back(Eigen::Triplet<double>(s.f_n + dy_r, s.v_n + dy_c, val * s.W_12(dy_r)));
IJV.push_back(Eigen::Triplet<double>(3 * s.f_n + dy_r, dy_c, val * s.W_21(dy_r)));
IJV.push_back(Eigen::Triplet<double>(3 * s.f_n + dy_r, s.v_n + dy_c, val * s.W_22(dy_r)));
}
}
}
else
{
/*A = [W11*Dx, W12*Dx, W13*Dx;
W11*Dy, W12*Dy, W13*Dy;
W11*Dz, W12*Dz, W13*Dz;
W21*Dx, W22*Dx, W23*Dx;
W21*Dy, W22*Dy, W23*Dy;
W21*Dz, W22*Dz, W23*Dz;
W31*Dx, W32*Dx, W33*Dx;
W31*Dy, W32*Dy, W33*Dy;
W31*Dz, W32*Dz, W33*Dz;];*/
IJV.reserve(9 * (s.Dx.outerSize() + s.Dy.outerSize() + s.Dz.outerSize()));
for (int k = 0; k < s.Dx.outerSize(); k++)
{
for (Eigen::SparseMatrix<double>::InnerIterator it(s.Dx, k); it; ++it)
{
int dx_r = it.row();
int dx_c = it.col();
double val = it.value();
IJV.push_back(Eigen::Triplet<double>(dx_r, dx_c, val * s.W_11(dx_r)));
IJV.push_back(Eigen::Triplet<double>(dx_r, s.v_n + dx_c, val * s.W_12(dx_r)));
IJV.push_back(Eigen::Triplet<double>(dx_r, 2 * s.v_n + dx_c, val * s.W_13(dx_r)));
IJV.push_back(Eigen::Triplet<double>(3 * s.f_n + dx_r, dx_c, val * s.W_21(dx_r)));
IJV.push_back(Eigen::Triplet<double>(3 * s.f_n + dx_r, s.v_n + dx_c, val * s.W_22(dx_r)));
IJV.push_back(Eigen::Triplet<double>(3 * s.f_n + dx_r, 2 * s.v_n + dx_c, val * s.W_23(dx_r)));
IJV.push_back(Eigen::Triplet<double>(6 * s.f_n + dx_r, dx_c, val * s.W_31(dx_r)));
IJV.push_back(Eigen::Triplet<double>(6 * s.f_n + dx_r, s.v_n + dx_c, val * s.W_32(dx_r)));
IJV.push_back(Eigen::Triplet<double>(6 * s.f_n + dx_r, 2 * s.v_n + dx_c, val * s.W_33(dx_r)));
}
}
for (int k = 0; k < s.Dy.outerSize(); k++)
{
for (Eigen::SparseMatrix<double>::InnerIterator it(s.Dy, k); it; ++it)
{
int dy_r = it.row();
int dy_c = it.col();
double val = it.value();
IJV.push_back(Eigen::Triplet<double>(s.f_n + dy_r, dy_c, val * s.W_11(dy_r)));
IJV.push_back(Eigen::Triplet<double>(s.f_n + dy_r, s.v_n + dy_c, val * s.W_12(dy_r)));
IJV.push_back(Eigen::Triplet<double>(s.f_n + dy_r, 2 * s.v_n + dy_c, val * s.W_13(dy_r)));
IJV.push_back(Eigen::Triplet<double>(4 * s.f_n + dy_r, dy_c, val * s.W_21(dy_r)));
IJV.push_back(Eigen::Triplet<double>(4 * s.f_n + dy_r, s.v_n + dy_c, val * s.W_22(dy_r)));
IJV.push_back(Eigen::Triplet<double>(4 * s.f_n + dy_r, 2 * s.v_n + dy_c, val * s.W_23(dy_r)));
IJV.push_back(Eigen::Triplet<double>(7 * s.f_n + dy_r, dy_c, val * s.W_31(dy_r)));
IJV.push_back(Eigen::Triplet<double>(7 * s.f_n + dy_r, s.v_n + dy_c, val * s.W_32(dy_r)));
IJV.push_back(Eigen::Triplet<double>(7 * s.f_n + dy_r, 2 * s.v_n + dy_c, val * s.W_33(dy_r)));
}
}
for (int k = 0; k < s.Dz.outerSize(); k++)
{
for (Eigen::SparseMatrix<double>::InnerIterator it(s.Dz, k); it; ++it)
{
int dz_r = it.row();
int dz_c = it.col();
double val = it.value();
IJV.push_back(Eigen::Triplet<double>(2 * s.f_n + dz_r, dz_c, val * s.W_11(dz_r)));
IJV.push_back(Eigen::Triplet<double>(2 * s.f_n + dz_r, s.v_n + dz_c, val * s.W_12(dz_r)));
IJV.push_back(Eigen::Triplet<double>(2 * s.f_n + dz_r, 2 * s.v_n + dz_c, val * s.W_13(dz_r)));
IJV.push_back(Eigen::Triplet<double>(5 * s.f_n + dz_r, dz_c, val * s.W_21(dz_r)));
IJV.push_back(Eigen::Triplet<double>(5 * s.f_n + dz_r, s.v_n + dz_c, val * s.W_22(dz_r)));
IJV.push_back(Eigen::Triplet<double>(5 * s.f_n + dz_r, 2 * s.v_n + dz_c, val * s.W_23(dz_r)));
IJV.push_back(Eigen::Triplet<double>(8 * s.f_n + dz_r, dz_c, val * s.W_31(dz_r)));
IJV.push_back(Eigen::Triplet<double>(8 * s.f_n + dz_r, s.v_n + dz_c, val * s.W_32(dz_r)));
IJV.push_back(Eigen::Triplet<double>(8 * s.f_n + dz_r, 2 * s.v_n + dz_c, val * s.W_33(dz_r)));
}
}
}
}
IGL_INLINE void buildRhs(igl::SLIMData& s, const Eigen::SparseMatrix<double> &A)
{
Eigen::VectorXd f_rhs(s.dim * s.dim * s.f_n);
f_rhs.setZero();
if (s.dim == 2)
{
/*b = [W11*R11 + W12*R21; (formula (36))
W11*R12 + W12*R22;
W21*R11 + W22*R21;
W21*R12 + W22*R22];*/
for (int i = 0; i < s.f_n; i++)
{
f_rhs(i + 0 * s.f_n) = s.W_11(i) * s.Ri(i, 0) + s.W_12(i) * s.Ri(i, 1);
f_rhs(i + 1 * s.f_n) = s.W_11(i) * s.Ri(i, 2) + s.W_12(i) * s.Ri(i, 3);
f_rhs(i + 2 * s.f_n) = s.W_21(i) * s.Ri(i, 0) + s.W_22(i) * s.Ri(i, 1);
f_rhs(i + 3 * s.f_n) = s.W_21(i) * s.Ri(i, 2) + s.W_22(i) * s.Ri(i, 3);
}
}
else
{
/*b = [W11*R11 + W12*R21 + W13*R31;
W11*R12 + W12*R22 + W13*R32;
W11*R13 + W12*R23 + W13*R33;
W21*R11 + W22*R21 + W23*R31;
W21*R12 + W22*R22 + W23*R32;
W21*R13 + W22*R23 + W23*R33;
W31*R11 + W32*R21 + W33*R31;
W31*R12 + W32*R22 + W33*R32;
W31*R13 + W32*R23 + W33*R33;];*/
for (int i = 0; i < s.f_n; i++)
{
f_rhs(i + 0 * s.f_n) = s.W_11(i) * s.Ri(i, 0) + s.W_12(i) * s.Ri(i, 1) + s.W_13(i) * s.Ri(i, 2);
f_rhs(i + 1 * s.f_n) = s.W_11(i) * s.Ri(i, 3) + s.W_12(i) * s.Ri(i, 4) + s.W_13(i) * s.Ri(i, 5);
f_rhs(i + 2 * s.f_n) = s.W_11(i) * s.Ri(i, 6) + s.W_12(i) * s.Ri(i, 7) + s.W_13(i) * s.Ri(i, 8);
f_rhs(i + 3 * s.f_n) = s.W_21(i) * s.Ri(i, 0) + s.W_22(i) * s.Ri(i, 1) + s.W_23(i) * s.Ri(i, 2);
f_rhs(i + 4 * s.f_n) = s.W_21(i) * s.Ri(i, 3) + s.W_22(i) * s.Ri(i, 4) + s.W_23(i) * s.Ri(i, 5);
f_rhs(i + 5 * s.f_n) = s.W_21(i) * s.Ri(i, 6) + s.W_22(i) * s.Ri(i, 7) + s.W_23(i) * s.Ri(i, 8);
f_rhs(i + 6 * s.f_n) = s.W_31(i) * s.Ri(i, 0) + s.W_32(i) * s.Ri(i, 1) + s.W_33(i) * s.Ri(i, 2);
f_rhs(i + 7 * s.f_n) = s.W_31(i) * s.Ri(i, 3) + s.W_32(i) * s.Ri(i, 4) + s.W_33(i) * s.Ri(i, 5);
f_rhs(i + 8 * s.f_n) = s.W_31(i) * s.Ri(i, 6) + s.W_32(i) * s.Ri(i, 7) + s.W_33(i) * s.Ri(i, 8);
}
}
Eigen::VectorXd uv_flat(s.dim *s.v_n);
for (int i = 0; i < s.dim; i++)
for (int j = 0; j < s.v_n; j++)
uv_flat(s.v_n * i + j) = s.V_o(j, i);
s.rhs = (f_rhs.transpose() * s.WGL_M.asDiagonal() * A).transpose() + s.proximal_p * uv_flat;
}
}
}
/// Slim Implementation
IGL_INLINE void igl::slim_precompute(
const Eigen::MatrixXd &V,
const Eigen::MatrixXi &F,
const Eigen::MatrixXd &V_init,
SLIMData &data,
SLIMData::SLIM_ENERGY slim_energy,
Eigen::VectorXi &b,
Eigen::MatrixXd &bc,
double soft_p)
{
data.V = V;
data.F = F;
data.V_o = V_init;
data.v_num = V.rows();
data.f_num = F.rows();
data.slim_energy = slim_energy;
data.b = b;
data.bc = bc;
data.soft_const_p = soft_p;
data.proximal_p = 0.0001;
igl::doublearea(V, F, data.M);
data.M /= 2.;
data.mesh_area = data.M.sum();
data.mesh_improvement_3d = false; // whether to use a jacobian derived from a real mesh or an abstract regular mesh (used for mesh improvement)
data.exp_factor = 1.0; // param used only for exponential energies (e.g exponential symmetric dirichlet)
assert (F.cols() == 3 || F.cols() == 4);
igl::slim::pre_calc(data);
data.energy = igl::slim::compute_energy(data,data.V_o) / data.mesh_area;
}
IGL_INLINE Eigen::MatrixXd igl::slim_solve(SLIMData &data, int iter_num)
{
for (int i = 0; i < iter_num; i++)
{
Eigen::MatrixXd dest_res;
dest_res = data.V_o;
// Solve Weighted Proxy
igl::slim::update_weights_and_closest_rotations(data,data.V, data.F, dest_res);
igl::slim::solve_weighted_arap(data,data.V, data.F, dest_res, data.b, data.bc);
double old_energy = data.energy;
std::function<double(Eigen::MatrixXd &)> compute_energy = [&](
Eigen::MatrixXd &aaa) { return igl::slim::compute_energy(data,aaa); };
data.energy = igl::flip_avoiding_line_search(data.F, data.V_o, dest_res, compute_energy,
data.energy * data.mesh_area) / data.mesh_area;
}
return data.V_o;
}
#ifdef IGL_STATIC_LIBRARY
// Explicit template instantiation
#endif
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