254 lines
6.5 KiB
C++
254 lines
6.5 KiB
C++
// This file is part of libigl, a simple c++ geometry processing library.
|
|
//
|
|
// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
|
|
//
|
|
// 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 "arap_linear_block.h"
|
|
#include "verbose.h"
|
|
#include "cotmatrix_entries.h"
|
|
#include <Eigen/Dense>
|
|
|
|
template <typename MatV, typename MatF, typename Scalar>
|
|
IGL_INLINE void igl::arap_linear_block(
|
|
const MatV & V,
|
|
const MatF & F,
|
|
const int d,
|
|
const igl::ARAPEnergyType energy,
|
|
Eigen::SparseMatrix<Scalar> & Kd)
|
|
{
|
|
switch(energy)
|
|
{
|
|
case ARAP_ENERGY_TYPE_SPOKES:
|
|
return igl::arap_linear_block_spokes(V,F,d,Kd);
|
|
break;
|
|
case ARAP_ENERGY_TYPE_SPOKES_AND_RIMS:
|
|
return igl::arap_linear_block_spokes_and_rims(V,F,d,Kd);
|
|
break;
|
|
case ARAP_ENERGY_TYPE_ELEMENTS:
|
|
return igl::arap_linear_block_elements(V,F,d,Kd);
|
|
break;
|
|
default:
|
|
verbose("Unsupported energy type: %d\n",energy);
|
|
assert(false);
|
|
}
|
|
}
|
|
|
|
|
|
template <typename MatV, typename MatF, typename Scalar>
|
|
IGL_INLINE void igl::arap_linear_block_spokes(
|
|
const MatV & V,
|
|
const MatF & F,
|
|
const int d,
|
|
Eigen::SparseMatrix<Scalar> & Kd)
|
|
{
|
|
using namespace std;
|
|
using namespace Eigen;
|
|
// simplex size (3: triangles, 4: tetrahedra)
|
|
int simplex_size = F.cols();
|
|
// Number of elements
|
|
int m = F.rows();
|
|
// Temporary output
|
|
Matrix<int,Dynamic,2> edges;
|
|
Kd.resize(V.rows(), V.rows());
|
|
vector<Triplet<Scalar> > Kd_IJV;
|
|
if(simplex_size == 3)
|
|
{
|
|
// triangles
|
|
Kd.reserve(7*V.rows());
|
|
Kd_IJV.reserve(7*V.rows());
|
|
edges.resize(3,2);
|
|
edges <<
|
|
1,2,
|
|
2,0,
|
|
0,1;
|
|
}else if(simplex_size == 4)
|
|
{
|
|
// tets
|
|
Kd.reserve(17*V.rows());
|
|
Kd_IJV.reserve(17*V.rows());
|
|
edges.resize(6,2);
|
|
edges <<
|
|
1,2,
|
|
2,0,
|
|
0,1,
|
|
3,0,
|
|
3,1,
|
|
3,2;
|
|
}
|
|
// gather cotangent weights
|
|
Matrix<Scalar,Dynamic,Dynamic> C;
|
|
cotmatrix_entries(V,F,C);
|
|
// should have weights for each edge
|
|
assert(C.cols() == edges.rows());
|
|
// loop over elements
|
|
for(int i = 0;i<m;i++)
|
|
{
|
|
// loop over edges of element
|
|
for(int e = 0;e<edges.rows();e++)
|
|
{
|
|
int source = F(i,edges(e,0));
|
|
int dest = F(i,edges(e,1));
|
|
double v = 0.5*C(i,e)*(V(source,d)-V(dest,d));
|
|
Kd_IJV.push_back(Triplet<Scalar>(source,dest,v));
|
|
Kd_IJV.push_back(Triplet<Scalar>(dest,source,-v));
|
|
Kd_IJV.push_back(Triplet<Scalar>(source,source,v));
|
|
Kd_IJV.push_back(Triplet<Scalar>(dest,dest,-v));
|
|
}
|
|
}
|
|
Kd.setFromTriplets(Kd_IJV.begin(),Kd_IJV.end());
|
|
Kd.makeCompressed();
|
|
}
|
|
|
|
template <typename MatV, typename MatF, typename Scalar>
|
|
IGL_INLINE void igl::arap_linear_block_spokes_and_rims(
|
|
const MatV & V,
|
|
const MatF & F,
|
|
const int d,
|
|
Eigen::SparseMatrix<Scalar> & Kd)
|
|
{
|
|
using namespace std;
|
|
using namespace Eigen;
|
|
// simplex size (3: triangles, 4: tetrahedra)
|
|
int simplex_size = F.cols();
|
|
// Number of elements
|
|
int m = F.rows();
|
|
// Temporary output
|
|
Kd.resize(V.rows(), V.rows());
|
|
vector<Triplet<Scalar> > Kd_IJV;
|
|
Matrix<int,Dynamic,2> edges;
|
|
if(simplex_size == 3)
|
|
{
|
|
// triangles
|
|
Kd.reserve(7*V.rows());
|
|
Kd_IJV.reserve(7*V.rows());
|
|
edges.resize(3,2);
|
|
edges <<
|
|
1,2,
|
|
2,0,
|
|
0,1;
|
|
}else if(simplex_size == 4)
|
|
{
|
|
// tets
|
|
Kd.reserve(17*V.rows());
|
|
Kd_IJV.reserve(17*V.rows());
|
|
edges.resize(6,2);
|
|
edges <<
|
|
1,2,
|
|
2,0,
|
|
0,1,
|
|
3,0,
|
|
3,1,
|
|
3,2;
|
|
// Not implemented yet for tets
|
|
assert(false);
|
|
}
|
|
// gather cotangent weights
|
|
Matrix<Scalar,Dynamic,Dynamic> C;
|
|
cotmatrix_entries(V,F,C);
|
|
// should have weights for each edge
|
|
assert(C.cols() == edges.rows());
|
|
// loop over elements
|
|
for(int i = 0;i<m;i++)
|
|
{
|
|
// loop over edges of element
|
|
for(int e = 0;e<edges.rows();e++)
|
|
{
|
|
int source = F(i,edges(e,0));
|
|
int dest = F(i,edges(e,1));
|
|
double v = C(i,e)*(V(source,d)-V(dest,d))/3.0;
|
|
// loop over edges again
|
|
for(int f = 0;f<edges.rows();f++)
|
|
{
|
|
int Rs = F(i,edges(f,0));
|
|
int Rd = F(i,edges(f,1));
|
|
if(Rs == source && Rd == dest)
|
|
{
|
|
Kd_IJV.push_back(Triplet<Scalar>(Rs,Rd,v));
|
|
Kd_IJV.push_back(Triplet<Scalar>(Rd,Rs,-v));
|
|
}else if(Rd == source)
|
|
{
|
|
Kd_IJV.push_back(Triplet<Scalar>(Rd,Rs,v));
|
|
}else if(Rs == dest)
|
|
{
|
|
Kd_IJV.push_back(Triplet<Scalar>(Rs,Rd,-v));
|
|
}
|
|
}
|
|
Kd_IJV.push_back(Triplet<Scalar>(source,source,v));
|
|
Kd_IJV.push_back(Triplet<Scalar>(dest,dest,-v));
|
|
}
|
|
}
|
|
Kd.setFromTriplets(Kd_IJV.begin(),Kd_IJV.end());
|
|
Kd.makeCompressed();
|
|
}
|
|
|
|
template <typename MatV, typename MatF, typename Scalar>
|
|
IGL_INLINE void igl::arap_linear_block_elements(
|
|
const MatV & V,
|
|
const MatF & F,
|
|
const int d,
|
|
Eigen::SparseMatrix<Scalar> & Kd)
|
|
{
|
|
using namespace std;
|
|
using namespace Eigen;
|
|
// simplex size (3: triangles, 4: tetrahedra)
|
|
int simplex_size = F.cols();
|
|
// Number of elements
|
|
int m = F.rows();
|
|
// Temporary output
|
|
Kd.resize(V.rows(), F.rows());
|
|
vector<Triplet<Scalar> > Kd_IJV;
|
|
Matrix<int,Dynamic,2> edges;
|
|
if(simplex_size == 3)
|
|
{
|
|
// triangles
|
|
Kd.reserve(7*V.rows());
|
|
Kd_IJV.reserve(7*V.rows());
|
|
edges.resize(3,2);
|
|
edges <<
|
|
1,2,
|
|
2,0,
|
|
0,1;
|
|
}else if(simplex_size == 4)
|
|
{
|
|
// tets
|
|
Kd.reserve(17*V.rows());
|
|
Kd_IJV.reserve(17*V.rows());
|
|
edges.resize(6,2);
|
|
edges <<
|
|
1,2,
|
|
2,0,
|
|
0,1,
|
|
3,0,
|
|
3,1,
|
|
3,2;
|
|
}
|
|
// gather cotangent weights
|
|
Matrix<Scalar,Dynamic,Dynamic> C;
|
|
cotmatrix_entries(V,F,C);
|
|
// should have weights for each edge
|
|
assert(C.cols() == edges.rows());
|
|
// loop over elements
|
|
for(int i = 0;i<m;i++)
|
|
{
|
|
// loop over edges of element
|
|
for(int e = 0;e<edges.rows();e++)
|
|
{
|
|
int source = F(i,edges(e,0));
|
|
int dest = F(i,edges(e,1));
|
|
double v = C(i,e)*(V(source,d)-V(dest,d));
|
|
Kd_IJV.push_back(Triplet<Scalar>(source,i,v));
|
|
Kd_IJV.push_back(Triplet<Scalar>(dest,i,-v));
|
|
}
|
|
}
|
|
Kd.setFromTriplets(Kd_IJV.begin(),Kd_IJV.end());
|
|
Kd.makeCompressed();
|
|
}
|
|
|
|
|
|
#ifdef IGL_STATIC_LIBRARY
|
|
// Explicit template instantiation
|
|
template IGL_INLINE void igl::arap_linear_block<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, double>(Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, Eigen::Matrix<int, -1, -1, 0, -1, -1> const&, int, igl::ARAPEnergyType, Eigen::SparseMatrix<double, 0, int>&);
|
|
#endif
|