// 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 "massmatrix.h"
#include "normalize_row_sums.h"
#include "sparse.h"
#include "doublearea.h"
#include "repmat.h"
#include <Eigen/Geometry>
#include <iostream>
template <typename DerivedV, typename DerivedF, typename Scalar>
IGL_INLINE void igl::massmatrix(
const Eigen::MatrixBase<DerivedV> & V,
const Eigen::MatrixBase<DerivedF> & F,
const MassMatrixType type,
Eigen::SparseMatrix<Scalar>& M)
{
using namespace Eigen;
using namespace std;
const int n = V.rows();
const int m = F.rows();
const int simplex_size = F.cols();
MassMatrixType eff_type = type;
// Use voronoi of for triangles by default, otherwise barycentric
if(type == MASSMATRIX_TYPE_DEFAULT)
{
eff_type = (simplex_size == 3?MASSMATRIX_TYPE_VORONOI:MASSMATRIX_TYPE_BARYCENTRIC);
}
// Not yet supported
assert(type!=MASSMATRIX_TYPE_FULL);
Matrix<int,Dynamic,1> MI;
Matrix<int,Dynamic,1> MJ;
Matrix<Scalar,Dynamic,1> MV;
if(simplex_size == 3)
{
// Triangles
// edge lengths numbered same as opposite vertices
Matrix<Scalar,Dynamic,3> l(m,3);
// loop over faces
for(int i = 0;i<m;i++)
{
l(i,0) = (V.row(F(i,1))-V.row(F(i,2))).norm();
l(i,1) = (V.row(F(i,2))-V.row(F(i,0))).norm();
l(i,2) = (V.row(F(i,0))-V.row(F(i,1))).norm();
}
Matrix<Scalar,Dynamic,1> dblA;
doublearea(l,dblA);
switch(eff_type)
{
case MASSMATRIX_TYPE_BARYCENTRIC:
// diagonal entries for each face corner
MI.resize(m*3,1); MJ.resize(m*3,1); MV.resize(m*3,1);
MI.block(0*m,0,m,1) = F.col(0);
MI.block(1*m,0,m,1) = F.col(1);
MI.block(2*m,0,m,1) = F.col(2);
MJ = MI;
repmat(dblA,3,1,MV);
MV.array() /= 6.0;
break;
case MASSMATRIX_TYPE_VORONOI:
{
// diagonal entries for each face corner
// http://www.alecjacobson.com/weblog/?p=874
MI.resize(m*3,1); MJ.resize(m*3,1); MV.resize(m*3,1);
MI.block(0*m,0,m,1) = F.col(0);
MI.block(1*m,0,m,1) = F.col(1);
MI.block(2*m,0,m,1) = F.col(2);
MJ = MI;
// Holy shit this needs to be cleaned up and optimized
Matrix<Scalar,Dynamic,3> cosines(m,3);
cosines.col(0) =
(l.col(2).array().pow(2)+l.col(1).array().pow(2)-l.col(0).array().pow(2))/(l.col(1).array()*l.col(2).array()*2.0);
cosines.col(1) =
(l.col(0).array().pow(2)+l.col(2).array().pow(2)-l.col(1).array().pow(2))/(l.col(2).array()*l.col(0).array()*2.0);
cosines.col(2) =
(l.col(1).array().pow(2)+l.col(0).array().pow(2)-l.col(2).array().pow(2))/(l.col(0).array()*l.col(1).array()*2.0);
Matrix<Scalar,Dynamic,3> barycentric = cosines.array() * l.array();
normalize_row_sums(barycentric,barycentric);
Matrix<Scalar,Dynamic,3> partial = barycentric;
partial.col(0).array() *= dblA.array() * 0.5;
partial.col(1).array() *= dblA.array() * 0.5;
partial.col(2).array() *= dblA.array() * 0.5;
Matrix<Scalar,Dynamic,3> quads(partial.rows(),partial.cols());
quads.col(0) = (partial.col(1)+partial.col(2))*0.5;
quads.col(1) = (partial.col(2)+partial.col(0))*0.5;
quads.col(2) = (partial.col(0)+partial.col(1))*0.5;
quads.col(0) = (cosines.col(0).array()<0).select( 0.25*dblA,quads.col(0));
quads.col(1) = (cosines.col(0).array()<0).select(0.125*dblA,quads.col(1));
quads.col(2) = (cosines.col(0).array()<0).select(0.125*dblA,quads.col(2));
quads.col(0) = (cosines.col(1).array()<0).select(0.125*dblA,quads.col(0));
quads.col(1) = (cosines.col(1).array()<0).select(0.25*dblA,quads.col(1));
quads.col(2) = (cosines.col(1).array()<0).select(0.125*dblA,quads.col(2));
quads.col(0) = (cosines.col(2).array()<0).select(0.125*dblA,quads.col(0));
quads.col(1) = (cosines.col(2).array()<0).select(0.125*dblA,quads.col(1));
quads.col(2) = (cosines.col(2).array()<0).select( 0.25*dblA,quads.col(2));
MV.block(0*m,0,m,1) = quads.col(0);
MV.block(1*m,0,m,1) = quads.col(1);
MV.block(2*m,0,m,1) = quads.col(2);
break;
}
case MASSMATRIX_TYPE_FULL:
assert(false && "Implementation incomplete");
break;
default:
assert(false && "Unknown Mass matrix eff_type");
}
}else if(simplex_size == 4)
{
assert(V.cols() == 3);
assert(eff_type == MASSMATRIX_TYPE_BARYCENTRIC);
MI.resize(m*4,1); MJ.resize(m*4,1); MV.resize(m*4,1);
MI.block(0*m,0,m,1) = F.col(0);
MI.block(1*m,0,m,1) = F.col(1);
MI.block(2*m,0,m,1) = F.col(2);
MI.block(3*m,0,m,1) = F.col(3);
MJ = MI;
// loop over tets
for(int i = 0;i<m;i++)
{
// http://en.wikipedia.org/wiki/Tetrahedron#Volume
Matrix<Scalar,3,1> v0m3 = V.row(F(i,0)) - V.row(F(i,3));
Matrix<Scalar,3,1> v1m3 = V.row(F(i,1)) - V.row(F(i,3));
Matrix<Scalar,3,1> v2m3 = V.row(F(i,2)) - V.row(F(i,3));
Scalar v = fabs(v0m3.dot(v1m3.cross(v2m3)))/6.0;
MV(i+0*m) = v/4.0;
MV(i+1*m) = v/4.0;
MV(i+2*m) = v/4.0;
MV(i+3*m) = v/4.0;
}
}else
{
// Unsupported simplex size
assert(false && "Unsupported simplex size");
}
sparse(MI,MJ,MV,n,n,M);
}
#ifdef IGL_STATIC_LIBRARY
// Explicit template specialization
// generated by autoexplicit.sh
template void igl::massmatrix<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 4, 0, -1, 4>, double>(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 4, 0, -1, 4> > const&, igl::MassMatrixType, Eigen::SparseMatrix<double, 0, int>&);
// generated by autoexplicit.sh
template void igl::massmatrix<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, double>(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, igl::MassMatrixType, Eigen::SparseMatrix<double, 0, int>&);
template void igl::massmatrix<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, double>(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::MassMatrixType, Eigen::SparseMatrix<double, 0, int>&);
#endif