167 lines
7.3 KiB
C++
167 lines
7.3 KiB
C++
// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla Public License
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// v. 2.0. If a copy of the MPL was not distributed with this file, You can
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// obtain one at http://mozilla.org/MPL/2.0/.
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#include "massmatrix.h"
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#include "normalize_row_sums.h"
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#include "sparse.h"
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#include "doublearea.h"
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#include "repmat.h"
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#include <Eigen/Geometry>
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#include <iostream>
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template <typename DerivedV, typename DerivedF, typename Scalar>
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IGL_INLINE void igl::massmatrix(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedF> & F,
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const MassMatrixType type,
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Eigen::SparseMatrix<Scalar>& M)
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{
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using namespace Eigen;
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using namespace std;
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const int n = V.rows();
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const int m = F.rows();
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const int simplex_size = F.cols();
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MassMatrixType eff_type = type;
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// Use voronoi of for triangles by default, otherwise barycentric
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if(type == MASSMATRIX_TYPE_DEFAULT)
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{
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eff_type = (simplex_size == 3?MASSMATRIX_TYPE_VORONOI:MASSMATRIX_TYPE_BARYCENTRIC);
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}
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// Not yet supported
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assert(type!=MASSMATRIX_TYPE_FULL);
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Matrix<int,Dynamic,1> MI;
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Matrix<int,Dynamic,1> MJ;
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Matrix<Scalar,Dynamic,1> MV;
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if(simplex_size == 3)
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{
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// Triangles
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// edge lengths numbered same as opposite vertices
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Matrix<Scalar,Dynamic,3> l(m,3);
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// loop over faces
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for(int i = 0;i<m;i++)
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{
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l(i,0) = (V.row(F(i,1))-V.row(F(i,2))).norm();
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l(i,1) = (V.row(F(i,2))-V.row(F(i,0))).norm();
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l(i,2) = (V.row(F(i,0))-V.row(F(i,1))).norm();
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}
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Matrix<Scalar,Dynamic,1> dblA;
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doublearea(l,0.,dblA);
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switch(eff_type)
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{
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case MASSMATRIX_TYPE_BARYCENTRIC:
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// diagonal entries for each face corner
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MI.resize(m*3,1); MJ.resize(m*3,1); MV.resize(m*3,1);
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MI.block(0*m,0,m,1) = F.col(0);
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MI.block(1*m,0,m,1) = F.col(1);
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MI.block(2*m,0,m,1) = F.col(2);
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MJ = MI;
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repmat(dblA,3,1,MV);
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MV.array() /= 6.0;
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break;
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case MASSMATRIX_TYPE_VORONOI:
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{
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// diagonal entries for each face corner
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// http://www.alecjacobson.com/weblog/?p=874
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MI.resize(m*3,1); MJ.resize(m*3,1); MV.resize(m*3,1);
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MI.block(0*m,0,m,1) = F.col(0);
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MI.block(1*m,0,m,1) = F.col(1);
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MI.block(2*m,0,m,1) = F.col(2);
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MJ = MI;
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// Holy shit this needs to be cleaned up and optimized
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Matrix<Scalar,Dynamic,3> cosines(m,3);
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cosines.col(0) =
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(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);
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cosines.col(1) =
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(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);
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cosines.col(2) =
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(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);
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Matrix<Scalar,Dynamic,3> barycentric = cosines.array() * l.array();
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normalize_row_sums(barycentric,barycentric);
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Matrix<Scalar,Dynamic,3> partial = barycentric;
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partial.col(0).array() *= dblA.array() * 0.5;
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partial.col(1).array() *= dblA.array() * 0.5;
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partial.col(2).array() *= dblA.array() * 0.5;
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Matrix<Scalar,Dynamic,3> quads(partial.rows(),partial.cols());
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quads.col(0) = (partial.col(1)+partial.col(2))*0.5;
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quads.col(1) = (partial.col(2)+partial.col(0))*0.5;
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quads.col(2) = (partial.col(0)+partial.col(1))*0.5;
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quads.col(0) = (cosines.col(0).array()<0).select( 0.25*dblA,quads.col(0));
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quads.col(1) = (cosines.col(0).array()<0).select(0.125*dblA,quads.col(1));
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quads.col(2) = (cosines.col(0).array()<0).select(0.125*dblA,quads.col(2));
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quads.col(0) = (cosines.col(1).array()<0).select(0.125*dblA,quads.col(0));
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quads.col(1) = (cosines.col(1).array()<0).select(0.25*dblA,quads.col(1));
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quads.col(2) = (cosines.col(1).array()<0).select(0.125*dblA,quads.col(2));
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quads.col(0) = (cosines.col(2).array()<0).select(0.125*dblA,quads.col(0));
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quads.col(1) = (cosines.col(2).array()<0).select(0.125*dblA,quads.col(1));
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quads.col(2) = (cosines.col(2).array()<0).select( 0.25*dblA,quads.col(2));
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MV.block(0*m,0,m,1) = quads.col(0);
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MV.block(1*m,0,m,1) = quads.col(1);
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MV.block(2*m,0,m,1) = quads.col(2);
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break;
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}
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case MASSMATRIX_TYPE_FULL:
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assert(false && "Implementation incomplete");
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break;
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default:
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assert(false && "Unknown Mass matrix eff_type");
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}
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}else if(simplex_size == 4)
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{
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assert(V.cols() == 3);
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assert(eff_type == MASSMATRIX_TYPE_BARYCENTRIC);
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MI.resize(m*4,1); MJ.resize(m*4,1); MV.resize(m*4,1);
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MI.block(0*m,0,m,1) = F.col(0);
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MI.block(1*m,0,m,1) = F.col(1);
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MI.block(2*m,0,m,1) = F.col(2);
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MI.block(3*m,0,m,1) = F.col(3);
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MJ = MI;
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// loop over tets
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for(int i = 0;i<m;i++)
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{
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// http://en.wikipedia.org/wiki/Tetrahedron#Volume
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Matrix<Scalar,3,1> v0m3,v1m3,v2m3;
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v0m3.head(V.cols()) = V.row(F(i,0)) - V.row(F(i,3));
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v1m3.head(V.cols()) = V.row(F(i,1)) - V.row(F(i,3));
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v2m3.head(V.cols()) = V.row(F(i,2)) - V.row(F(i,3));
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Scalar v = fabs(v0m3.dot(v1m3.cross(v2m3)))/6.0;
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MV(i+0*m) = v/4.0;
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MV(i+1*m) = v/4.0;
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MV(i+2*m) = v/4.0;
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MV(i+3*m) = v/4.0;
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}
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}else
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{
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// Unsupported simplex size
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assert(false && "Unsupported simplex size");
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}
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sparse(MI,MJ,MV,n,n,M);
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}
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#ifdef IGL_STATIC_LIBRARY
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// Explicit template instantiation
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// generated by autoexplicit.sh
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template void igl::massmatrix<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, double>(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::MassMatrixType, Eigen::SparseMatrix<double, 0, int>&);
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// generated by autoexplicit.sh
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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>&);
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// generated by autoexplicit.sh
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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>&);
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template void igl::massmatrix<Eigen::Matrix<double, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, double>(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, igl::MassMatrixType, Eigen::SparseMatrix<double, 0, int>&);
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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>&);
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#endif
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