119 lines
3.4 KiB
C++
119 lines
3.4 KiB
C++
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// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2015 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 "LinSpaced.h"
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#include "normal_derivative.h"
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#include "cotmatrix_entries.h"
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#include "slice.h"
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#include <cassert>
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template <
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typename DerivedV,
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typename DerivedEle,
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typename Scalar>
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IGL_INLINE void igl::normal_derivative(
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const Eigen::PlainObjectBase<DerivedV> & V,
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const Eigen::PlainObjectBase<DerivedEle> & Ele,
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Eigen::SparseMatrix<Scalar>& DD)
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{
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using namespace Eigen;
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using namespace std;
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// Element simplex-size
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const size_t ss = Ele.cols();
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assert( ((ss==3) || (ss==4)) && "Only triangles or tets");
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// cotangents
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Matrix<Scalar,Dynamic,Dynamic> C;
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cotmatrix_entries(V,Ele,C);
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vector<Triplet<Scalar> > IJV;
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// Number of elements
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const size_t m = Ele.rows();
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// Number of vertices
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const size_t n = V.rows();
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switch(ss)
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{
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default:
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assert(false);
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return;
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case 4:
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{
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const MatrixXi DDJ =
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slice(
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Ele,
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(VectorXi(24)<<
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1,0,2,0,3,0,2,1,3,1,0,1,3,2,0,2,1,2,0,3,1,3,2,3).finished(),
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2);
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MatrixXi DDI(m,24);
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for(size_t f = 0;f<4;f++)
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{
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const auto & I = (igl::LinSpaced<VectorXi >(m,0,m-1).array()+f*m).eval();
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for(size_t r = 0;r<6;r++)
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{
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DDI.col(f*6+r) = I;
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}
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}
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const DiagonalMatrix<Scalar,24,24> S =
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(Matrix<Scalar,2,1>(1,-1).template replicate<12,1>()).asDiagonal();
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Matrix<Scalar,Dynamic,Dynamic> DDV =
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slice(
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C,
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(VectorXi(24)<<
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2,2,1,1,3,3,0,0,4,4,2,2,5,5,1,1,0,0,3,3,4,4,5,5).finished(),
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2);
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DDV *= S;
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IJV.reserve(DDV.size());
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for(size_t f = 0;f<6*4;f++)
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{
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for(size_t e = 0;e<m;e++)
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{
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IJV.push_back(Triplet<Scalar>(DDI(e,f),DDJ(e,f),DDV(e,f)));
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}
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}
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DD.resize(m*4,n);
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DD.setFromTriplets(IJV.begin(),IJV.end());
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break;
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}
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case 3:
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{
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const MatrixXi DDJ =
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slice(Ele,(VectorXi(12)<<2,0,1,0,0,1,2,1,1,2,0,2).finished(),2);
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MatrixXi DDI(m,12);
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for(size_t f = 0;f<3;f++)
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{
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const auto & I = (igl::LinSpaced<VectorXi >(m,0,m-1).array()+f*m).eval();
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for(size_t r = 0;r<4;r++)
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{
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DDI.col(f*4+r) = I;
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}
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}
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const DiagonalMatrix<Scalar,12,12> S =
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(Matrix<Scalar,2,1>(1,-1).template replicate<6,1>()).asDiagonal();
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Matrix<Scalar,Dynamic,Dynamic> DDV =
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slice(C,(VectorXi(12)<<1,1,2,2,2,2,0,0,0,0,1,1).finished(),2);
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DDV *= S;
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IJV.reserve(DDV.size());
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for(size_t f = 0;f<12;f++)
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{
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for(size_t e = 0;e<m;e++)
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{
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IJV.push_back(Triplet<Scalar>(DDI(e,f),DDJ(e,f),DDV(e,f)));
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}
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}
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DD.resize(m*3,n);
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DD.setFromTriplets(IJV.begin(),IJV.end());
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break;
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}
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}
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}
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#ifdef IGL_STATIC_LIBRARY
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// Explicit template instantiation
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template void igl::normal_derivative<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, double>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::SparseMatrix<double, 0, int>&);
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#endif
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