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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) 2017 Oded Stein <oded.stein@columbia.edu>
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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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+
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+
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+#include "isolines.h"
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+
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+#include <vector>
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+#include <array>
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+#include <iostream>
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+
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+#include "sort.h"
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+#include "remove_duplicate_vertices.h"
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+
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+
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+template <typename DerivedV,
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+typename DerivedF,
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+typename DerivedZ,
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+typename DerivedIsoV,
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+typename DerivedIsoE>
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+IGL_INLINE void igl::isolines(
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+ const Eigen::MatrixBase<DerivedV>& V,
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+ const Eigen::MatrixBase<DerivedF>& F,
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+ const Eigen::MatrixBase<DerivedZ>& z,
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+ const int n,
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+ Eigen::PlainObjectBase<DerivedIsoV>& isoV,
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+ Eigen::PlainObjectBase<DerivedIsoE>& isoE)
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+{
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+ //Constants
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+ const int dim = V.cols();
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+ assert(dim==2 || dim==3);
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+ const int nVerts = V.rows();
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+ assert(z.rows() == nVerts &&
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+ "There must be as many function entries as vertices");
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+ const int nFaces = F.rows();
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+ const int np1 = n+1;
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+ const double min = z.minCoeff(), max = z.maxCoeff();
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+
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+
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+ //Following http://www.alecjacobson.com/weblog/?p=2529
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+ typedef typename DerivedZ::Scalar Scalar;
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+ typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vec;
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+ Vec iso(np1);
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+ for(int i=0; i<np1; ++i)
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+ iso(i) = Scalar(i)/Scalar(n)*(max-min) + min;
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+
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+ typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
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+ std::array<Matrix,3> t{{Matrix(nFaces, np1),
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+ Matrix(nFaces, np1), Matrix(nFaces, np1)}};
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+ for(int i=0; i<nFaces; ++i) {
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+ for(int k=0; k<3; ++k) {
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+ const Scalar z1=z(F(i,k)), z2=z(F(i,(k+1)%3));
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+ for(int j=0; j<np1; ++j) {
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+ t[k](i,j) = (iso(j)-z1) / (z2-z1);
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+ if(t[k](i,j)<0 || t[k](i,j)>1)
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+ t[k](i,j) = std::numeric_limits<Scalar>::quiet_NaN();
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+ }
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+ }
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+ }
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+
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+ std::array<std::vector<int>,3> Fij, Iij;
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+ for(int i=0; i<nFaces; ++i) {
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+ for(int j=0; j<np1; ++j) {
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+ for(int k=0; k<3; ++k) {
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+ const int kp1=(k+1)%3, kp2=(k+2)%3;
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+ if(std::isfinite(t[kp1](i,j)) && std::isfinite(t[kp2](i,j))) {
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+ Fij[k].push_back(i);
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+ Iij[k].push_back(j);
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+ }
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+ }
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+ }
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+ }
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+
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+ const int K = Fij[0].size()+Fij[1].size()+Fij[2].size();
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+ isoV.resize(2*K, dim);
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+ int b = 0;
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+ for(int k=0; k<3; ++k) {
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+ const int kp1=(k+1)%3, kp2=(k+2)%3;
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+ for(int i=0; i<Fij[k].size(); ++i) {
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+ isoV.row(b+i) = (1.-t[kp1](Fij[k][i],Iij[k][i]))*
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+ V.row(F(Fij[k][i],kp1)) +
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+ t[kp1](Fij[k][i],Iij[k][i])*V.row(F(Fij[k][i],kp2));
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+ isoV.row(K+b+i) = (1.-t[kp2](Fij[k][i],Iij[k][i]))*
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+ V.row(F(Fij[k][i],kp2)) +
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+ t[kp2](Fij[k][i],Iij[k][i])*V.row(F(Fij[k][i],k));
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+ }
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+ b += Fij[k].size();
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+ }
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+
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+ isoE.resize(K,2);
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+ for(int i=0; i<K; ++i)
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+ isoE.row(i) << i, K+i;
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+
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+
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+ //Remove double entries
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+ typedef typename DerivedIsoV::Scalar LScalar;
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+ typedef typename DerivedIsoE::Scalar LInt;
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+ typedef Eigen::Matrix<LInt, Eigen::Dynamic, 1> LIVec;
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+ typedef Eigen::Matrix<LScalar, Eigen::Dynamic, Eigen::Dynamic> LMat;
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+ typedef Eigen::Matrix<LInt, Eigen::Dynamic, Eigen::Dynamic> LIMat;
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+ LIVec dummy1, dummy2;
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+ igl::remove_duplicate_vertices(LMat(isoV), LIMat(isoE),
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+ 1e-12, isoV, dummy1, dummy2, isoE);
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+
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+}
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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::isolines<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, int const, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > &, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > &);
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+#endif
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+
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Oded Stein