general polyvector field

Former-commit-id: 3092be447ba623a52706e1e069531a2eaeae48e2

include/igl/n_polyvector_general.cpp

@@ -0,0 +1,491 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2014 Olga Diamanti <olga.diam@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 <igl/n_polyvector_general.h>
+#include <igl/edge_topology.h>
+#include <igl/local_basis.h>
+#include <igl/nchoosek.h>
+#include <igl/slice.h>
+#include <igl/polyroots.h>
+#include <Eigen/Sparse>
+
+#include <iostream>
+
+namespace igl {
+  template <typename DerivedV, typename DerivedF>
+  class GeneralPolyVectorFieldFinder
+  {
+  private:
+    const Eigen::PlainObjectBase<DerivedV> &V;
+    const Eigen::PlainObjectBase<DerivedF> &F; int numF;
+    const int n;
+
+    Eigen::MatrixXi EV; int numE;
+    Eigen::MatrixXi F2E;
+    Eigen::MatrixXi E2F;
+    Eigen::VectorXd K;
+
+    Eigen::VectorXi isBorderEdge;
+    int numInteriorEdges;
+    Eigen::Matrix<int,Eigen::Dynamic,2> E2F_int;
+    Eigen::VectorXi indInteriorToFull;
+    Eigen::VectorXi indFullToInterior;
+
+    Eigen::PlainObjectBase<DerivedV> B1, B2, FN;
+
+    IGL_INLINE void computek();
+    IGL_INLINE void setFieldFromGeneralCoefficients(const  std::vector<Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic,1>> &coeffs,
+                                                    std::vector<Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, 2> > &pv);
+    IGL_INLINE void computeCoefficientLaplacian(int n, Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > &D);
+    IGL_INLINE void getGeneralCoeffConstraints(const Eigen::VectorXi &isConstrained,
+                                    const Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, Eigen::Dynamic> &cfW,
+                                    int k,
+                                    const Eigen::VectorXi &rootsIndex,
+                                    Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic,1> &Ck);
+    IGL_INLINE void precomputeInteriorEdges();
+
+
+    IGL_INLINE void minQuadWithKnownMini(const Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > &Q,
+                                         const Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > &f,
+                                         const Eigen::VectorXi isConstrained,
+                                         const Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic, 1> &xknown,
+                                         Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic, 1> &x);
+
+  public:
+    IGL_INLINE GeneralPolyVectorFieldFinder(const Eigen::PlainObjectBase<DerivedV> &_V,
+                                     const Eigen::PlainObjectBase<DerivedF> &_F,
+                                     const int &_n);
+    IGL_INLINE bool solve(const Eigen::VectorXi &isConstrained,
+               const Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, Eigen::Dynamic> &cfW,
+               const Eigen::VectorXi &rootsIndex,
+               Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, Eigen::Dynamic> &output);
+
+  };
+}
+
+template<typename DerivedV, typename DerivedF>
+IGL_INLINE igl::GeneralPolyVectorFieldFinder<DerivedV, DerivedF>::
+          GeneralPolyVectorFieldFinder(const Eigen::PlainObjectBase<DerivedV> &_V,
+                                const Eigen::PlainObjectBase<DerivedF> &_F,
+                                const int &_n):
+V(_V),
+F(_F),
+numF(_F.rows()),
+n(_n)
+{
+
+  igl::edge_topology(V,F,EV,F2E,E2F);
+  numE = EV.rows();
+
+
+  precomputeInteriorEdges();
+
+  igl::local_basis(V,F,B1,B2,FN);
+
+  computek();
+
+};
+
+
+template<typename DerivedV, typename DerivedF>
+IGL_INLINE void igl::GeneralPolyVectorFieldFinder<DerivedV, DerivedF>::
+precomputeInteriorEdges()
+{
+  // Flag border edges
+  numInteriorEdges = 0;
+  isBorderEdge.setZero(numE,1);
+  indFullToInterior = -1.*Eigen::VectorXi::Ones(numE,1);
+
+  for(unsigned i=0; i<numE; ++i)
+  {
+    if ((E2F(i,0) == -1) || ((E2F(i,1) == -1)))
+      isBorderEdge[i] = 1;
+      else
+      {
+        indFullToInterior[i] = numInteriorEdges;
+        numInteriorEdges++;
+      }
+  }
+
+  E2F_int.resize(numInteriorEdges, 2);
+  indInteriorToFull.setZero(numInteriorEdges,1);
+  int ii = 0;
+  for (int k=0; k<numE; ++k)
+  {
+    if (isBorderEdge[k])
+      continue;
+    E2F_int.row(ii) = E2F.row(k);
+    indInteriorToFull[ii] = k;
+    ii++;
+  }
+
+}
+
+
+template<typename DerivedV, typename DerivedF>
+IGL_INLINE void igl::GeneralPolyVectorFieldFinder<DerivedV, DerivedF>::
+minQuadWithKnownMini(const Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > &Q,
+                          const Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > &f,
+                     const Eigen::VectorXi isConstrained,
+                          const Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic, 1> &xknown,
+                          Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic, 1> &x)
+{
+  int N = Q.rows();
+
+  int nc = xknown.rows();
+  Eigen::VectorXi known; known.setZero(nc,1);
+  Eigen::VectorXi unknown; unknown.setZero(N-nc,1);
+
+  int indk = 0, indu = 0;
+  for (int i = 0; i<N; ++i)
+    if (isConstrained[i])
+    {
+      known[indk] = i;
+      indk++;
+    }
+    else
+    {
+      unknown[indu] = i;
+      indu++;
+    }
+
+  Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar>> Quu, Quk;
+
+  igl::slice(Q,unknown, unknown, Quu);
+  igl::slice(Q,unknown, known, Quk);
+
+
+  std::vector<typename Eigen::Triplet<std::complex<typename DerivedV::Scalar> > > tripletList;
+
+  Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > fu(N-nc,1);
+
+  igl::slice(f,unknown, Eigen::VectorXi::Zero(1,1), fu);
+
+  Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > rhs = (Quk*xknown).sparseView()+.5*fu;
+
+  Eigen::SparseLU< Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar>>> solver;
+  solver.compute(-Quu);
+  if(solver.info()!=Eigen::Success)
+  {
+    std::cerr<<"Decomposition failed!"<<std::endl;
+    return;
+  }
+  Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar>>  b  = solver.solve(rhs);
+  if(solver.info()!=Eigen::Success)
+  {
+    std::cerr<<"Solving failed!"<<std::endl;
+    return;
+  }
+
+  indk = 0, indu = 0;
+  x.setZero(N,1);
+  for (int i = 0; i<N; ++i)
+    if (isConstrained[i])
+      x[i] = xknown[indk++];
+    else
+      x[i] = b.coeff(indu++,0);
+
+}
+
+
+
+template<typename DerivedV, typename DerivedF>
+IGL_INLINE bool igl::GeneralPolyVectorFieldFinder<DerivedV, DerivedF>::
+                     solve(const Eigen::VectorXi &isConstrained,
+                           const Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, Eigen::Dynamic> &cfW,
+                           const Eigen::VectorXi &rootsIndex,
+                           Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, Eigen::Dynamic> &output)
+{
+
+  // polynomial is of the form:
+  // z^(2n) +
+  // -c[0]z^(2n-1) +
+  // c[1]z^(2n-2) +
+  // -c[2]z^(2n-3) +
+  // ... +
+  // (-1)^n c[n-1]
+
+  std::vector<Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic,1>> coeffs(n,Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic,1>::Zero(numF, 1));
+
+  for (int i =0; i<n; ++i)
+  {
+    int degree = i+1;
+
+    Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic,1> Ck;
+    getGeneralCoeffConstraints(isConstrained,
+                               cfW,
+                               i,
+                               rootsIndex,
+                               Ck);
+
+    Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > DD;
+    computeCoefficientLaplacian(degree, DD);
+    Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > f; f.resize(numF,1);
+
+    minQuadWithKnownMini(DD, f, isConstrained, Ck, coeffs[i]);
+  }
+
+  std::vector<Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, 2> > pv;
+  setFieldFromGeneralCoefficients(coeffs, pv);
+
+  output.setZero(numF,3*n);
+  for (int fi=0; fi<numF; ++fi)
+  {
+    const Eigen::Matrix<typename DerivedV::Scalar, 1, 3> &b1 = B1.row(fi);
+    const Eigen::Matrix<typename DerivedV::Scalar, 1, 3> &b2 = B2.row(fi);
+    for (int i=0; i<n; ++i)
+      output.block(fi,3*i, 1, 3) = pv[i](fi,0)*b1 + pv[i](fi,1)*b2;
+  }
+  return true;
+}
+
+template<typename DerivedV, typename DerivedF>
+IGL_INLINE void igl::GeneralPolyVectorFieldFinder<DerivedV, DerivedF>::setFieldFromGeneralCoefficients(const  std::vector<Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic,1>> &coeffs,
+                                                            std::vector<Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, 2>> &pv)
+{
+  pv.assign(n, Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, 2>::Zero(numF, 2));
+  for (int i = 0; i <numF; ++i)
+  {
+
+    //    poly coefficients: 1, 0, -Acoeff, 0, Bcoeff
+    //    matlab code from roots (given there are no trailing zeros in the polynomial coefficients)
+    Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic,1> polyCoeff;
+    polyCoeff.setZero(n+1,1);
+    polyCoeff[0] = 1.;
+    int sign = 1;
+    for (int k =0; k<n; ++k)
+    {
+      sign = -sign;
+      int degree = k+1;
+      polyCoeff[degree] = (1.*sign)*coeffs[k](i);
+    }
+
+    Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic,1> roots;
+    igl::polyRoots<std::complex<typename DerivedV::Scalar>, typename DerivedV::Scalar >(polyCoeff,roots);
+    for (int k=0; k<n; ++k)
+    {
+      pv[k](i,0) = real(roots[k]);
+      pv[k](i,1) = imag(roots[k]);
+    }
+  }
+
+}
+
+
+template<typename DerivedV, typename DerivedF>
+IGL_INLINE void igl::GeneralPolyVectorFieldFinder<DerivedV, DerivedF>::computeCoefficientLaplacian(int n, Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > &D)
+{
+  std::vector<Eigen::Triplet<std::complex<typename DerivedV::Scalar> >> tripletList;
+
+  // For every non-border edge
+  for (unsigned eid=0; eid<numE; ++eid)
+  {
+    if (!isBorderEdge[eid])
+    {
+      int fid0 = E2F(eid,0);
+      int fid1 = E2F(eid,1);
+
+      tripletList.push_back(Eigen::Triplet<std::complex<typename DerivedV::Scalar> >(fid0,
+                                           fid0,
+                                           std::complex<typename DerivedV::Scalar>(1.)));
+      tripletList.push_back(Eigen::Triplet<std::complex<typename DerivedV::Scalar> >(fid1,
+                                           fid1,
+                                           std::complex<typename DerivedV::Scalar>(1.)));
+      tripletList.push_back(Eigen::Triplet<std::complex<typename DerivedV::Scalar> >(fid0,
+                                           fid1,
+                                                                                     -1.*std::polar(1.,-1.*n*K[eid])));
+      tripletList.push_back(Eigen::Triplet<std::complex<typename DerivedV::Scalar> >(fid1,
+                                           fid0,
+                                                                                     -1.*std::polar(1.,1.*n*K[eid])));
+
+    }
+  }
+  D.resize(numF,numF);
+  D.setFromTriplets(tripletList.begin(), tripletList.end());
+
+
+}
+
+//this gives the coefficients without the (-1)^k that multiplies them
+template<typename DerivedV, typename DerivedF>
+IGL_INLINE void igl::GeneralPolyVectorFieldFinder<DerivedV, DerivedF>::getGeneralCoeffConstraints(const Eigen::VectorXi &isConstrained,
+                                                       const Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, Eigen::Dynamic> &cfW,
+                                                       int k,
+                                                       const Eigen::VectorXi &rootsIndex,
+                                                       Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic,1> &Ck)
+{
+  int numConstrained = isConstrained.sum();
+  Ck.resize(numConstrained,1);
+  // int n = rootsIndex.cols();
+
+  std::vector<std::vector<int>> allCombs;
+  igl::nchoosek(0,k+1,n,allCombs);
+
+  int ind = 0;
+  for (int fi = 0; fi <numF; ++fi)
+  {
+    const Eigen::Matrix<typename DerivedV::Scalar, 1, 3> &b1 = B1.row(fi);
+    const Eigen::Matrix<typename DerivedV::Scalar, 1, 3> &b2 = B2.row(fi);
+    if(isConstrained[fi])
+    {
+      std::complex<typename DerivedV::Scalar> ck(0);
+
+      for (int j = 0; j < allCombs.size(); ++j)
+      {
+        std::complex<typename DerivedV::Scalar> tk(1.);
+        //collect products
+        for (int i = 0; i < allCombs[j].size(); ++i)
+        {
+          int index = allCombs[j][i];
+
+          int ri = rootsIndex[index];
+          Eigen::Matrix<typename DerivedV::Scalar, 1, 3> w;
+          if (ri>0)
+            w = cfW.block(fi,3*(ri-1),1,3);
+          else
+            w = -cfW.block(fi,3*(-ri-1),1,3);
+          typename DerivedV::Scalar w0 = w.dot(b1);
+          typename DerivedV::Scalar w1 = w.dot(b2);
+          std::complex<typename DerivedV::Scalar> u(w0,w1);
+          tk*= u;
+        }
+        //collect sum
+        ck += tk;
+      }
+      Ck(ind) = ck;
+      ind ++;
+    }
+  }
+
+
+}
+
+template<typename DerivedV, typename DerivedF>
+IGL_INLINE void igl::GeneralPolyVectorFieldFinder<DerivedV, DerivedF>::computek()
+{
+  K.setZero(numE);
+  // For every non-border edge
+  for (unsigned eid=0; eid<numE; ++eid)
+  {
+    if (!isBorderEdge[eid])
+    {
+      int fid0 = E2F(eid,0);
+      int fid1 = E2F(eid,1);
+
+      Eigen::Matrix<typename DerivedV::Scalar, 1, 3> N0 = FN.row(fid0);
+      Eigen::Matrix<typename DerivedV::Scalar, 1, 3> N1 = FN.row(fid1);
+
+      // find common edge on triangle 0 and 1
+      int fid0_vc = -1;
+      int fid1_vc = -1;
+      for (unsigned i=0;i<3;++i)
+      {
+        if (F2E(fid0,i) == eid)
+          fid0_vc = i;
+        if (F2E(fid1,i) == eid)
+          fid1_vc = i;
+      }
+      assert(fid0_vc != -1);
+      assert(fid1_vc != -1);
+
+      Eigen::Matrix<typename DerivedV::Scalar, 1, 3> common_edge = V.row(F(fid0,(fid0_vc+1)%3)) - V.row(F(fid0,fid0_vc));
+      common_edge.normalize();
+
+      // Map the two triangles in a new space where the common edge is the x axis and the N0 the z axis
+      Eigen::Matrix<typename DerivedV::Scalar, 3, 3> P;
+      Eigen::Matrix<typename DerivedV::Scalar, 1, 3> o = V.row(F(fid0,fid0_vc));
+      Eigen::Matrix<typename DerivedV::Scalar, 1, 3> tmp = -N0.cross(common_edge);
+      P << common_edge, tmp, N0;
+//      P.transposeInPlace();
+
+
+      Eigen::Matrix<typename DerivedV::Scalar, 3, 3> V0;
+      V0.row(0) = V.row(F(fid0,0)) -o;
+      V0.row(1) = V.row(F(fid0,1)) -o;
+      V0.row(2) = V.row(F(fid0,2)) -o;
+
+      V0 = (P*V0.transpose()).transpose();
+
+//      assert(V0(0,2) < 1e-10);
+//      assert(V0(1,2) < 1e-10);
+//      assert(V0(2,2) < 1e-10);
+
+      Eigen::Matrix<typename DerivedV::Scalar, 3, 3> V1;
+      V1.row(0) = V.row(F(fid1,0)) -o;
+      V1.row(1) = V.row(F(fid1,1)) -o;
+      V1.row(2) = V.row(F(fid1,2)) -o;
+      V1 = (P*V1.transpose()).transpose();
+
+//      assert(V1(fid1_vc,2) < 10e-10);
+//      assert(V1((fid1_vc+1)%3,2) < 10e-10);
+
+      // compute rotation R such that R * N1 = N0
+      // i.e. map both triangles to the same plane
+      double alpha = -atan2(V1((fid1_vc+2)%3,2),V1((fid1_vc+2)%3,1));
+
+      Eigen::Matrix<typename DerivedV::Scalar, 3, 3> R;
+      R << 1,          0,            0,
+      0, cos(alpha), -sin(alpha) ,
+      0, sin(alpha),  cos(alpha);
+      V1 = (R*V1.transpose()).transpose();
+
+//      assert(V1(0,2) < 1e-10);
+//      assert(V1(1,2) < 1e-10);
+//      assert(V1(2,2) < 1e-10);
+
+      // measure the angle between the reference frames
+      // k_ij is the angle between the triangle on the left and the one on the right
+      Eigen::Matrix<typename DerivedV::Scalar, 1, 3> ref0 = V0.row(1) - V0.row(0);
+      Eigen::Matrix<typename DerivedV::Scalar, 1, 3> ref1 = V1.row(1) - V1.row(0);
+
+      ref0.normalize();
+      ref1.normalize();
+
+      double ktemp = atan2(ref1(1),ref1(0)) - atan2(ref0(1),ref0(0));
+
+      // just to be sure, rotate ref0 using angle ktemp...
+      Eigen::Matrix<typename DerivedV::Scalar, 2, 2> R2;
+      R2 << cos(ktemp), -sin(ktemp), sin(ktemp), cos(ktemp);
+
+      Eigen::Matrix<typename DerivedV::Scalar, 1, 2> tmp1 = R2*(ref0.head(2)).transpose();
+
+//      assert(tmp1(0) - ref1(0) < 1e-10);
+//      assert(tmp1(1) - ref1(1) < 1e-10);
+
+      K[eid] = ktemp;
+    }
+  }
+
+}
+
+
+IGL_INLINE void igl::n_polyvector_general(const Eigen::MatrixXd &V,
+                             const Eigen::MatrixXi &F,
+                             const Eigen::VectorXi& b,
+                             const Eigen::MatrixXd& bc,
+                             const Eigen::VectorXi &I,
+                             Eigen::MatrixXd &output)
+{
+  Eigen::VectorXi isConstrained = Eigen::VectorXi::Constant(F.rows(),0);
+  Eigen::MatrixXd cfW = Eigen::MatrixXd::Constant(F.rows(),bc.cols(),0);
+
+  for(unsigned i=0; i<b.size();++i)
+  {
+    isConstrained(b(i)) = 1;
+    cfW.row(b(i)) << bc.row(i);
+  }
+
+  int n = I.rows();
+  igl::GeneralPolyVectorFieldFinder<Eigen::MatrixXd, Eigen::MatrixXi> pvff(V,F,n);
+  pvff.solve(isConstrained, cfW, I, output);
+}
+
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template specialization
+#endif

include/igl/n_polyvector_general.h

@@ -0,0 +1,41 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2014 Olga Diamanti <olga.diam@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/.
+
+#ifndef IGL_N_POLYVECTOR_GENERAL
+#define IGL_N_POLYVECTOR_GENERAL
+#include "igl_inline.h"
+
+#include <Eigen/Core>
+
+namespace igl {
+  //todo
+  /// Given 2 vectors centered on origin calculate the rotation matrix from first to the second
+
+  // Inputs:
+  //   v0, v1         the two #3 by 1 vectors
+  //   normalized     boolean, if false, then the vectors are normalized prior to the calculation
+  // Output:
+  //                  3 by 3 rotation matrix that takes v0 to v1
+  //
+
+  IGL_INLINE void n_polyvector_general(const Eigen::MatrixXd& V,
+                               const Eigen::MatrixXi& F,
+                               const Eigen::VectorXi& b,
+                               const Eigen::MatrixXd& bc,
+                               const Eigen::VectorXi &I,
+                               Eigen::MatrixXd &output);
+
+};
+
+
+#ifndef IGL_STATIC_LIBRARY
+#include "n_polyvector_general.cpp"
+#endif
+
+
+#endif /* defined(IGL_N_POLYVECTOR) */

tutorial/511_PolyVectorFieldGeneral/CMakeLists.txt

@@ -0,0 +1,11 @@
+cmake_minimum_required(VERSION 2.6)
+project(511_PolyVectorFieldGeneral)
+
+include("../CMakeLists.shared")
+
+set(SOURCES
+${PROJECT_SOURCE_DIR}/main.cpp
+)
+
+add_executable(${PROJECT_NAME}_bin ${SOURCES} ${SHARED_SOURCES})
+target_link_libraries(${PROJECT_NAME}_bin ${SHARED_LIBRARIES} ${LIBCOMISO_LIBRARY})

tutorial/511_PolyVectorFieldGeneral/main.cpp

@@ -0,0 +1,138 @@
+#include <igl/readOBJ.h>
+#include <igl/readDMAT.h>
+#include <igl/viewer/Viewer.h>
+#include <igl/barycenter.h>
+#include <igl/avg_edge_length.h>
+#include <vector>
+#include <igl/n_polyvector_general.h>
+#include <igl/n_polyvector.h>
+#include <igl/local_basis.h>
+#include <stdlib.h>
+#include <igl/jet.h>
+#include <fstream>
+// Input mesh
+Eigen::MatrixXd V;
+Eigen::MatrixXi F;
+
+// Per face bases
+Eigen::MatrixXd B1,B2,B3;
+
+// Face barycenters
+Eigen::MatrixXd B;
+
+// Scale for visualizing the fields
+double global_scale;
+
+// Random length factor
+double rand_factor = 5;
+
+// Create a random set of tangent vectors
+Eigen::VectorXd random_constraints(const
+                                   Eigen::VectorXd& b1, const
+                                   Eigen::VectorXd& b2, int n)
+{
+  Eigen::VectorXd r(n*3);
+  for (unsigned i=0; i<n;++i)
+  {
+    double a = (double(rand())/RAND_MAX)*2*M_PI;
+    double s = 1 + ((double(rand())/RAND_MAX)) * rand_factor;
+    Eigen::Vector3d t = s * (cos(a) * b1 + sin(a) * b2);
+    r.block(i*3,0,3,1) = t;
+  }
+  return r;
+}
+
+bool key_down(igl::Viewer& viewer, unsigned char key, int modifier)
+{
+  using namespace std;
+  using namespace Eigen;
+
+  if (key <'1' || key >'8')
+    return false;
+
+  viewer.data.lines.resize(0,9);
+
+  int num = key  - '0';
+
+  // Interpolate
+  cerr << "Interpolating " << num  << "-PolyVector field" << endl;
+
+  VectorXi b(3);
+  b << 1511, 603, 506;
+
+  int numConstraintsToGenerate;
+  // if it's not a 2-PV or a 1-PV, include a line direction (2 opposite vectors)
+  // in the field
+  if (num>=5)
+    numConstraintsToGenerate  = num-2;
+  else
+    if (num>=3)
+      numConstraintsToGenerate  = num-1;
+    else
+      numConstraintsToGenerate  = num;
+
+
+  MatrixXd bc(b.size(),numConstraintsToGenerate*3);
+  for (unsigned i=0; i<b.size(); ++i)
+  {
+    VectorXd t = random_constraints(B1.row(b(i)),B2.row(b(i)),numConstraintsToGenerate);
+    bc.row(i) = t;
+  }
+  VectorXi rootsIndex(num);
+  for (int i =0; i<numConstraintsToGenerate; ++i)
+    rootsIndex[i] = i+1;
+  if (num>=5)
+    rootsIndex[num-2] = -2;
+    if (num>=3)
+      rootsIndex[num-1] = -1;
+
+  // Interpolated PolyVector field
+  Eigen::MatrixXd pvf;
+  igl::n_polyvector_general(V, F, b, bc, rootsIndex, pvf);
+
+  // Highlight in red the constrained faces
+  MatrixXd C = MatrixXd::Constant(F.rows(),3,1);
+  for (unsigned i=0; i<b.size();++i)
+    C.row(b(i)) << 1, 0, 0;
+  viewer.data.set_colors(C);
+
+  for (int n=0; n<num; ++n)
+  {
+    const MatrixXd &VF = pvf.block(0,n*3,F.rows(),3);
+    VectorXd c = VF.rowwise().norm();
+    MatrixXd C2;
+    igl::jet(c,1,1+rand_factor,C2);
+    // viewer.data.add_edges(B - global_scale*VF, B + global_scale*VF , C2);
+    viewer.data.add_edges(B, B + global_scale*VF , C2);
+  }
+
+
+  return false;
+}
+
+int main(int argc, char *argv[])
+{
+  using namespace Eigen;
+  using namespace std;
+  // Load a mesh in OBJ format
+  igl::readOBJ("../../shared/snail.obj", V, F);
+
+  // Compute local basis for faces
+  igl::local_basis(V,F,B1,B2,B3);
+
+  // Compute face barycenters
+  igl::barycenter(V, F, B);
+
+  // Compute scale for visualizing fields
+  global_scale =  .1*igl::avg_edge_length(V, F);
+
+  // Make the example deterministic
+  srand(0);
+
+  igl::Viewer viewer;
+  viewer.data.set_mesh(V, F);
+  viewer.callback_key_down = &key_down;
+  viewer.core.show_lines = false;
+  key_down(viewer,'3',0);
+  viewer.launch();
+}