libigl_Martin/include/igl/bijective_composite_harmonic_mapping.cpp

// This file is part of libigl, a simple c++ geometry processing library.
// 
// Copyright (C) 2017 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 "bijective_composite_harmonic_mapping.h"

#include "slice.h"
#include "doublearea.h"
#include "harmonic.h"

template <
  typename DerivedV,
  typename DerivedF,
  typename Derivedb,
  typename Derivedbc,
  typename DerivedU>
IGL_INLINE bool igl::bijective_composite_harmonic_mapping(
  const Eigen::MatrixBase<DerivedV> & V,
  const Eigen::MatrixBase<DerivedF> & F,
  const Eigen::MatrixBase<Derivedb> & b,
  const Eigen::MatrixBase<Derivedbc> & bc,
  Eigen::PlainObjectBase<DerivedU> & U)
{
  typedef typename Derivedbc::Scalar Scalar;
  assert(V.cols() == 2 && bc.cols() == 2 && "Input should be 2D");
  assert(F.cols() == 3 && "F should contain triangles");
  int tries = 0;
  const int min_steps = 1;
  const int max_steps = 64;
  int nsteps = min_steps;
  Derivedbc bc0;
  slice(V,b,1,bc0);

  // It's difficult to check for flips "robustly" in the sense that the input
  // mesh might not have positive/consistent sign to begin with. 

  while(nsteps<=max_steps)
  {
    U = V;
    int flipped = 0;
    int nans = 0;
    for(int step = 0;step<=nsteps;step++)
    {
      const Scalar t = ((Scalar)step)/((Scalar)nsteps);
      // linearly interpolate boundary conditions
      // TODO: replace this with something that guarantees a homotopic "morph"
      // of the boundary conditions. Something like "Homotopic Morphing of
      // Planar Curves" [Dym et al. 2015] but also handling multiple connected
      // components.
      Derivedbc bct = bc0 + t*(bc - bc0);
      // Compute dsicrete harmonic map using metric of previous step
      const int ninnersteps = 8;
      for(int iter = 0;iter<8;iter++)
      {
        //std::cout<<nsteps<<" t: "<<t<<" iter: "<<iter;
        harmonic(DerivedU(U),F,b,bct,1,U);
        Eigen::Matrix<Scalar,Eigen::Dynamic,1> A;
        doublearea(U,F,A);
        flipped = (A.array() < 0 ).count();
        //std::cout<<"  "<<flipped<<"  nan? "<<(U.array() != U.array()).any()<<std::endl;
        nans = (U.array() != U.array()).count();
        if(flipped == 0 && nans == 0) break;
        igl::slice(U,b,1,bct);
      }
      if(flipped > 0 || nans>0) break;
    }
    if(flipped == 0 && nans == 0)
    {
      return true;
    }
    nsteps *= 2;
  }
  return false;
}

#ifdef IGL_STATIC_LIBRARY
// Explicit template specialization
// generated by autoexplicit.sh
template bool igl::bijective_composite_harmonic_mapping<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -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, 1, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -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&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> >&);
#endif