libigl_Martin/include/igl/outer_element.cpp

// This file is part of libigl, a simple c++ geometry processing library.
// 
// Copyright (C) 2015 Qingnan Zhou <qnzhou@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 "outer_element.h"
#include <iostream>
#include <vector>

template <
     typename DerivedV,
     typename DerivedF,
     typename DerivedI,
     typename IndexType,
     typename DerivedA
     >
IGL_INLINE void igl::outer_vertex(
        const Eigen::PlainObjectBase<DerivedV> & V,
        const Eigen::PlainObjectBase<DerivedF> & F,
        const Eigen::PlainObjectBase<DerivedI> & I,
        IndexType & v_index,
        Eigen::PlainObjectBase<DerivedA> & A)
{
  // Algorithm: 
  //    Find an outer vertex (i.e. vertex reachable from infinity)
  //    Return the vertex with the largest X value.
  //    If there is a tie, pick the one with largest Y value.
  //    If there is still a tie, pick the one with the largest Z value.
  //    If there is still a tie, then there are duplicated vertices within the
  //    mesh, which violates the precondition.
  const size_t INVALID = std::numeric_limits<size_t>::max();
  const size_t num_selected_faces = I.rows();
  std::vector<size_t> candidate_faces;
  size_t outer_vid = INVALID;
  typename DerivedV::Scalar outer_val = 0;
  for (size_t i=0; i<num_selected_faces; i++)
  {
    size_t f = I(i);
    for (size_t j=0; j<3; j++)
    {
      auto v = F(f, j);
      auto vx = V(v, 0);
      if (outer_vid == INVALID || vx > outer_val)
      {
        outer_val = vx;
        outer_vid = v;
        candidate_faces = {f};
      } else if (v == outer_vid)
      {
        candidate_faces.push_back(f);
      } else if (vx == outer_val)
      {
        // Break tie.
        auto vy = V(v,1);
        auto vz = V(v, 2);
        auto outer_y = V(outer_vid, 1);
        auto outer_z = V(outer_vid, 2);
        assert(!(vy == outer_y && vz == outer_z));
        bool replace = (vy > outer_y) ||
          ((vy == outer_y) && (vz > outer_z));
        if (replace)
        {
          outer_val = vx;
          outer_vid = v;
          candidate_faces = {f};
        }
      }
    }
  }

  assert(outer_vid != INVALID);
  assert(candidate_faces.size() > 0);
  v_index = outer_vid;
  A.resize(candidate_faces.size());
  std::copy(candidate_faces.begin(), candidate_faces.end(), A.data());
}

template<
    typename DerivedV,
    typename DerivedF,
    typename DerivedI,
    typename IndexType,
    typename DerivedA
    >
IGL_INLINE void igl::outer_edge(
       const Eigen::PlainObjectBase<DerivedV> & V,
       const Eigen::PlainObjectBase<DerivedF> & F,
       const Eigen::PlainObjectBase<DerivedI> & I,
       IndexType & v1,
       IndexType & v2,
       Eigen::PlainObjectBase<DerivedA> & A) {
   // Algorithm:
   //    Find an outer vertex first.
   //    Find the incident edge with largest slope when projected onto XY
   //      plane.
   //    If there is still a tie, break it using the projected slope onto ZX
   //      plane.
   //    If there is still a tie, then there are multiple overlapping edges,
   //      which violates the precondition.
   typedef typename DerivedV::Scalar Scalar;
   typedef typename DerivedV::Index Index;
   typedef typename Eigen::Matrix<Scalar, 3, 1> ScalarArray3;
   typedef typename Eigen::Matrix<typename DerivedF::Scalar, 3, 1> IndexArray3;
   const size_t INVALID = std::numeric_limits<size_t>::max();

   Index outer_vid;
   Eigen::Matrix<Index,Eigen::Dynamic,1> candidate_faces;
   outer_vertex(V, F, I, outer_vid, candidate_faces);
   const ScalarArray3& outer_v = V.row(outer_vid);
   assert(candidate_faces.size() > 0);

   auto get_vertex_index = [&](const IndexArray3& f, Index vid) -> Index 
   {
     if (f[0] == vid) return 0;
     if (f[1] == vid) return 1;
     if (f[2] == vid) return 2;
     assert(false);
     return -1;
   };

   Scalar outer_slope_YX = 0;
   Scalar outer_slope_ZX = 0;
   size_t outer_opp_vid = INVALID;
   bool infinite_slope_detected = false;
   std::vector<Index> incident_faces;
   auto check_and_update_outer_edge = [&](Index opp_vid, Index fid) {
     if (opp_vid == outer_opp_vid)
     {
       incident_faces.push_back(fid);
       return;
     }

     const ScalarArray3 opp_v = V.row(opp_vid);
     if (!infinite_slope_detected && outer_v[0] != opp_v[0]) 
     {
       // Finite slope
       const ScalarArray3 diff = opp_v - outer_v;
       const Scalar slope_YX = diff[1] / diff[0];
       const Scalar slope_ZX = diff[2] / diff[0];
       if (outer_opp_vid == INVALID ||
               slope_YX > outer_slope_YX ||
               (slope_YX == outer_slope_YX &&
                slope_ZX > outer_slope_ZX)) {
           outer_opp_vid = opp_vid;
           outer_slope_YX = slope_YX;
           outer_slope_ZX = slope_ZX;
           incident_faces = {fid};
       }
     } else if (!infinite_slope_detected)
     {
       // Infinite slope
       outer_opp_vid = opp_vid;
       infinite_slope_detected = true;
       incident_faces = {fid};
     }
   };

   const size_t num_candidate_faces = candidate_faces.size();
   for (size_t i=0; i<num_candidate_faces; i++) 
   {
     const Index fid = candidate_faces(i);
     const IndexArray3& f = F.row(fid);
     size_t id = get_vertex_index(f, outer_vid);
     Index next_vid = f((id+1)%3);
     Index prev_vid = f((id+2)%3);
     check_and_update_outer_edge(next_vid, fid);
     check_and_update_outer_edge(prev_vid, fid);
   }

   v1 = outer_vid;
   v2 = outer_opp_vid;
   A.resize(incident_faces.size());
   std::copy(incident_faces.begin(), incident_faces.end(), A.data());
}

template<
    typename DerivedV,
    typename DerivedF,
    typename DerivedN,
    typename DerivedI,
    typename IndexType
    >
IGL_INLINE void igl::outer_facet(
        const Eigen::PlainObjectBase<DerivedV> & V,
        const Eigen::PlainObjectBase<DerivedF> & F,
        const Eigen::PlainObjectBase<DerivedN> & N,
        const Eigen::PlainObjectBase<DerivedI> & I,
        IndexType & f,
        bool & flipped) {
    // Algorithm:
    //    Find an outer edge.
    //    Find the incident facet with the largest absolute X normal component.
    //    If there is a tie, keep the one with positive X component.
    //    If there is still a tie, pick the face with the larger signed index
    //    (flipped face has negative index).
    typedef typename DerivedV::Scalar Scalar;
    typedef typename DerivedV::Index Index;
    const size_t INVALID = std::numeric_limits<size_t>::max();

    Index v1,v2;
    Eigen::Matrix<Index,Eigen::Dynamic,1> incident_faces;
    outer_edge(V, F, I, v1, v2, incident_faces);
    assert(incident_faces.size() > 0);

    auto generic_fabs = [&](const Scalar& val) -> const Scalar {
        if (val >= 0) return val;
        else return -val;
    };

    Scalar max_nx = 0;
    size_t outer_fid = INVALID;
    const size_t num_incident_faces = incident_faces.size();
    for (size_t i=0; i<num_incident_faces; i++) 
    {
        const auto& fid = incident_faces(i);
        const Scalar nx = N(fid, 0);
        if (outer_fid == INVALID) {
            max_nx = nx;
            outer_fid = fid;
        } else {
            if (generic_fabs(nx) > generic_fabs(max_nx)) {
                max_nx = nx;
                outer_fid = fid;
            } else if (nx == -max_nx && nx > 0) {
                max_nx = nx;
                outer_fid = fid;
            } else if (nx == max_nx) {
                if ((max_nx >= 0 && outer_fid < fid) ||
                    (max_nx <  0 && outer_fid > fid)) {
                    max_nx = nx;
                    outer_fid = fid;
                }
            }
        }
    }

    assert(outer_fid != INVALID);
    f = outer_fid;
    flipped = max_nx < 0;
}


#ifdef IGL_STATIC_LIBRARY
// Explicit template specialization
template void igl::outer_facet<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<long, -1, 1, 0, -1, 1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> > const&, int&, bool&);
template void igl::outer_facet<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 1, -1, -1>, Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 1, -1, -1>, unsigned long>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 1, -1, -1> > const&, unsigned long&, bool&);
template void igl::outer_facet<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, int&, bool&);
template void igl::outer_facet<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<int, -1, 1, 0, -1, 1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, int&, bool&);
#endif