// Copyright (c) 2017 GeometryFactory Sarl (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
// You can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL: https://github.com/CGAL/cgal/blob/releases/CGAL-4.14.3/Classification/include/CGAL/Classification/Local_eigen_analysis.h $
// $Id: Local_eigen_analysis.h 267b1f4 2018-06-28T11:13:35+02:00 Simon Giraudot
// SPDX-License-Identifier: GPL-3.0+
//
// Author(s)     : Simon Giraudot

#ifndef CGAL_CLASSIFICATION_LOCAL_EIGEN_ANALYSIS_H
#define CGAL_CLASSIFICATION_LOCAL_EIGEN_ANALYSIS_H

#include <CGAL/license/Classification.h>

#include <vector>

#include <CGAL/Classification/compressed_float.h>
#include <CGAL/Search_traits_3.h>
#include <CGAL/Fuzzy_sphere.h>
#include <CGAL/Orthogonal_k_neighbor_search.h>
#include <CGAL/Default_diagonalize_traits.h>
#include <CGAL/centroid.h>
#include <CGAL/squared_distance_3.h>
#include <CGAL/array.h>
#include <CGAL/PCA_util.h>
#include <CGAL/boost/graph/properties.h>

#include <boost/graph/graph_traits.hpp>
#include <boost/make_shared.hpp>

#ifdef CGAL_LINKED_WITH_TBB
#include <tbb/parallel_for.h>
#include <tbb/blocked_range.h>
#include <tbb/scalable_allocator.h>
#include <tbb/mutex.h>
#endif // CGAL_LINKED_WITH_TBB

namespace CGAL {

namespace Classification {

  /*!
    \ingroup PkgClassificationDataStructures

    \brief Class that precomputes and stores the eigenvectors and
    eigenvalues of the covariance matrices of all points of a point
    set using a local neighborhood.

    This class can be used to compute eigen features (see
    \ref PkgClassificationFeatures) and to estimate local normal vectors
    and tangent planes.

  */
class Local_eigen_analysis
{
public:
  typedef CGAL::cpp11::array<float, 3> Eigenvalues; ///< Eigenvalues (sorted in ascending order)
  
private:

#ifdef CGAL_LINKED_WITH_TBB
  template <typename PointRange, typename PointMap, typename NeighborQuery, typename DiagonalizeTraits>
  class Compute_eigen_values
  {
    Local_eigen_analysis& m_eigen;
    const PointRange& m_input;
    PointMap m_point_map;
    const NeighborQuery& m_neighbor_query;
    float& m_mean_range;
    tbb::mutex& m_mutex;
    
  public:
    
    Compute_eigen_values (Local_eigen_analysis& eigen,
                          const PointRange& input,
                          PointMap point_map,
                          const NeighborQuery& neighbor_query,
                          float& mean_range,
                          tbb::mutex& mutex)
      : m_eigen (eigen), m_input (input), m_point_map (point_map),
        m_neighbor_query (neighbor_query), m_mean_range (mean_range), m_mutex (mutex)
    { }
    
    void operator()(const tbb::blocked_range<std::size_t>& r) const
    {
      std::vector<std::size_t> neighbors;
      for (std::size_t i = r.begin(); i != r.end(); ++ i)
      {
        neighbors.clear();
        m_neighbor_query (get(m_point_map, *(m_input.begin()+i)), std::back_inserter (neighbors));

        std::vector<typename PointMap::value_type> neighbor_points;
        neighbor_points.reserve(neighbors.size());
        for (std::size_t j = 0; j < neighbors.size(); ++ j)
          neighbor_points.push_back (get(m_point_map, *(m_input.begin()+neighbors[j])));

        m_mutex.lock();
        m_mean_range += float(CGAL::sqrt
                              (CGAL::squared_distance (get(m_point_map, *(m_input.begin() + i)),
                                                       get(m_point_map, *(m_input.begin() + neighbors.back())))));
        m_mutex.unlock();
          
        m_eigen.compute<typename PointMap::value_type,
                        DiagonalizeTraits> (i, get(m_point_map, *(m_input.begin()+i)), neighbor_points);
      }
    }

  };

  template <typename FaceListGraph, typename NeighborQuery, typename DiagonalizeTraits>
  class Compute_eigen_values_graph
  {
    typedef typename boost::graph_traits<FaceListGraph>::face_descriptor face_descriptor;
    typedef typename boost::property_map<FaceListGraph, CGAL::face_index_t>::type::value_type face_index;
    typedef typename boost::graph_traits<FaceListGraph>::face_iterator face_iterator;
    
    Local_eigen_analysis& m_eigen;
    const FaceListGraph& m_input;
    const NeighborQuery& m_neighbor_query;
    float& m_mean_range;
    tbb::mutex& m_mutex;
    
  public:
    
    Compute_eigen_values_graph (Local_eigen_analysis& eigen,
                                const FaceListGraph& input,
                                const NeighborQuery& neighbor_query,
                                float& mean_range,
                                tbb::mutex& mutex)
      : m_eigen (eigen), m_input (input),
        m_neighbor_query (neighbor_query), m_mean_range (mean_range), m_mutex (mutex)
    { }
    
    void operator()(const tbb::blocked_range<std::size_t>& r) const
    {
      face_iterator begin = faces(m_input).first;
      for (std::size_t i = r.begin(); i != r.end(); ++ i)
      {
        face_descriptor fd = *(begin + i);
        std::vector<face_index> neighbors;
        m_neighbor_query (fd, std::back_inserter (neighbors));

        m_mutex.lock();
        m_mean_range += m_eigen.face_radius(fd, m_input);
        m_mutex.unlock();
        
        m_eigen.compute_triangles<FaceListGraph, DiagonalizeTraits>
          (m_input, fd, neighbors);
      }
    }

  };
#endif
  
  template <typename ClusterRange, typename DiagonalizeTraits>
  class Compute_clusters_eigen_values
  {
    Local_eigen_analysis& m_eigen;
    const ClusterRange& m_input;
    
  public:
    
    Compute_clusters_eigen_values (Local_eigen_analysis& eigen,
                                   const ClusterRange& input)
      : m_eigen (eigen), m_input (input)
    { }

#ifdef CGAL_LINKED_WITH_TBB
    void operator()(const tbb::blocked_range<std::size_t>& r) const
    {
      for (std::size_t i = r.begin(); i != r.end(); ++ i)
        apply (i);
    }
#endif

    inline void apply (std::size_t i) const
    {
      typedef typename ClusterRange::value_type Cluster;
      typedef typename Cluster::Item Item;
      const Cluster& cluster = m_input[i];

      std::vector<typename ClusterRange::value_type::Item> points;
      for (std::size_t j = 0; j < cluster.size(); ++ j)
        points.push_back (cluster[j]);

      m_eigen.compute<Item, DiagonalizeTraits> (i, Item(0.,0.,0.), points);
    }

  };

  typedef CGAL::cpp11::array<float, 3> float3;
  typedef CGAL::cpp11::array<float, 2> float2;
  typedef CGAL::cpp11::array<compressed_float, 2> cfloat2;
  
  struct Content
  {
    std::vector<cfloat2> eigenvalues;
    std::vector<float3> centroids;
    std::vector<float2> smallest_eigenvectors;
    float mean_range;
  };

  boost::shared_ptr<Content> m_content; // To avoid copies with named constructors
  
public:

  /// \cond SKIP_IN_MANUAL
  Local_eigen_analysis () { }
  /// \endcond

  /// \name Named Constructors
  /// @{

  /*! 
    \brief Computes the local eigen analysis of an input point set
    based on a local neighborhood.

    \tparam PointRange model of `ConstRange`. Its iterator type is
    `RandomAccessIterator` and its value type is the key type of
    `PointMap`.
    \tparam PointMap model of `ReadablePropertyMap` whose key
    type is the value type of the iterator of `PointRange` and value type
    is `CGAL::Point_3`.
    \tparam NeighborQuery model of `NeighborQuery`
    \tparam ConcurrencyTag enables sequential versus parallel
    algorithm. Possible values are `Parallel_tag` (default value is %CGAL
    is linked with TBB) or `Sequential_tag` (default value otherwise).
    \tparam DiagonalizeTraits model of `DiagonalizeTraits` used for
    matrix diagonalization. It can be omitted if Eigen 3 (or greater)
    is available and `CGAL_EIGEN3_ENABLED` is defined. In that case,
    an overload using `Eigen_diagonalize_traits` is provided.

    \param input point range.
    \param point_map property map to access the input points.
    \param neighbor_query object used to access neighborhoods of points.
  */
  template <typename PointRange,
            typename PointMap,
            typename NeighborQuery,
#if defined(DOXYGEN_RUNNING)
            typename ConcurrencyTag,
#elif defined(CGAL_LINKED_WITH_TBB)
            typename ConcurrencyTag = CGAL::Parallel_tag,
#else
            typename ConcurrencyTag = CGAL::Sequential_tag,
#endif
#if defined(DOXYGEN_RUNNING)
            typename DiagonalizeTraits>
#else
            typename DiagonalizeTraits = CGAL::Default_diagonalize_traits<float, 3> >
#endif
  static Local_eigen_analysis create_from_point_set(const PointRange& input,
                                                    PointMap point_map,
                                                    const NeighborQuery& neighbor_query,
                                                    const ConcurrencyTag& = ConcurrencyTag(),
                                                    const DiagonalizeTraits& = DiagonalizeTraits())
  {
    Local_eigen_analysis out;
    out.m_content = boost::make_shared<Content>();
    out.m_content->eigenvalues.resize (input.size());
    out.m_content->centroids.resize (input.size());
    out.m_content->smallest_eigenvectors.resize (input.size());
    
    out.m_content->mean_range = 0.;
      
#ifndef CGAL_LINKED_WITH_TBB
    CGAL_static_assertion_msg (!(boost::is_convertible<ConcurrencyTag, Parallel_tag>::value),
                               "Parallel_tag is enabled but TBB is unavailable.");
#else
    if (boost::is_convertible<ConcurrencyTag,Parallel_tag>::value)
    {
      tbb::mutex mutex;
      Compute_eigen_values<PointRange, PointMap, NeighborQuery, DiagonalizeTraits>
        f(out, input, point_map, neighbor_query, out.m_content->mean_range, mutex);
      tbb::parallel_for(tbb::blocked_range<size_t>(0, input.size ()), f);
    }
    else
#endif
    {
      for (std::size_t i = 0; i < input.size(); i++)
      {
        std::vector<std::size_t> neighbors;
        neighbor_query (get(point_map, *(input.begin()+i)), std::back_inserter (neighbors));

        std::vector<typename PointMap::value_type> neighbor_points;
        for (std::size_t j = 0; j < neighbors.size(); ++ j)
          neighbor_points.push_back (get(point_map, *(input.begin()+neighbors[j])));

        out.m_content->mean_range += float(CGAL::sqrt (CGAL::squared_distance
                                          (get(point_map, *(input.begin() + i)),
                                           get(point_map, *(input.begin() + neighbors.back())))));
        
        out.compute<typename PointMap::value_type, DiagonalizeTraits>
          (i, get(point_map, *(input.begin()+i)), neighbor_points);
      }
    }
    out.m_content->mean_range /= input.size();

    return out;
  }
  
  
  /*! 
    \brief Computes the local eigen analysis of an input face graph
    based on a local neighborhood.

    \tparam FaceListGraph model of `FaceListGraph`. 
    \tparam NeighborQuery model of `NeighborQuery`
    \tparam ConcurrencyTag enables sequential versus parallel
    algorithm. Possible values are `Parallel_tag` (default value is %CGAL
    is linked with TBB) or `Sequential_tag` (default value otherwise).
    \tparam DiagonalizeTraits model of `DiagonalizeTraits` used for
    matrix diagonalization. It can be omitted: if Eigen 3 (or greater)
    is available and `CGAL_EIGEN3_ENABLED` is defined then an overload
    using `Eigen_diagonalize_traits` is provided. Otherwise, the
    internal implementation `Diagonalize_traits` is used.

    \param input face graph.
    \param neighbor_query object used to access neighborhoods of points.
  */
  template <typename FaceListGraph,
            typename NeighborQuery,
#if defined(DOXYGEN_RUNNING)
            typename ConcurrencyTag,
#elif defined(CGAL_LINKED_WITH_TBB)
            typename ConcurrencyTag = CGAL::Parallel_tag,
#else
            typename ConcurrencyTag = CGAL::Sequential_tag,
#endif
#if defined(DOXYGEN_RUNNING)
            typename DiagonalizeTraits>
#else
            typename DiagonalizeTraits = CGAL::Default_diagonalize_traits<float, 3> >
#endif
  static Local_eigen_analysis create_from_face_graph (const FaceListGraph& input,
                                                      const NeighborQuery& neighbor_query,
                                                      const ConcurrencyTag& = ConcurrencyTag(),
                                                      const DiagonalizeTraits& = DiagonalizeTraits())
  {
    typedef typename boost::graph_traits<FaceListGraph>::face_descriptor face_descriptor;
    typedef typename boost::graph_traits<FaceListGraph>::face_iterator face_iterator;
    typedef typename CGAL::Iterator_range<face_iterator> Face_range;
    typedef typename boost::property_map<FaceListGraph, CGAL::face_index_t>::type::value_type face_index;

    Local_eigen_analysis out;
    out.m_content = boost::make_shared<Content>();
    
    Face_range range (faces(input));

    out.m_content->eigenvalues.resize (range.size());
    out.m_content->centroids.resize (range.size());
    out.m_content->smallest_eigenvectors.resize (range.size());
    
    out.m_content->mean_range = 0.;
      
#ifndef CGAL_LINKED_WITH_TBB
    CGAL_static_assertion_msg (!(boost::is_convertible<ConcurrencyTag, Parallel_tag>::value),
                               "Parallel_tag is enabled but TBB is unavailable.");
#else
    if (boost::is_convertible<ConcurrencyTag,Parallel_tag>::value)
    {
      tbb::mutex mutex;
      Compute_eigen_values_graph<FaceListGraph, NeighborQuery, DiagonalizeTraits>
        f(out, input, neighbor_query, out.m_content->mean_range, mutex);

      tbb::parallel_for(tbb::blocked_range<std::size_t>(0, range.size()), f);
    }
    else
#endif
    {
      BOOST_FOREACH(face_descriptor fd, range)
      {
        std::vector<face_index> neighbors;
        neighbor_query (fd, std::back_inserter (neighbors));

        out.m_content->mean_range += out.face_radius(fd, input);
      
        out.compute_triangles<FaceListGraph, DiagonalizeTraits>
          (input, fd, neighbors);

      }
    }
    
    out.m_content->mean_range /= range.size();
    return out;
  }
  
  /*! 
    \brief Computes the local eigen analysis of an input set of point
    clusters based on a local neighborhood.

    \tparam ClusterRange model of `ConstRange`. Its iterator type is
    `RandomAccessIterator` and its value type is the key type of
    `PointMap`.
    \tparam ConcurrencyTag enables sequential versus parallel
    algorithm. Possible values are `Parallel_tag` (default value is %CGAL
    is linked with TBB) or `Sequential_tag` (default value otherwise).
    \tparam DiagonalizeTraits model of `DiagonalizeTraits` used for
    matrix diagonalization. It can be omitted: if Eigen 3 (or greater)
    is available and `CGAL_EIGEN3_ENABLED` is defined then an overload
    using `Eigen_diagonalize_traits` is provided. Otherwise, the
    internal implementation `Diagonalize_traits` is used.

    \param input cluster range.
  */
  template <typename ClusterRange,
#if defined(DOXYGEN_RUNNING)
            typename ConcurrencyTag,
#elif defined(CGAL_LINKED_WITH_TBB)
            typename ConcurrencyTag = CGAL::Parallel_tag,
#else
            typename ConcurrencyTag = CGAL::Sequential_tag,
#endif
#if defined(DOXYGEN_RUNNING)
            typename DiagonalizeTraits>
#else
            typename DiagonalizeTraits = CGAL::Default_diagonalize_traits<float, 3> >
#endif
  static Local_eigen_analysis create_from_point_clusters (const ClusterRange& input,
                                                          const ConcurrencyTag& = ConcurrencyTag(),
                                                          const DiagonalizeTraits& = DiagonalizeTraits())
  {
    Local_eigen_analysis out;
    out.m_content = boost::make_shared<Content>();
    
    out.m_content->eigenvalues.resize (input.size());
    out.m_content->centroids.resize (input.size());
    out.m_content->smallest_eigenvectors.resize (input.size());
    
    out.m_content->mean_range = 0.;

    Compute_clusters_eigen_values<ClusterRange, DiagonalizeTraits>
    f(out, input);

    
#ifndef CGAL_LINKED_WITH_TBB
    CGAL_static_assertion_msg (!(boost::is_convertible<ConcurrencyTag, Parallel_tag>::value),
                               "Parallel_tag is enabled but TBB is unavailable.");
#else
    if (boost::is_convertible<ConcurrencyTag,Parallel_tag>::value)
    {
      tbb::parallel_for(tbb::blocked_range<size_t>(0, input.size ()), f);
    }
    else
#endif
    {
      for (std::size_t i = 0; i < input.size(); ++ i)
        f.apply (i);
    }
    return out;
  }


  /// @}

  /// \name Analysis
  /// @{

  /*!
    \brief Returns the estimated unoriented normal vector of the point at position `index`.
    \tparam GeomTraits model of \cgal Kernel.
  */
  template <typename GeomTraits>
  typename GeomTraits::Vector_3 normal_vector (std::size_t index) const
  {
    return typename GeomTraits::Vector_3(double(m_content->smallest_eigenvectors[index][0]),
                                         double(m_content->smallest_eigenvectors[index][1]),
                                         double(1. - (m_content->smallest_eigenvectors[index][0] +
                                                      m_content->smallest_eigenvectors[index][1])));
  }

  /*!
    \brief Returns the estimated local tangent plane of the point at position `index`.
    \tparam GeomTraits model of \cgal Kernel.
  */
  template <typename GeomTraits>
  typename GeomTraits::Plane_3 plane (std::size_t index) const
  {
    return typename GeomTraits::Plane_3
      (typename GeomTraits::Point_3 (double(m_content->centroids[index][0]),
                                      double(m_content->centroids[index][1]),
                                      double(m_content->centroids[index][2])),
       normal_vector<GeomTraits>(index));
  }

  /*!
    \brief Returns the normalized eigenvalues of the point at position `index`.
  */
  Eigenvalues eigenvalue (std::size_t index) const
  {
    const cfloat2& uc = m_content->eigenvalues[index];
    Eigenvalues out;
    out[1] = decompress_float(uc[0]);
    out[2] = decompress_float(uc[1]);
    out[0] = 1.f - (out[1] + out[2]);
    return out;
  }

  /// @}

  /// \cond SKIP_IN_MANUAL
  float mean_range() const { return m_content->mean_range; }
  /// \endcond

private:

  template <typename FaceListGraph>
  float face_radius (typename boost::graph_traits<FaceListGraph>::face_descriptor& fd,
                     const FaceListGraph& g)
  {
    typedef typename boost::graph_traits<FaceListGraph>::halfedge_descriptor halfedge_descriptor;
    
    float out = 0.f;
    BOOST_FOREACH(halfedge_descriptor hd, halfedges_around_face(halfedge(fd, g), g))
    {
      out = (std::max)(out,
                       float(CGAL::squared_distance (get(get (CGAL::vertex_point, g), source(hd,g)),
                                                     get(get (CGAL::vertex_point, g), target(hd,g)))));
    }
    return out;
  }

  template <typename Point, typename DiagonalizeTraits>
  void compute (std::size_t index, const Point& query, std::vector<Point>& neighbor_points)
  {
    typedef typename Kernel_traits<Point>::Kernel::Vector_3 Vector;
      
    if (neighbor_points.size() == 0)
    {
      m_content->eigenvalues[index] = make_array (compressed_float(0), compressed_float(0));
      m_content->centroids[index] = make_array(float(query.x()), float(query.y()), float(query.z()) );
      m_content->smallest_eigenvectors[index] = make_array( 0.f, 0.f );
      return;
    }

    Point centroid = CGAL::centroid (neighbor_points.begin(), neighbor_points.end());
    m_content->centroids[index] = make_array( float(centroid.x()), float(centroid.y()), float(centroid.z()) );
    
    CGAL::cpp11::array<float, 6> covariance = make_array( 0.f, 0.f, 0.f, 0.f, 0.f, 0.f );
      
    for (std::size_t i = 0; i < neighbor_points.size(); ++ i)
    {
      Vector d = neighbor_points[i] - centroid;
      covariance[0] += float(d.x () * d.x ());
      covariance[1] += float(d.x () * d.y ());
      covariance[2] += float(d.x () * d.z ());
      covariance[3] += float(d.y () * d.y ());
      covariance[4] += float(d.y () * d.z ());
      covariance[5] += float(d.z () * d.z ());
    }

    CGAL::cpp11::array<float, 3> evalues = make_array( 0.f, 0.f, 0.f );
    CGAL::cpp11::array<float, 9> evectors = make_array( 0.f, 0.f, 0.f,
                                               0.f, 0.f, 0.f,
                                               0.f, 0.f, 0.f );

    DiagonalizeTraits::diagonalize_selfadjoint_covariance_matrix
      (covariance, evalues, evectors);

    // Normalize
    float sum = evalues[0] + evalues[1] + evalues[2];
    if (sum > 0.f)
      for (std::size_t i = 0; i < 3; ++ i)
        evalues[i] = evalues[i] / sum;
    
    m_content->eigenvalues[index] = make_array(compress_float (evalues[1]),
                                               compress_float (evalues[2]));
    
    sum = evectors[0] + evectors[1] + evectors[2];
    if (sum > 0.f)
      for (std::size_t i = 0; i < 3; ++ i)
        evectors[i] = evectors[i] / sum;
    m_content->smallest_eigenvectors[index] = make_array( float(evectors[0]), float(evectors[1]) );
  }

  template <typename FaceListGraph, typename DiagonalizeTraits>
  void compute_triangles (const FaceListGraph& g,
                          typename boost::graph_traits<FaceListGraph>::face_descriptor& query,
                          std::vector<typename boost::property_map<FaceListGraph, CGAL::face_index_t>::type::value_type>& neighbor_faces)
  {
    typedef typename boost::property_map<FaceListGraph, boost::vertex_point_t>::type::value_type Point;
    typedef typename Kernel_traits<Point>::Kernel Kernel;
    typedef typename Kernel::Triangle_3 Triangle;
        
    typedef typename boost::graph_traits<FaceListGraph>::face_descriptor face_descriptor;
    typedef typename boost::graph_traits<FaceListGraph>::face_iterator face_iterator;

    if (neighbor_faces.size() == 0)
    {
      m_content->eigenvalues[get(get(CGAL::face_index,g), query)]
        = make_array(compressed_float(0), compressed_float(0));

      CGAL::cpp11::array<Triangle,1> tr
        = {{ Triangle (get(get (CGAL::vertex_point, g), target(halfedge(query, g), g)),
                       get(get (CGAL::vertex_point, g), target(next(halfedge(query, g), g), g)),
                       get(get (CGAL::vertex_point, g), target(next(next(halfedge(query, g), g), g), g))) }};
      Point c = CGAL::centroid(tr.begin(),
                               tr.end(), Kernel(), CGAL::Dimension_tag<2>());

      m_content->centroids[get(get(CGAL::face_index,g), query)] = {{ float(c.x()), float(c.y()), float(c.z()) }};
      
      m_content->smallest_eigenvectors[get(get(CGAL::face_index,g), query)] = {{ 0.f, 0.f }};
      return;
    }

    std::vector<Triangle> triangles;
    triangles.reserve(neighbor_faces.size());

    face_iterator begin = faces(g).first;
    for (std::size_t i = 0; i < neighbor_faces.size(); ++ i)
    {
      face_descriptor fd = *(begin + std::size_t(neighbor_faces[i]));
      triangles.push_back
        (Triangle (get(get (CGAL::vertex_point, g), target(halfedge(fd, g), g)),
                   get(get (CGAL::vertex_point, g), target(next(halfedge(fd, g), g), g)),
                   get(get (CGAL::vertex_point, g), target(next(next(halfedge(fd, g), g), g), g))));
    }

    CGAL::cpp11::array<float, 6> covariance = {{ 0.f, 0.f, 0.f, 0.f, 0.f, 0.f }};
    Point c = CGAL::centroid(triangles.begin(),
                             triangles.end(), Kernel(), CGAL::Dimension_tag<2>());

    CGAL::internal::assemble_covariance_matrix_3 (triangles.begin(), triangles.end(), covariance,
                                                  c, Kernel(), (Triangle*)NULL, CGAL::Dimension_tag<2>(),
                                                  DiagonalizeTraits());
      
    m_content->centroids[get(get(CGAL::face_index,g), query)] = {{ float(c.x()), float(c.y()), float(c.z()) }};
    
    CGAL::cpp11::array<float, 3> evalues = {{ 0.f, 0.f, 0.f }};
    CGAL::cpp11::array<float, 9> evectors = {{ 0.f, 0.f, 0.f,
                                               0.f, 0.f, 0.f,
                                               0.f, 0.f, 0.f }};

    DiagonalizeTraits::diagonalize_selfadjoint_covariance_matrix
      (covariance, evalues, evectors);

    // Normalize
    float sum = evalues[0] + evalues[1] + evalues[2];
    if (sum > 0.f)
      for (std::size_t i = 0; i < 3; ++ i)
        evalues[i] = evalues[i] / sum;

    m_content->eigenvalues[get(get(CGAL::face_index,g), query)]
      = make_array(compress_float (evalues[1]),
                   compress_float (evalues[2]));
    
    sum = evectors[0] + evectors[1] + evectors[2];
    if (sum > 0.f)
      for (std::size_t i = 0; i < 3; ++ i)
        evectors[i] = evectors[i] / sum;
    m_content->smallest_eigenvectors[get(get(CGAL::face_index,g), query)] = {{ float(evectors[0]), float(evectors[1]), }};
  }
  
};
  

}
  
}


#endif // CGAL_CLASSIFICATION_LOCAL_EIGEN_ANALYSIS_H
