// Copyright (c) 2007-09  INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.0.1/Point_set_processing_3/include/CGAL/mst_orient_normals.h $
// $Id: include/CGAL/mst_orient_normals.h 50cfbde3b84 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s) : Laurent Saboret and Andreas Fabri

#ifndef CGAL_MST_ORIENT_NORMALS_H
#define CGAL_MST_ORIENT_NORMALS_H

#include <CGAL/license/Point_set_processing_3.h>

#include <CGAL/disable_warnings.h>

#include <CGAL/IO/trace.h>
#include <CGAL/Point_set_processing_3/internal/Neighbor_query.h>
#include <CGAL/property_map.h>
#include <CGAL/Index_property_map.h>
#include <CGAL/Memory_sizer.h>
#include <CGAL/assertions.h>
#include <CGAL/use.h>

#include <CGAL/Named_function_parameters.h>
#include <CGAL/boost/graph/named_params_helper.h>

#include <iterator>
#include <list>
#include <climits>
#include <math.h>

#if defined(BOOST_MSVC)
#  pragma warning(push)
#  pragma warning(disable:4172) // Address warning inside boost named parameters
#endif

#include <CGAL/property_map.h>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/dijkstra_shortest_paths.hpp>
#include <boost/graph/prim_minimum_spanning_tree.hpp>

#if defined(BOOST_MSVC)
#  pragma warning(pop)
#endif

namespace CGAL {


// ----------------------------------------------------------------------------
// Private section
// ----------------------------------------------------------------------------
/// \cond SKIP_IN_MANUAL
namespace internal {

/// Generalization of std::distance() to compute the distance between 2 integers
inline std::size_t
distance(std::size_t _First, std::size_t _Last)
{
  // return int difference
  return _Last - _First;
}

// Bring std::distance() to scope
using std::distance;


/// Helper class: Riemannian graph.
///
/// This class is used internally by mst_orient_normals()
/// to encode:
/// - the adjacency relations of vertices in a K-neighboring.
/// - vertices contain the corresponding input point iterator.
/// - the edge weight = edge weight = 1 - | normal1 * normal2 |
///   where normal1 and normal2 are the normal at the edge extremities.

template <typename ForwardIterator> ///< Input point iterator
struct Riemannian_graph_vertex_properties {
    ForwardIterator input_point; ///< Input point
};
template <typename ForwardIterator> ///< Input point iterator
class Riemannian_graph
  : public boost::adjacency_list< boost::vecS, boost::vecS,
                                  boost::undirectedS,
                                  Riemannian_graph_vertex_properties<ForwardIterator>,
                                  boost::property<boost::edge_weight_t, float> >
{
};


/// Helper class: MST graph
///
/// This class is used internally by mst_orient_normals()
/// to encode:
/// - the adjacency relations of vertices in a Minimum Spanning Tree.
/// - vertices contain the corresponding input point iterator
//    and a boolean indicating if the normal is oriented.

template <typename ForwardIterator> ///< Input point iterator
struct MST_graph_vertex_properties {
    ForwardIterator input_point; ///< Input point
    bool is_oriented; ///< Is input point's normal oriented?
};
template <typename ForwardIterator, ///< Input point iterator
          typename NormalMap, ///< property map: value_type of ForwardIterator -> Normal
          typename Kernel ///< Geometric traits class
>
class MST_graph
  : public boost::adjacency_list< boost::vecS, boost::vecS,
                                  boost::directedS,
                                  MST_graph_vertex_properties<ForwardIterator> >
{
public:
    MST_graph(NormalMap normal_map) : m_normal_map(normal_map) {}

// Public data
    const NormalMap m_normal_map;
};

template <typename ForwardIterator>
class Default_constrained_map
{
public:

  typedef boost::readable_property_map_tag     category;
  typedef typename std::iterator_traits<
            ForwardIterator>::value_type       key_type;
  typedef bool                                 value_type;
  typedef value_type                           reference;

private:

  ForwardIterator m_source_point;

public:

  Default_constrained_map () { }
  Default_constrained_map (ForwardIterator source_point)
    : m_source_point (source_point) { }

  /// Free function to access the map elements.
  friend inline
  value_type get(const Default_constrained_map& map, const key_type& p)
  {
    return (p == *map.m_source_point);
  }

};

/// Helper class: Propagate_normal_orientation
///
/// This class is used internally by mst_orient_normals()
/// to propagate the normal orientation, starting from a source point
/// and following the adjacency relations of vertices in a Minimum Spanning Tree.
/// It does not orient normals that are already oriented.
/// It does not propagate the orientation if the angle between 2 normals > angle_max.
///
/// \pre Normals must be unit vectors
/// \pre `0 < angle_max <= PI/2`
///
/// @tparam ForwardIterator iterator over input points.
/// @tparam NormalMap is a model of `ReadWritePropertyMap`.
/// @tparam Kernel Geometric traits class.

template <typename ForwardIterator, ///< Input point iterator
          typename NormalMap, ///< property map: value_type of ForwardIterator -> Normal
          typename Kernel
>
struct Propagate_normal_orientation
  : public boost::base_visitor< Propagate_normal_orientation<ForwardIterator, NormalMap, Kernel> >
{
    typedef internal::MST_graph<ForwardIterator, NormalMap, Kernel> MST_graph;
    typedef typename MST_graph::vertex_descriptor vertex_descriptor;
    typedef boost::on_examine_edge event_filter;

    Propagate_normal_orientation(vertex_descriptor source,
                               double angle_max = CGAL_PI/2.) ///< max angle to propagate the normal orientation (radians)
      : m_source(source), m_angle_max(angle_max)
    {
        // Precondition: 0 < angle_max <= PI/2
        CGAL_precondition(0 < angle_max && angle_max <= CGAL_PI/2.);
    }

    template <class Edge>
    void operator()(Edge& edge, const MST_graph& mst_graph)
    {
        typedef typename boost::property_traits<NormalMap>::reference Vector_ref;

        // Gets source
        vertex_descriptor source_vertex = source(edge, mst_graph);

        // Gets target
        vertex_descriptor target_vertex = target(edge, mst_graph);
        bool& target_normal_is_oriented = ((MST_graph&)mst_graph)[target_vertex].is_oriented;

        // special case if vertex is source vertex (and thus has no related point/normal)
        if (source_vertex == m_source)
        {
          target_normal_is_oriented = true;
          return;
        }

        // Gets source normal
        Vector_ref source_normal = get(mst_graph.m_normal_map, *(mst_graph[source_vertex].input_point) );
        const bool source_normal_is_oriented = mst_graph[source_vertex].is_oriented;

        // Gets target
        Vector_ref target_normal = get( mst_graph.m_normal_map, *(mst_graph[target_vertex].input_point) );

        if ( ! target_normal_is_oriented )
        {
          //             ->                        ->
          // Orients target_normal parallel to source_normal
          double normals_dot = source_normal * target_normal;
          if (normals_dot < 0)
          {
            put( mst_graph.m_normal_map, *(mst_graph[target_vertex].input_point), -target_normal );
          }

          // Is orientation robust?
          target_normal_is_oriented
            = source_normal_is_oriented &&
              (std::abs(normals_dot) >= std::cos(m_angle_max)); // oriented iff angle <= m_angle_max
        }
    }

// Data
// Implementation note: boost::breadth_first_search() makes copies of this object => data must be constant or shared.
private:
    vertex_descriptor m_source;
    const double m_angle_max; ///< max angle to propagate the normal orientation (radians).
};

/// Orients the normal of the point with maximum Z towards +Z axis.
///
/// @tparam ForwardIterator iterator over input points.
/// @tparam PointMap is a model of `ReadablePropertyMap` with a value_type = Point_3<Kernel>.
/// @tparam NormalMap is a model of `ReadWritePropertyMap` with a value_type = Vector_3<Kernel>.
/// @tparam Kernel Geometric traits class.
///
/// @return iterator over the top point.
template <typename ForwardIterator,
          typename PointMap,
          typename NormalMap,
          typename Kernel
>
ForwardIterator
mst_find_source(
    ForwardIterator first,   ///< iterator over the first input point.
    ForwardIterator beyond,  ///< past-the-end iterator over the input points.
    PointMap point_map, ///< property map: value_type of ForwardIterator -> Point_3
    NormalMap normal_map, ///< property map: value_type of ForwardIterator -> Vector_3
    const Kernel& /*kernel*/)    ///< geometric traits.
{
  CGAL_TRACE_STREAM << "  mst_find_source()\n";

    // Input points types
    typedef typename boost::property_traits<NormalMap>::value_type Vector;
    typedef typename boost::property_traits<NormalMap>::reference Vector_ref;

    // Precondition: at least one element in the container
    CGAL_precondition(first != beyond);

    // Find top point
    ForwardIterator top_point = first;
    for (ForwardIterator v = ++first; v != beyond; v++)
    {

      double top_z = get(point_map,*top_point).z(); // top_point's Z coordinate
      double z = get(point_map,*v).z();

      if (top_z < z)
        top_point = v;
    }

    // Orients its normal towards +Z axis
    Vector_ref normal = get(normal_map,*top_point);
    const Vector Z(0, 0, 1);
    if (Z * normal < 0) {
      CGAL_TRACE_STREAM << "  Flip top point normal\n";
      put(normal_map,*top_point, -normal);
    }

    return top_point;
}

/// Iterates over input points and creates Riemannian Graph:
/// - vertices are numbered like the input points index.
/// - vertices contain the corresponding input point iterator.
/// - we add the edge (i, j) if either vertex i is in the k-neighborhood of vertex j,
///   or vertex j is in the k-neighborhood of vertex i.
///
/// \pre Normals must be unit vectors.
/// \pre `k >= 2`
///
/// @tparam ForwardIterator iterator over input points.
/// @tparam IndexMap is a model of `ReadablePropertyMap` with an integral value_type.
/// @tparam PointMap is a model of `ReadablePropertyMap` with a value_type = Point_3<Kernel>.
/// @tparam NormalMap is a model of `ReadWritePropertyMap` with a value_type = Vector_3<Kernel>.
/// @tparam Kernel Geometric traits class.
///
/// @return the Riemannian graph
template <typename PointRange,
          typename PointMap,
          typename NormalMap,
          typename IndexMap,
          typename ConstrainedMap,
          typename Kernel
>
Riemannian_graph<typename PointRange::iterator>
create_riemannian_graph(
    PointRange& points, ///< input points
    PointMap point_map, ///< property map: value_type of ForwardIterator -> Point_3
    NormalMap normal_map, ///< property map: value_type of ForwardIterator -> Vector_3
    IndexMap index_map, ///< property map ForwardIterator -> index
    ConstrainedMap constrained_map, ///< property map ForwardIterator -> bool
    unsigned int k, ///< number of neighbors
    typename Kernel::FT neighbor_radius,
    const Kernel& /*kernel*/) ///< geometric traits.
{
    // Input points types
    typedef typename boost::property_traits<PointMap>::reference Point_ref;
    typedef typename boost::property_traits<NormalMap>::reference Vector_ref;

    // Types for K nearest neighbors search structure
    typedef typename PointRange::iterator ForwardIterator;
    typedef Point_set_processing_3::internal::Neighbor_query<Kernel, PointRange&, PointMap> Neighbor_query;

    // Riemannian_graph types
    typedef internal::Riemannian_graph<ForwardIterator> Riemannian_graph;
    typedef typename boost::property_map<Riemannian_graph, boost::edge_weight_t>::type Riemannian_graph_weight_map;

    // Precondition: at least 2 nearest neighbors
    CGAL_precondition(k >= 2);

    // Number of input points
    const std::size_t num_input_points = points.size();

    std::size_t memory = CGAL::Memory_sizer().virtual_size();
    CGAL_TRACE_STREAM << (memory >> 20) << " Mb allocated\n";
    CGAL_TRACE_STREAM << "  Creates KD-tree\n";

    Neighbor_query neighbor_query (points, point_map);

    memory = CGAL::Memory_sizer().virtual_size();
    CGAL_TRACE_STREAM << (memory >> 20) << " Mb allocated\n";
    CGAL_TRACE_STREAM << "  Creates Riemannian Graph\n";

    // Iterates over input points and creates Riemannian Graph:
    // - vertices are numbered like the input points index.
    // - vertices contain the corresponding input point iterator.
    // - we add the edge (i, j) if either vertex i is in the k-neighborhood of vertex j,
    //   or vertex j is in the k-neighborhood of vertex i.
    Riemannian_graph riemannian_graph;
    //
    // add vertices
    for (ForwardIterator it = points.begin(); it != points.end(); it++)
    {
        typename Riemannian_graph::vertex_descriptor v = add_vertex(riemannian_graph);
        CGAL_assertion(v == get(index_map,it));
        riemannian_graph[v].input_point = it;
    }

    // add source vertex (virtual, does not correspond to a point)
    add_vertex(riemannian_graph);
    std::size_t source_point_index = num_input_points;

    //
    // add edges
    Riemannian_graph_weight_map riemannian_graph_weight_map = get(boost::edge_weight, riemannian_graph);
    for (ForwardIterator it = points.begin(); it != points.end(); it++)
    {
        std::size_t it_index = get(index_map,it);
        Vector_ref it_normal_vector = get(normal_map,*it);

        Point_ref point = get(point_map, *it);
        std::vector<ForwardIterator> neighbor_points;
        neighbor_query.get_iterators (point, k, neighbor_radius, std::back_inserter(neighbor_points));

        for (std::size_t i = 0; i < neighbor_points.size(); ++ i)
        {
            ForwardIterator neighbor = neighbor_points[i];
            std::size_t neighbor_index = get(index_map,neighbor);
            if (neighbor_index > it_index) // undirected graph
            {
                // Add edge
                typename boost::graph_traits<Riemannian_graph>::edge_descriptor e;
                bool inserted;
                boost::tie(e, inserted) = add_edge(vertex(it_index, riemannian_graph),
                                                   vertex(neighbor_index, riemannian_graph),
                                                   riemannian_graph);
                CGAL_assertion(inserted);

                //                               ->        ->
                // Computes edge weight = 1 - | normal1 * normal2 |
                // where normal1 and normal2 are the normal at the edge extremities.

                Vector_ref neighbor_normal_vector = get(normal_map,*neighbor);
                double weight = 1.0 - std::abs(it_normal_vector * neighbor_normal_vector);
                if (weight < 0)
                    weight = 0; // safety check
                riemannian_graph_weight_map[e] = (float)weight;
            }
        }

        // Check if point is source
        if (get(constrained_map, *it))
        {
          typename boost::graph_traits<Riemannian_graph>::edge_descriptor e;
          bool inserted;
          boost::tie(e, inserted) = add_edge(vertex(it_index, riemannian_graph),
                                             vertex(source_point_index, riemannian_graph),
                                             riemannian_graph);
          CGAL_assertion(inserted);

          riemannian_graph_weight_map[e] = 0.;
        }

    }

    return riemannian_graph;
}

/// Computes Minimum Spanning Tree and store it in a Boost graph:
/// - vertices are numbered like the input points index.
/// - vertices contain the corresponding input point iterator.
/// - we add the edge (predecessor[i], i) for each element of the MST.
///
/// \pre Normals must be unit vectors.
///
/// @tparam ForwardIterator iterator over input points.
/// @tparam IndexMap is a model of `ReadablePropertyMap` with an integral value_type.
/// @tparam PointMap is a model of `ReadablePropertyMap` with a value_type = Point_3<Kernel>.
/// @tparam NormalMap is a model of `ReadWritePropertyMap` with a value_type = Vector_3<Kernel>.
/// @tparam Kernel Geometric traits class.
///
/// @return the MST graph.
template <typename ForwardIterator,
          typename PointMap,
          typename NormalMap,
          typename IndexMap,
          typename Kernel
>
MST_graph<ForwardIterator, NormalMap, Kernel>
create_mst_graph(
    ForwardIterator first,  ///< iterator over the first input point.
    ForwardIterator beyond, ///< past-the-end iterator over the input points.
    PointMap point_map, ///< property map: value_type of ForwardIterator -> Point_3
    NormalMap normal_map, ///< property map: value_type of ForwardIterator -> Vector_3
    IndexMap index_map, ///< property map ForwardIterator -> index
    unsigned int k, ///< number of neighbors
    const Kernel& kernel, ///< geometric traits.
    const Riemannian_graph<ForwardIterator>& riemannian_graph) ///< graph connecting each vertex to its knn
{
    // prevents warnings
    CGAL_USE(point_map);
    CGAL_USE(k);
    CGAL_USE(kernel);
    CGAL_USE(index_map);

    // Bring private stuff to scope
    using namespace internal;

    // Riemannian_graph types
    typedef internal::Riemannian_graph<ForwardIterator> Riemannian_graph;
    typedef typename boost::property_map<Riemannian_graph, boost::edge_weight_t>::const_type Riemannian_graph_weight_map;

    // MST_graph types
    typedef internal::MST_graph<ForwardIterator, NormalMap, Kernel> MST_graph;

    // Precondition: at least one element in the container.
    CGAL_precondition(first != beyond);

    // Number of input points
    const std::size_t num_input_points = num_vertices(riemannian_graph) - 1;

    std::size_t memory = CGAL::Memory_sizer().virtual_size();
    CGAL_TRACE_STREAM << (memory >> 20) << " Mb allocated\n";
    CGAL_TRACE_STREAM << "  Calls boost::prim_minimum_spanning_tree()\n";

    // Computes Minimum Spanning Tree.
    std::size_t source_point_index = num_input_points;

    Riemannian_graph_weight_map riemannian_graph_weight_map = get(boost::edge_weight, riemannian_graph);
    typedef std::vector<typename Riemannian_graph::vertex_descriptor> PredecessorMap;
    PredecessorMap predecessor(num_input_points + 1);
    boost::prim_minimum_spanning_tree(riemannian_graph, &predecessor[0],
                                      weight_map( riemannian_graph_weight_map )
                                     .root_vertex( vertex(source_point_index, riemannian_graph) ));

    memory = CGAL::Memory_sizer().virtual_size();
    CGAL_TRACE_STREAM << (memory >> 20) << " Mb allocated\n";
    CGAL_TRACE_STREAM << "  Creates MST Graph\n";

    // Converts predecessor map to a MST graph:
    // - vertices are numbered like the input points index.
    // - vertices contain the corresponding input point iterator.
    // - we add the edge (predecessor[i], i) for each element of the predecessor map.
    MST_graph mst_graph(normal_map);
    //
    // Add vertices. source_point is the unique point marked "oriented".
    for (ForwardIterator it = first; it != beyond; it++)
    {
        // With C++11, the following line triggers a bug in Boost versions
        // 1.56 and 1.57:
        //   https://svn.boost.org/trac/boost/ticket/10382
        typename MST_graph::vertex_descriptor v = add_vertex(mst_graph);
        CGAL_assertion(v == get(index_map,it));
        mst_graph[v].input_point = it;
        mst_graph[v].is_oriented = false;
    }

    typename MST_graph::vertex_descriptor v = add_vertex(mst_graph);
    CGAL_assertion(v == source_point_index);
    mst_graph[v].is_oriented = true;

    // add edges
    for (std::size_t i=0; i < predecessor.size(); i++) // add edges
    {
        if (i != predecessor[i])
        {
            // check that bi-directed graph is useless
            CGAL_assertion(predecessor[predecessor[i]] != i);

            add_edge(vertex(predecessor[i], mst_graph),
                     vertex(i,     mst_graph),
                     mst_graph);
        }
    }

    return mst_graph;
}

} /* namespace internal */
/// \endcond

// ----------------------------------------------------------------------------
// Public section
// ----------------------------------------------------------------------------

/**
   \ingroup PkgPointSetProcessing3Algorithms
   Orients the normals of the range of `points` using the propagation
   of a seed orientation through a minimum spanning tree of the Riemannian graph.
   This method modifies the order of input points so as to pack all successfully oriented points first,
   and returns an iterator over the first point with an unoriented normal (see erase-remove idiom).
   For this reason it should not be called on sorted containers.
   It is based on \cgalCite{cgal:hddms-srup-92}.

   \pre Normals must be unit vectors
   \pre `k >= 2`

   \tparam PointRange is a model of `Range`. The value type of
   its iterator is the key type of the named parameter `point_map`.

   \param points input point range
   \param k number of neighbors.
   \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below

   \cgalNamedParamsBegin
     \cgalParamNBegin{point_map}
       \cgalParamDescription{a property map associating points to the elements of the point set `points`}
       \cgalParamType{a model of `ReadablePropertyMap` whose key type is the value type
                      of the iterator of `PointRange` and whose value type is `geom_traits::Point_3`}
       \cgalParamDefault{`CGAL::Identity_property_map<geom_traits::Point_3>`}
     \cgalParamNEnd

     \cgalParamNBegin{normal_map}
       \cgalParamDescription{a property map associating normals to the elements of the point set `points`}
       \cgalParamType{a model of `WritablePropertyMap` whose key type is the value type
                      of the iterator of `PointRange` and whose value type is `geom_traits::Vector_3`}
     \cgalParamNEnd

     \cgalParamNBegin{neighbor_radius}
       \cgalParamDescription{the spherical neighborhood radius}
       \cgalParamType{floating scalar value}
       \cgalParamDefault{`0` (no limit)}
       \cgalParamExtra{If provided, the neighborhood of a query point is computed with a fixed spherical
                       radius instead of a fixed number of neighbors. In that case, the parameter
                       `k` is used as a limit on the number of points returned by each spherical
                       query (to avoid overly large number of points in high density areas).}
     \cgalParamNEnd

     \cgalParamNBegin{point_is_constrained_map}
       \cgalParamDescription{a property map containing information about points being constrained or not}
       \cgalParamType{a class model of `ReadablePropertyMap` with `PointRange::iterator::value_type`
                      as key type and `bool` as value type}
       \cgalParamDefault{If this parameter is omitted, the highest point (highest Z coordinate)
                         will be used as the unique seed with an upward oriented.}
       \cgalParamExtra{Points with a `true` value will be used as seed points: their normal
                       will be considered as already oriented, it won't be altered
                       and it will be propagated to its neighbors.}
     \cgalParamNEnd

     \cgalParamNBegin{geom_traits}
       \cgalParamDescription{an instance of a geometric traits class}
       \cgalParamType{a model of `Kernel`}
       \cgalParamDefault{a \cgal Kernel deduced from the point type, using `CGAL::Kernel_traits`}
     \cgalParamNEnd
   \cgalNamedParamsEnd

   \return iterator over the first point with an unoriented normal.
*/
template <typename PointRange,
          typename NamedParameters = parameters::Default_named_parameters
>
typename PointRange::iterator
mst_orient_normals(
  PointRange& points,
  unsigned int k,
  const NamedParameters& np = parameters::default_values())
{
    using parameters::choose_parameter;
    using parameters::get_parameter;
    using parameters::is_default_parameter;

    CGAL_TRACE_STREAM << "Calls mst_orient_normals()\n";

    typedef Point_set_processing_3_np_helper<PointRange, NamedParameters> NP_helper;
    typedef typename NP_helper::Point_map PointMap;
    typedef typename NP_helper::Normal_map NormalMap;
    typedef typename NP_helper::Geom_traits Kernel;
    typedef typename Point_set_processing_3::GetIsConstrainedMap<PointRange, NamedParameters>::type ConstrainedMap;

    CGAL_assertion_msg(NP_helper::has_normal_map(points, np), "Error: no normal map");

    PointMap point_map = NP_helper::get_point_map(points, np);
    NormalMap normal_map = NP_helper::get_normal_map(points, np);
    typename Kernel::FT neighbor_radius = choose_parameter(get_parameter(np, internal_np::neighbor_radius),
                                                           typename Kernel::FT(0));
    ConstrainedMap constrained_map = choose_parameter<ConstrainedMap>(get_parameter(np, internal_np::point_is_constrained));
    Kernel kernel;

  // Bring private stuff to scope
    using namespace internal;

    // Input points types
    typedef typename std::iterator_traits<typename PointRange::iterator>::value_type Enriched_point; // actual type of input points
    // Property map typename PointRange::iterator -> index
    typedef Index_property_map<typename PointRange::iterator> IndexMap;

    // Riemannian_graph types
    typedef Riemannian_graph<typename PointRange::iterator> Riemannian_graph;

    // MST_graph types
    typedef MST_graph<typename PointRange::iterator, NormalMap, Kernel> MST_graph;

    // Precondition: at least one element in the container.
    CGAL_precondition(points.begin() != points.end());

    // Precondition: at least 2 nearest neighbors
    CGAL_precondition(k >= 2);

    std::size_t memory = CGAL::Memory_sizer().virtual_size();
    CGAL_TRACE_STREAM << (memory >> 20) << " Mb allocated\n";
    CGAL_TRACE_STREAM << "  Create Index_property_map\n";

    // Create a property map Iterator -> index.
    // - if typename PointRange::iterator is a random access iterator (typically vector and deque),
    // get() just calls std::distance() and is very efficient;
    // - else, the property map allocates a std::map to store indices
    // and get() requires a lookup in the map.
    IndexMap index_map(points.begin(), points.end());

    // Iterates over input points and creates Riemannian Graph:
    // - vertices are numbered like the input points index.
    // - vertices are empty.
    // - we add the edge (i, j) if either vertex i is in the k-neighborhood of vertex j,
    //   or vertex j is in the k-neighborhood of vertex i.
    Riemannian_graph riemannian_graph;

    if (is_default_parameter<NamedParameters, internal_np::point_is_constrained_t>::value)
      riemannian_graph = create_riemannian_graph(points,
                                                 point_map, normal_map, index_map,
                                                 Default_constrained_map<typename PointRange::iterator>
                                                 (mst_find_source(points.begin(), points.end(),
                                                                  point_map, normal_map,
                                                                  kernel)),
                                                 k,
                                                 neighbor_radius,
                                                 kernel);
    else
      riemannian_graph = create_riemannian_graph(points,
                                                 point_map, normal_map, index_map,
                                                 constrained_map,
                                                 k,
                                                 neighbor_radius,
                                                 kernel);

    // Creates a Minimum Spanning Tree starting at source_point
    MST_graph mst_graph = create_mst_graph(points.begin(), points.end(),
                                           point_map, normal_map, index_map,
                                           k,
                                           kernel,
                                           riemannian_graph);

    memory = CGAL::Memory_sizer().virtual_size();
    CGAL_TRACE_STREAM << (memory >> 20) << " Mb allocated\n";
    CGAL_TRACE_STREAM << "  Calls boost::breadth_first_search()\n";

    const std::size_t num_input_points = distance(points.begin(), points.end());
    std::size_t source_point_index = num_input_points;

    // Traverse the point set along the MST to propagate source_point's orientation
    Propagate_normal_orientation<typename PointRange::iterator, NormalMap, Kernel> orienter(source_point_index);

    boost::breadth_first_search(mst_graph,
                                vertex(source_point_index, mst_graph), // source
                                visitor(boost::make_bfs_visitor(orienter)));

    // Copy points with robust normal orientation to oriented_points[], the others to unoriented_points[].
    std::deque<Enriched_point> oriented_points, unoriented_points;
    for (typename PointRange::iterator it = points.begin(); it != points.end(); it++)
    {
        std::size_t it_index = get(index_map,it);
        typename MST_graph::vertex_descriptor v = vertex(it_index, mst_graph);
        if (mst_graph[v].is_oriented)
          oriented_points.push_back(*it);
        else
          unoriented_points.push_back(*it);
    }

    // Replaces [points.begin(), points.end()) range by the content of oriented_points[], then unoriented_points[].
    typename PointRange::iterator first_unoriented_point =
      std::copy(oriented_points.begin(), oriented_points.end(), points.begin());
    std::copy(unoriented_points.begin(), unoriented_points.end(), first_unoriented_point);

    // At this stage, we have typically 0 unoriented normals if k is large enough
    CGAL_TRACE_STREAM << "  => " << unoriented_points.size() << " normals are unoriented\n";

    memory = CGAL::Memory_sizer().virtual_size();
    CGAL_TRACE_STREAM << (memory >> 20) << " Mb allocated\n";
    CGAL_TRACE_STREAM << "End of mst_orient_normals()\n";

    return first_unoriented_point;
}

} //namespace CGAL

#include <CGAL/enable_warnings.h>

#endif // CGAL_MST_ORIENT_NORMALS_H

