#include <Rcpp.h>
// Copyright (c) 2008,2011  INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v5.6.1/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/AABB_tree_with_join.h $
// $Id: AABB_tree_with_join.h 98e4718 2021-08-26T11:33:39+02:00 Sébastien Loriot
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Camille Wormser, Pierre Alliez, Stephane Tayeb

#ifndef CGAL_AABB_TREE_WITH_JOIN_H
#define CGAL_AABB_TREE_WITH_JOIN_H

#include <CGAL/license/Minkowski_sum_2.h>


#include <vector>
#include <iterator>
#include <CGAL/Minkowski_sum_2/AABB_traversal_traits_with_join.h>
#include <CGAL/Minkowski_sum_2/AABB_node_with_join.h>
#include <CGAL/AABB_tree/internal/AABB_search_tree.h>
#include <CGAL/AABB_tree/internal/Has_nested_type_Shared_data.h>
#include <CGAL/AABB_tree/internal/Primitive_helper.h>
#include <boost/optional.hpp>

#ifdef CGAL_HAS_THREADS
#include <CGAL/mutex.h>
#endif

/// \file AABB_tree.h

namespace CGAL {

/// \addtogroup PkgAABBTreeRef
/// @{

  /**
   * Class AABB_tree is a static data structure for efficient
   * intersection and distance computations in 3D. It builds a
   * hierarchy of axis-aligned bounding boxes (an AABB tree) from a set
   * of 3D geometric objects, and can receive intersection and distance
   * queries, provided that the corresponding predicates are
   * implemented in the traits class AABBTraits.
   * An instance of the class `AABBTraits` is internally stored.
   *
   * \sa `AABBTraits`
   * \sa `AABBPrimitive`
   *
   */
  template <typename AABBTraits>
  class AABB_tree_with_join
  {
  private:
    // internal KD-tree used to accelerate the distance queries
    typedef AABB_search_tree<AABBTraits> Search_tree;

    // type of the primitives container
    typedef std::vector<typename AABBTraits::Primitive> Primitives;

  public:
    typedef AABBTraits AABB_traits;

    /// \name Types
    ///@{

    /// Number type returned by the distance queries.
    typedef typename AABBTraits::FT FT;


    /// Type of 3D point.
    typedef typename AABBTraits::Point_3 Point;

    /// Type of input primitive.
    typedef typename AABBTraits::Primitive Primitive;
    /// Identifier for a primitive in the tree.
    typedef typename Primitive::Id Primitive_id;
    /// Unsigned integral size type.
    typedef typename Primitives::size_type size_type;
    /// Type of bounding box.
    typedef typename AABBTraits::Bounding_box Bounding_box;
    ///
    typedef typename AABBTraits::Point_and_primitive_id Point_and_primitive_id;
    typedef typename AABBTraits::Object_and_primitive_id Object_and_primitive_id;

    /*!
    An alias to `AABBTraits::Intersection_and_primitive_id<Query>`
    */
    #ifdef DOXYGEN_RUNNING
    template<typename Query>
    using Intersection_and_primitive_id = AABBTraits::Intersection_and_primitive_id<Query>;
    #else
    template<typename Query>
    struct Intersection_and_primitive_id {
      typedef typename AABBTraits::template Intersection_and_primitive_id<Query>::Type Type;
    };
    #endif


    ///@}

  public:
    /// \name Creation
    ///@{

    /// Constructs an empty tree, and initializes the internally stored traits
    /// class using `traits`.
    AABB_tree_with_join(const AABBTraits& traits = AABBTraits());

    /**
     * @brief Builds the datastructure from a sequence of primitives.
     * @param first iterator over first primitive to insert
     * @param beyond past-the-end iterator
     *
     * It is equivalent to constructing an empty tree and calling `insert(first,last,t...)`.
     * The tree stays empty if the memory allocation is not successful.
     */
    template<typename InputIterator,typename ... T>
    AABB_tree_with_join(InputIterator first, InputIterator beyond,T...);

    ///@}

    /// \name Operations
    ///@{

    /// Equivalent to calling `clear()` and then `insert(first,last,t...)`.
    template<typename ConstPrimitiveIterator,typename ... T>
    void rebuild(ConstPrimitiveIterator first, ConstPrimitiveIterator beyond,T...);

    /// Add a sequence of primitives to the set of primitives of the AABB tree.
    /// `%InputIterator` is any iterator and the parameter pack `T` are any types
    /// such that `Primitive` has a constructor with the following signature:
    /// `Primitive(%InputIterator, T...)`. If `Primitive` is a model of the concept
    /// `AABBPrimitiveWithSharedData`, a call to `AABBTraits::set_shared_data(t...)`
    /// is made using the internally stored traits.
    template<typename InputIterator,typename ... T>
    void insert(InputIterator first, InputIterator beyond,T...);

    /// Adds a primitive to the set of primitives of the tree.
    inline void insert(const Primitive& p);

    /// Clears and destroys the tree.
    ~AABB_tree_with_join()
    {
      clear();
    }
    /// Returns a const reference to the internally stored traits class.
    const AABBTraits& traits() const{
      return m_traits;
    }

    /// Clears the tree.
    void clear()
    {
      // clear AABB tree
      clear_nodes();
      m_primitives.clear();
      clear_search_tree();
    }

    /// Returns the axis-aligned bounding box of the whole tree.
    /// \pre `!empty()`
    const Bounding_box bbox() const {
      CGAL_precondition(!empty());
      if(size() > 1)
        return root_node()->bbox();
      else
        return AABB_traits().compute_bbox_object()(m_primitives.begin(),
                                                   m_primitives.end());
    }

    /// Returns the number of primitives in the tree.
    size_type size() const { return m_primitives.size(); }

    /// Returns \c true, iff the tree contains no primitive.
    bool empty() const { return m_primitives.empty(); }
    ///@}

    /// \name Advanced
    ///@{

    /// After one or more calls to `AABB_tree_with_join::insert()` the internal data
    /// structure of the tree must be reconstructed. This procedure
    /// has a complexity of \f$O(n log(n))\f$, where \f$n\f$ is the number of
    /// primitives of the tree.  This procedure is called implicitly
    /// at the first call to a query member function. You can call
    /// AABB_tree_with_join::build() explicitly to ensure that the next call to
    /// query functions will not trigger the reconstruction of the
    /// data structure.
    void build();

    ///@}

private:
    template <typename ... T>
    void set_primitive_data_impl(CGAL::Boolean_tag<false>,T ... ){}
    template <typename ... T>
    void set_primitive_data_impl(CGAL::Boolean_tag<true>,T ... t)
    {m_traits.set_shared_data(t...);}

    template <typename ... T>
    void set_shared_data(T...t){
      set_primitive_data_impl(CGAL::Boolean_tag<internal::Has_nested_type_Shared_data<Primitive>::value>(),t...);
    }

    template<typename ConstPointIterator>
    bool accelerate_distance_queries_impl(ConstPointIterator first,
                                          ConstPointIterator beyond) const;
public:

    /// \name Intersection Tests
    ///@{

    /// Returns `true`, iff the query intersects at least one of
    /// the input primitives. \tparam Query must be a type for
    /// which `do_intersect` predicates are
    /// defined in the traits class `AABBTraits`.
    template<typename Query>
    bool do_intersect(const Query& query) const;

    /// Returns `true`, iff at least one pair of primitives in the
    /// two trees intersect. The `other` tree is translated by
    /// `translation` before this is tested. The traits class `AABBTraits`
    /// needs to define `do_intersect` predicates for the tree's primitive.
    bool do_intersect(const AABB_tree_with_join &other,
                      const Point &translation) const;

    /// Returns the number of primitives intersected by the
    /// query. \tparam Query must be a type for which
    /// `do_intersect` predicates are defined
    /// in the traits class `AABBTraits`.
    template<typename Query>
    size_type number_of_intersected_primitives(const Query& query) const;

    /// Outputs to the iterator the list of all intersected primitives
    /// ids. This function does not compute the intersection points
    /// and is hence faster than the function `all_intersections()`
    /// function below. \tparam Query must be a type for which
    /// `do_intersect` predicates are defined
    /// in the traits class `AABBTraits`.
    template<typename Query, typename OutputIterator>
    OutputIterator all_intersected_primitives(const Query& query, OutputIterator out) const;


    /// Returns the first encountered intersected primitive id, iff
    /// the query intersects at least one of the input primitives. No
    /// particular order is guaranteed over the tree traversal, such
    /// that, e.g, the primitive returned is not necessarily the
    /// closest from the source point of a ray query. \tparam Query
    /// must be a type for which
    /// `do_intersect` predicates are defined
    /// in the traits class `AABBTraits`.
    template <typename Query>
    boost::optional<Primitive_id> any_intersected_primitive(const Query& query) const;

    ///@}

    /// \name Intersections
    ///@{

    /// Outputs the list of all intersections, as objects of
    /// `Intersection_and_primitive_id<Query>::%Type`,
    /// between the query and the input data to
    /// the iterator. `do_intersect()`
    /// predicates and intersections must be defined for `Query`
    /// in the `AABBTraits` class.
    template<typename Query, typename OutputIterator>
    OutputIterator all_intersections(const Query& query, OutputIterator out) const;


    /// Returns the first encountered intersection. No particular
    /// order is guaranteed over the tree traversal, e.g, the
    /// primitive returned is not necessarily the closest from the
    /// source point of a ray query. Type `Query` must be a type
    /// for which `do_intersect` predicates
    /// and intersections are defined in the traits class AABBTraits.
    template <typename Query>
    boost::optional< typename Intersection_and_primitive_id<Query>::Type >
    any_intersection(const Query& query) const;

    ///@}

    /// \name Distance Queries
    ///@{

    /// Returns the minimum squared distance between the query point
    /// and all input primitives. Method
    /// `accelerate_distance_queries()` should be called before the
    /// first distance query, so that an internal secondary search
    /// structure is build, for improving performance.
    /// \pre `!empty()`
    FT squared_distance(const Point& query) const;

    /// Returns the point in the union of all input primitives which
    /// is closest to the query. In case there are several closest
    /// points, one arbitrarily chosen closest point is
    /// returned. Method `accelerate_distance_queries()` should be
    /// called before the first distance query, so that an internal
    /// secondary search structure is build, for improving
    /// performance.
    /// \pre `!empty()`
    Point closest_point(const Point& query) const;


    /// Returns a `Point_and_primitive_id` which realizes the
    /// smallest distance between the query point and all input
    /// primitives. Method `accelerate_distance_queries()` should be
    /// called before the first distance query, so that an internal
    /// secondary search structure is build, for improving
    /// performance.
    /// \pre `!empty()`
    Point_and_primitive_id closest_point_and_primitive(const Point& query) const;


    ///@}

    /// \name Accelerating the Distance Queries
    ///
    /// In the following paragraphs, we discuss details of the
    /// implementation of the distance queries. We explain the
    /// internal use of hints, how the user can pass his own hints to
    /// the tree, and how the user can influence the construction of
    /// the secondary data structure used for accelerating distance
    /// queries.
    /// Internally, the distance queries algorithms are initialized
    /// with some hint, which has the same type as the return type of
    /// the query, and this value is refined along a traversal of the
    /// tree, until it is optimal, that is to say until it realizes
    /// the shortest distance to the primitives. In particular, the
    /// exact specification of these internal algorithms is that they
    /// minimize the distance to the object composed of the union of
    /// the primitives and the hint.
    /// It follows that
    /// - in order to return the exact distance to the set of
    /// primitives, the algorithms need the hint to be exactly on the
    /// primitives;
    /// - if this is not the case, and if the hint happens to be closer
    /// to the query point than any of the primitives, then the hint
    /// is returned.
    ///
    /// This second observation is reasonable, in the sense that
    /// providing a hint to the algorithm means claiming that this
    /// hint belongs to the union of the primitives. These
    /// considerations about the hints being exactly on the primitives
    /// or not are important: in the case where the set of primitives
    /// is a triangle soup, and if some of the primitives are large,
    /// one may want to provide a much better hint than a vertex of
    /// the triangle soup could be. It could be, for example, the
    /// barycenter of one of the triangles. But, except with the use
    /// of an exact constructions kernel, one cannot easily construct
    /// points other than the vertices, that lie exactly on a triangle
    /// soup. Hence, providing a good hint sometimes means not being
    /// able to provide it exactly on the primitives. In rare
    /// occasions, this hint can be returned as the closest point.
    /// In order to accelerate distance queries significantly, the
    /// AABB tree builds an internal KD-tree containing a set of
    /// potential hints, when the method
    /// `accelerate_distance_queries()` is called. This KD-tree
    /// provides very good hints that allow the algorithms to run much
    /// faster than with a default hint (such as the
    /// `reference_point` of the first primitive). The set of
    /// potential hints is a sampling of the union of the primitives,
    /// which is obtained, by default, by calling the method
    /// `reference_point` of each of the primitives. However, such
    /// a sampling with one point per primitive may not be the most
    /// relevant one: if some primitives are very large, it helps
    /// inserting more than one sample on them. Conversely, a sparser
    /// sampling with less than one point per input primitive is
    /// relevant in some cases.
    ///@{

    /// Constructs internal search tree from
    /// a point set taken on the internal primitives
    /// returns `true` iff successful memory allocation
    bool accelerate_distance_queries() const;

    /// Constructs an internal KD-tree containing the specified point
    /// set, to be used as the set of potential hints for accelerating
    /// the distance queries.
    /// \tparam ConstPointIterator is an iterator with
    /// value type `Point_and_primitive_id`.
    template<typename ConstPointIterator>
    bool accelerate_distance_queries(ConstPointIterator first,
                                     ConstPointIterator beyond) const
    {
      #ifdef CGAL_HAS_THREADS
      //this ensures that this is done once at a time
      CGAL_SCOPED_LOCK(kd_tree_mutex);
      #endif
      clear_search_tree();
      return accelerate_distance_queries_impl(first,beyond);

    }

    /// Returns the minimum squared distance between the query point
    /// and all input primitives. The internal KD-tree is not used.
    /// \pre `!empty()`
    FT squared_distance(const Point& query, const Point& hint) const;

    /// Returns the point in the union of all input primitives which
    /// is closest to the query. In case there are several closest
    /// points, one arbitrarily chosen closest point is returned. The
    /// internal KD-tree is not used.
    /// \pre `!empty()`
    Point closest_point(const Point& query, const Point& hint) const;

    /// Returns a `Point_and_primitive_id` which realizes the
    /// smallest distance between the query point and all input
    /// primitives. The internal KD-tree is not used.
    /// \pre `!empty()`
    Point_and_primitive_id closest_point_and_primitive(const Point& query, const Point_and_primitive_id& hint) const;

    ///@}

  private:
    // clear nodes
    void clear_nodes()
    {
      if( size() > 1 ) {
        delete [] m_p_root_node;
      }
      m_p_root_node = nullptr;
    }

    // clears internal KD tree
    void clear_search_tree() const
    {
      if ( m_search_tree_constructed )
      {
        CGAL_assertion( m_p_search_tree!=nullptr );
        delete m_p_search_tree;
        m_p_search_tree = nullptr;
        m_search_tree_constructed = false;
        m_default_search_tree_constructed = false;
                        }
    }

  public:

    /// \internal
    template <class Query, class Traversal_traits>
    void traversal(const Query& query, Traversal_traits& traits) const
    {
      switch(size())
      {
      case 0:
        break;
      case 1:
        traits.intersection(query, singleton_data());
        break;
      default: // if(size() >= 2)
        root_node()->template traversal<Traversal_traits,Query>(query, traits, m_primitives.size());
      }
    }

    /// \internal
    template <class Traversal_traits>
    void traversal(const AABB_tree_with_join &other_tree, Traversal_traits &traits) const
    {
      if (size() > 1 && other_tree.size() > 1)
      {
        root_node()->template traversal<Traversal_traits>(*(other_tree.root_node()),
                                                          traits,
                                                          m_primitives.size(),
                                                          other_tree.m_primitives.size(),
                                                          true);
      }
      else // at least tree has less than 2 primitives
      {
          // TODO not implemented yet, cannot happen with two polygons
      }
    }

  private:
    typedef AABB_node_with_join<AABBTraits> Node;


  public:
    // returns a point which must be on one primitive
    Point_and_primitive_id any_reference_point_and_id() const
    {
      CGAL_assertion(!empty());
      return Point_and_primitive_id(
        internal::Primitive_helper<AABB_traits>::get_reference_point(m_primitives[0],m_traits), m_primitives[0].id()
      );
    }

  public:
    Point_and_primitive_id best_hint(const Point& query) const
    {
      if(m_search_tree_constructed)
        return m_p_search_tree->closest_point(query);
      else
        return this->any_reference_point_and_id();
    }

  private:
    //Traits class
    AABBTraits m_traits;
    // set of input primitives
    Primitives m_primitives;
    // single root node
    Node* m_p_root_node;
    #ifdef CGAL_HAS_THREADS
    mutable CGAL_MUTEX internal_tree_mutex;//mutex used to protect const calls inducing build()
    mutable CGAL_MUTEX kd_tree_mutex;//mutex used to protect calls to accelerate_distance_queries
    #endif

    const Node* root_node() const {
      CGAL_assertion(size() > 1);
      if(m_need_build){
        #ifdef CGAL_HAS_THREADS
        //this ensures that build() will be called once
        CGAL_SCOPED_LOCK(internal_tree_mutex);
        if(m_need_build)
        #endif
          const_cast< AABB_tree_with_join<AABBTraits>* >(this)->build();
      }
      return m_p_root_node;
    }

    const Primitive& singleton_data() const {
      CGAL_assertion(size() == 1);
      return *m_primitives.begin();
    }

    // search KD-tree
    mutable const Search_tree* m_p_search_tree;
    mutable bool m_search_tree_constructed;
    mutable bool m_default_search_tree_constructed;
    bool m_need_build;

  private:
    // Disabled copy constructor & assignment operator
    typedef AABB_tree_with_join<AABBTraits> Self;
    AABB_tree_with_join(const Self& src);
    Self& operator=(const Self& src);

  };  // end class AABB_tree_with_join

/// @}

  template<typename Tr>
  AABB_tree_with_join<Tr>::AABB_tree_with_join(const Tr& traits)
    : m_traits(traits)
    , m_primitives()
    , m_p_root_node(nullptr)
    , m_p_search_tree(nullptr)
    , m_search_tree_constructed(false)
    , m_default_search_tree_constructed(false)
    , m_need_build(false)
  {}

   template<typename Tr>
  template<typename ConstPrimitiveIterator, typename ... T>
  AABB_tree_with_join<Tr>::AABB_tree_with_join(ConstPrimitiveIterator first,
                           ConstPrimitiveIterator beyond,
                           T ... t)
    : m_traits()
    , m_primitives()
    , m_p_root_node(nullptr)
    , m_p_search_tree(nullptr)
    , m_search_tree_constructed(false)
    , m_default_search_tree_constructed(false)
    , m_need_build(false)
  {
    // Insert each primitive into tree
    insert(first, beyond,t...);
   }

  template<typename Tr>
  template<typename ConstPrimitiveIterator, typename ... T>
  void AABB_tree_with_join<Tr>::insert(ConstPrimitiveIterator first,
                             ConstPrimitiveIterator beyond,
                             T ... t)
  {
    set_shared_data(t...);
    while(first != beyond)
    {
      m_primitives.push_back(Primitive(first,t...));
      ++first;
    }
    m_need_build = true;
  }

  // Clears tree and insert a set of primitives
  template<typename Tr>
  template<typename ConstPrimitiveIterator, typename ... T>
  void AABB_tree_with_join<Tr>::rebuild(ConstPrimitiveIterator first,
                              ConstPrimitiveIterator beyond,
                              T ... t)
  {
    // cleanup current tree and internal KD tree
    clear();

    // inserts primitives
    insert(first, beyond,t...);

    build();
  }

  template<typename Tr>
  void AABB_tree_with_join<Tr>::insert(const Primitive& p)
  {
    m_primitives.push_back(p);
    m_need_build = true;
  }

  // Build the data structure, after calls to insert(..)
  template<typename Tr>
  void AABB_tree_with_join<Tr>::build()
  {
    clear_nodes();

    if(m_primitives.size() > 1) {

      // allocates tree nodes
      m_p_root_node = new Node[m_primitives.size()-1]();
      if(m_p_root_node == nullptr)
      {
        Rcpp::Rcerr << "Unable to allocate memory for AABB tree" << std::endl;
        CGAL_assertion(m_p_root_node != nullptr);
        m_primitives.clear();
        clear();
      }

      // constructs the tree
      m_p_root_node->expand(m_primitives.begin(), m_primitives.end(),
                            m_primitives.size(), m_traits);
    }

    // In case the users has switched on the accelerated distance query
    // data structure with the default arguments, then it has to be
    // rebuilt.
    if(m_default_search_tree_constructed)
      accelerate_distance_queries();

    m_need_build = false;
  }


  // constructs the search KD tree from given points
  // to accelerate the distance queries
  template<typename Tr>
  template<typename ConstPointIterator>
  bool AABB_tree_with_join<Tr>::accelerate_distance_queries_impl(ConstPointIterator first,
    ConstPointIterator beyond) const
  {
    m_p_search_tree = new Search_tree(first, beyond);
    if(m_p_search_tree != nullptr)
    {
      m_search_tree_constructed = true;
      return true;
    }
    else
    {
      Rcpp::Rcerr << "Unable to allocate memory for accelerating distance queries" << std::endl;
      return false;
    }
  }

  // constructs the search KD tree from internal primitives
  template<typename Tr>
  bool AABB_tree_with_join<Tr>::accelerate_distance_queries() const
  {
    if(m_primitives.empty()) return true;
    #ifdef CGAL_HAS_THREADS
    //this ensures that this function will be done once
    CGAL_SCOPED_LOCK(kd_tree_mutex);
    #endif

    //we only redo computation only if needed
    if (!m_need_build && m_default_search_tree_constructed)
      return m_search_tree_constructed;

    // iterate over primitives to get reference points on them
    std::vector<Point_and_primitive_id> points;
    points.reserve(m_primitives.size());
    typename Primitives::const_iterator it;
    for(it = m_primitives.begin(); it != m_primitives.end(); ++it)
      points.push_back(
        Point_and_primitive_id(
          internal::Primitive_helper<AABB_traits>::get_reference_point(*it,m_traits), it->id()
        )
      );

    // clears current KD tree
    clear_search_tree();
    m_default_search_tree_constructed = true;
    return accelerate_distance_queries_impl(points.begin(), points.end());
  }

  template<typename Tr>
  template<typename Query>
  bool
    AABB_tree_with_join<Tr>::do_intersect(const Query& query) const
  {
    using namespace CGAL::internal::AABB_tree_with_join;
    typedef typename AABB_tree_with_join<Tr>::AABB_traits AABBTraits;
    Do_intersect_traits<AABBTraits, Query> traversal_traits(m_traits);
    this->traversal(query, traversal_traits);
    return traversal_traits.is_intersection_found();
  }

  template<typename Tr>
  bool AABB_tree_with_join<Tr>::do_intersect(const AABB_tree_with_join &other,
    const Point &translation) const
  {
    using namespace CGAL::internal::AABB_tree_with_join;
    typedef typename AABB_tree_with_join<Tr>::AABB_traits AABBTraits;
    Do_intersect_joined_traits<AABBTraits> traversal_traits(translation);
    this->traversal(other, traversal_traits);
    return traversal_traits.is_intersection_found();
  }

  template<typename Tr>
  template<typename Query>
  typename AABB_tree_with_join<Tr>::size_type
    AABB_tree_with_join<Tr>::number_of_intersected_primitives(const Query& query) const
  {
    using namespace CGAL::internal::AABB_tree_with_join;
    using CGAL::internal::AABB_tree_with_join::Counting_output_iterator;
    typedef typename AABB_tree_with_join<Tr>::AABB_traits AABBTraits;
    typedef Counting_output_iterator<Primitive_id, size_type> Counting_iterator;

    size_type counter = 0;
    Counting_iterator out(&counter);

    Listing_primitive_traits<AABBTraits,
      Query, Counting_iterator> traversal_traits(out,m_traits);
    this->traversal(query, traversal_traits);
    return counter;
  }

  template<typename Tr>
  template<typename Query, typename OutputIterator>
  OutputIterator
    AABB_tree_with_join<Tr>::all_intersected_primitives(const Query& query,
    OutputIterator out) const
  {
    using namespace CGAL::internal::AABB_tree_with_join;
    typedef typename AABB_tree_with_join<Tr>::AABB_traits AABBTraits;
    Listing_primitive_traits<AABBTraits,
      Query, OutputIterator> traversal_traits(out,m_traits);
    this->traversal(query, traversal_traits);
    return out;
  }

  template<typename Tr>
  template<typename Query, typename OutputIterator>
  OutputIterator
    AABB_tree_with_join<Tr>::all_intersections(const Query& query,
    OutputIterator out) const
  {
    using namespace CGAL::internal::AABB_tree_with_join;
    typedef typename AABB_tree_with_join<Tr>::AABB_traits AABBTraits;
    Listing_intersection_traits<AABBTraits,
      Query, OutputIterator> traversal_traits(out,m_traits);
    this->traversal(query, traversal_traits);
    return out;
  }


  template <typename Tr>
  template <typename Query>
  boost::optional< typename AABB_tree_with_join<Tr>::template Intersection_and_primitive_id<Query>::Type >
    AABB_tree_with_join<Tr>::any_intersection(const Query& query) const
  {
    using namespace CGAL::internal::AABB_tree_with_join;
    typedef typename AABB_tree_with_join<Tr>::AABB_traits AABBTraits;
    First_intersection_traits<AABBTraits, Query> traversal_traits(m_traits);
    this->traversal(query, traversal_traits);
    return traversal_traits.result();
  }

  template <typename Tr>
  template <typename Query>
  boost::optional<typename AABB_tree_with_join<Tr>::Primitive_id>
    AABB_tree_with_join<Tr>::any_intersected_primitive(const Query& query) const
  {
    using namespace CGAL::internal::AABB_tree_with_join;
    typedef typename AABB_tree_with_join<Tr>::AABB_traits AABBTraits;
    First_primitive_traits<AABBTraits, Query> traversal_traits(m_traits);
    this->traversal(query, traversal_traits);
    return traversal_traits.result();
  }

  // closest point with user-specified hint
  template<typename Tr>
  typename AABB_tree_with_join<Tr>::Point
    AABB_tree_with_join<Tr>::closest_point(const Point& query,
    const Point& hint) const
  {
    CGAL_precondition(!empty());
    typename Primitive::Id hint_primitive = m_primitives[0].id();
    using namespace CGAL::internal::AABB_tree_with_join;
    typedef typename AABB_tree_with_join<Tr>::AABB_traits AABBTraits;
    Projection_traits<AABBTraits> projection_traits(hint,hint_primitive,m_traits);
    this->traversal(query, projection_traits);
    return projection_traits.closest_point();
  }

  // closest point without hint, the search KD-tree is queried for the
  // first closest neighbor point to get a hint
  template<typename Tr>
  typename AABB_tree_with_join<Tr>::Point
    AABB_tree_with_join<Tr>::closest_point(const Point& query) const
  {
    CGAL_precondition(!empty());
    const Point_and_primitive_id hint = best_hint(query);
    return closest_point(query,hint.first);
  }

  // squared distance with user-specified hint
  template<typename Tr>
  typename AABB_tree_with_join<Tr>::FT
    AABB_tree_with_join<Tr>::squared_distance(const Point& query,
    const Point& hint) const
  {
    CGAL_precondition(!empty());
    const Point closest = this->closest_point(query, hint);
    return Tr().squared_distance_object()(query, closest);
  }

  // squared distance without user-specified hint
  template<typename Tr>
  typename AABB_tree_with_join<Tr>::FT
    AABB_tree_with_join<Tr>::squared_distance(const Point& query) const
  {
    CGAL_precondition(!empty());
    const Point closest = this->closest_point(query);
    return Tr().squared_distance_object()(query, closest);
  }

  // closest point with user-specified hint
  template<typename Tr>
  typename AABB_tree_with_join<Tr>::Point_and_primitive_id
    AABB_tree_with_join<Tr>::closest_point_and_primitive(const Point& query) const
  {
    CGAL_precondition(!empty());
    return closest_point_and_primitive(query,best_hint(query));
  }

  // closest point with user-specified hint
  template<typename Tr>
  typename AABB_tree_with_join<Tr>::Point_and_primitive_id
    AABB_tree_with_join<Tr>::closest_point_and_primitive(const Point& query,
    const Point_and_primitive_id& hint) const
  {
    CGAL_precondition(!empty());
    using namespace CGAL::internal::AABB_tree_with_join;
    typedef typename AABB_tree_with_join<Tr>::AABB_traits AABBTraits;
    Projection_traits<AABBTraits> projection_traits(hint.first,hint.second,m_traits);
    this->traversal(query, projection_traits);
    return projection_traits.closest_point_and_primitive();
  }

} // end namespace CGAL

#endif // CGAL_AABB_TREE_WITH_JOIN_H

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