added functors for accessing Sphere_d

Orthtree/doc/Orthtree/Concepts/CollectionPartitioningOrthtreeTraits.h

@@ -23,7 +23,7 @@ public:
   /// @{
 
   /*!
-   * Sphere type used for the shrinking-sphere approach for neighbor queries
+   * Sphere Type used for the shrinking-sphere approach for neighbor queries; needs to be copy assignable.
    */
   using Sphere_d = unspecified_type;
 
@@ -48,11 +48,50 @@ public:
    */
   using Squared_distance_of_element = unspecified_type;
 
+  /*!
+   * \brief Functor with an operator that constructs a `Sphere_d` from a provided center and squared radius.
+   *
+   * Provides the operator:
+   * `Sphere_d operator()(const Point_d&, const FT&)`
+  */
+  using Construct_sphere_3 = unspecified_type;
+
+  /*!
+   * \brief Functor with an operator that provides the center of a `Sphere_d`.
+   *
+   * Provides the operator:
+   * `Point_d operator()(const Sphere_d&)`
+  */
+  using Construct_center_3 = unspecified_type;
+
+  /*!
+   * \brief Functor with an operator that provides the squared radius of a `Sphere_d`.
+   *
+   * Provides the operator:
+   * `FT operator()(const Sphere_d&)`
+  */
+  using Compute_squared_radius_3 = unspecified_type;
+
   /// @}
 
   /// \name Operations
   /// @{
 
+  /*!
+   * constructs an object of type `ConstructSphere_3`.
+   */
+  Construct_sphere_3 get_construct_sphere_3_object() const;
+
+  /*!
+   * constructs an object of type `ConstructCenter_3`.
+   */
+  Construct_center_3 get_construct_center_3_object() const;
+
+  /*!
+   * constructs an object of type `ComputeSquaredRadius_3`.
+   */
+  Compute_squared_radius_3 get_compute_squared_radius_3_object() const;
+
   /*!
    * constructs an object of type `Squared_distance_of_element`.
    */

Orthtree/include/CGAL/Orthtree/Nearest_neighbors.h

@@ -38,10 +38,10 @@ void nearest_k_neighbors_recursive(const Tree& orthtree,
 
       // Pair that element with its distance from the search point
       Result current_element_with_distance =
-        {e, orthtree.traits().get_squared_distance_of_element_object()(e, search_bounds.center())};
+        {e, orthtree.traits().get_squared_distance_of_element_object()(e, orthtree.traits().get_construct_center_3_object()(search_bounds))};
 
       // Check if the new element is within the bounds
-      if (current_element_with_distance.distance < search_bounds.squared_radius()) {
+      if (current_element_with_distance.distance < orthtree.traits().get_compute_squared_radius_3_object()(search_bounds)) {
 
         // Check if the results list is full
         if (results.size() == results.capacity()) {
@@ -62,7 +62,7 @@ void nearest_k_neighbors_recursive(const Tree& orthtree,
         if (results.size() == results.capacity()) {
 
           // Set the search radius
-          search_bounds = typename Tree::Sphere(search_bounds.center(), results.back().distance + epsilon);
+          search_bounds = orthtree.traits().get_construct_sphere_3_object()(orthtree.traits().get_construct_center_3_object()(search_bounds), results.back().distance + epsilon);
         }
       }
     }
@@ -89,7 +89,7 @@ void nearest_k_neighbors_recursive(const Tree& orthtree,
       // Add a child to the list, with its distance
       children_with_distances.emplace_back(
         child_node,
-        CGAL::squared_distance(search_bounds.center(), orthtree.barycenter(child_node))
+        CGAL::squared_distance(orthtree.traits().get_construct_center_3_object()(search_bounds), orthtree.barycenter(child_node))
       );
     }
 
@@ -182,7 +182,7 @@ template <typename Tree, typename OutputIterator>
 OutputIterator nearest_neighbors(const Tree& orthtree, const typename Tree::Point& query,
                                  std::size_t k,
                                  OutputIterator output) {
-  typename Tree::Sphere query_sphere(query, (std::numeric_limits<typename Tree::FT>::max)());
+  typename Tree::Sphere query_sphere = orthtree.traits().get_construct_sphere_3_object()(query, (std::numeric_limits<typename Tree::FT>::max)());
   return nearest_k_neighbors_in_radius(orthtree, query_sphere, k, output);
 }
 

Orthtree/include/CGAL/Orthtree_traits_point.h

@@ -163,6 +163,24 @@ public:
     };
   }
 
+  auto get_construct_sphere_3_object() const {
+    return [](const typename Self::Point_d& center, const typename Self::FT& squared_radius) -> typename Self::Sphere_d {
+      return typename Self::Sphere_d(center, squared_radius);
+      };
+  }
+
+  auto get_construct_center_3_object() const {
+    return [](const typename Self::Sphere_d& sphere) -> typename Self::Point_d {
+      return sphere.center();
+      };
+  }
+
+  auto get_compute_squared_radius_3_object() const {
+    return [](const typename Self::Sphere_d& sphere) -> typename Self::FT {
+      return sphere.squared_radius();
+      };
+  }
+
   auto get_squared_distance_of_element_object() const {
     return [&](const Node_data_element& index, const typename Self::Point_d& point) -> typename Self::FT {
       return CGAL::squared_distance(get(m_point_map, index), point);