diff --git a/Orthtree/doc/Orthtree/Concepts/CollectionPartitioningOrthtreeTraits.h b/Orthtree/doc/Orthtree/Concepts/CollectionPartitioningOrthtreeTraits.h
index ddf2218fda3..079c75ac726 100644
--- a/Orthtree/doc/Orthtree/Concepts/CollectionPartitioningOrthtreeTraits.h
+++ b/Orthtree/doc/Orthtree/Concepts/CollectionPartitioningOrthtreeTraits.h
@@ -13,7 +13,7 @@
   \cgalRefines{OrthtreeTraits}
 
   \cgalHasModelsBegin
-  \cgalHasModels{CGAL::Orthtree_traits_point<GeomTraits, PointSet, PointMap, DimensionTag>}
+  \cgalHasModels{CGAL::Orthtree_traits_point<GeomTraits, PointRange, PointMap, DimensionTag>}
   \cgalHasModelsEnd
 */
 class CollectionPartitioningOrthtreeTraits {
@@ -39,7 +39,7 @@ public:
   /*!
    * \brief Functor with an operator to produce a geometric object from a `Node_data_element`.
    *
-   * The return type of the functor must be a valid argument to `CGAL::squared_distance`.
+   * The return type of the functor must be a valid argument to `CGAL::squared_distance()`.
    */
   using Get_geometric_object_for_element = unspecified_type;
 
diff --git a/Orthtree/doc/Orthtree/Concepts/OrthtreeTraits.h b/Orthtree/doc/Orthtree/Concepts/OrthtreeTraits.h
index 2307d925ff2..409d53bb7a1 100644
--- a/Orthtree/doc/Orthtree/Concepts/OrthtreeTraits.h
+++ b/Orthtree/doc/Orthtree/Concepts/OrthtreeTraits.h
@@ -6,7 +6,7 @@
   template parameter of the `CGAL::Orthtree` class.
 
   \cgalHasModelsBegin
-  \cgalHasModels{CGAL::Orthtree_traits_point<GeomTraits, PointSet, PointMap, DimensionTag>}
+  \cgalHasModels{CGAL::Orthtree_traits_point<GeomTraits, PointRange, PointMap, DimensionTag>}
   \cgalHasModels{CGAL::Orthtree_traits_face_graph<PolygonMesh, VPM>}
   \cgalHasModelsEnd
 */
diff --git a/Orthtree/include/CGAL/Orthtree_traits_base_for_dimension.h b/Orthtree/include/CGAL/Orthtree_traits_base_for_dimension.h
index 1c878049013..eb3b6520ddc 100644
--- a/Orthtree/include/CGAL/Orthtree_traits_base_for_dimension.h
+++ b/Orthtree/include/CGAL/Orthtree_traits_base_for_dimension.h
@@ -26,12 +26,12 @@ namespace CGAL {
   \ingroup PkgOrthtreeTraits
 
   The class `Orthtree_traits_base_for_dimension` is a base class providing common choices for types and functors.
-  The base class is extended by `CGAL::Orthtree_traits_point<GeomTraits, PointSet, PointMap, DimensionTag>` and by `CGAL::Orthtree_traits_face_graph<PolygonMesh, VertexPointMap>`.
+  The base class is extended by `CGAL::Orthtree_traits_point<GeomTraits, PointRange, PointMap, DimensionTag>` and by `CGAL::Orthtree_traits_face_graph<PolygonMesh, VertexPointMap>`.
 
   \tparam K model of `Kernel`.
   \tparam DimensionTag is a tag representing the dimension of the ambient Euclidean space. Must be `Dimension_tag<d>` where `d` is an integer.
 
-  \sa `CGAL::Orthtree_traits_point<GeomTraits, PointSet, PointMap, DimensionTag>`
+  \sa `CGAL::Orthtree_traits_point<GeomTraits, PointRange, PointMap, DimensionTag>`
   \sa `CGAL::Orthtree_traits_face_graph<PolygonMesh, VertexPointMap>`
 */
 
diff --git a/Orthtree/include/CGAL/Orthtree_traits_point.h b/Orthtree/include/CGAL/Orthtree_traits_point.h
index 9546dddaa9b..6688a8e5663 100644
--- a/Orthtree/include/CGAL/Orthtree_traits_point.h
+++ b/Orthtree/include/CGAL/Orthtree_traits_point.h
@@ -66,7 +66,7 @@ void reassign_points(
   the `Orthtree` class.
 
   \tparam GeomTraits model of `Kernel`.
-  \tparam PointSet must be a model of range whose value type is the key type of `PointMap`
+  \tparam PointRange must be a model of `Range` whose value type is the key type of `PointMap`
   \tparam PointMap must be a model of `ReadablePropertyMap` whose value type is `GeomTraits::Traits::Point_d`
 
   \warning The input point set is not copied. It is used directly
@@ -80,10 +80,10 @@ void reassign_points(
 */
 template <
   typename GeomTraits,
-  typename PointSet,
-  typename PointMap = Identity_property_map<typename std::iterator_traits<typename PointSet::iterator>::value_type>,
+  typename PointRange,
+  typename PointMap = Identity_property_map<typename std::iterator_traits<typename PointRange::iterator>::value_type>,
   typename DimensionTag = Ambient_dimension<
-    typename std::iterator_traits<typename PointSet::iterator>::value_type,
+    typename std::iterator_traits<typename PointRange::iterator>::value_type,
     GeomTraits
   >
 >
@@ -93,18 +93,18 @@ public:
   /// \name Types
   /// @{
 
-  using Self = Orthtree_traits_point<GeomTraits, PointSet, PointMap, DimensionTag>;
+  using Self = Orthtree_traits_point<GeomTraits, PointRange, PointMap, DimensionTag>;
   using Tree = Orthtree<Self>;
 
-  using Node_data = boost::iterator_range<typename PointSet::iterator>;
-  using Node_data_element = typename std::iterator_traits<typename PointSet::iterator>::value_type;
+  using Node_data = boost::iterator_range<typename PointRange::iterator>;
+  using Node_data_element = typename std::iterator_traits<typename PointRange::iterator>::value_type;
 
   /// @}
 
   Orthtree_traits_point(
-    PointSet& point_set,
+    PointRange& points,
     PointMap point_map = PointMap()
-  ) : m_point_set(point_set), m_point_map(point_map) {}
+  ) : m_points(points), m_point_map(point_map) {}
 
   /// \name Operations
   /// @{
@@ -117,7 +117,7 @@ public:
 
       // init bbox with first values found
       {
-        const typename Self::Point_d& point = get(m_point_map, *(m_point_set.begin()));
+        const typename Self::Point_d& point = get(m_point_map, *(m_points.begin()));
         std::size_t i = 0;
         for (const typename Self::FT& x: cartesian_range(point)) {
           bbox_min[i] = x;
@@ -126,7 +126,7 @@ public:
         }
       }
       // Expand bbox to contain all points
-      for (const auto& p: m_point_set) {
+      for (const auto& p: m_points) {
         const typename Self::Point_d& point = get(m_point_map, p);
         std::size_t i = 0;
         for (const typename Self::FT& x: cartesian_range(point)) {
@@ -143,7 +143,7 @@ public:
 
   auto construct_root_node_contents_object() const {
     return [&]() -> typename Self::Node_data {
-      return {m_point_set.begin(), m_point_set.end()};
+      return {m_points.begin(), m_points.end()};
     };
   }
 
@@ -164,7 +164,7 @@ public:
 
 private:
 
-  PointSet& m_point_set;
+  PointRange& m_points;
   PointMap m_point_map;
 };