diff --git a/Point_set_shape_detection_3/doc/Point_set_shape_detection_3/Concepts/EfficientRANSACTraits.h b/Point_set_shape_detection_3/doc/Point_set_shape_detection_3/Concepts/EfficientRANSACTraits.h
index 70510865e62..037bed81038 100644
--- a/Point_set_shape_detection_3/doc/Point_set_shape_detection_3/Concepts/EfficientRANSACTraits.h
+++ b/Point_set_shape_detection_3/doc/Point_set_shape_detection_3/Concepts/EfficientRANSACTraits.h
@@ -20,10 +20,10 @@ public:
   /// It must provide `Geom_traits::FT`, `Geom_traits::Point_3` and `Geom_traits::Vector_3`.
   /// `Geom_traits::FT` must be a floating point number type like `double` or `float`.
   typedef unspecified_type Geom_traits;
-  /// Random access iterator used to get the input points and normals.
-  typedef InputIt Input_iterator;
-  /// a model of `ReadablePropertyMap` with `Input_iterator` as key type and `Geom_traits::Point_3` as value type
-  typedef Ppmap Point_map;
-  /// a model of `ReadablePropertyMap` with `Input_iterator` as key type and `Geom_traits::Vector_3` as value type
-  typedef Npmap Normal_map;
+  /// Model of the concept `boost:RandomAccessRange` providing input points and normals.
+  typedef unspecified_type Input_range;
+  /// a model of `ReadablePropertyMap` with `Input_range::iterator` as key type and `Geom_traits::Point_3` as value type.
+  typedef unspecified_type Point_map;
+  /// a model of `ReadablePropertyMap` with `Input_range::iterator` as key type and `Geom_traits::Vector_3` as value type.
+  typedef unspecified_type Normal_map;
 };
diff --git a/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_basic.cpp b/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_basic.cpp
index d826c65c553..e382f05a8cf 100644
--- a/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_basic.cpp
+++ b/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_basic.cpp
@@ -18,7 +18,7 @@ typedef CGAL::Normal_of_point_with_normal_pmap<Kernel>      Normal_map;
 // In Efficient_RANSAC_traits the basic types, i.e., Point and Vector types
 // as well as iterator type and property maps, are defined.
 typedef CGAL::Shape_detection_3::Efficient_RANSAC_traits
-  <Kernel, Pwn_vector::iterator, Point_map, Normal_map>   Traits;
+  <Kernel, Pwn_vector, Point_map, Normal_map>   Traits;
 typedef CGAL::Shape_detection_3::Efficient_RANSAC<Traits>   Efficient_ransac;
 typedef CGAL::Shape_detection_3::Plane<Traits>              Plane;
 
diff --git a/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_parameters.cpp b/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_parameters.cpp
index 4233701e877..5f14d27c6ea 100644
--- a/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_parameters.cpp
+++ b/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_parameters.cpp
@@ -21,7 +21,7 @@ typedef CGAL::Normal_of_point_with_normal_pmap<Kernel>      Normal_map;
 // In Efficient_RANSAC_traits the basic types, i.e., Point and Vector types
 // as well as iterator type and property maps, are defined.
 typedef CGAL::Shape_detection_3::Efficient_RANSAC_traits<Kernel,
-  Pwn_vector::iterator, Point_map, Normal_map>            Traits;
+  Pwn_vector, Point_map, Normal_map>            Traits;
 typedef CGAL::Shape_detection_3::Efficient_RANSAC<Traits> Efficient_ransac;
 typedef CGAL::Shape_detection_3::Cone<Traits>             Cone;
 typedef CGAL::Shape_detection_3::Cylinder<Traits>         Cylinder;
diff --git a/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_point_access.cpp b/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_point_access.cpp
index d83db2fa0bf..d559737e942 100644
--- a/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_point_access.cpp
+++ b/Point_set_shape_detection_3/examples/Point_set_shape_detection_3/efficient_RANSAC_point_access.cpp
@@ -21,7 +21,7 @@ typedef CGAL::Normal_of_point_with_normal_pmap<Kernel>      Normal_map;
 // In Efficient_RANSAC_traits the basic types, i.e., Point and Vector types
 // as well as iterator type and property maps, are defined.
 typedef CGAL::Shape_detection_3::Efficient_RANSAC_traits<Kernel,
-  Pwn_vector::iterator, Point_map, Normal_map>            Traits;
+  Pwn_vector, Point_map, Normal_map>            Traits;
 typedef CGAL::Shape_detection_3::Efficient_RANSAC<Traits>   Efficient_ransac;
 typedef CGAL::Shape_detection_3::Plane<Traits>              Plane;
 
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cone.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cone.h
index cec2dc03a49..65f368d0f73 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cone.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cone.h
@@ -51,8 +51,6 @@ namespace CGAL {
   class Cone : public Shape_base<Traits> {
   public:
     /// \cond SKIP_IN_MANUAL
-    typedef typename Traits::Input_iterator Input_iterator;
-     ///< random access iterator for input data.
     typedef typename Traits::Point_map Point_map;
      ///< property map to access the location of an input point.
     typedef typename Traits::Normal_map Normal_map;
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cylinder.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cylinder.h
index 978b97e7584..af423ebd79f 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cylinder.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Cylinder.h
@@ -49,8 +49,6 @@ namespace CGAL {
   class Cylinder : public Shape_base<Traits> {
   public:
     /// \cond SKIP_IN_MANUAL
-    typedef typename Traits::Input_iterator Input_iterator;
-     ///< random access iterator for input data.
     typedef typename Traits::Point_map Point_map;
      ///< property map to access the location of an input point.
     typedef typename Traits::Normal_map Normal_map;
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Efficient_RANSAC.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Efficient_RANSAC.h
index 685101cc42b..449749630d8 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Efficient_RANSAC.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Efficient_RANSAC.h
@@ -88,8 +88,7 @@ shape. The implementation follows \cgalCite{Schnabel07}.
 
     /// \name Types 
     /// @{    
-    typedef typename Traits::Input_iterator Input_iterator;
-    ///< random access iterator for input data.
+    typedef typename Traits::Input_range::iterator Input_iterator;
     typedef typename Traits::Geom_traits::FT FT; ///< number type.
     typedef typename Traits::Geom_traits::Point_3 Point; ///< point type.
     typedef typename Traits::Geom_traits::Vector_3 Vector; ///< vector type.
@@ -109,7 +108,7 @@ shape. The implementation follows \cgalCite{Schnabel07}.
     ///< Range of extracted shapes with typ `Shape *`. Model of the `ConstRange` concept.
 
 #ifdef DOXYGEN_RUNNING
-    typedef unspecified_type Point_index_range;    ///< Range of indices of points of type `std::size_t` into the provided Input_iterator. Model of the `boost::BidirectionalRange` concept.
+    typedef unspecified_type Point_index_range;    ///< Range of indices of points of type `std::size_t` into the provided input point range. Model of the `boost::BidirectionalRange` concept.
 
 #else 
     typedef typename boost::iterator_range<Point_index_iterator>
@@ -184,10 +183,9 @@ shape. The implementation follows \cgalCite{Schnabel07}.
       results is required. The data in the input range is reordered during
       `detect()` and `build_octrees()`. `clear()` is first called by this function.
     */
-    template <class RandomAccessInputRange>
     void set_input_data(
-      ///< Range of input data providing 'Input_iterator' for random access. Model of the 'boost:RandomAccessRange'.
-      RandomAccessInputRange &input_range,
+      ///< Range of input data points.
+      typename Traits::Input_range& input_range,
       ///< past-the-end random access iterator over the input points.
       Point_map point_pmap = Point_map(),
       ///< property map to access the position of an input point.
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Efficient_RANSAC_traits.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Efficient_RANSAC_traits.h
index 2ef21278caf..34ac1a6f6b6 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Efficient_RANSAC_traits.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Efficient_RANSAC_traits.h
@@ -42,14 +42,14 @@ namespace CGAL {
               `key_type = InputIterator` and `value_type = Gt::Vector_3`.
     */
   template <class Gt,
-            class InputIterator,
+            class InputRange,
             class Ppmap,
             class Npmap>
   struct Efficient_RANSAC_traits {
     ///
     typedef Gt Geom_traits;
     ///
-    typedef InputIterator Input_iterator;
+    typedef InputRange Input_range;
     ///
     typedef Ppmap Point_map;
     ///
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Octree.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Octree.h
index bb49ba1b84e..5d3ce503cec 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Octree.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Octree.h
@@ -48,7 +48,7 @@ namespace CGAL {
     class DirectPointAccessor {
     public:
       typedef Sdt Sd_traits;
-      typedef typename Sd_traits::Input_iterator Input_iterator;
+      typedef typename Sd_traits::Input_range::iterator Input_iterator;
 
       DirectPointAccessor() {}
       DirectPointAccessor(const Input_iterator &begin,
@@ -104,7 +104,7 @@ namespace CGAL {
     class IndexedPointAccessor {
     public:
       typedef Sdt Sd_traits;
-      typedef typename Sd_traits::Input_iterator Input_iterator;
+      typedef typename Sd_traits::Input_range::iterator Input_iterator;
 
       IndexedPointAccessor() {}
       IndexedPointAccessor(const Input_iterator &begin,
@@ -165,7 +165,7 @@ namespace CGAL {
     class Octree : public PointAccessor {
 
       typedef typename PointAccessor::Sd_traits Sd_traits;
-      typedef typename Sd_traits::Input_iterator Input_iterator;
+      typedef typename Sd_traits::Input_range::iterator Input_iterator;
       typedef Shape_base<Sd_traits> Shape;
       typedef typename Sd_traits::Geom_traits::Point_3 Point;
       typedef typename Sd_traits::Geom_traits::Vector_3 Vector;
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Plane.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Plane.h
index 044d8ff856a..33d57981bd4 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Plane.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Plane.h
@@ -38,8 +38,6 @@ namespace CGAL {
   class Plane : public Shape_base<Traits> {
   public:
     /// \cond SKIP_IN_MANUAL
-    typedef typename Traits::Input_iterator Input_iterator;
-     ///< random access iterator for input data.
     typedef typename Traits::Point_map Point_map;
      ///< property map to access the location of an input point.
     typedef typename Traits::Normal_map Normal_map;
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Shape_base.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Shape_base.h
index 124cb4990e8..f9efef94e09 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Shape_base.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Shape_base.h
@@ -67,7 +67,7 @@ namespace CGAL {
 
   public:
     /// \cond SKIP_IN_MANUAL
-    typedef typename Traits::Input_iterator Input_iterator;
+    typedef typename Traits::Input_range::iterator Input_iterator;
       ///< random access iterator for input data.
     typedef typename Traits::Point_map Point_map;
       ///< property map to access the location of an input point.
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Sphere.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Sphere.h
index d62a8510917..70568da38b0 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Sphere.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Sphere.h
@@ -39,8 +39,6 @@ namespace CGAL {
   class Sphere : public Shape_base<Traits> {
   public:    
     /// \cond SKIP_IN_MANUAL
-    typedef typename Traits::Input_iterator Input_iterator;
-      ///< random access iterator for input data.
     typedef typename Traits::Point_map Point_map;
       ///< property map to access the location of an input point.
     typedef typename Traits::Normal_map Normal_map;
diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Torus.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Torus.h
index 43f2905b337..645c5219b66 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Torus.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Torus.h
@@ -42,8 +42,6 @@ namespace CGAL {
   class Torus : public Shape_base<Traits> {
   public:
     /// \cond SKIP_IN_MANUAL
-    typedef typename Traits::Input_iterator Input_iterator;
-     ///< random access iterator for input data.
     typedef typename Traits::Point_map Point_map;
      ///< property map to access the location of an input point.
     typedef typename Traits::Normal_map Normal_map;
diff --git a/Polyhedron/demo/Polyhedron/Polyhedron_demo_point_set_shape_detection_plugin.cpp b/Polyhedron/demo/Polyhedron/Polyhedron_demo_point_set_shape_detection_plugin.cpp
index 504b418a670..099dfdc2577 100644
--- a/Polyhedron/demo/Polyhedron/Polyhedron_demo_point_set_shape_detection_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Polyhedron_demo_point_set_shape_detection_plugin.cpp
@@ -112,7 +112,7 @@ void Polyhedron_demo_point_set_shape_detection_plugin::on_actionDetect_triggered
     typedef CGAL::Identity_property_map<Point_set::Point_with_normal> PointPMap;
     typedef CGAL::Normal_of_point_with_normal_pmap<Point_set::Geom_traits> NormalPMap;
 
-    typedef CGAL::Shape_detection_3::Efficient_RANSAC_traits<Epic_kernel, Point_set::iterator, PointPMap, NormalPMap> Traits;
+    typedef CGAL::Shape_detection_3::Efficient_RANSAC_traits<Epic_kernel, Point_set, PointPMap, NormalPMap> Traits;
     typedef CGAL::Shape_detection_3::Efficient_RANSAC<Traits> Shape_detection;
 
     Shape_detection shape_detection;