diff --git a/Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_curve_2.h b/Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_curve_2.h
index 8229a8ced98..b6a89ed0613 100644
--- a/Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_curve_2.h
+++ b/Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_curve_2.h
@@ -33,6 +33,7 @@
 #include <deque>
 #include <vector>
 #include <list>
+#include <CGAL/Arr_enums.h>
 #include <ostream>
 
 namespace CGAL {
@@ -414,6 +415,36 @@ public:
     return (this->_rep()._ctrl_pts.size());
   }
 
+  bool has_left() const
+  {
+    return true;
+  }
+
+  bool has_right() const
+  {
+    return true;
+  }
+
+  Arr_parameter_space right_infinite_in_x () const
+  {
+    return ARR_INTERIOR;
+  }
+
+  Arr_parameter_space right_infinite_in_y () const
+  {
+    return ARR_INTERIOR;
+  }
+
+  Arr_parameter_space left_infinite_in_x () const
+  {
+    return ARR_INTERIOR;
+  }
+
+  Arr_parameter_space left_infinite_in_y () const
+  {
+    return ARR_INTERIOR;
+  }
+
   /*!
    * Get the i'th control point.
    * \pre i must be between 0 and n - 1, where n is the number of control
diff --git a/Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_x_monotone_2.h b/Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_x_monotone_2.h
index db40c8aaf1d..52da852d4a4 100644
--- a/Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_x_monotone_2.h
+++ b/Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Bezier_x_monotone_2.h
@@ -29,6 +29,7 @@
 #include <CGAL/Arr_geometry_traits/Bezier_curve_2.h>
 #include <CGAL/Arr_geometry_traits/Bezier_point_2.h>
 #include <CGAL/Arr_geometry_traits/Bezier_cache.h>
+#include <CGAL/Arr_enums.h>
 #include <ostream>
 
 namespace CGAL {
@@ -250,6 +251,36 @@ public:
     return (_pt);
   }
 
+  bool has_left() const
+  {
+    return true;
+  }
+
+  bool has_right() const
+  {
+    return true;
+  }
+
+  Arr_parameter_space right_infinite_in_x () const
+  {
+    return ARR_INTERIOR;
+  }
+
+  Arr_parameter_space right_infinite_in_y () const
+  {
+    return ARR_INTERIOR;
+  }
+
+  Arr_parameter_space left_infinite_in_x () const
+  {
+    return ARR_INTERIOR;
+  }
+
+  Arr_parameter_space left_infinite_in_y () const
+  {
+    return ARR_INTERIOR;
+  }
+
   /*!
    * Get the left endpoint (the lexicographically smaller one).
    */
diff --git a/Arrangement_on_surface_2/include/CGAL/Arr_segment_traits_2.h b/Arrangement_on_surface_2/include/CGAL/Arr_segment_traits_2.h
index 34fdb72b982..430c8fb292a 100644
--- a/Arrangement_on_surface_2/include/CGAL/Arr_segment_traits_2.h
+++ b/Arrangement_on_surface_2/include/CGAL/Arr_segment_traits_2.h
@@ -31,6 +31,7 @@
 #include <CGAL/Arr_tags.h>
 #include <CGAL/Arr_geometry_traits/Segment_assertions.h>
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Arr_enums.h> 
 #include <fstream>
 
 
@@ -296,6 +297,36 @@ public:
       return (is_vert);
     }
 
+    bool has_left() const
+    {
+      return true;
+    }
+
+    bool has_right() const
+    {
+      return true;
+    }
+
+    Arr_parameter_space right_infinite_in_x () const
+    {
+      return ARR_INTERIOR;
+    }
+
+    Arr_parameter_space right_infinite_in_y () const
+    {
+      return ARR_INTERIOR;
+    }
+
+    Arr_parameter_space left_infinite_in_x () const
+    {
+      return ARR_INTERIOR;
+    }
+
+    Arr_parameter_space left_infinite_in_y () const
+    {
+      return ARR_INTERIOR;
+    }
+
     /*!
      * Check if the curve is directed lexicographic from left to right
      */