diff --git a/Visibility_2/doc/Visibility_2/CGAL/Preprocessed_rotational_sweep_visibility_2.h b/Visibility_2/doc/Visibility_2/CGAL/Preprocessed_rotational_sweep_visibility_2.h
index 09f3fe3b6c6..fec2afad89e 100644
--- a/Visibility_2/doc/Visibility_2/CGAL/Preprocessed_rotational_sweep_visibility_2.h
+++ b/Visibility_2/doc/Visibility_2/CGAL/Preprocessed_rotational_sweep_visibility_2.h
@@ -91,7 +91,7 @@ Preprocessed_rotational_sweep_visibility_2();
 /*! 
 Constructs a `Preprocessed_rotational_sweep_visibility_2` object that is attached to `arr`.
 */ 
-Preprocessed_rotational_sweep_visibility_2(Input_arrangement_2& arr);
+Preprocessed_rotational_sweep_visibility_2(const Input_arrangement_2& arr);
 
 /// @}
 
@@ -108,7 +108,7 @@ Attaches the given arrangement to the visibility object and applies preprocessin
 In case the object is already attached to another arrangement, 
 the visibility object gets detached before being attached to `arr`.
 */
-  void attach(Input_arrangement_2& arr);
+  void attach(const Input_arrangement_2& arr);
 
 /*!
 Detaches the arrangement from the visibility object it is currently attached to
diff --git a/Visibility_2/doc/Visibility_2/CGAL/Rotational_sweep_visibility_2.h b/Visibility_2/doc/Visibility_2/CGAL/Rotational_sweep_visibility_2.h
index cab0a3bdc90..04c28d34d93 100644
--- a/Visibility_2/doc/Visibility_2/CGAL/Rotational_sweep_visibility_2.h
+++ b/Visibility_2/doc/Visibility_2/CGAL/Rotational_sweep_visibility_2.h
@@ -85,7 +85,7 @@ Rotational_sweep_visibility_2();
 /*! 
 Constructs a `Rotational_sweep_visibility_2` object that is attached to `arr`.
 */ 
-Rotational_sweep_visibility_2(Input_arrangement_2& arr); 
+Rotational_sweep_visibility_2(const Input_arrangement_2& arr); 
 
 /// @}
 
@@ -102,7 +102,7 @@ Attaches the given arrangement to the visibility object.
 In case the object is already attached to another arrangement, 
 the visibility object gets detached before being attached to `arr`.
 */
-  void attach(Input_arrangement_2& arr);
+  void attach(const Input_arrangement_2& arr);
   
 /*!
 Detaches the arrangement from the visibility object it is currently attached to
diff --git a/Visibility_2/doc/Visibility_2/CGAL/Simple_polygon_visibility_2.h b/Visibility_2/doc/Visibility_2/CGAL/Simple_polygon_visibility_2.h
index be0b84dc55b..ab7caeaeb37 100644
--- a/Visibility_2/doc/Visibility_2/CGAL/Simple_polygon_visibility_2.h
+++ b/Visibility_2/doc/Visibility_2/CGAL/Simple_polygon_visibility_2.h
@@ -98,7 +98,7 @@ Simple_polygon_visibility_2();
 /*! 
 Constructs a `Simple_polygon_visibility_2` object that is attached to `arr`.
 */ 
-Simple_polygon_visibility_2(Input_arrangement_2& arr); 
+Simple_polygon_visibility_2(const Input_arrangement_2& arr); 
 
 /// @}
 
@@ -115,7 +115,7 @@ Attaches the given arrangement to the visibility object.
 In case the object is already attached to another arrangement, 
 the visibility object gets detached before being attached to `arr`.
 */
-  void attach(Input_arrangement_2& arr);
+  void attach(const Input_arrangement_2& arr);
 
 /*!
 Detaches the arrangement from the visibility object it is currently attached to
diff --git a/Visibility_2/doc/Visibility_2/CGAL/Triangular_expansion_visibility_2.h b/Visibility_2/doc/Visibility_2/CGAL/Triangular_expansion_visibility_2.h
index 0559a516127..b30945183ba 100644
--- a/Visibility_2/doc/Visibility_2/CGAL/Triangular_expansion_visibility_2.h
+++ b/Visibility_2/doc/Visibility_2/CGAL/Triangular_expansion_visibility_2.h
@@ -92,7 +92,7 @@ Triangular_expansion_visibility_2();
 /*! 
 Constructs a `Triangular_expansion_visibility_2` object that is attached to `arr`.
 */ 
-Triangular_expansion_visibility_2(Input_arrangement_2& arr);
+Triangular_expansion_visibility_2(const Input_arrangement_2& arr);
 
 /// @}
 
@@ -112,7 +112,7 @@ also changes the stored restricted triangulation which in the worst may again ta
 In case the object is already attached to another arrangement, 
 the visibility object gets detached before being attached to `arr`.
 */
-  void attach(Input_arrangement_2& arr);
+  void attach(const Input_arrangement_2& arr);
 
 /*!
 Detaches the arrangement from the visibility object it is currently attached to
diff --git a/Visibility_2/doc/Visibility_2/Concepts/Visibility_2.h b/Visibility_2/doc/Visibility_2/Concepts/Visibility_2.h
index a287fd589cc..3ec4510341d 100644
--- a/Visibility_2/doc/Visibility_2/Concepts/Visibility_2.h
+++ b/Visibility_2/doc/Visibility_2/Concepts/Visibility_2.h
@@ -74,7 +74,7 @@ Visibility_2();
 /*! 
 Constructs a `Visibility_2` object that is attached to `arr`.
 */ 
-Visibility_2(Input_arrangement_2& arr);
+Visibility_2(const Input_arrangement_2& arr);
 
 /// @}
 
@@ -92,7 +92,7 @@ Attaches the given arrangement `arr` to the visibility object.
 In case the object is already attached to another arrangement, 
 the visibility object gets detached before being attached to `arr`.
 */
-  void attach(Input_arrangement_2& arr);
+  void attach(const Input_arrangement_2& arr);
 
   
 /*!
diff --git a/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h b/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h
index 62c4886ff85..d480de53355 100644
--- a/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h
+++ b/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h
@@ -66,7 +66,7 @@ public:
 
 
   Rotational_sweep_visibility_2(): p_arr(NULL) {}
-  Rotational_sweep_visibility_2(Input_arrangement_2& arr): p_arr(&arr) {}
+  Rotational_sweep_visibility_2(const Input_arrangement_2& arr): p_arr(&arr) {}
 
 
   Face_handle compute_visibility(const Point_2& q, const Halfedge_const_handle e, Arrangement_2& out_arr) {
@@ -175,7 +175,7 @@ bool is_attached() {
   return (p_arr != NULL);
 }
 
-void attach(Input_arrangement_2& arr) {
+void attach(const Input_arrangement_2& arr) {
   p_arr = &arr;
 //  geom_traits = p_arr->geometry_traits();
 }
diff --git a/Visibility_2/include/CGAL/Simple_polygon_visibility_2.h b/Visibility_2/include/CGAL/Simple_polygon_visibility_2.h
index fa77a9e81bf..046ba5173e9 100644
--- a/Visibility_2/include/CGAL/Simple_polygon_visibility_2.h
+++ b/Visibility_2/include/CGAL/Simple_polygon_visibility_2.h
@@ -63,7 +63,7 @@ public:
   Simple_polygon_visibility_2() : p_arr(NULL), geom_traits(NULL) {};
 
   /*! Constructor given an arrangement and the Regularization tag. */
-  Simple_polygon_visibility_2(Input_arrangement_2& arr): 
+  Simple_polygon_visibility_2(const Input_arrangement_2& arr): 
     p_arr(&arr) {
     geom_traits = p_arr->geometry_traits();
     query_pt_is_vertex = false;
@@ -73,7 +73,7 @@ public:
     return (p_arr != NULL);
   }
 
-  void attach(Input_arrangement_2& arr) {
+  void attach(const Input_arrangement_2& arr) {
     p_arr = &arr;
     geom_traits = p_arr->geometry_traits();
     query_pt_is_vertex = false;
diff --git a/Visibility_2/include/CGAL/Simple_polygon_visibility_2_.h b/Visibility_2/include/CGAL/Simple_polygon_visibility_2_.h
index 39870299b53..aef49c646ed 100644
--- a/Visibility_2/include/CGAL/Simple_polygon_visibility_2_.h
+++ b/Visibility_2/include/CGAL/Simple_polygon_visibility_2_.h
@@ -65,7 +65,7 @@ public:
   Simple_polygon_visibility_2_() : p_arr(NULL), geom_traits(NULL) {};
 
   /*! Constructor given an arrangement and the Regularization tag. */
-  Simple_polygon_visibility_2_(Input_arrangement_2& arr): 
+  Simple_polygon_visibility_2_(const Input_arrangement_2& arr): 
     p_arr(&arr) {
     geom_traits = p_arr->geometry_traits();
   };
@@ -74,7 +74,7 @@ public:
     return (p_arr != NULL);
   }
 
-  void attach(Input_arrangement_2& arr) {
+  void attach(const Input_arrangement_2& arr) {
     p_arr = &arr;
     geom_traits = p_arr->geometry_traits();
   }
diff --git a/Visibility_2/include/CGAL/Triangular_expansion_visibility_2_.h b/Visibility_2/include/CGAL/Triangular_expansion_visibility_2_.h
index 73717481188..e108cfdf47a 100644
--- a/Visibility_2/include/CGAL/Triangular_expansion_visibility_2_.h
+++ b/Visibility_2/include/CGAL/Triangular_expansion_visibility_2_.h
@@ -77,7 +77,7 @@ public:
   Triangular_expansion_visibility_2() : p_arr(NULL){}
 
   /*! Constructor given an arrangement and the Regularization tag. */
-  Triangular_expansion_visibility_2 (Input_arrangement_2& arr)
+  Triangular_expansion_visibility_2 (const Input_arrangement_2& arr)
     : p_arr(&arr){
     //std::cout << "Triangular_expansion_visibility_2" << std::endl;
     init_cdt(); 
@@ -88,7 +88,7 @@ public:
     return (p_arr != NULL);
   }
 
-  void attach(Input_arrangement_2& arr) {
+  void attach(const Input_arrangement_2& arr) {
     //std::cout << "attach" << std::endl;
     // todo observe changes in arr; 
     p_arr = &arr;