Support for isolated vertices on the boundary

Arrangement_on_surface_2/examples/Arrangement_on_surface_2/spherical_degenerate_insert.cpp

@@ -0,0 +1,43 @@
+//! \file examples/Arrangement_on_surface_2/aggregated_insertion.cpp
+// Using the global aggregated insertion functions.
+
+#include <list>
+
+#include <CGAL/basic.h>
+#include <CGAL/Exact_rational.h>
+#include <CGAL/Cartesian.h>
+#include <CGAL/Arrangement_on_surface_2.h>
+#include <CGAL/Arr_geodesic_arc_on_sphere_traits_2.h>
+#include <CGAL/Arr_spherical_topology_traits_2.h>
+
+typedef CGAL::Exact_rational                               Number_type;
+typedef CGAL::Cartesian<Number_type>                       Kernel;
+typedef CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel>  Geom_traits_2;
+typedef Geom_traits_2::Point_2                             Point_2;
+typedef Geom_traits_2::X_monotone_curve_2                  X_monotone_curve_2;
+typedef CGAL::Arr_spherical_topology_traits_2<Geom_traits_2> Topol_traits_2;
+typedef CGAL::Arrangement_on_surface_2<Geom_traits_2, Topol_traits_2>
+                                                           Arrangement_2;
+typedef Arrangement_2::Vertex_handle                       Vertex_handle;
+
+int main()
+{
+  Arrangement_2 arr;
+  Point_2 sp(0, 0, -1);
+  Point_2 np(0, 0, 1);
+  Vertex_handle spv = arr.insert_in_face_interior(sp, arr.reference_face());
+  X_monotone_curve_2 xcv1(Point_2(0, 0, -1), Point_2(1, 0, 0));
+  X_monotone_curve_2 xcv2(Point_2(0, 0, -1), Point_2(1, 1, 0));
+  arr.insert_from_left_vertex(xcv1, spv);
+  arr.insert_from_left_vertex(xcv2, spv);
+
+  // Print the size of the arrangement.
+  std::cout << "The arrangement size:" << std::endl
+            << "   V = " << arr.number_of_vertices()
+            << ",  E = " << arr.number_of_edges()
+            << ",  F = " << arr.number_of_faces() << std::endl;
+
+  std::cout << "arr: " << arr << std::endl;
+
+  return 0;
+}

Arrangement_on_surface_2/include/CGAL/Arr_observer.h

@@ -12,10 +12,6 @@
 // This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 // WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 //
-// $URL$
-// $Id$
-// 
-//
 // Author(s)     : Ron Wein          <wein@post.tau.ac.il>
 
 #ifndef CGAL_ARR_OBSERVER_H
@@ -33,11 +29,10 @@ namespace CGAL {
  * A base class for arrangement observers.
  * The Arrangement parameter corresponds to an arrangement instantiation.
  */
-template <class Arrangement_>
+template <typename Arrangement_>
 class Arr_observer
 {
 public:
-
   typedef Arrangement_                                     Arrangement_2;
   typedef Arr_observer<Arrangement_2>                      Self;
 
@@ -47,43 +42,38 @@ public:
   typedef typename Arrangement_2::Vertex_handle            Vertex_handle;
   typedef typename Arrangement_2::Halfedge_handle          Halfedge_handle;
   typedef typename Arrangement_2::Face_handle              Face_handle;
-  typedef typename Arrangement_2::Ccb_halfedge_circulator  
+  typedef typename Arrangement_2::Ccb_halfedge_circulator
                                                       Ccb_halfedge_circulator;
 
 private:
-
-  Arrangement_2  *p_arr;           // The associated arrangement.
+  Arrangement_2* p_arr;           // The associated arrangement.
 
   /*! Copy constructor - not supported. */
-  Arr_observer (const Self& );
+  Arr_observer(const Self&);
 
   /*! Assignment operator - not supported. */
-  Self& operator= (const Self& );
+  Self& operator=(const Self&);
 
 public:
-
   /// \name Construction and destruction functions.
   //@{
 
   /*! Default constructor. */
-  Arr_observer () :
-    p_arr (NULL)
-  {}
+  Arr_observer() : p_arr(NULL) {}
 
   /*! Constructor with an associated arrangement. */
-  Arr_observer (Arrangement_2& arr) :
-    p_arr (&arr)
+  Arr_observer(Arrangement_2& arr) : p_arr(&arr)
   {
     // Register the observer object in the arrangement.
-    p_arr->_register_observer (this);
+    p_arr->_register_observer(this);
   }
 
   /*! Destructor. */
-  virtual ~Arr_observer ()
+  virtual ~Arr_observer()
   {
     // Unregister the observer object from the arrangement.
     if (p_arr != NULL)
-      p_arr->_unregister_observer (this);
+      p_arr->_unregister_observer(this);
   }
   //@}
 
@@ -91,132 +81,96 @@ public:
   //@{
 
   /*! Get the associated arrangement (non-const version). */
-  const Arrangement_2* arrangement () const
-  {
-    return (p_arr);
-  }
+  const Arrangement_2* arrangement() const { return (p_arr); }
 
   /*! Get the associated arrangement (non-const version). */
-  Arrangement_2* arrangement ()
-  {
-    return (p_arr);
-  }
+  Arrangement_2* arrangement() { return (p_arr); }
 
-  /*!
-   * Attach the observer to an arrangement. 
+  /*! Attach the observer to an arrangement.
    * \pre The observer is not already attached to an arrangement.
    */
-  void attach (Arrangement_2& arr)
+  void attach(Arrangement_2& arr)
   {
     // Do nothing if the associated arrangement is not changed.
-    if (p_arr == &arr)
-      return;
+    if (p_arr == &arr) return;
 
     // The observer is not already attached to an arrangement.
-    CGAL_precondition (p_arr == NULL);
+    CGAL_precondition(p_arr == NULL);
 
-    if (p_arr != NULL)
-      return;
+    if (p_arr != NULL) return;
 
     // Notify the concrete oberver (the sub-class) about the attachment.
-    before_attach (arr);
+    before_attach(arr);
 
     // Register the observer object in the new arrangement.
     p_arr = &arr;
-    p_arr->_register_observer (this);
+    p_arr->_register_observer(this);
 
     // Notify the concrete oberver that the attachment took place.
     after_attach();
-
-    return;
   }
 
   /*! Detach the observer from the arrangement. */
-  void detach ()
+  void detach()
   {
-    if (p_arr == NULL)
-      return;
+    if (p_arr == NULL) return;
 
     // Notify the concrete oberver (the sub-class) about the detachment.
     before_detach ();
 
     // Unregister the observer object from the current arrangement, and mark
     // that the oberver is not attached to an arrangement.
-    p_arr->_unregister_observer (this);
+    p_arr->_unregister_observer(this);
     p_arr = NULL;
-   
+
     // Notify the concrete oberver that the detachment took place.
     after_detach();
-
-    return;
   }
   //@}
 
   /// \name Notification functions on global arrangement operations.
   //@{
 
-  /*! 
-   * Notification before the arrangement is assigned with another
+  /*! Notification before the arrangement is assigned with another
    * arrangement.
    * \param arr The arrangement to be copied.
    */
-  virtual void before_assign (const Arrangement_2& /* arr */)
-  {}
+  virtual void before_assign(const Arrangement_2& /* arr */) {}
 
-  /*!
-   * Notification after the arrangement has been assigned with another
+  /*! Notification after the arrangement has been assigned with another
    * arrangement.
    */
-  virtual void after_assign ()
-  {}
+  virtual void after_assign() {}
 
   /*! Notification before the arrangement is cleared. */
-  virtual void before_clear ()
-  {}
+  virtual void before_clear() {}
 
-  /*!
-   * Notification after the arrangement is cleared.
-   */
-  virtual void after_clear ()
-  {}
+  /*! Notification after the arrangement is cleared. */
+  virtual void after_clear() {}
 
   /*! Notification before a global operation modifies the arrangement. */
-  virtual void before_global_change ()
-  {}
+  virtual void before_global_change() {}
 
   /*! Notification after a global operation is completed. */
-  virtual void after_global_change ()
-  {}
+  virtual void after_global_change() {}
   //@}
 
   /// \name Notification functions on observer attachment or detachment.
   //@{
 
-  /*! 
-   * Notification before the observer is attached to an arrangement.
+  /*! Notification before the observer is attached to an arrangement.
    * \param arr The arrangement we are about to attach the observer to.
    */
-  virtual void before_attach (const Arrangement_2& /* arr */)
-  {}
+  virtual void before_attach(const Arrangement_2& /* arr */) {}
 
-  /*!
-   * Notification after the observer has been attached to an arrangement.
-   */
-  virtual void after_attach ()
-  {}
+  /*! Notification after the observer has been attached to an arrangement. */
+  virtual void after_attach() {}
 
-  /*! 
-   * Notification before the observer is detached from the arrangement.
-   */
-  virtual void before_detach ()
-  {}
+  /*! Notification before the observer is detached from the arrangement. */
+  virtual void before_detach() {}
 
-  /*!
-   * Notification after the observer has been detached to the arrangement.
-   */
-  virtual void after_detach ()
-
-  {}
+  /*! Notification after the observer has been detached to the arrangement. */
+  virtual void after_detach() {}
   //@}
 
   /// \name Notification functions on local changes in the arrangement.
@@ -227,449 +181,388 @@ public:
    * \param p The point to be associated with the vertex.
    *          This point cannot lies on the surface boundaries.
    */
-  virtual void before_create_vertex (const Point_2& /* p */)
-  {}
+  virtual void before_create_vertex(const Point_2& /* p */) {}
 
-  /*!
-   * Notification after the creation of a new vertex.
+  /*! Notification after the creation of a new vertex.
    * \param v A handle to the created vertex.
    */
-  virtual void after_create_vertex (Vertex_handle /* v */)
+  virtual void after_create_vertex(Vertex_handle /* v */)
   {}
 
-  /*!
-   * Notification before the creation of a new boundary vertex.
+  /*! Notification before the creation of a new boundary vertex.
+   * \param p The on the surface boundary.
+   * \param ps_x The boundary condition of the vertex in x.
+   * \param ps_y The boundary condition of the vertex in y.
+   */
+  virtual void before_create_boundary_vertex(const Point_2& /* p */,
+                                             Arr_parameter_space /* ps_x */,
+                                             Arr_parameter_space /* ps_y */)
+  {}
+
+  /*! Notification before the creation of a new boundary vertex.
    * \param cv The curve incident to the surface boundary.
    * \param ind The relevant curve-end.
    * \param ps_x The boundary condition of the vertex in x.
    * \param ps_y The boundary condition of the vertex in y.
    */
-  virtual void before_create_boundary_vertex (const X_monotone_curve_2& /*cv*/,
-                                              Arr_curve_end /* ind */,
-                                              Arr_parameter_space /* ps_x */,
-                                              Arr_parameter_space /* ps_y */)
+  virtual void before_create_boundary_vertex(const X_monotone_curve_2& /* cv */,
+                                             Arr_curve_end /* ind */,
+                                             Arr_parameter_space /* ps_x */,
+                                             Arr_parameter_space /* ps_y */)
   {}
 
-  /*!
-   * Notification after the creation of a new vertex at infinity.
+  /*! Notification after the creation of a new vertex at infinity.
    * \param v A handle to the created vertex.
    */
-  virtual void after_create_boundary_vertex (Vertex_handle /* v */)
-  {}
+  virtual void after_create_boundary_vertex(Vertex_handle /* v */) {}
 
-  /*!
-   * Notification before the creation of a new edge.
+  /*! Notification before the creation of a new edge.
    * \param c The x-monotone curve to be associated with the edge.
    * \param v1 A handle to the first end-vertex of the edge.
    * \param v2 A handle to the second end-vertex of the edge.
    */
-  virtual void before_create_edge (const X_monotone_curve_2& /* c */,
-                                   Vertex_handle /* v1 */,
-                                   Vertex_handle /* v2 */)
+  virtual void before_create_edge(const X_monotone_curve_2& /* c */,
+                                  Vertex_handle /* v1 */,
+                                  Vertex_handle /* v2 */)
   {}
 
-  /*!
-   * Notification after the creation of a new edge.
+  /*! Notification after the creation of a new edge.
    * \param e A handle to one of the twin halfedges that were created.
    */
-  virtual void after_create_edge (Halfedge_handle /* e */)
-  {}
+  virtual void after_create_edge(Halfedge_handle /* e */) {}
 
-  /*!
-   * Notification before the modification of an existing vertex.
+  /*! Notification before the modification of an existing vertex.
    * \param v A handle to the vertex to be updated.
    * \param p The point to be associated with the vertex.
    */
-  virtual void before_modify_vertex (Vertex_handle /* v */,
-                                     const Point_2& /* p */)
+  virtual void before_modify_vertex(Vertex_handle /* v */,
+                                    const Point_2& /* p */)
   {}
 
-  /*!
-   * Notification after a vertex was modified.
+  /*! Notification after a vertex was modified.
    * \param v A handle to the updated vertex.
    */
-  virtual void after_modify_vertex (Vertex_handle /* v */)
-  {}
+  virtual void after_modify_vertex(Vertex_handle /* v */) {}
 
-  /*!
-   * Notification before the modification of an existing edge.
+  /*! Notification before the modification of an existing edge.
    * \param e A handle to one of the twin halfedges to be updated.
    * \param c The x-monotone curve to be associated with the edge.
    */
-  virtual void before_modify_edge (Halfedge_handle /* e */,
-                                   const X_monotone_curve_2& /* c */)
+  virtual void before_modify_edge(Halfedge_handle /* e */,
+                                  const X_monotone_curve_2& /* c */)
   {}
 
-  /*!
-   * Notification after an edge was modified.
+  /*! Notification after an edge was modified.
    * \param e A handle to one of the twin halfedges that were updated.
    */
-  virtual void after_modify_edge (Halfedge_handle /* e */)
-  {}
+  virtual void after_modify_edge(Halfedge_handle /* e */) {}
 
-  /*!
-   * Notification before the splitting of an edge into two.
+  /*! Notification before the splitting of an edge into two.
    * \param e A handle to one of the existing halfedges.
    * \param v A vertex representing the split point.
    * \param c1 The x-monotone curve to be associated with the first edge.
    * \param c2 The x-monotone curve to be associated with the second edge.
    */
-  virtual void before_split_edge (Halfedge_handle /* e */,
-                                  Vertex_handle /* v */,
-                                  const X_monotone_curve_2& /* c1 */,
-                                  const X_monotone_curve_2& /* c2 */)
+  virtual void before_split_edge(Halfedge_handle /* e */,
+                                 Vertex_handle /* v */,
+                                 const X_monotone_curve_2& /* c1 */,
+                                 const X_monotone_curve_2& /* c2 */)
   {}
 
-  /*!
-   * Notification after an edge was split.
+  /*! Notification after an edge was split.
    * \param e1 A handle to one of the twin halfedges forming the first edge.
    * \param e2 A handle to one of the twin halfedges forming the second edge.
    */
-  virtual void after_split_edge (Halfedge_handle /* e1 */,
-                                 Halfedge_handle /* e2 */)
+  virtual void after_split_edge(Halfedge_handle /* e1 */,
+                                Halfedge_handle /* e2 */)
   {}
 
-  /*!
-   * Notification before the splitting of a fictitious edge into two.
+  /*! Notification before the splitting of a fictitious edge into two.
    * \param e A handle to one of the existing halfedges.
    * \param v A vertex representing the unbounded split point.
    */
-  virtual void before_split_fictitious_edge (Halfedge_handle /* e */,
-                                             Vertex_handle /* v */)
+  virtual void before_split_fictitious_edge(Halfedge_handle /* e */,
+                                            Vertex_handle /* v */)
   {}
 
-  /*!
-   * Notification after a fictitious edge was split.
+  /*! Notification after a fictitious edge was split.
    * \param e1 A handle to one of the twin halfedges forming the first edge.
    * \param e2 A handle to one of the twin halfedges forming the second edge.
    */
-  virtual void after_split_fictitious_edge (Halfedge_handle /* e1 */,
-                                            Halfedge_handle /* e2 */)
+  virtual void after_split_fictitious_edge(Halfedge_handle /* e1 */,
+                                           Halfedge_handle /* e2 */)
   {}
 
-  /*!
-   * Notification before the splitting of a face into two.
+  /*! Notification before the splitting of a face into two.
    * \param f A handle to the existing face.
    * \param e The new edge whose insertion causes the face to split.
    */
-  virtual void before_split_face (Face_handle /* f */,
-                                  Halfedge_handle /* e */)
+  virtual void before_split_face(Face_handle /* f */,
+                                 Halfedge_handle /* e */)
   {}
 
-  /*!
-   * Notification after a face was split.
+  /*! Notification after a face was split.
    * \param f A handle to the face we have just split.
    * \param new_f A handle to the new face that has been created.
    * \param is_hole Whether the new face forms a hole inside f.
    */
-  virtual void after_split_face (Face_handle /* f */,
-                                 Face_handle /* new_f */,
+  virtual void after_split_face(Face_handle /* f */,
+                                Face_handle /* new_f */,
                                  bool /* is_hole */)
   {}
 
-  /*!
-   * Notification before the splitting of an outer CCB into two.
+  /*! Notification before the splitting of an outer CCB into two.
    * \param f A handle to the face that owns the outer CCB.
    * \param h A circulator representing the component boundary.
    * \param e The new edge whose removal causes the outer CCB to split.
    */
-  virtual void before_split_outer_ccb (Face_handle /* f */,
-                                       Ccb_halfedge_circulator /* h */,
-                                       Halfedge_handle /* e */)
+  virtual void before_split_outer_ccb(Face_handle /* f */,
+                                      Ccb_halfedge_circulator /* h */,
+                                      Halfedge_handle /* e */)
   {}
 
-  /*!
-   * Notification after an outer CCB was split.
+  /*! Notification after an outer CCB was split.
    * \param f A handle to the face that owns the outer CCBs.
    * \param h1 A circulator representing the boundary of the first component.
    * \param h2 A circulator representing the boundary of the second component.
    */
-  virtual void after_split_outer_ccb (Face_handle /* f */,
-                                      Ccb_halfedge_circulator /* h1 */,
-                                      Ccb_halfedge_circulator /* h2 */)
+  virtual void after_split_outer_ccb(Face_handle /* f */,
+                                     Ccb_halfedge_circulator /* h1 */,
+                                     Ccb_halfedge_circulator /* h2 */)
   {}
 
-  /*!
-   * Notification before the splitting of an inner CCB into two.
+  /*! Notification before the splitting of an inner CCB into two.
    * \param f A handle to the face containing the inner CCB.
    * \param h A circulator representing the component boundary.
    * \param e The new edge whose removal causes the inner CCB to split.
    */
-  virtual void before_split_inner_ccb (Face_handle /* f */,
-                                       Ccb_halfedge_circulator /* h */,
-                                       Halfedge_handle /* e */)
+  virtual void before_split_inner_ccb(Face_handle /* f */,
+                                      Ccb_halfedge_circulator /* h */,
+                                      Halfedge_handle /* e */)
   {}
 
-  /*!
-   * Notification after an inner CCB was split.
+  /*! Notification after an inner CCB was split.
    * \param f A handle to the face containing the inner CCBs.
    * \param h1 A circulator representing the boundary of the first component.
    * \param h2 A circulator representing the boundary of the second component.
    */
-  virtual void after_split_inner_ccb (Face_handle /* f */,
-                                      Ccb_halfedge_circulator /* h1 */,
-                                      Ccb_halfedge_circulator /* h2 */)
+  virtual void after_split_inner_ccb(Face_handle /* f */,
+                                     Ccb_halfedge_circulator /* h1 */,
+                                     Ccb_halfedge_circulator /* h2 */)
   {}
 
-  /*!
-   * Notification before the creation of a new outer CCB of a face.
+  /*! Notification before the creation of a new outer CCB of a face.
    * \param f A handle to the face that owns the outer CCB.
    * \param e A halfedge along the new outer CCB.
    */
-  virtual void before_add_outer_ccb (Face_handle /* f */,
-                                     Halfedge_handle /* e */)
+  virtual void before_add_outer_ccb(Face_handle /* f */,
+                                    Halfedge_handle /* e */)
   {}
 
-  /*!
-   * Notification after an outer CCB was added to a face.
+  /*! Notification after an outer CCB was added to a face.
    * \param h A circulator representing the boundary of the new outer CCB.
    */
-  virtual void after_add_outer_ccb (Ccb_halfedge_circulator /* h */)
-  {}
+  virtual void after_add_outer_ccb(Ccb_halfedge_circulator /* h */) {}
 
-  /*!
-   * Notification before the creation of a new inner CCB inside a face.
+  /*! Notification before the creation of a new inner CCB inside a face.
    * \param f A handle to the face containing the inner CCB.
    * \param e The new halfedge that forms the new inner CCB.
    */
-  virtual void before_add_inner_ccb (Face_handle /* f */,
-                                     Halfedge_handle /* e */)
+  virtual void before_add_inner_ccb(Face_handle /* f */,
+                                    Halfedge_handle /* e */)
   {}
 
-  /*!
-   * Notification after an inner CCB was created inside a face.
+  /*! Notification after an inner CCB was created inside a face.
    * \param h A circulator representing the boundary of the new inner CCB.
    */
-  virtual void after_add_inner_ccb (Ccb_halfedge_circulator /* h */)
-  {}
+  virtual void after_add_inner_ccb(Ccb_halfedge_circulator /* h */) {}
 
-  /*!
-   * Notification before the creation of a new isolated vertex inside a face.
+  /*! Notification before the creation of a new isolated vertex inside a face.
    * \param f A handle to the face containing the isolated vertex.
    * \param v The isolated vertex.
    */
-  virtual void before_add_isolated_vertex (Face_handle /* f */,
-                                           Vertex_handle /* v */)
+  virtual void before_add_isolated_vertex(Face_handle /* f */,
+                                          Vertex_handle /* v */)
   {}
 
-  /*!
-   * Notification after an isolated vertex was created inside a face.
+  /*! Notification after an isolated vertex was created inside a face.
    * \param v The isolated vertex.
    */
-  virtual void after_add_isolated_vertex (Vertex_handle /* v */)
-  {}
+  virtual void after_add_isolated_vertex(Vertex_handle /* v */) {}
 
-  /*!
-   * Notification before the merging of two edges.
+  /*! Notification before the merging of two edges.
    * \param e1 A handle to one of the halfedges forming the first edge.
    * \param e2 A handle to one of the halfedges forming the second edge.
    * \param c The x-monotone curve to be associated with the merged edge.
    */
-  virtual void before_merge_edge (Halfedge_handle /* e1 */,
-                                  Halfedge_handle /* e2 */,
-                                  const X_monotone_curve_2& /* c */)
+  virtual void before_merge_edge(Halfedge_handle /* e1 */,
+                                 Halfedge_handle /* e2 */,
+                                 const X_monotone_curve_2& /* c */)
   {}
 
-  /*!
-   * Notification after an edge was merged.
+  /*! Notification after an edge was merged.
    * \param e A handle to one of the twin halfedges forming the merged edge.
    */
-  virtual void after_merge_edge (Halfedge_handle /* e */)
-  {}
+  virtual void after_merge_edge(Halfedge_handle /* e */) {}
 
-  /*!
-   * Notification before the merging of two fictitious edges.
+  /*! Notification before the merging of two fictitious edges.
    * \param e1 A handle to one of the halfedges forming the first edge.
    * \param e2 A handle to one of the halfedges forming the second edge.
    */
-  virtual void before_merge_fictitious_edge (Halfedge_handle /* e1 */,
-                                             Halfedge_handle /* e2 */)
+  virtual void before_merge_fictitious_edge(Halfedge_handle /* e1 */,
+                                            Halfedge_handle /* e2 */)
   {}
 
-  /*!
-   * Notification after a fictitious edge was merged.
+  /*! Notification after a fictitious edge was merged.
    * \param e A handle to one of the twin halfedges forming the merged edge.
    */
-  virtual void after_merge_fictitious_edge (Halfedge_handle /* e */)
-  {}
+  virtual void after_merge_fictitious_edge(Halfedge_handle /* e */) {}
 
-  /*!
-   * Notification before the merging of two faces.
+  /*! Notification before the merging of two faces.
    * \param f1 A handle to the first face.
    * \param f2 A handle to the second face.
    * \param e The edge whose removal causes the faces to merge.
    */
-  virtual void before_merge_face (Face_handle /* f1 */,
-                                  Face_handle /* f2 */,
-                                  Halfedge_handle /* e */)
+  virtual void before_merge_face(Face_handle /* f1 */,
+                                 Face_handle /* f2 */,
+                                 Halfedge_handle /* e */)
   {}
 
-  /*!
-   * Notification after a face was merged.
+  /*! Notification after a face was merged.
    * \param f A handle to the merged face.
    */
-  virtual void after_merge_face (Face_handle /* f */)
-  {}
+  virtual void after_merge_face(Face_handle /* f */) {}
 
-  /*!
-   * Notification before the merging of two outer CCBs.
+  /*! Notification before the merging of two outer CCBs.
    * \param f A handle to the face that owns the outer CCBs.
    * \param h1 A circulator representing the boundary of the first component.
    * \param h2 A circulator representing the boundary of the second component.
    * \param e The edge whose insertion or removal causes the CCBs to merge.
    */
-  virtual void before_merge_outer_ccb (Face_handle /* f */,
-                                       Ccb_halfedge_circulator /* h1 */,
-                                       Ccb_halfedge_circulator /* h2 */,
-                                       Halfedge_handle /* e */)
+  virtual void before_merge_outer_ccb(Face_handle /* f */,
+                                      Ccb_halfedge_circulator /* h1 */,
+                                      Ccb_halfedge_circulator /* h2 */,
+                                      Halfedge_handle /* e */)
   {}
 
-  /*!
-   * Notification after an outer CCB was merged.
+  /*! Notification after an outer CCB was merged.
    * \param f A handle to the face that owns the outer CCBs.
    * \param h A circulator representing the boundary of the merged component.
    */
-  virtual void after_merge_outer_ccb (Face_handle /* f */,
-                                      Ccb_halfedge_circulator /* h */)
+  virtual void after_merge_outer_ccb(Face_handle /* f */,
+                                     Ccb_halfedge_circulator /* h */)
   {}
 
-  /*!
-   * Notification before the merging of two inner CCBs (holes).
+  /*! Notification before the merging of two inner CCBs (holes).
    * \param f A handle to the face that contains the inner CCBs.
    * \param h1 A circulator representing the boundary of the first component.
    * \param h2 A circulator representing the boundary of the second component.
    * \param e The edge whose insertion causes the inner CCBs to merge.
    */
-  virtual void before_merge_inner_ccb (Face_handle /* f */,
-                                       Ccb_halfedge_circulator /* h1 */,
-                                       Ccb_halfedge_circulator /* h2 */,
-                                       Halfedge_handle /* e */)
+  virtual void before_merge_inner_ccb(Face_handle /* f */,
+                                      Ccb_halfedge_circulator /* h1 */,
+                                      Ccb_halfedge_circulator /* h2 */,
+                                      Halfedge_handle /* e */)
   {}
 
-  /*!
-   * Notification after an inner CCB was merged.
+  /*! Notification after an inner CCB was merged.
    * \param f A handle to the face that contains the inner CCBs.
    * \param h A circulator representing the boundary of the merged component.
    */
-  virtual void after_merge_inner_ccb (Face_handle /* f */,
-                                      Ccb_halfedge_circulator /* h */)
+  virtual void after_merge_inner_ccb(Face_handle /* f */,
+                                     Ccb_halfedge_circulator /* h */)
   {}
 
-  /*!
-   * Notification before an outer CCB is moved from one face to another.
+  /*! Notification before an outer CCB is moved from one face to another.
    * \param from_f A handle to the face that currently owns the outer CCB.
    * \param to_f A handle to the face that should own the outer CCB.
    * \param h A circulator representing the boundary of the component.
    */
-  virtual void before_move_outer_ccb (Face_handle /* from_f */,
-                                      Face_handle /* to_f */,
-                                      Ccb_halfedge_circulator /* h */)
+  virtual void before_move_outer_ccb(Face_handle /* from_f */,
+                                     Face_handle /* to_f */,
+                                     Ccb_halfedge_circulator /* h */)
   {}
 
-  /*!
-   * Notification after an outer CCB is moved from one face to another.
+  /*! Notification after an outer CCB is moved from one face to another.
    * \param h A circulator representing the boundary of the component.
    */
-  virtual void after_move_outer_ccb (Ccb_halfedge_circulator /* h */)
-  {}
+  virtual void after_move_outer_ccb(Ccb_halfedge_circulator /* h */) {}
 
 
-  /*!
-   * Notification before an inner CCB is moved from one face to another.
+  /*! Notification before an inner CCB is moved from one face to another.
    * \param from_f A handle to the face currently containing the inner CCB.
    * \param to_f A handle to the face that should contain the inner CCB.
    * \param h A circulator representing the boundary of the component.
    */
-  virtual void before_move_inner_ccb (Face_handle /* from_f */,
-                                      Face_handle /* to_f */,
-                                      Ccb_halfedge_circulator /* h */)
+  virtual void before_move_inner_ccb(Face_handle /* from_f */,
+                                     Face_handle /* to_f */,
+                                     Ccb_halfedge_circulator /* h */)
   {}
 
   /*!
    * Notification after an inner CCB is moved from one face to another.
    * \param h A circulator representing the boundary of the component.
    */
-  virtual void after_move_inner_ccb (Ccb_halfedge_circulator /* h */)
-  {}
+  virtual void after_move_inner_ccb(Ccb_halfedge_circulator /* h */) {}
 
-  /*!
-   * Notification before an isolated vertex is moved from one face to another.
+  /*! Notification before an isolated vertex is moved from one face to another.
    * \param from_f A handle to the face currently containing the vertex.
    * \param to_f A handle to the face that should contain the vertex.
    * \param v The isolated vertex.
    */
-  virtual void before_move_isolated_vertex (Face_handle /* from_f */,
-                                            Face_handle /* to_f */,
-                                            Vertex_handle /* v */)
+  virtual void before_move_isolated_vertex(Face_handle /* from_f */,
+                                           Face_handle /* to_f */,
+                                           Vertex_handle /* v */)
   {}
 
-  /*!
-   * Notification after an isolated vertex is moved from one face to another.
+  /*! Notification after an isolated vertex is moved from one face to another.
    * \param v The isolated vertex.
    */
-  virtual void after_move_isolated_vertex (Vertex_handle /* v */)
-  {}
+  virtual void after_move_isolated_vertex(Vertex_handle /* v */) {}
 
-  /*!
-   * Notificaion before the removal of a vertex.
+  /*! Notificaion before the removal of a vertex.
    * \param v A handle to the vertex to be deleted.
    */
-  virtual void before_remove_vertex (Vertex_handle /* v */)
-  {}
+  virtual void before_remove_vertex(Vertex_handle /* v */) {}
 
-  /*!
-   * Notificaion after the removal of a vertex.
-   */
-  virtual void after_remove_vertex ()
-  {}
+  /*! Notificaion after the removal of a vertex. */
+  virtual void after_remove_vertex() {}
 
-  /*!
-   * Notification before the removal of an edge.
+  /*! Notification before the removal of an edge.
    * \param e A handle to one of the twin halfedges to be deleted.
    */
-  virtual void before_remove_edge (Halfedge_handle /* e */)
-  {}
+  virtual void before_remove_edge(Halfedge_handle /* e */) {}
 
-  /*!
-   * Notificaion after the removal of an edge.
-   */
-  virtual void after_remove_edge ()
-  {}
+  /*! Notificaion after the removal of an edge. */
+  virtual void after_remove_edge() {}
 
-  /*!
-   * Notification before the removal of an outer CCB.
+  /*! Notification before the removal of an outer CCB.
    * \param f The face that owns the outer CCB.
    * \param h A circulator representing the boundary of the component.
    */
-  virtual void before_remove_outer_ccb (Face_handle /* f */,
-                                        Ccb_halfedge_circulator /* h */)
+  virtual void before_remove_outer_ccb(Face_handle /* f */,
+                                       Ccb_halfedge_circulator /* h */)
   {}
 
-  /*!
-   * Notificaion after the removal of an outer CCB.
+  /*! Notificaion after the removal of an outer CCB.
    * \param f The face that used to own the outer CCB.
    */
-  virtual void after_remove_outer_ccb (Face_handle /* f */)
-  {}
+  virtual void after_remove_outer_ccb(Face_handle /* f */) {}
 
-  /*!
-   * Notification before the removal of an inner CCB.
+  /*! Notification before the removal of an inner CCB.
    * \param f The face containing the inner CCB.
    * \param h A circulator representing the boundary of the component.
    */
-  virtual void before_remove_inner_ccb (Face_handle /* f */,
-                                        Ccb_halfedge_circulator /* h */)
+  virtual void before_remove_inner_ccb(Face_handle /* f */,
+                                       Ccb_halfedge_circulator /* h */)
   {}
 
-  /*!
-   * Notificaion after the removal of an inner CCB.
+  /*! Notificaion after the removal of an inner CCB.
    * \param f The face that used to contain the inner CCB.
    */
-  virtual void after_remove_inner_ccb (Face_handle /* f */)
-  {}
+  virtual void after_remove_inner_ccb(Face_handle /* f */) {}
 
   //@}
-
 };
 
 } //namespace CGAL

Arrangement_on_surface_2/include/CGAL/Arr_spherical_topology_traits_2.h

@@ -12,11 +12,9 @@
 // This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 // WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 //
-// $URL$
-// $Id$
-//
 // Author(s)     : Efi Fogel         <efif@post.tau.ac.il>
 //                 Eric Berberich    <ericb@post.tau.ac.il>
+//                 Efi Fogel         <efif@post.tau.ac.il>
 
 #ifndef CGAL_ARR_SPHERICAL_TOPOLOGY_TRAITS_2_H
 #define CGAL_ARR_SPHERICAL_TOPOLOGY_TRAITS_2_H
@@ -243,13 +241,13 @@ public:
    * \param v the vertex.
    * \todo why is this needed, and where used?
    */
-  bool is_valid_vertex (const Vertex* /* v */) const { return true; }
+  bool is_valid_vertex(const Vertex* /* v */) const { return true; }
 
   /*! Obtain the number of valid vertices. */
   Size number_of_valid_vertices() const { return (m_dcel.size_of_vertices()); }
 
   /*! Determine whether the given halfedge is valid. */
-  bool is_valid_halfedge (const Halfedge* /* he */) const { return true; }
+  bool is_valid_halfedge(const Halfedge* /* he */) const { return true; }
 
   /*! Obtain the number of valid halfedges. */
   Size number_of_valid_halfedges() const
@@ -473,7 +471,19 @@ public:
   //@{
 
   /*! Receive a notification on the creation of a new boundary vertex that
-   * corresponds to the given curve end.
+   * corresponds to a point.
+   * \param v The new boundary vertex.
+   * \param p The point.
+   * \param ps_x The boundary condition of the curve end in x.
+   * \param ps_y The boundary condition of the curve end in y.
+   */
+  void notify_on_boundary_vertex_creation(Vertex* v,
+                                          const Point_2& p,
+                                          Arr_parameter_space ps_x,
+                                          Arr_parameter_space ps_y);
+
+  /*! Receive a notification on the creation of a new boundary vertex that
+   * corresponds to a given curve end.
    * \param v The new boundary vertex.
    * \param xc The x-monotone curve.
    * \param ind The curve end.
@@ -496,13 +506,12 @@ public:
    * \param swap_predecessors Output swap predeccesors or not;
    *        set correctly only if true is returned
    */
-  bool let_me_decide_the_outer_ccb(std::pair< CGAL::Sign, CGAL::Sign> signs1,
-                                   std::pair< CGAL::Sign, CGAL::Sign> signs2,
+  bool let_me_decide_the_outer_ccb(std::pair<CGAL::Sign, CGAL::Sign> signs1,
+                                   std::pair<CGAL::Sign, CGAL::Sign> signs2,
                                    bool& swap_predecessors) const;
 
 
-  /*!
-   * Given signs of two ccbs that show up when splitting upon insertion of
+  /*! Given signs of two ccbs that show up when splitting upon insertion of
    * curve into two, determine what happens to the face(s).
    * \param signs1 signs in x and y of the first implied ccb
    * \param signs2 signs in x and y of the secondd implied ccb
@@ -511,10 +520,10 @@ public:
    *         will form a hole in the original face.
    */
   std::pair<bool, bool>
-  face_split_after_edge_insertion(std::pair< CGAL::Sign,
-                                             CGAL::Sign > /* signs1 */,
-                                  std::pair< CGAL::Sign,
-                                             CGAL::Sign > /* signs2 */) const
+  face_split_after_edge_insertion(std::pair<CGAL::Sign,
+                                            CGAL::Sign> /* signs1 */,
+                                  std::pair<CGAL::Sign,
+                                            CGAL::Sign> /* signs2 */) const
   {
     // In case of a spherical topology, connecting two vertices on the same
     // inner CCB closes a new face that becomes a hole in the original face:
@@ -569,8 +578,7 @@ public:
                                      Arr_parameter_space ps_x,
                                      Arr_parameter_space ps_y);
 
-  /*!
-   * Locate the predecessor halfedge for the given curve around a given
+  /*! Locate the predecessor halfedge for the given curve around a given
    * vertex with boundary conditions.
    * \param v The vertex.
    * \param cv The x-monotone curve.
@@ -644,10 +652,9 @@ public:
 
   //! reference_face (non-const version).
   /*! The function returns a reference face of the arrangement.
-      All reference faces of arrangements of the same type have a common
-      point.
-      \return A pointer to the reference face.
-  */
+   * All reference faces of arrangements of the same type have a common point.
+   * \return A pointer to the reference face.
+   */
   Face* reference_face() { return spherical_face(); }
   //@}
 
@@ -684,7 +691,6 @@ protected:
    * on the line of discontinuity.
    */
   Face* _face_below_vertex_on_discontinuity(Vertex* v) const;
-
   //@}
 };
 

Arrangement_on_surface_2/include/CGAL/Arr_topology_traits/Arr_spherical_topology_traits_2_impl.h

@@ -28,7 +28,7 @@
 
 namespace CGAL {
 
-/*! \brief constructs default */
+  //! \brief constructs default.
 template <typename GeomTraits, typename Dcel>
 Arr_spherical_topology_traits_2<GeomTraits, Dcel>::
 Arr_spherical_topology_traits_2() :
@@ -41,7 +41,7 @@ Arr_spherical_topology_traits_2() :
   m_boundary_vertices = Vertex_map(Vertex_key_comparer(m_geom_traits));
 }
 
-/*! \brief constructs from a geometry-traits object. */
+//! \brief constructs from a geometry-traits object.
 template <typename GeomTraits, typename Dcel>
 Arr_spherical_topology_traits_2<GeomTraits, Dcel>::
 Arr_spherical_topology_traits_2(const Geometry_traits_2* traits) :
@@ -54,7 +54,7 @@ Arr_spherical_topology_traits_2(const Geometry_traits_2* traits) :
   m_boundary_vertices = Vertex_map(Vertex_key_comparer(m_geom_traits));
 }
 
-/*! \brief destructs */
+//! \brief destructs.
 template <typename GeomTraits, typename Dcel>
 Arr_spherical_topology_traits_2<GeomTraits, Dcel>::
 ~Arr_spherical_topology_traits_2()
@@ -68,10 +68,9 @@ Arr_spherical_topology_traits_2<GeomTraits, Dcel>::
   }
 }
 
-/*! \brief assigns the contents of another topology-traits class */
+//! \brief assigns the contents of another topology-traits class.
 template <typename GeomTraits, typename Dcel>
-void Arr_spherical_topology_traits_2<GeomTraits, Dcel>::
-assign(const Self& other)
+void Arr_spherical_topology_traits_2<GeomTraits, Dcel>::assign(const Self& other)
 {
   // Clear the current DCEL and duplicate the other DCEL.
   m_dcel.delete_all();
@@ -96,7 +95,7 @@ assign(const Self& other)
   dcel_updated();
 }
 
-/*! \brief initializes an empty DCEL structure. */
+//! \brief initializes an empty DCEL structure.
 template <typename GeomTraits_, typename Dcel_>
 void Arr_spherical_topology_traits_2<GeomTraits_, Dcel_>::dcel_updated()
 {
@@ -138,7 +137,7 @@ void Arr_spherical_topology_traits_2<GeomTraits_, Dcel_>::dcel_updated()
   CGAL_assertion(m_spherical_face != NULL);
 }
 
-/*! \brief initializes an empty DCEL structure. */
+//! \brief initializes an empty DCEL structure.
 template <typename GeomTraits, typename Dcel>
 void Arr_spherical_topology_traits_2<GeomTraits, Dcel>::init_dcel()
 {
@@ -156,7 +155,7 @@ void Arr_spherical_topology_traits_2<GeomTraits, Dcel>::init_dcel()
   m_south_pole = NULL;
 }
 
-/*! \brief determines whether a point lies in the interior of a given face. */
+//! \brief determines whether a point lies in the interior of a given face.
 template <typename GeomTraits, typename Dcel>
 bool Arr_spherical_topology_traits_2<GeomTraits, Dcel>::
 is_in_face(const Face* f, const Point_2& p, const Vertex* v) const
@@ -418,7 +417,7 @@ is_in_face(const Face* f, const Point_2& p, const Vertex* v) const
   return (num_intersections& 0x1);
 }
 
-/*! \brief compares the relative y-position of a point and a halfedge */
+//! \brief compares the relative y-position of a point and a halfedge.
 template <typename GeomTraits, typename Dcel>
 Comparison_result
 Arr_spherical_topology_traits_2<GeomTraits, Dcel>::
@@ -428,7 +427,7 @@ compare_y_at_x(const Point_2& p, const Halfedge* he) const
   return m_geom_traits->compare_y_at_x_2_object()(p, he->curve());
 }
 
-/*! \brief determine whether a vertex is associated with a curve end */
+//! \brief determine whether a vertex is associated with a curve end.
 template <typename GeomTraits, typename Dcel>
 bool Arr_spherical_topology_traits_2<GeomTraits, Dcel>::
 are_equal(const Vertex* v,
@@ -465,7 +464,30 @@ are_equal(const Vertex* v,
   return (m_geom_traits->compare_y_on_boundary_2_object()(p1, p2) == EQUAL);
 }
 
-/*! \brief receives a notification on the creation of a new boundary vertex */
+//! \brief receives a notification on the creation of a new boundary vertex.
+template <typename GeomTraits, typename Dcel>
+void
+Arr_spherical_topology_traits_2<GeomTraits, Dcel>::
+notify_on_boundary_vertex_creation(Vertex* v,
+                                   const Point_2& p,
+                                   Arr_parameter_space
+                                     CGAL_assertion_code(ps_x),
+                                   Arr_parameter_space ps_y)
+{
+  // std::cout << "notify_on_boundary_vertex_creation()" << std::endl;
+  if (ps_y == ARR_BOTTOM_BOUNDARY) {
+    m_south_pole = v;
+    return;
+  }
+  if (ps_y == ARR_TOP_BOUNDARY) {
+    m_north_pole = v;
+    return;
+  }
+  CGAL_assertion(ps_x != ARR_INTERIOR);
+  m_boundary_vertices.insert(Vertex_value(p, v));
+}
+
+//! \brief receives a notification on the creation of a new boundary vertex.
 template <typename GeomTraits, typename Dcel>
 void
 Arr_spherical_topology_traits_2<GeomTraits, Dcel>::
@@ -517,7 +539,8 @@ let_me_decide_the_outer_ccb(std::pair< CGAL::Sign, CGAL::Sign> signs1,
 
 /*! \brief given a curve end with boundary conditions and a face that contains
  * the interior of the curve, find a place for a boundary vertex that will
- * represent the curve end along the face boundary */
+ * represent the curve end along the face boundary.
+ */
 template <typename GeomTraits, typename Dcel>
 CGAL::Object
 Arr_spherical_topology_traits_2<GeomTraits, Dcel>::
@@ -553,7 +576,8 @@ place_boundary_vertex(Face* /* f */,
 }
 
 /*! \brief locate the predecessor halfedge for the given curve around a given
- * vertex with boundary conditions. */
+ * vertex with boundary conditions.
+ */
 template <typename GeomTraits, typename Dcel>
 typename Arr_spherical_topology_traits_2<GeomTraits, Dcel>::Halfedge*
 Arr_spherical_topology_traits_2<GeomTraits,Dcel>::
@@ -633,13 +657,13 @@ locate_curve_end(const X_monotone_curve_2& xc, Arr_curve_end ind,
   return CGAL::make_object(_face_below_vertex_on_discontinuity(v));
 }
 
-/*! \brief determines whether a given boundary vertex is redundant */
+//! \brief determines whether a given boundary vertex is redundant.
 template <typename GeomTraits, typename Dcel>
 bool Arr_spherical_topology_traits_2<GeomTraits, Dcel>::
 is_redundant(const Vertex* v) const
 { return (v->halfedge() == NULL); }
 
-/* \brief erases a given redundant vertex */
+//! \brief erases a given redundant vertex.
 template <typename GeomTraits, typename Dcel>
 typename Arr_spherical_topology_traits_2<GeomTraits, Dcel>::Halfedge*
 Arr_spherical_topology_traits_2<GeomTraits, Dcel>::

Arrangement_on_surface_2/include/CGAL/Arrangement_2/Arrangement_on_surface_2_impl.h

@@ -12,10 +12,6 @@
 // This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 // WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 //
-// $URL$
-// $Id$
-//
-//
 // Author(s)     : Ron Wein          <wein@post.tau.ac.il>
 //                 Efi Fogel         <efif@post.tau.ac.il>
 //                 Eric Berberich    <eric.berberich@cgal.org>
@@ -173,16 +169,13 @@ void Arrangement_on_surface_2<GeomTraits, TopTraits>::assign(const Self& arr)
   m_topol_traits.assign(arr.m_topol_traits);
 
   // Go over the vertices and create duplicates of the stored points.
-  Point_2* dup_p;
-  DVertex* p_v;
-
   typename Dcel::Vertex_iterator vit;
   for (vit = _dcel().vertices_begin(); vit != _dcel().vertices_end(); ++vit) {
-    p_v = &(*vit);
+    DVertex* p_v = &(*vit);
 
     if (! p_v->has_null_point()) {
       // Create the duplicate point and store it in the points container.
-      dup_p = _new_point(p_v->point());
+      Point_2* dup_p = _new_point(p_v->point());
 
       // Associate the vertex with the duplicated point.
       p_v->set_point(dup_p);
@@ -296,15 +289,29 @@ insert_in_face_interior(const Point_2& p, Face_handle f)
   std::cout << "face : " << &(*f) << std::endl;
 #endif
 
+  // Obtain the boundary conditions:
+  const Arr_parameter_space ps_x =
+    m_geom_traits->parameter_space_in_x_2_object()(p);
+  const Arr_parameter_space ps_y =
+    m_geom_traits->parameter_space_in_y_2_object()(p);
+
   // Create a new vertex associated with the given point.
-  // We assume the point has no boundary conditions.
-  DVertex* v = _create_vertex(p);
-  Vertex_handle vh(v);
+  // The point is either the interior of the parameter space or on the boundary.
+  DVertex* v(NULL);
+  if ((ps_x == ARR_INTERIOR) && (ps_y == ARR_INTERIOR))
+    v = _create_vertex(p);
+  else {
+    v = _create_boundary_vertex(p, ps_x, ps_y);
+
+    // Notify the topology traits on the creation of the boundary vertex.
+    m_topol_traits.notify_on_boundary_vertex_creation(v, p, ps_x, ps_y);
+  }
 
   // Insert v as an isolated vertex inside the given face.
   _insert_isolated_vertex(p_f, v);
 
   // Return a handle to the new isolated vertex.
+  Vertex_handle vh(v);
   return vh;
 }
 
@@ -2095,6 +2102,30 @@ _create_vertex(const Point_2& p)
   return v;
 }
 
+// Create a new vertex on boundary
+//
+template <typename GeomTraits, typename TopTraits>
+typename Arrangement_on_surface_2<GeomTraits, TopTraits>::DVertex*
+Arrangement_on_surface_2<GeomTraits, TopTraits>::
+_create_boundary_vertex(const Point_2& p,
+                        Arr_parameter_space ps_x, Arr_parameter_space ps_y)
+{
+  CGAL_precondition((ps_x != ARR_INTERIOR) || (ps_y != ARR_INTERIOR));
+
+  // Notify the observers that we are about to create a new boundary vertex.
+  _notify_before_create_boundary_vertex(p, ps_x, ps_y);
+
+  // Create a new vertex and set its boundary conditions.
+  DVertex* v = _dcel().new_vertex();
+  v->set_boundary(ps_x, ps_y);
+  v->set_point(_new_point(p));
+
+  // Notify the observers that we have just created a new boundary vertex.
+  _notify_after_create_boundary_vertex(Vertex_handle(v));
+
+  return v;
+}
+
 //-----------------------------------------------------------------------------
 // Create a new vertex on boundary
 //
@@ -2129,12 +2160,58 @@ _create_boundary_vertex(const X_monotone_curve_2& cv, Arr_curve_end ind,
   }
 
   // Notify the observers that we have just created a new boundary vertex.
-  Vertex_handle   vh(v);
-  _notify_after_create_boundary_vertex(vh);
+  _notify_after_create_boundary_vertex(Vertex_handle(v));
 
   return v;
 }
 
+//-----------------------------------------------------------------------------
+// Locate the DCEL features that will be used for inserting the given point,
+// which has a boundary condition, and set a proper vertex there.
+//
+template <typename GeomTraits, typename TopTraits>
+typename Arrangement_on_surface_2<GeomTraits, TopTraits>::DVertex*
+Arrangement_on_surface_2<GeomTraits, TopTraits>::
+_place_and_set_point(DFace* f, const Point_2& p,
+                     Arr_parameter_space ps_x, Arr_parameter_space ps_y)
+{
+  // Use the topology traits to locate the DCEL feature that contains the
+  // given point.
+  CGAL::Object obj = m_topol_traits.place_boundary_vertex(f, p, ps_x, ps_y);
+  DVertex* v;
+
+  // Act according to the result type.
+  DHalfedge* fict_he;
+  if (CGAL::assign(fict_he, obj)) {
+    // The point is located on a fictitious edge.
+    // Create a new vertex that corresponds to the point.
+    v = _create_boundary_vertex(p, ps_x, ps_y);
+
+    // Split the fictitious halfedge at the newly created vertex.
+    // The returned halfedge is the predecessor for the insertion of the curve
+    // end around v.
+    _notify_before_split_fictitious_edge(Halfedge_handle(fict_he),
+                                         Vertex_handle(v));
+    DHalfedge* p_pred = m_topol_traits.split_fictitious_edge(fict_he, v);
+    _notify_after_split_fictitious_edge(Halfedge_handle(p_pred),
+                                        Halfedge_handle((*p_pred)->next()));
+  }
+  else if (obj.is_empty()) {
+    // Create a new vertex that reprsents the given point.
+    v = _create_boundary_vertex(p, ps_x, ps_y);
+
+    // Notify the topology traits on the creation of the boundary vertex.
+    m_topol_traits.notify_on_boundary_vertex_creation(v, p, ps_x, ps_y);
+  }
+  else {
+    CGAL_assertion(CGAL::assign(v, obj));
+    // The vertex cpoincides with an existing vertex that represents the point.
+    // Do nothing.
+  }
+
+  return v;     // return the vertex that represents the point.
+}
+
 //-----------------------------------------------------------------------------
 // Locate the DCEL features that will be used for inserting the given curve
 // end, which has a boundary condition, and set the proper vertex there.

Arrangement_on_surface_2/include/CGAL/Arrangement_on_surface_2.h

@@ -1907,6 +1907,18 @@ protected:
    */
   DVertex* _create_vertex(const Point_2& p);
 
+  /*!
+   * Create a new boundary vertex.
+   * \param p The point on the boundary.
+   * \param bx The boundary condition in x.
+   * \param by The boundary condition in y.
+   * \pre Either bx or by does not equal ARR_INTERIOR.
+   * \return A pointer to the newly created vertex.
+   */
+  DVertex* _create_boundary_vertex(const Point_2& p,
+                                   Arr_parameter_space bx,
+                                   Arr_parameter_space by);
+
   /*!
    * Create a new boundary vertex.
    * \param cv The curve incident to the boundary.
@@ -1921,6 +1933,20 @@ protected:
                                    Arr_parameter_space bx,
                                    Arr_parameter_space by);
 
+  /*!
+   * Locate the DCEL features that will be used for inserting the given point,
+   * which has a boundary condition, and set a proper vertex there.
+   * \param f The face that contains the point.
+   * \param p The point.
+   * \param bx The boundary condition at the point x-coordinate.
+   * \param by The boundary condition at the point y-coordinate.
+   * \return The vertex that corresponds to the point.
+   */
+  DVertex* _place_and_set_point(DFace* f,
+                                const Point_2& p,
+                                Arr_parameter_space bx,
+                                Arr_parameter_space by);
+
   /*!
    * Locate the DCEL features that will be used for inserting the given curve
    * end, which has a boundary condition, and set a proper vertex there.
@@ -2259,6 +2285,17 @@ protected:
       (*iter)->after_create_vertex(v);
   }
 
+  void _notify_before_create_boundary_vertex(const Point_2& p,
+                                             Arr_parameter_space bx,
+                                             Arr_parameter_space by)
+  {
+    Observers_iterator iter;
+    Observers_iterator end = m_observers.end();
+
+    for (iter = m_observers.begin(); iter != end; ++iter)
+      (*iter)->before_create_boundary_vertex(p, bx, by);
+  }
+
   void _notify_before_create_boundary_vertex(const X_monotone_curve_2& cv,
                                              Arr_curve_end ind,
                                              Arr_parameter_space bx,