diff --git a/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2/Arc_2.h b/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2/Arc_2.h
index c7d93b8773a..1a47492df29 100755
--- a/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2/Arc_2.h
+++ b/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2/Arc_2.h
@@ -254,6 +254,33 @@ public:
             return arc._maxpoint();
         }
         
+        // TODO move to SfA_2l
+        /*!\brief
+         * reverse rebind, i.e., extracts original arc type from a 
+         * rebound instance
+         */
+        Self operator()(const Rebound_arc_2& arc) {
+            Rep rep;
+            
+            rep._m_min = typename New_point_2::Rebind()(arc._minpoint());
+            rep._m_max = typename New_point_2::Rebind()(arc._maxpoint());
+            
+            rep._m_support = arc.ptr()->_m_support;
+            
+            rep._m_arcno = arc.ptr()->_m_arcno;
+            rep._m_arcno_min = arc.ptr()->_m_arcno_min;
+            rep._m_arcno_max = arc.ptr()->_m_arcno_max;
+
+            rep._m_is_vertical = arc.ptr()->_m_is_vertical;
+
+            rep._m_interval_id = arc.ptr()->_m_interval_id;
+
+            rep._m_boundary_in_interval = 
+                arc.ptr()->_m_boundary_in_interval;
+            
+            return Self(rep);
+        }
+
     protected:
         //! collect common assignments
         void copy_members(const Self& arc, New_rep& newrep) {
diff --git a/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2/Point_2.h b/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2/Point_2.h
index 3f094938d50..e55a9d742f2 100755
--- a/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2/Point_2.h
+++ b/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2/Point_2.h
@@ -199,6 +199,25 @@ public:
             newrep._m_location = pt.ptr()->_m_location;
             return Rebound_point_2(newrep);
         }
+
+        // TODO move to SfP_2l
+        /*!\brief
+         * reverse rebind, i.e., extracts original point type from a 
+         * rebound instance
+         */
+        Self operator()(const Rebound_point_2& pt) {
+            Rep rep;
+            rep._m_xy = pt.ptr()->_m_xy;
+            rep._m_x = pt.ptr()->_m_x;
+            rep._m_curve = pt.ptr()->_m_curve;
+            rep._m_arcno = pt.ptr()->_m_arcno;
+            if (pt.is_finite()) {
+                rep._m_location = CGAL::ARR_INTERIOR;
+            } else {
+                rep._m_location = pt.ptr()->_m_location;
+            }
+            return Self(rep);
+        }
     };
     
 public:
diff --git a/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2l/Surface_arc_2l.h b/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2l/Surface_arc_2l.h
index 611a0dfc710..cf1fbf83739 100644
--- a/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2l/Surface_arc_2l.h
+++ b/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2l/Surface_arc_2l.h
@@ -762,7 +762,13 @@ public:
      */
     Projected_arc_2 projected_arc() const {
         CGAL_precondition(!this->is_z_vertical());
-        CGAL_precondition(this->ptr()->_m_projected_arc);
+        if (!this->ptr()->_m_projected_arc) {
+            CGAL_precondition(dynamic_cast< const Kernel_arc_2* >(this));
+            this->ptr()->_m_projected_arc = 
+                typename Kernel_arc_2::Rebind()(
+                        *dynamic_cast< const Kernel_arc_2* >(this)
+                );
+        }
         return *(this->ptr()->_m_projected_arc);
     }
 
@@ -886,6 +892,8 @@ protected:
             replaced.first.ptr()->_m_sheet_max = sheet2;
         }
         
+        replaced.first.ptr()->_m_projected_arc = boost::none;
+        
         return replaced;
     }
 
diff --git a/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2l/Surface_point_2l.h b/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2l/Surface_point_2l.h
index c1e26cc38d0..30812aa4df7 100644
--- a/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2l/Surface_point_2l.h
+++ b/Curved_kernel_via_analysis_2/include/CGAL/Curved_kernel_via_analysis_2l/Surface_point_2l.h
@@ -161,7 +161,7 @@ public:
     Curve_analysis_2;
 
     //! type of kernel point
-    typedef typename Curved_kernel_via_analysis_2l::Point_2 Kernel_point;
+    typedef typename Curved_kernel_via_analysis_2l::Point_2 Kernel_point_2;
     
     //! type of Approximation
     typedef typename Rep::Approximation_3 Approximation_3;
@@ -191,7 +191,7 @@ public:
                      const Surface_3& surface, 
                      int sheet) :
         Base(Rebind()(pt)) {
-
+        
         this->copy_on_write();
         
         this->ptr()->_m_projected_point = pt;
@@ -271,8 +271,14 @@ public:
      * returns projected point
      */
     inline
-    const Projected_point_2& projected_point() const {
-        CGAL_precondition(this->ptr()->_m_projected_point);
+    Projected_point_2 projected_point() const {
+        if (!this->ptr()->_m_projected_point) {
+            CGAL_precondition(dynamic_cast< const Kernel_point_2* >(this));
+            this->ptr()->_m_projected_point = 
+                typename Kernel_point_2::Rebind()(
+                        *dynamic_cast< const Kernel_point_2* >(this)
+                );
+        }
         return *this->ptr()->_m_projected_point;
     }
 
@@ -321,17 +327,17 @@ public:
     //!
     //!\pre compared points have finite x/y-coordinates
     inline
-    CGAL::Comparison_result compare_xyz(const Kernel_point& q, 
-                                       bool equal_xy = false) const {
+    CGAL::Comparison_result compare_xyz(const Kernel_point_2& q, 
+                                        bool equal_xy = false) const {
         CGAL_precondition(this->is_finite());
         CGAL_precondition(q.is_finite());
         
         CGAL_CKvA_2l_GRAB_CK_FUNCTOR_FOR_POINT(Compare_xyz_3, 
                                                compare_xyz_3,
                                                compare_xyz_3_object);
-        CGAL_precondition(dynamic_cast< const Kernel_point* >(this));
+        CGAL_precondition(dynamic_cast< const Kernel_point_2* >(this));
         return compare_xyz_3(
-                *dynamic_cast< const Kernel_point* >(this), q, equal_xy
+                *dynamic_cast< const Kernel_point_2* >(this), q, equal_xy
         );
     }