diff --git a/Nef_S2/include/CGAL/Nef_S2/Sphere_circle.h b/Nef_S2/include/CGAL/Nef_S2/Sphere_circle.h
index e360c0c8ede..c1e956c0cff 100644
--- a/Nef_S2/include/CGAL/Nef_S2/Sphere_circle.h
+++ b/Nef_S2/include/CGAL/Nef_S2/Sphere_circle.h
@@ -67,7 +67,7 @@ between $p$ and $q$. If $p$ and $q$ are antipodal of each other then we
 create any great circle that contains $p$ and $q$.}*/ 
 { Point_3 p1(0,0,0), p4 = CGAL::ORIGIN + ((Base*) this)->orthogonal_vector();
   if ( p != q.antipode() ) {
-    if ( CGAL::orientation(p1,p,q,p4) != CGAL::POSITIVE )
+    if (R_().orientation_3_object()(p1,p,q,p4) != CGAL::POSITIVE )
       *this = Self(opposite());
   } else {
     /* previous method was: *this = Self(Plane_3(p1,q-p)); 
diff --git a/Nef_S2/include/CGAL/Nef_S2/Sphere_point.h b/Nef_S2/include/CGAL/Nef_S2/Sphere_point.h
index 63f2bf7252d..b4764664cda 100644
--- a/Nef_S2/include/CGAL/Nef_S2/Sphere_point.h
+++ b/Nef_S2/include/CGAL/Nef_S2/Sphere_point.h
@@ -21,6 +21,7 @@
 #define CGAL_SPHERE_POINT_H
 
 #include <CGAL/basic.h>
+#include <CGAL/Origin.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -123,8 +124,8 @@ Sphere_point<R> antipode() const
 }; // Sphere_point<R>
 
 template <typename R>
-CGAL::Point_3<R> operator+(
-  const CGAL::Point_3<R>& p, const Sphere_point<R>& q)
+typename R::Point_3 operator+
+  (const typename R::Point_3& p, const Sphere_point<R>& q)
 { return p + (q-CGAL::ORIGIN); }
 
 CGAL_END_NAMESPACE
diff --git a/Nef_S2/include/CGAL/Nef_S2/Sphere_segment.h b/Nef_S2/include/CGAL/Nef_S2/Sphere_segment.h
index 0839b4e2695..dcfd8211895 100644
--- a/Nef_S2/include/CGAL/Nef_S2/Sphere_segment.h
+++ b/Nef_S2/include/CGAL/Nef_S2/Sphere_segment.h
@@ -61,7 +61,7 @@ Sphere_segment_rep(const Circle& c1,
 { CGAL_assertion(!equal_as_sets(c1,c2)); 
   ps_ = intersection(c1,c2);
   pt_ = ps_.antipode();
-  if ( orientation(Point_3(0,0,0),ps_,pt_,
+  if ( R_::orientation(Point_3(0,0,0),ps_,pt_,
                    CGAL::ORIGIN + c_.orthogonal_vector()) !=
        CGAL::POSITIVE ) std::swap(ps_,pt_);
 }
@@ -188,15 +188,16 @@ void split_halfcircle(Sphere_segment<R>& s1,
 
 bool is_short() const 
 /*{\Mop a segment is short iff it is shorter than a halfcircle.}*/
-{ return CGAL::orientation(Point_3(0,0,0), source(), target(),
-                           CGAL::ORIGIN + this->ptr()->c_.orthogonal_vector()) 
-         == CGAL::POSITIVE; }
+{ 
+  return R().orientation_3_object()(Point_3(0,0,0), source(), target(),
+				    CGAL::ORIGIN + this->ptr()->c_.orthogonal_vector()) 
+    == CGAL::POSITIVE; }
 
 bool is_long() const 
 /*{\Mop a segment is long iff it is longer than a halfcircle.}*/
-{ return CGAL::orientation(Point_3(0,0,0), source(), target(),
-                           CGAL::ORIGIN + this->ptr()->c_.orthogonal_vector()) 
-         == CGAL::NEGATIVE; }
+{ return R().orientation_3_object()(Point_3(0,0,0), source(), target(),
+				    CGAL::ORIGIN + this->ptr()->c_.orthogonal_vector()) 
+    == CGAL::NEGATIVE; }
 
 bool is_degenerate() const { return source() == target(); }
 /*{\Mop return true iff |\Mvar| is degenerate.}*/