diff --git a/Nef_S2/include/CGAL/Nef_S2/Sphere_geometry_OGL.h b/Nef_S2/include/CGAL/Nef_S2/Sphere_geometry_OGL.h
index e7904529787..f0527bb932b 100644
--- a/Nef_S2/include/CGAL/Nef_S2/Sphere_geometry_OGL.h
+++ b/Nef_S2/include/CGAL/Nef_S2/Sphere_geometry_OGL.h
@@ -71,6 +71,23 @@ VVector convert(const CGAL::Vector_3<R>& v)
                  CGAL::to_double(v.y()),
                  CGAL::to_double(v.z())); }
 
+template <typename R>
+VVector normalize_and_convert(const CGAL::Vector_3<R>& v)
+{
+  typename R::FT xa = CGAL::abs(v.x());
+  typename R::FT ya = CGAL::abs(v.y());
+  typename R::FT za = CGAL::abs(v.z());
+  typename R::FT m = (std::max)((std::max)(xa,ya),za);
+  if (m==0) {
+      return VVector(0,0,0);
+  } else {
+      double xd = CGAL::to_double(v.x()/m);
+      double yd = CGAL::to_double(v.y()/m);
+      double zd = CGAL::to_double(v.z()/m);
+      VVector u(xd,yd,zd);
+      return u / CGAL_NTS sqrt(u*u) ; // normalize
+  }
+}
 
 const double refinement_angle = 0.1;
 const double shrink_fac = 0.995;
@@ -80,8 +97,7 @@ class Approximator {
 
  public:
   static VPoint approximate(const CGAL::Sphere_point<R>& p) {
-    VVector v = convert(p-CGAL::ORIGIN);
-    v = v / CGAL_NTS sqrt(v*v) ; // normalize
+    VVector v = normalize_and_convert(p-CGAL::ORIGIN);
     return CGAL::ORIGIN+v;
   }
    
diff --git a/Nef_S2/include/CGAL/Nef_polyhedron_S2.h b/Nef_S2/include/CGAL/Nef_polyhedron_S2.h
index 7a5dc5ffc9d..c980fabd6f3 100644
--- a/Nef_S2/include/CGAL/Nef_polyhedron_S2.h
+++ b/Nef_S2/include/CGAL/Nef_polyhedron_S2.h
@@ -350,6 +350,11 @@ public:
             f->mark() == true);
   }
 
+  bool is_sphere() const
+  {
+    return is_plane();
+  }
+
   void extract_complement()
   { CGAL_NEF_TRACEN("extract complement");
     if ( this->is_shared() ) clone_rep();
@@ -375,7 +380,7 @@ public:
     SHalfedge_iterator e;
     CGAL_forall_svertices(v,D) v->mark() = false;
     CGAL_forall_sedges(e,D) e->mark() = false;
-    if ( D.has_sloop() ) D.shalfloop()->mark() = false;
+    if ( D.has_shalfloop() ) D.shalfloop()->mark() = false;
     D.simplify();
   }
 
@@ -390,7 +395,7 @@ public:
     CGAL_forall_svertices(v,D) v->mark() = true;
     CGAL_forall_sedges(e,D)    e->mark() = true;
     CGAL_forall_sfaces(f,D)    f->mark() = false;
-    if ( D.has_sloop() )       D.shalfloop()->mark() = D.shalfoop()->twin() = true;
+    if ( D.has_shalfloop() )       D.shalfloop()->mark() = D.shalfoop()->twin()->mark() = true;
     D.simplify();
   }