diff --git a/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/CMakeLists.txt b/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/CMakeLists.txt
index ee478c44946..dd04cdd3318 100644
--- a/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/CMakeLists.txt
+++ b/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/CMakeLists.txt
@@ -57,6 +57,6 @@ include_directories( BEFORE ../../include )
 
 include( CGAL_CreateSingleSourceCGALProgram )
 
-create_single_source_cgal_program( "polygon_mesh_slicer_test.cpp" )
+create_single_source_cgal_program( "polygon_mesh_slicer.cpp" )
 
 
diff --git a/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/polygon_mesh_slicer.cpp b/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/polygon_mesh_slicer.cpp
index 60e37de0a07..88cfd93b77c 100644
--- a/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/polygon_mesh_slicer.cpp
+++ b/Polygon_mesh_processing/benchmark/Polygon_mesh_processing/polygon_mesh_slicer.cpp
@@ -97,7 +97,7 @@ int main(int argc, char* argv[])
 {
   std::ifstream input(argv[1]);
   Mesh m;
-  int N = 10;
+  int N = 100;
   if (!input || !(input >> m)){
     std::cerr << "Error: can not read file.\n";
     return 1;
@@ -116,6 +116,7 @@ int main(int argc, char* argv[])
   CGAL::Polygon_mesh_slicer_3<Mesh, K> slicer(m);
 
 
+  std::ofstream out("out.off");
   int polycount = 0;
   int vertex_count = 0;
   for(int i=0; i < N; i++){
@@ -125,11 +126,11 @@ int main(int argc, char* argv[])
     polycount += polylines.size();
     BOOST_FOREACH(Polyline pl, polylines){
       vertex_count += pl.size();
-      std::cout << pl.size();
+      out << pl.size();
       BOOST_FOREACH(Point_3 p, pl){
-        std::cout << " " << p;
+        out << " " << p;
       }
-      std::cout << std::endl;
+      out << std::endl;
     }
     t.start();
     
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/compute_normal.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/compute_normal.h
index bbc07cc5402..41894fb97a6 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/compute_normal.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/compute_normal.h
@@ -28,10 +28,23 @@ namespace CGAL{
 
 namespace Polygon_mesh_processing{
 
+#ifndef DOXYGEN_RUNNING
+template <class PolygonMesh>
+typename Kernel_traits<typename boost::property_traits<typename boost::property_map<PolygonMesh,CGAL::vertex_point_t>::type>::value_type>::Kernel::Vector_3
+compute_facet_normal(
+  typename boost::graph_traits<PolygonMesh>::face_descriptor f,
+  const PolygonMesh& pmesh)
+{
+  typedef typename Kernel_traits<typename boost::property_traits<typename boost::property_map<PolygonMesh,CGAL::vertex_point_t>::type>::value_type>::Kernel Kernel;
+  return compute_facet_normal(f, pmesh, Kernel());
+}
+#endif
+
+  // %CGAL `Kernel` with `FT` a model of `FieldWithSqrt`. This
 /**
 * \ingroup PkgPolygonMeshProcessing
 * computes the outward unit vector normal to facet `f`.
-* @tparam Kernel a %CGAL `Kernel` with `FT` a model of `FieldWithSqrt`
+* @tparam Kernel Geometric traits class. It can be omitted and deduced automatically from the point type of `PolygonMesh`.
 * @tparam PolygonMesh a model of `FaceGraph`
 *
 * @param f the facet on which the normal is computed
@@ -41,13 +54,14 @@ template <class Kernel, class PolygonMesh>
 typename Kernel::Vector_3
 compute_facet_normal(
   typename boost::graph_traits<PolygonMesh>::face_descriptor f,
-  const PolygonMesh& pmesh)
+  const PolygonMesh& pmesh,
+  const Kernel& )
 {
   typedef typename Kernel::Point_3 Point;
   typedef typename Kernel::Vector_3 Vector;
 
-  typename boost::property_map<PolygonMesh, boost::vertex_point_t>::const_type
-    ppmap = get(boost::vertex_point, pmesh);
+  typename boost::property_map<PolygonMesh, CGAL::vertex_point_t>::const_type
+    ppmap = get(CGAL::vertex_point, pmesh);
 
   Vector normal = CGAL::NULL_VECTOR;
   typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor halfedge_descriptor;
@@ -67,6 +81,19 @@ compute_facet_normal(
   return normal / std::sqrt(normal * normal);
 }
 
+
+#ifndef DOXYGEN_RUNNING
+template <class PolygonMesh>
+typename Kernel_traits<typename boost::property_traits<typename boost::property_map<PolygonMesh,CGAL::vertex_point_t>::type>::value_type>::Kernel::Vector_3
+compute_vertex_normal(
+  typename boost::graph_traits<PolygonMesh>::vertex_descriptor v,
+  const PolygonMesh& pmesh)
+{
+  typedef typename Kernel_traits<typename boost::property_traits<typename boost::property_map<PolygonMesh,CGAL::vertex_point_t>::type>::value_type>::Kernel Kernel;
+  return compute_vertex_normal(v, pmesh, Kernel());
+}
+#endif
+
 /**
 * \ingroup PkgPolygonMeshProcessing
 * computes the unit normal at vertex `v` as the average of the normals of incident facets.
@@ -80,7 +107,8 @@ template<typename Kernel, typename PolygonMesh>
 typename Kernel::Vector_3
 compute_vertex_normal(
     typename boost::graph_traits<PolygonMesh>::vertex_descriptor v,
-    const PolygonMesh& pmesh)
+    const PolygonMesh& pmesh,
+                      const Kernel& k)
 {
   typedef typename Kernel::Vector_3 Vector;
   typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor halfedge_descriptor;
@@ -92,7 +120,7 @@ compute_vertex_normal(
   {
     if (!is_border(he, pmesh))
     {
-      Vector n = compute_facet_normal<Kernel>(face(he, pmesh), pmesh);
+      Vector n = compute_facet_normal(face(he, pmesh), pmesh, k);
       normal = normal + (n / std::sqrt(n*n));
     }
     he = opposite(next(he, pmesh), pmesh);
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/is_oriented.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/is_oriented.h
index 959c93c844b..2efeef2338d 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/is_oriented.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/is_oriented.h
@@ -52,7 +52,16 @@ namespace internal{
 
   };
 } // end of namespace internal
-
+#ifndef DOXYGEN_RUNNING
+template <class PolygonMesh>
+bool
+is_outward_oriented(
+  const PolygonMesh& pmesh)
+{
+  typedef typename Kernel_traits<typename boost::property_traits<typename boost::property_map<PolygonMesh,CGAL::vertex_point_t>::type>::value_type>::Kernel Kernel;
+  return is_outward_oriented(pmesh, Kernel());
+}
+#endif
 /**
  * \ingroup PkgPolygonMeshProcessing
  * Tests whether a closed surface polygon mesh has a positive orientation.
@@ -76,10 +85,9 @@ namespace internal{
  * }
  * @endcode
  */
-template< class PolygonMesh >
-bool is_outward_oriented(const PolygonMesh& pmesh)
+  template<class Kernel, class PolygonMesh >
+  bool is_outward_oriented(const PolygonMesh& pmesh, const Kernel&k)
 {
-  typedef typename CGAL::Kernel_traits<typename PolygonMesh::Point>::Kernel Kernel;
   CGAL_warning(CGAL::is_closed(pmesh));
   CGAL_precondition(CGAL::is_valid(pmesh));
 
@@ -94,7 +102,7 @@ bool is_outward_oriented(const PolygonMesh& pmesh)
     = std::min_element(vbegin, vend, less_xyz);
 
   const typename Kernel::Vector_3&
-    normal_v_min = compute_vertex_normal<Kernel>(*v_min, pmesh);
+    normal_v_min = compute_vertex_normal(*v_min, pmesh, k);
 
   return normal_v_min[0] < 0 || (
             normal_v_min[0] == 0 && (
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/orient_polygon_mesh_test.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/orient_polygon_mesh_test.cpp
index a006709eea2..ac391901efb 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/orient_polygon_mesh_test.cpp
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/orient_polygon_mesh_test.cpp
@@ -1,6 +1,8 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Polyhedron_3.h>
+#include <CGAL/boost/graph/properties_Polyhedron_3.h>
 #include <CGAL/Surface_mesh.h>
+#include <CGAL/boost/graph/properties_Surface_mesh.h>
 #include <CGAL/Polygon_mesh_processing/is_oriented.h>
 
 #include <CGAL/IO/Polyhedron_iostream.h>