diff --git a/Kernel_23/include/CGAL/Kernel_23/internal/Projection_traits_3.h b/Kernel_23/include/CGAL/Kernel_23/internal/Projection_traits_3.h
index dd4e24005a4..1cc09421944 100644
--- a/Kernel_23/include/CGAL/Kernel_23/internal/Projection_traits_3.h
+++ b/Kernel_23/include/CGAL/Kernel_23/internal/Projection_traits_3.h
@@ -20,6 +20,7 @@
 
 #include <CGAL/Kernel/global_functions_2.h>
 #include <CGAL/Kernel_23/internal/Has_boolean_tags.h>
+#include <CGAL/Triangulation_structural_filtering_traits.h>
 
 namespace CGAL {
 
@@ -1210,6 +1211,14 @@ public:
 };
 
 
-} } //namespace CGAL::internal
+
+} // namespace internal
+
+template <class R, int dim>
+struct Triangulation_structural_filtering_traits<::CGAL::internal::Projection_traits_3<R,dim> > {
+  typedef typename Triangulation_structural_filtering_traits<R>::Use_structural_filtering_tag  Use_structural_filtering_tag;
+};
+
+ } //namespace CGAL
 
 #endif // CGAL_INTERNAL_PROJECTION_TRAITS_3_H
diff --git a/Triangulation_2/include/CGAL/Triangulation_2.h b/Triangulation_2/include/CGAL/Triangulation_2.h
index 14e8604640f..c0f2c7ba50e 100644
--- a/Triangulation_2/include/CGAL/Triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Triangulation_2.h
@@ -35,6 +35,7 @@
 #include <CGAL/Triangulation_2/internal/Triangulation_line_face_circulator_2.h>
 #include <CGAL/spatial_sort.h>
 #include <CGAL/Spatial_sort_traits_adapter_2.h>
+#include <CGAL/Kernel_23/internal/Projection_traits_3.h>
 
 #include <CGAL/double.h>
 
@@ -434,6 +435,81 @@ protected:
   bool has_inexact_negative_orientation(const Point &p, const Point &q,
                                         const Point &r) const;
 
+
+
+template <class T>
+inline
+bool
+projection_traits_has_inexact_negative_orientation(const Point &p, const Point &q, const Point &r,
+                                                   const T& ) const
+{
+  // So that this code works well with Lazy_kernel
+  internal::Static_filters_predicates::Get_approx<Point> get_approx;
+
+  const double px = to_double(get_approx(p).x());
+  const double py = to_double(get_approx(p).y());
+  const double qx = to_double(get_approx(q).x());
+  const double qy = to_double(get_approx(q).y());
+  const double rx = to_double(get_approx(r).x());
+  const double ry = to_double(get_approx(r).y());
+
+  const double pqx = qx - px;
+  const double pqy = qy - py;
+  const double prx = rx - px;
+  const double pry = ry - py;
+
+  return ( determinant(pqx, pqy, prx, pry) < 0);
+}
+
+template <class T>
+inline
+bool
+projection_traits_has_inexact_negative_orientation(const Point &p, const Point &q, const Point &r,
+                                                   const ::CGAL::internal::Projection_traits_3<T,0>& ) const
+{  // So that this code works well with Lazy_kernel
+  internal::Static_filters_predicates::Get_approx<Point> get_approx;
+
+  const double px = to_double(get_approx(p).y());
+  const double py = to_double(get_approx(p).z());
+  const double qx = to_double(get_approx(q).y());
+  const double qy = to_double(get_approx(q).z());
+  const double rx = to_double(get_approx(r).y());
+  const double ry = to_double(get_approx(r).z());
+
+  const double pqx = qx - px;
+  const double pqy = qy - py;
+  const double prx = rx - px;
+  const double pry = ry - py;
+
+  return ( determinant(pqx, pqy, prx, pry) < 0);
+}
+
+
+template <class T>
+inline
+bool
+projection_traits_has_inexact_negative_orientation(const Point &p, const Point &q, const Point &r,
+                                                   const ::CGAL::internal::Projection_traits_3<T,1>& ) const
+{  // So that this code works well with Lazy_kernel
+  internal::Static_filters_predicates::Get_approx<Point> get_approx;
+
+  const double px = to_double(get_approx(p).x());
+  const double py = to_double(get_approx(p).z());
+  const double qx = to_double(get_approx(q).x());
+  const double qy = to_double(get_approx(q).z());
+  const double rx = to_double(get_approx(r).x());
+  const double ry = to_double(get_approx(r).z());
+
+  const double pqx = qx - px;
+  const double pqy = qy - py;
+  const double prx = rx - px;
+  const double pry = ry - py;
+
+  return ( determinant(pqx, pqy, prx, pry) < 0);
+}
+
+
+
 public:
   Face_handle
   inexact_locate(const Point& p,
@@ -3152,6 +3228,7 @@ inexact_locate(const Point & t, Face_handle start, int n_of_turns) const
   return c;
 }
 
+
 template <class Gt, class Tds >
 inline
 bool
@@ -3159,22 +3236,8 @@ Triangulation_2<Gt, Tds>::
 has_inexact_negative_orientation(const Point &p, const Point &q,
                                  const Point &r) const
 {
-  // So that this code works well with Lazy_kernel
-  internal::Static_filters_predicates::Get_approx<Point> get_approx;
-
-  const double px = to_double(get_approx(p).x());
-  const double py = to_double(get_approx(p).y());
-  const double qx = to_double(get_approx(q).x());
-  const double qy = to_double(get_approx(q).y());
-  const double rx = to_double(get_approx(r).x());
-  const double ry = to_double(get_approx(r).y());
-
-  const double pqx = qx - px;
-  const double pqy = qy - py;
-  const double prx = rx - px;
-  const double pry = ry - py;
-
-  return ( determinant(pqx, pqy, prx, pry) < 0);
+  Gt gt;
+  return projection_traits_has_inexact_negative_orientation(p,q,r,gt);
 }
 #endif