diff --git a/Periodic_2_triangulation_2/include/CGAL/Periodic_2_triangulation_2/internal/Functor_with_offset_points_adaptor_2.h b/Periodic_2_triangulation_2/include/CGAL/Periodic_2_triangulation_2/internal/Functor_with_offset_points_adaptor_2.h
index 7cff0fd5f76..d14518d7da4 100644
--- a/Periodic_2_triangulation_2/include/CGAL/Periodic_2_triangulation_2/internal/Functor_with_offset_points_adaptor_2.h
+++ b/Periodic_2_triangulation_2/include/CGAL/Periodic_2_triangulation_2/internal/Functor_with_offset_points_adaptor_2.h
@@ -29,7 +29,6 @@ class Functor_with_offset_points_adaptor_2
   typedef typename Kernel::Construct_point_2    Construct_point_2;
 
 public:
-  typedef typename Functor::result_type         result_type;
 
   Functor_with_offset_points_adaptor_2(const Functor& functor,
                                        const Construct_point_2& cp)
@@ -39,24 +38,24 @@ public:
   // gives access to function calls without offset
   using Functor::operator();
 
-  result_type operator()(const Point& p0, const Point& p1,
-                         const Offset& o0, const Offset& o1) const {
+  decltype(auto) operator()(const Point& p0, const Point& p1,
+                            const Offset& o0, const Offset& o1) const {
     return operator()(cp(p0,o0), cp(p1,o1));
   }
-  result_type operator()(const Point& p0, const Point& p1, const Point& p2,
-                         const Offset& o0, const Offset& o1, const Offset& o2) const {
+  decltype(auto) operator()(const Point& p0, const Point& p1, const Point& p2,
+                            const Offset& o0, const Offset& o1, const Offset& o2) const {
     return operator()(cp(p0,o0), cp(p1,o1), cp(p2,o2));
   }
-  result_type operator()(const Point& p0, const Point& p1,
-                         const Point& p2, const Point& p3,
-                         const Offset& o0, const Offset& o1,
-                         const Offset& o2, const Offset& o3) const {
+  decltype(auto) operator()(const Point& p0, const Point& p1,
+                            const Point& p2, const Point& p3,
+                            const Offset& o0, const Offset& o1,
+                            const Offset& o2, const Offset& o3) const {
     return operator()(cp(p0,o0), cp(p1,o1), cp(p2,o2), cp(p3,o3));
   }
-  result_type operator()(const Point& p0, const Point& p1,
-                         const Point& p2, const Point& p3, const Point& p4,
-                         const Offset& o0, const Offset& o1, const Offset& o2,
-                         const Offset& o3, const Offset& o4) const {
+  decltype(auto) operator()(const Point& p0, const Point& p1,
+                            const Point& p2, const Point& p3, const Point& p4,
+                            const Offset& o0, const Offset& o1, const Offset& o2,
+                            const Offset& o3, const Offset& o4) const {
     return operator()(cp(p0,o0), cp(p1,o1), cp(p2,o2), cp(p3,o3), cp(p4,o4));
   }
 
diff --git a/Periodic_2_triangulation_2/include/CGAL/Periodic_2_triangulation_2/internal/Static_filters/Periodic_2_orientation_2.h b/Periodic_2_triangulation_2/include/CGAL/Periodic_2_triangulation_2/internal/Static_filters/Periodic_2_orientation_2.h
index 255f72b4e63..75fdaf59853 100644
--- a/Periodic_2_triangulation_2/include/CGAL/Periodic_2_triangulation_2/internal/Static_filters/Periodic_2_orientation_2.h
+++ b/Periodic_2_triangulation_2/include/CGAL/Periodic_2_triangulation_2/internal/Static_filters/Periodic_2_orientation_2.h
@@ -92,12 +92,12 @@ public:
   typedef typename Kernel::Iso_rectangle_2        Iso_rectangle_2;
   typedef typename Kernel::Periodic_2_offset_2    Offset_2;
 
+  typedef typename Kernel:: Orientation            Orientation;
+
 public:
   const Iso_rectangle_2 * const _dom;
 
 public:
-  typedef typename Base::result_type  result_type;
-
   Periodic_2_orientation_2(const Iso_rectangle_2 * const dom,
                            const Base& o2b)
     : Base(o2b), _dom(dom)
@@ -106,7 +106,7 @@ public:
   using Base::operator();
 
   /// Normal static orientation test, copied from Orientation_2
-  result_type operator()(const Point_2 &p, const Point_2 &q, const Point_2 &r) const
+  Orientation operator()(const Point_2 &p, const Point_2 &q, const Point_2 &r) const
   {
     CGAL_PROFILER("Periodic_2_orientation_2 calls");
 
@@ -161,7 +161,7 @@ public:
 
 
   /// Static orientation test with offsets
-  result_type operator()(const Point_2 &p, const Point_2 &q, const Point_2 &r,
+  Orientation operator()(const Point_2 &p, const Point_2 &q, const Point_2 &r,
                          const Offset_2 &o_p, const Offset_2 &o_q, const Offset_2 &o_r) const
   {
 
diff --git a/Periodic_2_triangulation_2/include/CGAL/Periodic_2_triangulation_2/internal/Static_filters/Periodic_2_side_of_oriented_circle_2.h b/Periodic_2_triangulation_2/include/CGAL/Periodic_2_triangulation_2/internal/Static_filters/Periodic_2_side_of_oriented_circle_2.h
index 996db9f975a..8484871d9e3 100644
--- a/Periodic_2_triangulation_2/include/CGAL/Periodic_2_triangulation_2/internal/Static_filters/Periodic_2_side_of_oriented_circle_2.h
+++ b/Periodic_2_triangulation_2/include/CGAL/Periodic_2_triangulation_2/internal/Static_filters/Periodic_2_side_of_oriented_circle_2.h
@@ -45,8 +45,6 @@ private:
   const Iso_rectangle_2 * _dom;
 
 public:
-  typedef typename Base::result_type  result_type;
-
   Periodic_2_side_of_oriented_circle_2(const Iso_rectangle_2 * dom,
                                        const Base& socb)
     : Base(socb), _dom(dom)
diff --git a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3/internal/Functor_with_offset_points_adaptor_3.h b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3/internal/Functor_with_offset_points_adaptor_3.h
index 0edd5d23426..f813e6e7345 100644
--- a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3/internal/Functor_with_offset_points_adaptor_3.h
+++ b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3/internal/Functor_with_offset_points_adaptor_3.h
@@ -34,8 +34,6 @@ class Functor_with_offset_points_adaptor_3
   typedef typename Kernel::Construct_point_3    Construct_point_3;
 
 public:
-  typedef typename Functor::result_type         result_type;
-
   Functor_with_offset_points_adaptor_3(const Functor& functor,
                                        const Construct_point_3& cp)
     : Functor_(functor), cp(cp)
@@ -44,24 +42,24 @@ public:
   // gives access to function calls without offset
   using Functor::operator();
 
-  result_type operator()(const Point& p0, const Point& p1,
-                         const Offset& o0, const Offset& o1) const {
+  decltype(auto) operator()(const Point& p0, const Point& p1,
+                            const Offset& o0, const Offset& o1) const {
     return operator()(cp(p0,o0), cp(p1,o1));
   }
-  result_type operator()(const Point& p0, const Point& p1, const Point& p2,
-                         const Offset& o0, const Offset& o1, const Offset& o2) const {
+  decltype(auto) operator()(const Point& p0, const Point& p1, const Point& p2,
+                            const Offset& o0, const Offset& o1, const Offset& o2) const {
     return operator()(cp(p0,o0), cp(p1,o1), cp(p2,o2));
   }
-  result_type operator()(const Point& p0, const Point& p1,
-                         const Point& p2, const Point& p3,
-                         const Offset& o0, const Offset& o1,
-                         const Offset& o2, const Offset& o3) const {
+  decltype(auto) operator()(const Point& p0, const Point& p1,
+                            const Point& p2, const Point& p3,
+                            const Offset& o0, const Offset& o1,
+                            const Offset& o2, const Offset& o3) const {
     return operator()(cp(p0,o0), cp(p1,o1), cp(p2,o2), cp(p3,o3));
   }
-  result_type operator()(const Point& p0, const Point& p1,
-                         const Point& p2, const Point& p3, const Point& p4,
-                         const Offset& o0, const Offset& o1, const Offset& o2,
-                         const Offset& o3, const Offset& o4) const {
+  decltype(auto) operator()(const Point& p0, const Point& p1,
+                            const Point& p2, const Point& p3, const Point& p4,
+                            const Offset& o0, const Offset& o1, const Offset& o2,
+                            const Offset& o3, const Offset& o4) const {
     return operator()(cp(p0,o0), cp(p1,o1), cp(p2,o2), cp(p3,o3), cp(p4,o4));
   }
 
diff --git a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3/internal/Static_filters/Periodic_3_orientation_3.h b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3/internal/Static_filters/Periodic_3_orientation_3.h
index 9b19c03f511..f858558c45f 100644
--- a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3/internal/Static_filters/Periodic_3_orientation_3.h
+++ b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3/internal/Static_filters/Periodic_3_orientation_3.h
@@ -42,12 +42,12 @@ public:
   typedef typename K::Sphere_3               Sphere_3;
   typedef typename K::Periodic_3_offset_3    Offset;
 
+  typedef typename K::Orientation            Orientation;
+
 public:
   const Iso_cuboid_3 * const _dom;
 
 public:
- typedef typename Base::result_type  result_type;
-
  Periodic_3_orientation_3(const Iso_cuboid_3 * const dom,
                           const Orientation_3_base& o3b)
    : Base(o3b), _dom(dom)
@@ -55,7 +55,7 @@ public:
 
   using Base::operator();
 
-  result_type
+  Orientation
   operator()(const Point_3 &p, const Point_3 &q,
              const Point_3 &r, const Point_3 &s) const
   {
@@ -157,7 +157,7 @@ public:
       return Base::operator()(p, q, r, s);
   }
 
-  result_type
+  Orientation
   operator()(const Point_3 &p, const Point_3 &q,
              const Point_3 &r, const Point_3 &s,
              const Offset &o_p, const Offset &o_q,
diff --git a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3/internal/Static_filters/Periodic_3_side_of_oriented_sphere_3.h b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3/internal/Static_filters/Periodic_3_side_of_oriented_sphere_3.h
index 992e60d1ee0..9c0eae4b8de 100644
--- a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3/internal/Static_filters/Periodic_3_side_of_oriented_sphere_3.h
+++ b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3/internal/Static_filters/Periodic_3_side_of_oriented_sphere_3.h
@@ -42,9 +42,6 @@ public:
   typedef typename K::Iso_cuboid_3                      Iso_cuboid_3;
   typedef typename K::Periodic_3_offset_3               Offset;
 
-public:
-  typedef typename Base::result_type  result_type;
-
 private:
   const Iso_cuboid_3 * _dom;