diff --git a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h
index a30f19dacb5..a7234b61810 100644
--- a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h
+++ b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h
@@ -27,6 +27,7 @@
 #include <boost/random/variate_generator.hpp>
 #include <boost/unordered_map.hpp>
 #include <CGAL/internal/Periodic_3_triangulation_iterators_3.h>
+#include <CGAL/result_of.h>
 #include <CGAL/Periodic_3_triangulation_ds_cell_base_3.h>
 #include <CGAL/Periodic_3_triangulation_ds_vertex_base_3.h>
 #include <CGAL/Periodic_3_triangulation_traits_3.h>
@@ -648,7 +649,8 @@ public:
   // but       point()          -like functions have return type Point
 
   template<typename P> // can be Point or Point_3
-  Point_3 construct_point(const P& p) const {
+  typename boost::result_of<const typename Geom_traits::Construct_point_3(const P&)>::type
+  construct_point(const P& p) const {
     return geom_traits().construct_point_3_object()(p);
   }
 
diff --git a/Triangulation_2/include/CGAL/Triangulation_2.h b/Triangulation_2/include/CGAL/Triangulation_2.h
index de91b826848..079dcc18a11 100644
--- a/Triangulation_2/include/CGAL/Triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Triangulation_2.h
@@ -45,6 +45,7 @@
 #include <boost/random/variate_generator.hpp>
 #include <CGAL/boost/iterator/transform_iterator.hpp>
 #include <boost/iterator/zip_iterator.hpp>
+#include <boost/utility/result_of.hpp>
 
 #ifndef CGAL_TRIANGULATION_2_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
 #include <CGAL/internal/info_check.h>
@@ -295,9 +296,13 @@ public:
                Face_handle &fr) const;
 
   // GEOMETRIC FEATURES AND CONSTRUCTION
-  Point_2 construct_point(const Point& p) const;
+  template <typename P> // Point or Point_2
+  typename boost::result_of<const typename Geom_traits::Construct_point_2(const P&)>::type
+  construct_point(const P& p) const { return geom_traits().construct_point_2_object()(p); }
+
   const Point& point(Face_handle c, int i) const;
   const Point& point(Vertex_handle v) const;
+
   Segment segment(Face_handle f, int i) const;
   Segment segment(const Edge& e) const;
   Segment segment(const Edge_circulator& ec) const;
@@ -1064,14 +1069,6 @@ is_face(Vertex_handle v1,
   return _tds.is_face(v1, v2, v3, fr);
 }
 
-template <class Gt, class Tds >
-typename Triangulation_2<Gt, Tds>::Point_2
-Triangulation_2<Gt, Tds>::
-construct_point(const Point& p) const
-{
-  return geom_traits().construct_point_2_object()(p);
-}
-
 template <class Gt, class Tds >
 const typename Triangulation_2<Gt, Tds>::Point&
 Triangulation_2<Gt, Tds>::
diff --git a/Triangulation_3/include/CGAL/Triangulation_3.h b/Triangulation_3/include/CGAL/Triangulation_3.h
index 6f2f1f6807f..b1aabfce09d 100644
--- a/Triangulation_3/include/CGAL/Triangulation_3.h
+++ b/Triangulation_3/include/CGAL/Triangulation_3.h
@@ -563,7 +563,8 @@ protected:
 
 public:
   template<typename P> // Point or Point_3
-  Point_3 construct_point(const P& p) const
+  typename boost::result_of<const typename Geom_traits::Construct_point_3(const P&)>::type
+  construct_point(const P& p) const
   {
     return geom_traits().construct_point_3_object()(p);
   }