diff --git a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
index ce58ca93cc4..e5b2c6f9de5 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
@@ -3341,8 +3341,17 @@ namespace CartesianKernelFunctors {
     typedef typename K::Segment_3  Segment_3;
     typedef typename K::Ray_3      Ray_3;
     typedef typename K::FT         FT;
+
   public:
-    typedef Point_3                result_type;
+    template<typename>
+    struct result {
+      typedef const Point_3 type;
+    };
+
+    template<typename F>
+    struct result<F(Point_3, Point_3)> {
+      typedef const Point_3& type;
+    };
 
     Point_3
     operator()( const Line_3& l, const Point_3& p ) const
@@ -3369,15 +3378,19 @@ namespace CartesianKernelFunctors {
 
     Point_3
     operator()( const Triangle_3& t, const Point_3& p ) const
-    { return CommonKernelFunctors::Construct_projected_point_3<K>()(p,t,K()); }
+    { return CommonKernelFunctors::Construct_projected_point_3<K>()(t,p,K()); }
 
     Point_3
     operator()( const Segment_3& s, const Point_3& p ) const
-    { return CommonKernelFunctors::Construct_projected_point_3<K>()(p,s,K()); }
+    { return CommonKernelFunctors::Construct_projected_point_3<K>()(s,p,K()); }
 
     Point_3
     operator()( const Ray_3& r, const Point_3& p ) const
-    { return CommonKernelFunctors::Construct_projected_point_3<K>()(p,r,K()); }
+    { return CommonKernelFunctors::Construct_projected_point_3<K>()(r,p,K()); }
+
+    const Point_3&
+    operator()( const Point_3& p, const Point_3& q) const
+    { return CommonKernelFunctors::Construct_projected_point_3<K>()(p,q,K()); }
   };
 
   template <class K>
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
index 8091a640d18..6f807504fff 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
@@ -3398,8 +3398,17 @@ namespace HomogeneousKernelFunctors {
     typedef typename K::Triangle_3 Triangle_3;
     typedef typename K::Segment_3  Segment_3;
     typedef typename K::Ray_3      Ray_3;
+
   public:
-    typedef Point_3          result_type;
+    template<typename>
+    struct result {
+      typedef const Point_3 type;
+    };
+
+    template<typename F>
+    struct result<F(Point_3, Point_3)> {
+      typedef const Point_3& type;
+    };
 
     Point_3
     operator()( const Line_3& l, const Point_3& p ) const
@@ -3429,15 +3438,19 @@ namespace HomogeneousKernelFunctors {
 
     Point_3
     operator()( const Triangle_3& t, const Point_3& p ) const
-    { return CommonKernelFunctors::Construct_projected_point_3<K>()(p,t,K()); }
+    { return CommonKernelFunctors::Construct_projected_point_3<K>()(t,p,K()); }
 
     Point_3
     operator()( const Segment_3& s, const Point_3& p ) const
-    { return CommonKernelFunctors::Construct_projected_point_3<K>()(p,s,K()); }
+    { return CommonKernelFunctors::Construct_projected_point_3<K>()(s,p,K()); }
 
     Point_3
     operator()( const Ray_3& r, const Point_3& p ) const
-    { return CommonKernelFunctors::Construct_projected_point_3<K>()(p,r,K()); }
+    { return CommonKernelFunctors::Construct_projected_point_3<K>()(r,p,K()); }
+
+    const Point_3&
+    operator()( const Point_3& p, const Point_3& q) const
+    { return CommonKernelFunctors::Construct_projected_point_3<K>()(p,q,K()); }
   };
 
   template <class K>
diff --git a/Kernel_23/include/CGAL/Kernel/function_objects.h b/Kernel_23/include/CGAL/Kernel/function_objects.h
index 06758a7d7a3..c3a7337aefb 100644
--- a/Kernel_23/include/CGAL/Kernel/function_objects.h
+++ b/Kernel_23/include/CGAL/Kernel/function_objects.h
@@ -2850,8 +2850,8 @@ namespace CommonKernelFunctors {
 
   public:
     typename K::Point_3
-    operator()(const typename K::Point_3& origin,
-               const typename K::Triangle_3& triangle,
+    operator()(const typename K::Triangle_3& triangle,
+               const typename K::Point_3& origin,
                const K& k)
     {
       typedef typename K::Point_3 Point_3;
@@ -2890,18 +2890,18 @@ namespace CommonKernelFunctors {
         if(linf_ab > linf_ac) {
           if(linf_ab > linf_bc) {
             // ab is the maximal segment
-            return this->operator()(origin, seg(a, b), k);
+            return this->operator()(seg(a, b), origin, k);
           } else {
             // ab > ac, bc >= ab, use bc
-            return this->operator()(origin, seg(b, c), k);
+            return this->operator()(seg(b, c), origin, k);
           }
         } else { // ab <= ac
           if(linf_ac > linf_bc) {
             // ac is the maximal segment
-            return this->operator()(origin, seg(a, c), k);
+            return this->operator()(seg(a, c), origin, k);
           } else {
             // ab <= ac, ac <= bc, use bc
-            return this->operator()(origin, seg(b, c), k);
+            return this->operator()(seg(b, c), origin, k);
           }
         }
       } // degenerate plane
@@ -2923,8 +2923,8 @@ namespace CommonKernelFunctors {
     }
 
     typename K::Point_3
-    operator()(const typename K::Point_3& query,
-               const typename K::Segment_3& segment,
+    operator()(const typename K::Segment_3& segment,
+               const typename K::Point_3& query,
                const K& k)
     {
 
@@ -2945,8 +2945,8 @@ namespace CommonKernelFunctors {
     }
 
     typename K::Point_3
-    operator()(const typename K::Point_3& query,
-               const typename K::Ray_3& ray,
+    operator()(const typename K::Ray_3& ray,
+               const typename K::Point_3& query,
                const K& k)
     {
       if ( ray.to_vector() * (query-ray.source()) <= 0)
@@ -2957,6 +2957,14 @@ namespace CommonKernelFunctors {
       }
     }
 
+    const typename K::Point_3&
+    operator()(const typename K::Point_3& point,
+               const typename K::Point_3&,
+               const K&)
+    {
+      return point;
+    }
+
     // code for operator for plane and point is defined in
     // CGAL/Cartesian/function_objects.h and CGAL/Homogeneous/function_objects.h
   };
@@ -3005,7 +3013,6 @@ namespace CommonKernelFunctors {
   public:
     typedef typename K::Boolean     result_type;
 
-    // There are 36 combinaisons, so I use a template.
     template <class T1, class T2>
     result_type
     operator()(const T1& t1, const T2& t2) const
@@ -3018,7 +3025,6 @@ namespace CommonKernelFunctors {
   public:
     typedef typename K::Boolean     result_type;
 
-    // There are x combinaisons, so I use a template.
     template <class T1, class T2>
     result_type
     operator()(const T1& t1, const T2& t2) const
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_fct_constructions_3.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_fct_constructions_3.h
index e45abb683e9..1931c2ae7e2 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_fct_constructions_3.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_fct_constructions_3.h
@@ -131,6 +131,8 @@ _test_fct_constructions_3(const R& r)
   assert( r.construct_projected_point_3_object()(ray, Point(-1,0,0)) == Point(0,0,0));
   assert( r.construct_projected_point_3_object()(s, Point(-1,0,0)) == Point(0,0,0));
   assert( r.construct_projected_point_3_object()(s, Point(2,0,0)) == Point(1,1,0));
+  assert( r.construct_projected_point_3_object()(Point(0,0,0), Point(2,0,0)) == Point(0,0,0));
+
   return true;
 }