diff --git a/Convex_hull_3/doc/Convex_hull_3/CGAL/Convex_hull_traits_3.h b/Convex_hull_3/doc/Convex_hull_3/CGAL/Convex_hull_traits_3.h
index fc7c70bfe46..c4c59b2141d 100644
--- a/Convex_hull_3/doc/Convex_hull_3/CGAL/Convex_hull_traits_3.h
+++ b/Convex_hull_3/doc/Convex_hull_3/CGAL/Convex_hull_traits_3.h
@@ -41,11 +41,6 @@ typedef unspecified_type Plane_3;
 
 /*!
 
-*/ 
-typedef R::Vector_3 Vector_3; 
-
-/*!
-
 */ 
 typedef Polyhedron_3<R> Polyhedron_3;
 
@@ -72,16 +67,7 @@ typedef R::Construct_triangle_3 Construct_triangle_3;
 /*!
 
 */ 
-typedef R::Construct_centroid_3 Construct_centroid_3; 
-
-/*!
-
-*/ 
-typedef R::Construct_vector_3 Construct_vector_3;
-/*!
-
-*/ 
-typedef R::Orientation_3 Orientation_3;
+typedef R::Construct_centroid_3 Construct_centroid_3;
 
 /*!
 
diff --git a/Convex_hull_3/doc/Convex_hull_3/Concepts/ConvexHullTraits_3.h b/Convex_hull_3/doc/Convex_hull_3/Concepts/ConvexHullTraits_3.h
index 4dc9f0a9d84..9b857d2165c 100644
--- a/Convex_hull_3/doc/Convex_hull_3/Concepts/ConvexHullTraits_3.h
+++ b/Convex_hull_3/doc/Convex_hull_3/Concepts/ConvexHullTraits_3.h
@@ -34,11 +34,6 @@ a 3D triangle
 */ 
 typedef unspecified_type Triangle_3; 
 
-/*!
-a 3D vector 
-*/ 
-typedef unspecified_type Vector_3; 
-
 /*!
 Function object type that provides 
 `Plane_3 operator()(Point_3 p, Point_3 q, Point_3 r)`, which constructs 
@@ -114,7 +109,7 @@ the 2D convex hull function `CGAL::ch_bykat()` such that `Traits::Point_2`
 is `Point_3`, and the 2D points considered in the algorithm are the projections
 of the 3D points in the `xy`-plane.
 If this type is not available, the function `CGAL::convex_hull_3()` will
-automatically use `CGAL::Projection_traits_xy< CGAL::Kernel_traits<Point_3>::Kernel >.`
+automatically use `CGAL::Projection_traits_xy< CGAL::Kernel_traits<Point_3>::%Kernel >.`
 */
 typedef unspecified_type Traits_xy_3;
 
@@ -128,24 +123,6 @@ Same as above but in the `xz`-plane
 */
 typedef unspecified_type Traits_xz_3;
 
-/*!
-Function object type that provides 
-`Vector_3 operator()(Point_3 p1, Point_3 p2)`, which 
-constructs and returns the vector `p1p2`, and
-`Vector_3 operator()(int x,int y,int z)` which constructs and returns
-a vector with integer Cartesian coordinates. 
-*/
-typedef unspecified_type Construct_vector_3;
-
-/*!
-Predicate object type that
-provides `CGAL::Orientation operator()(Vector_3 u, Vector_3 v, Vector_3 w)`
-which returns `CGAL::NEGATIVE` if u, v and w are negatively oriented,
-`CGAL::POSITIVE` if u, v and w are positively oriented and
-`CGAL::COPLANAR` if u, v and w are coplanar. 
-*/
-typedef unspecified_type Orientation_3;
-
 /// @}
 
 /// \name Creation 
diff --git a/Convex_hull_3/include/CGAL/convex_hull_3.h b/Convex_hull_3/include/CGAL/convex_hull_3.h
index 4056ed21ce3..4f6c7b7cb0e 100644
--- a/Convex_hull_3/include/CGAL/convex_hull_3.h
+++ b/Convex_hull_3/include/CGAL/convex_hull_3.h
@@ -312,12 +312,8 @@ struct Projection_traits<T,true>{
 template <class InputIterator, class Point_3, class Polyhedron_3, class Traits>
 void coplanar_3_hull(InputIterator first, InputIterator beyond,
                      const Point_3& p1, const Point_3& p2, const Point_3& p3, 
-                     Polyhedron_3& P, const Traits& traits)
+                     Polyhedron_3& P, const Traits& /* traits */)
 {
-  typedef typename Traits::Vector_3              Vector_3;
-  typedef typename Traits::Construct_vector_3    Construct_vector_3;
-  typedef typename Traits::Orientation_3         Orientation_3;
-
   typedef typename internal::Convex_hull_3::Projection_traits<Traits> PTraits;
   typedef typename PTraits::Traits_xy_3 Traits_xy_3;
   typedef typename PTraits::Traits_yz_3 Traits_yz_3;
@@ -326,31 +322,26 @@ void coplanar_3_hull(InputIterator first, InputIterator beyond,
   std::list<Point_3> CH_2;
   typedef typename std::list<Point_3>::iterator  CH_2_iterator;
  
-  Construct_vector_3 vector_3 = traits.construct_vector_3_object();
-  Orientation_3 orientation = traits.orientation_3_object();
-  Vector_3 v1 = vector_3(p1,p2);
-  Vector_3 v2 = vector_3(p1,p3);
- 
-  Vector_3 vx = vector_3(1,0,0);
-  
- 
-
-  if ( orientation(v1, v2, vx) != COPLANAR  )
+  Traits_xy_3 traits_xy;
+  typename Traits_xy_3::Left_turn_2 left_turn_in_xy = traits_xy.left_turn_2_object();
+  if ( left_turn_in_xy(p1,p2,p3) || left_turn_in_xy(p2,p1,p3) )
      convex_hull_points_2( first, beyond,
                            std::back_inserter(CH_2),
-                           Traits_yz_3() );
+                           traits_xy );
   else{
-    Vector_3 vy = vector_3(0,1,0);
-    if ( orientation(v1,v2,vy) != COPLANAR )
+    Traits_yz_3 traits_yz;
+    typename Traits_yz_3::Left_turn_2 left_turn_in_yz = traits_yz.left_turn_2_object();
+    if ( left_turn_in_yz(p1,p2,p3) || left_turn_in_yz(p2,p1,p3) )
        convex_hull_points_2( first, beyond,
                              std::back_inserter(CH_2),
-                             Traits_xz_3() );
+                             traits_yz );
     else{
-      CGAL_assertion_code( Vector_3 vz = vector_3(0,0,1); )
-      CGAL_assertion( orientation(v1,v2,vz) != COPLANAR );
-      convex_hull_points_2( first, beyond,
-                             std::back_inserter(CH_2),
-                             Traits_xy_3() );
+      Traits_xz_3 traits_xz;
+      CGAL_assertion_code( typename Traits_xz_3::Left_turn_2 left_turn_in_xz = traits_xz.left_turn_2_object(); )
+      CGAL_assertion( left_turn_in_xz(p1,p2,p3) || left_turn_in_xz(p2,p1,p3) );
+         convex_hull_points_2( first, beyond,
+                               std::back_inserter(CH_2),
+                               traits_xz );
     }
   }