diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_3.h
index db82d2b78fa..d696e1917a3 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_3.h
@@ -143,17 +143,7 @@ public:
 
   Plane_3
   transform(const Plane_3& p) const
-  {
-    if(is_scaling()){
-      return this->Ptr()->transform(p);
-    }
-    if (is_even())
-      return Plane_3(transform(p.point()),
-                 transpose().inverse().transform(p.orthogonal_direction()));
-    else
-      return Plane_3(transform(p.point()),
-               - transpose().inverse().transform(p.orthogonal_direction()));
-  }
+  { return this->Ptr()->transform(p); }
 
   Plane_3
   operator()(const Plane_3& p) const
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_rep_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_rep_3.h
index 98a69b3a568..813a452f026 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_rep_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_rep_3.h
@@ -134,7 +134,12 @@ public:
 
   virtual Plane_3 transform(const Plane_3& p) const
   {
-      return p; // fix or never call
+      if (is_even())
+      return Plane_3(transform(p.point()),
+                 transpose().inverse().transform(p.orthogonal_direction()));
+    else
+      return Plane_3(transform(p.point()),
+               - transpose().inverse().transform(p.orthogonal_direction()));
   }
 
 
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Translation_rep_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Translation_rep_3.h
index eb897160252..488dc17f4e4 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Translation_rep_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Translation_rep_3.h
@@ -57,9 +57,13 @@ public:
     return d;
   }
 
-  virtual Plane_3 transform(const Plane_3 &d) const
+  virtual Plane_3 transform(const Plane_3 &p) const
   {
-    return d;  // fix or never call it
+    // direction ( which is (p.a(), p.b(), p.c())) does not change
+    return Plane_3(p.a(),
+                   p.b(),
+                   p.c(),
+                   p.d()  - ( p.a()*translationvector_.x() + p.b()*translationvector_.y() + p.c()*translationvector_.z()));
   }
 
   virtual Aff_transformation_3 operator*(const Transformation_base_3 &t) const