really use the GT given as a parameter

When the geom_traits given as parameter of `circumcenter` and/or
`weighted_circumcenter` was deriving from the cell base GT
(first template parameter), the gt was up-casted to the
cell base GT, and the function construct_circumcenter_3_object()
(or construct_weighted_circumcenter_3_object()) not
called on the right geom traits type --> possibly missing
the actual input of the function (the robust_circumcenter_traits in Mesh_3)

we add a static assert to check at compile time that both geom traits
are compatible

Mesh_3/include/CGAL/Compact_mesh_cell_base_3.h

@@ -38,6 +38,9 @@
 #include <CGAL/Regular_triangulation_cell_base_3.h>
 #include <CGAL/Mesh_3/io_signature.h>
 
+#include <boost/static_assert.hpp>
+#include <boost/core/is_same.hpp>
+
 #ifdef CGAL_LINKED_WITH_TBB
 # include <tbb/atomic.h>
 #endif
@@ -474,9 +477,18 @@ public:
     V[3] = v3;
   }
 
-  const Bare_point &
+  template<typename GT_>
-  weighted_circumcenter(const Geom_traits& gt = Geom_traits()) const
+  const Bare_point& weighted_circumcenter(const GT_& gt) const
   {
+    std::cout << "Point : " << typeid(Bare_point).name() << std::endl;
+    std::cout << "GT_ : " << typeid(GT_).name() << std::endl;
+    std::cout << "GT_::Construct_weighted_circumcenter_3 : "
+      << typeid(GT_::Construct_weighted_circumcenter_3).name() << std::endl;
+    std::cout << "result_type : " << typeid(GT_::Construct_weighted_circumcenter_3::result_type).name() << std::endl;
+
+    //BOOST_STATIC_ASSERT(boost::is_same<Bare_point,
+    //  typename GT_::Construct_weighted_circumcenter_3::result_type>::value);
+
     if (circumcenter_ == NULL) {
       this->try_to_set_circumcenter(
         new Bare_point(gt.construct_weighted_circumcenter_3_object()
@@ -494,6 +506,10 @@ public:
     return *circumcenter_;
   }
 
+  const Bare_point & weighted_circumcenter() const
+  {
+    return weighted_circumcenter(Geom_traits());
+  }
 
   // Returns the index of the cell of the input complex that contains the cell
   Subdomain_index subdomain_index() const { return subdomain_index_; }

Triangulation_3/include/CGAL/Delaunay_triangulation_cell_base_3.h

@@ -32,6 +32,9 @@
 #include <CGAL/Triangulation_ds_cell_base_3.h>
 #include <CGAL/Triangulation_cell_base_3.h>
 
+#include <boost/core/is_same.hpp>
+#include <boost/static_assert.hpp>
+
 namespace CGAL {
 
 template < typename GT, typename Cb = Triangulation_ds_cell_base_3<> >

Triangulation_3/include/CGAL/Regular_triangulation_cell_base_3.h

@@ -32,6 +32,9 @@
 
 #include <list>
 
+#include <boost/core/is_same.hpp>
+#include <boost/static_assert.hpp>
+
 namespace CGAL {
 
 template < typename GT,
@@ -121,8 +124,11 @@ public:
   //note this function is not requested by the RegularTriangulationCellBase_3
   //it should be replaced everywhere by weighted_circumcenter()
   // but remains here for backward compatibility
-  Point_3 circumcenter(const Geom_traits& gt = Geom_traits()) const
+  template<typename GT_>
+  Point_3 circumcenter(const GT_& gt) const
   {
+    BOOST_STATIC_ASSERT(boost::is_same<Point_3,
+      typename GT_::Construct_weighted_circumcenter_3::result_type>::value);
       return gt.construct_weighted_circumcenter_3_object()
         (this->vertex(0)->point(),
          this->vertex(1)->point(),
@@ -130,8 +136,16 @@ public:
          this->vertex(3)->point());
   }
 
-  Point_3 weighted_circumcenter(const Geom_traits& gt = Geom_traits()) const
+  Point_3 circumcenter() const
   {
+    return circumcenter(Geom_traits());
+  }
+
+  template<typename GT_>
+  Point_3 weighted_circumcenter(const GT_& gt) const
+  {
+    BOOST_STATIC_ASSERT(boost::is_same<Point_3,
+      typename GT_::Construct_weighted_circumcenter_3::result_type>::value);
       return gt.construct_weighted_circumcenter_3_object()
         (this->vertex(0)->point(),
          this->vertex(1)->point(),
@@ -139,6 +153,11 @@ public:
          this->vertex(3)->point());
   }
 
+  Point_3 weighted_circumcenter() const
+  {
+    return weighted_circumcenter(Geom_traits());
+  }
+
 private:
   Point_container _hidden;
 };