diff --git a/Mesh_3/include/CGAL/Mesh_3/Is_mesh_domain_field_3.h b/Mesh_3/include/CGAL/Mesh_3/Is_mesh_domain_field_3.h
new file mode 100644
index 00000000000..4cfc99a9231
--- /dev/null
+++ b/Mesh_3/include/CGAL/Mesh_3/Is_mesh_domain_field_3.h
@@ -0,0 +1,66 @@
+// Copyright (c) 2019 GeometryFactory Sarl  (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+// You can redistribute it and/or modify it under the terms of the GNU
+// General Public License as published by the Free Software Foundation,
+// either version 3 of the License, or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0+
+//
+//
+// Author(s)     : Laurent Rineau
+//
+//******************************************************************************
+// File Description :
+// Mesh_facet_criteria_3 class.
+//******************************************************************************
+
+#ifndef CGAL_MESH_3_IS_MESH_DOMAIN_FIELD_3_H
+#define CGAL_MESH_3_IS_MESH_DOMAIN_FIELD_3_H
+
+#include <CGAL/license/Mesh_3.h>
+
+#include <boost/config.hpp>
+#if BOOST_VERSION >= 106600
+#  include <boost/callable_traits/is_invocable.hpp>
+#else
+#  include <boost/mpl/has_xxx.hpp>
+#endif
+
+#include <CGAL/tags.h>
+
+namespace CGAL {
+  namespace Mesh_3 {
+#if BOOST_VERSION >= 106600
+    template <typename Tr, typename Type>
+    struct Is_mesh_domain_field_3 :
+      public CGAL::Boolean_tag
+      <
+        boost::callable_traits::is_invocable_r<
+          typename Tr::FT,
+          Type,
+          typename Tr::Bare_point,
+          int,
+          typename Tr::Vertex::Index
+        >::value
+      >
+    {};
+#else // Boost before 1.66
+    BOOST_MPL_HAS_XXX_TRAIT_DEF(FT)
+    template <typename Tr, typename Type>
+    struct Is_mesh_domain_field_3 : public Boolean_tag<has_FT<Type>::value>
+    {};
+#endif // Boost before 1.66
+  } // end namespace Mesh_3
+} // end namespace CGAL
+
+#endif // CGAL_MESH_3_IS_MESH_DOMAIN_FIELD_3_H
diff --git a/Mesh_3/include/CGAL/Mesh_cell_criteria_3.h b/Mesh_3/include/CGAL/Mesh_cell_criteria_3.h
index 2be2396971f..7cca176c3eb 100644
--- a/Mesh_3/include/CGAL/Mesh_cell_criteria_3.h
+++ b/Mesh_3/include/CGAL/Mesh_cell_criteria_3.h
@@ -27,6 +27,14 @@
 
 
 #include <CGAL/Mesh_3/mesh_standard_cell_criteria.h>
+#include <CGAL/Mesh_3/Is_mesh_domain_field_3.h>
+
+#include <boost/config.hpp>
+#if BOOST_VERSION >= 106600
+#  include <boost/callable_traits/is_invocable.hpp>
+#endif
+
+#include <type_traits>
 
 namespace CGAL {
   
@@ -65,13 +73,16 @@ public:
       init_radius_edge(radius_edge_bound);
   }
   
-  // Nb: SFINAE (dummy) to avoid wrong matches with built-in numerical types
+  // Nb: SFINAE to avoid wrong matches with built-in numerical types
   // as int.
   template <typename Sizing_field>
   Mesh_cell_criteria_3(const FT& radius_edge_bound,
                        const Sizing_field& radius_bound,
-                       typename Sizing_field::FT /*dummy*/ = 0)
-  { 
+                       typename std::enable_if<
+                         Mesh_3::Is_mesh_domain_field_3<Tr,Sizing_field>::value
+                       >::type* = 0
+                       )
+  {
     init_radius(radius_bound);
 
     if ( FT(0) != radius_edge_bound )
diff --git a/Mesh_3/include/CGAL/Mesh_edge_criteria_3.h b/Mesh_3/include/CGAL/Mesh_edge_criteria_3.h
index 67e5851640d..da35d8b33dd 100644
--- a/Mesh_3/include/CGAL/Mesh_edge_criteria_3.h
+++ b/Mesh_3/include/CGAL/Mesh_edge_criteria_3.h
@@ -30,7 +30,8 @@
 
 
 #include <CGAL/Mesh_constant_domain_field_3.h>
-#include <boost/type_traits.hpp>
+#include <CGAL/Mesh_3/Is_mesh_domain_field_3.h>
+#include <type_traits>
 
 namespace CGAL {
 namespace Mesh_3 {
@@ -55,24 +56,22 @@ namespace internal {
     virtual Sizing_field_interface* clone() const = 0;
   };
   
-  template < typename Sizing_field >
+  template < typename Sizing_field,
+             typename FT,
+             typename Point_3,
+             typename Index>
   struct Sizing_field_container
-    : public Sizing_field_interface < typename Sizing_field::FT,
-                                      typename Sizing_field::Point_3,
-                                      typename Sizing_field::Index >
+    : public Sizing_field_interface < FT,
+                                      Point_3,
+                                      Index >
   {
-    typedef Sizing_field_interface <
-              typename Sizing_field::FT,
-              typename Sizing_field::Point_3,
-              typename Sizing_field::Index > Base;
-    
-    typedef Sizing_field_container<Sizing_field> Self;
+    typedef Sizing_field_interface < FT,
+                                     Point_3,
+                                     Index > Base;
+
+    typedef Sizing_field_container<Sizing_field, FT, Point_3, Index> Self;
     
   public:
-    typedef typename Base::FT       FT;
-    typedef typename Base::Point_3  Point_3;
-    typedef typename Base::Index    Index;
-    
     Sizing_field_container(const Sizing_field& s) : s_(s) {}
     virtual ~Sizing_field_container() {}
     
@@ -109,23 +108,25 @@ public:
   /// Constructors
   Mesh_edge_criteria_3(const FT& value)
     : p_size_(new Mesh_3::internal::Sizing_field_container<
-                Mesh_constant_domain_field_3<Gt,Index> >(value))
+                Mesh_constant_domain_field_3<Gt,Index> ,
+                FT,
+                Point_3,
+                Index>(value))
   {}
-  
-  // Nb: SFINAE (dummy) to avoid wrong matches with built-in numerical types
+
+  // Nb: SFINAE to avoid wrong matches with built-in numerical types
   // as int.
   template < typename Sizing_field >
-  Mesh_edge_criteria_3(const Sizing_field& size,
-                       typename Sizing_field::FT /*dummy*/ = 0 )
+  Mesh_edge_criteria_3
+  (
+   const Sizing_field& size,
+   typename std::enable_if<Mesh_3::Is_mesh_domain_field_3<Tr, Sizing_field>::value>::type* = 0
+   )
   {
-    CGAL_static_assertion((boost::is_same<typename Sizing_field::FT,
-                                          FT>::value));
-    CGAL_static_assertion((boost::is_same<typename Sizing_field::Point_3,
-                                          Point_3>::value));
-    CGAL_static_assertion((boost::is_same<typename Sizing_field::Index,
-                                          Index>::value));
-                          
-    p_size_ = new Mesh_3::internal::Sizing_field_container<Sizing_field>(size);
+    p_size_ = new Mesh_3::internal::Sizing_field_container<Sizing_field,
+                                                           FT,
+                                                           Point_3,
+                                                           Index>(size);
   }
 
   Mesh_edge_criteria_3(const Self& rhs)
diff --git a/Mesh_3/include/CGAL/Mesh_facet_criteria_3.h b/Mesh_3/include/CGAL/Mesh_facet_criteria_3.h
index d16fbcf8e3c..5ad322f3b3b 100644
--- a/Mesh_3/include/CGAL/Mesh_facet_criteria_3.h
+++ b/Mesh_3/include/CGAL/Mesh_facet_criteria_3.h
@@ -32,6 +32,7 @@
 
 #include <CGAL/Mesh_3/mesh_standard_facet_criteria.h>
 #include <CGAL/Mesh_facet_topology.h>
+#include <CGAL/Mesh_3/Is_mesh_domain_field_3.h>
 
 namespace CGAL {
   
@@ -59,83 +60,21 @@ public:
   /**
    * @brief Constructor
    */
-  Mesh_facet_criteria_3(const FT& angle_bound,
-                        const FT& radius_bound,
-                        const FT& distance_bound,
-                        const Mesh_facet_topology topology =
-                          FACET_VERTICES_ON_SURFACE)
-  {
-    if ( FT(0) != angle_bound )
-      init_aspect(angle_bound);
-    
-    if ( FT(0) != radius_bound )
-      init_radius_bound(radius_bound);
-    
-    if ( FT(0) != distance_bound )
-      init_distance_bound(distance_bound);
-    
-    init_topo(topology);
-  }
-
-  // Nb: SFINAE (dummy) to avoid wrong matches with built-in numerical types
-  // as int.
-  template < typename Sizing_field >
-  Mesh_facet_criteria_3(const FT& angle_bound,
-                        const Sizing_field& radius_bound,
-                        const FT& distance_bound,
-                        const Mesh_facet_topology topology = 
-                          FACET_VERTICES_ON_SURFACE,
-                        typename Sizing_field::FT /*dummy*/ = 0)
-  {
-    if ( FT(0) != angle_bound )
-      init_aspect(angle_bound);
-    
-    init_radius_field(radius_bound);
-    
-    if ( FT(0) != distance_bound )
-      init_distance_bound(distance_bound);
-    
-    init_topo(topology);  
-  }
-  
-  // Nb: SFINAE (dummy) to avoid wrong matches with built-in numerical types
-  // as int.
-  template < typename Sizing_field >
-  Mesh_facet_criteria_3(const FT& angle_bound,
-                        const FT& radius_bound,
-                        const Sizing_field& distance_bound,
-                        const Mesh_facet_topology topology =
-                          FACET_VERTICES_ON_SURFACE,
-                        typename Sizing_field::FT /*dummy*/ = 0)
-  {
-    if ( FT(0) != angle_bound )
-      init_aspect(angle_bound);
-
-    if ( FT(0) != radius_bound )
-      init_radius_bound(radius_bound);
-
-    init_distance_field(distance_bound);
-
-    init_topo(topology);
-  }
-
-  // Nb: SFINAE (dummy) to avoid wrong matches with built-in numerical types
-  // as int.
   template < typename Sizing_field, typename Sizing_field2 >
   Mesh_facet_criteria_3(const FT& angle_bound,
                         const Sizing_field & radius_bound,
                         const Sizing_field2& distance_bound,
                         const Mesh_facet_topology topology =
-                          FACET_VERTICES_ON_SURFACE,
-                        typename Sizing_field::FT /*dummy*/ = 0,
-                        typename Sizing_field2::FT /*dummy*/ = 0)
+                          FACET_VERTICES_ON_SURFACE)
   {
     if ( FT(0) != angle_bound )
       init_aspect(angle_bound);
 
-    init_radius_field(radius_bound);
+    init_radius(radius_bound,
+                Mesh_3::Is_mesh_domain_field_3<Tr, Sizing_field>());
 
-    init_distance_field(distance_bound);
+    init_distance(distance_bound,
+                  Mesh_3::Is_mesh_domain_field_3<Tr, Sizing_field2>());
 
     init_topo(topology);
   }
@@ -169,27 +108,29 @@ private:
     criteria_.add(new Aspect_criterion(angle_bound));
   }
   
-  void init_radius_bound(const FT& radius_bound)
+  void init_radius(const FT& radius_bound, Tag_false)
   {
+    if(FT(0) == radius_bound) return;
     typedef Mesh_3::Uniform_size_criterion<Tr,Visitor> Uniform_size_criterion;
     criteria_.add(new Uniform_size_criterion(radius_bound));
   }
   
   template <typename Sizing_field>
-  void init_radius_field(const Sizing_field& radius_bound)
+  void init_radius(const Sizing_field& radius_bound, Tag_true)
   {
     typedef Mesh_3::Variable_size_criterion<Tr,Visitor,Sizing_field> Variable_size_criterion;
     criteria_.add(new Variable_size_criterion(radius_bound));
   }
   
-  void init_distance_bound(const FT& distance_bound)
+  void init_distance(const FT& distance_bound, Tag_false)
   {
+    if(FT(0) == distance_bound) return;
     typedef Mesh_3::Uniform_curvature_size_criterion<Tr,Visitor> Criterion;
     criteria_.add(new Criterion(distance_bound));
   }
   
   template <typename Sizing_field>
-  void init_distance_field(const Sizing_field& distance_bound)
+  void init_distance(const Sizing_field& distance_bound, Tag_true)
   {
     typedef Mesh_3::Variable_curvature_size_criterion<Tr,
                                                       Visitor,
diff --git a/Mesh_3/test/Mesh_3/test_mesh_capsule_var_distance_bound.cpp b/Mesh_3/test/Mesh_3/test_mesh_capsule_var_distance_bound.cpp
index bde524dbaa5..6844be0e5f4 100644
--- a/Mesh_3/test/Mesh_3/test_mesh_capsule_var_distance_bound.cpp
+++ b/Mesh_3/test/Mesh_3/test_mesh_capsule_var_distance_bound.cpp
@@ -7,6 +7,8 @@
 #include <CGAL/Labeled_mesh_domain_3.h>
 #include <CGAL/make_mesh_3.h>
 
+#include <boost/version.hpp>
+
 // Domain
 typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
 typedef K::FT FT;
@@ -42,7 +44,14 @@ FT capsule_function(const Point& p)
   else if(z < FT(-5)) return base+CGAL::square(z+5);
   else return base;
 }
-
+#if BOOST_VERSION >= 106600
+auto field = [](const Point& p, const int, const Mesh_domain::Index)
+             {
+               if(p.z() > 2) return 0.025;
+               if(p.z() < -3) return 0.01;
+               else return 1.;
+             };
+#else
 struct Field {
   typedef ::FT FT;
   
@@ -52,6 +61,7 @@ struct Field {
     else return 1;
   }
 } field;
+#endif
 
 int main()
 {