diff --git a/BGL/include/CGAL/boost/parameter.h b/BGL/include/CGAL/boost/parameter.h
index 6549eba09d9..785a8ab97a5 100644
--- a/BGL/include/CGAL/boost/parameter.h
+++ b/BGL/include/CGAL/boost/parameter.h
@@ -111,6 +111,7 @@ BOOST_PARAMETER_NAME( (dump_after_perturb_prefix, tag ) dump_after_perturb_prefi
 BOOST_PARAMETER_NAME( (dump_after_exude_prefix, tag ) dump_after_exude_prefix_)
 BOOST_PARAMETER_NAME( (number_of_initial_points, tag) number_of_initial_points_)
 BOOST_PARAMETER_NAME( (maximal_number_of_vertices, tag ) maximal_number_of_vertices_)
+BOOST_PARAMETER_NAME( (nonlinear_growth_of_balls, tag ) nonlinear_growth_of_balls_)
 BOOST_PARAMETER_NAME( (pointer_to_error_code, tag ) pointer_to_error_code_)
 BOOST_PARAMETER_NAME( (pointer_to_stop_atomic_boolean, tag ) pointer_to_stop_atomic_boolean_)
 
diff --git a/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h b/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h
index 2f23191b16b..5d26b1f5af8 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h
@@ -44,6 +44,7 @@
 #include <CGAL/Mesh_3/utilities.h>
 #include <CGAL/Mesh_3/Triangulation_helpers.h>
 #include <CGAL/iterator.h>
+#include <CGAL/Mesh_error_code.h>
 #if CGAL_MESH_3_PROTECTION_DEBUG
 #  include <CGAL/Mesh_3/Dump_c3t3.h>
 #endif
@@ -55,6 +56,7 @@
 #include <CGAL/iterator.h>
 #include <CGAL/number_utils.h>
 #include <CGAL/Delaunay_triangulation_3.h>
+#include <CGAL/atomic.h>
 
 #include <CGAL/boost/iterator/transform_iterator.hpp>
 
@@ -148,7 +150,13 @@ public:
   Protect_edges_sizing_field(C3T3& c3t3,
                              const MeshDomain& domain,
                              SizingFunction size=SizingFunction(),
-                             const FT minimal_size = FT());
+                             const FT minimal_size = FT(),
+                             std::size_t maximal_number_of_vertices = 0,
+                             Mesh_error_code* error_code = 0
+#ifndef CGAL_NO_ATOMIC
+                             , CGAL::cpp11::atomic<bool>* stop_ptr = 0
+#endif
+                             );
 
   void operator()(const bool refine = true);
 
@@ -156,6 +164,27 @@ public:
     nonlinear_growth_of_balls = b;
   }
 
+  bool forced_stop() const {
+#ifndef CGAL_NO_ATOMIC
+    if(stop_ptr_ != 0 &&
+       stop_ptr_->load(CGAL::cpp11::memory_order_acquire) == true)
+    {
+      if(error_code_ != 0) *error_code_ = CGAL_MESH_3_STOPPED;
+      return true;
+    }
+#endif // not defined CGAL_NO_ATOMIC
+    if(maximal_number_of_vertices_ != 0 &&
+       c3t3_.triangulation().number_of_vertices() >=
+       maximal_number_of_vertices_)
+    {
+      if(error_code_ != 0) {
+        *error_code_ = CGAL_MESH_3_MAXIMAL_NUMBER_OF_VERTICES_REACHED;
+      }
+      return true;
+    }
+    return false;
+  }
+
 private:
   typedef std::vector<std::pair<Curve_index,Bare_point> >    Incident_edges;
   typedef std::vector<Vertex_handle>                         Vertex_vector;
@@ -440,13 +469,25 @@ private:
   Vertex_set unchecked_vertices_;
   int refine_balls_iteration_nb;
   bool nonlinear_growth_of_balls;
+  std::size_t maximal_number_of_vertices_;
+  Mesh_error_code* const error_code_;
+#ifndef CGAL_NO_ATOMIC
+  /// Pointer to the atomic Boolean that can stop the process
+  CGAL::cpp11::atomic<bool>* const stop_ptr_;
+#endif
 };
 
 
 template <typename C3T3, typename MD, typename Sf>
 Protect_edges_sizing_field<C3T3, MD, Sf>::
 Protect_edges_sizing_field(C3T3& c3t3, const MD& domain,
-                           Sf size, const FT minimal_size)
+                           Sf size, const FT minimal_size,
+                           std::size_t maximal_number_of_vertices,
+                           Mesh_error_code* error_code
+#ifndef CGAL_NO_ATOMIC
+                           , CGAL::cpp11::atomic<bool>* stop_ptr
+#endif
+                           )
   : c3t3_(c3t3)
   , domain_(domain)
   , size_(size)
@@ -454,6 +495,11 @@ Protect_edges_sizing_field(C3T3& c3t3, const MD& domain,
   , minimal_weight_(CGAL::square(minimal_size))
   , refine_balls_iteration_nb(0)
   , nonlinear_growth_of_balls(false)
+  , maximal_number_of_vertices_(maximal_number_of_vertices)
+  , error_code_(error_code)
+#ifndef CGAL_NO_ATOMIC
+  , stop_ptr_(stop_ptr)
+#endif
 {
 #ifndef CGAL_MESH_3_NO_PROTECTION_NON_LINEAR
   set_nonlinear_growth_of_balls();
@@ -491,7 +537,7 @@ operator()(const bool refine)
 #endif
 
   // Solve problems
-  if ( refine )
+  if ( refine && !forced_stop())
   {
     refine_balls();
 #ifdef CGAL_MESH_3_VERBOSE
@@ -523,6 +569,7 @@ insert_corners()
   for ( typename Initial_corners::iterator it = corners.begin(),
        end = corners.end() ; it != end ; ++it )
   {
+    if(forced_stop()) break;
     const Bare_point& p = it->second;
     dt.insert(p);
   }
@@ -530,6 +577,7 @@ insert_corners()
   for ( typename Initial_corners::iterator cit = corners.begin(),
           end = corners.end() ; cit != end ; ++cit )
   {
+    if(forced_stop()) break;
     const Bare_point& p = cit->second;
     Index p_index = domain_.index_from_corner_index(cit->first);
 
@@ -907,6 +955,7 @@ insert_balls_on_edges()
   for ( typename Input_features::iterator fit = input_features.begin(),
        end = input_features.end() ; fit != end ; ++fit )
   {
+    if(forced_stop()) break;
     const Curve_index& curve_index = std::get<0>(*fit);
     if ( ! is_treated(curve_index) )
     {
@@ -1148,6 +1197,7 @@ insert_balls(const Vertex_handle& vp,
                            dim,
                            index,
                            out);
+      if(forced_stop()) return out;
       const Vertex_handle new_vertex = pair.first;
       out = pair.second;
       const FT sn = get_radius(new_vertex);
@@ -1277,6 +1327,7 @@ refine_balls()
   while ( (!unchecked_vertices_.empty() || restart) &&
           this->refine_balls_iteration_nb < refine_balls_max_nb_of_loops)
   {
+    if(forced_stop()) break;
 #ifdef CGAL_MESH_3_DUMP_FEATURES_PROTECTION_ITERATIONS
     std::ostringstream oss;
     oss << "dump_protecting_balls_" << refine_balls_iteration_nb << ".cgal";
@@ -1296,6 +1347,7 @@ refine_balls()
     for(typename Tr::Finite_edges_iterator eit = tr.finite_edges_begin(),
         end = tr.finite_edges_end(); eit != end; ++eit)
     {
+      if(forced_stop()) break;
       const Vertex_handle& va = eit->first->vertex(eit->second);
       const Vertex_handle& vb = eit->first->vertex(eit->third);
 
@@ -1342,6 +1394,7 @@ refine_balls()
         }
       }
     }
+    if(forced_stop()) new_sizes.clear();
 
     // The std::map with Vertex_handle as the key is not robust, because
     // the time stamp of vertices can change during the following loop. The
@@ -1356,6 +1409,7 @@ refine_balls()
           end = new_sizes_copy.end();
           it != end ; ++it )
     {
+      if(forced_stop()) break;
       const Vertex_handle v = it->first;
       const FT new_size = it->second;
       // Set size of the ball to new value
@@ -1379,7 +1433,9 @@ refine_balls()
     dump_c3t3_edges(c3t3_, "dump-before-check_and_repopulate_edges");
 #endif
     // Check edges
-    check_and_repopulate_edges();
+    if(!forced_stop()) {
+      check_and_repopulate_edges();
+    }
   }
 
   if(this->refine_balls_iteration_nb == refine_balls_max_nb_of_loops)
@@ -1553,6 +1609,7 @@ check_and_repopulate_edges()
   // Fix edges
   while ( !vertices.empty() )
   {
+    if(forced_stop()) break;
     Vertex_handle v = *vertices.begin();
     vertices.erase(vertices.begin());
 
@@ -1779,6 +1836,7 @@ walk_along_edge(const Vertex_handle& start, const Vertex_handle& next,
   // and current intersects enough
   while ( ! is_sampling_dense_enough(previous, current, curve_index, orientation) )
   {
+    if(forced_stop()) return out;
     *out++ = current;
 
     // Don't go through corners
@@ -1887,6 +1945,7 @@ repopulate(InputIterator begin, InputIterator last,
 #endif // CGAL_MESH_3_PROTECTION_DEBUG
     *out++ = *current;
     c3t3_.triangulation().remove(*current);
+    if(forced_stop()) return out;
   }
 
   // Repopulate edge
diff --git a/Mesh_3/include/CGAL/make_mesh_3.h b/Mesh_3/include/CGAL/make_mesh_3.h
index d55ed2075a8..abd460b1468 100644
--- a/Mesh_3/include/CGAL/make_mesh_3.h
+++ b/Mesh_3/include/CGAL/make_mesh_3.h
@@ -197,13 +197,28 @@ template < typename C3T3, typename MeshDomain, typename MeshCriteria>
 void init_c3t3_with_features(C3T3& c3t3,
                              const MeshDomain& domain,
                              const MeshCriteria& criteria,
-                             bool nonlinear = false)
+                             bool nonlinear = false,
+                             std::size_t maximal_number_of_vertices = 0,
+                             Mesh_error_code* pointer_to_error_code = 0
+#ifndef CGAL_NO_ATOMIC
+                             , CGAL::cpp11::atomic<bool>* pointer_to_stop = 0
+#endif
+                             )
 {
   typedef typename MeshCriteria::Edge_criteria Edge_criteria;
   typedef Edge_criteria_sizing_field_wrapper<Edge_criteria> Sizing_field;
 
   CGAL::Mesh_3::Protect_edges_sizing_field<C3T3,MeshDomain,Sizing_field>
-    protect_edges(c3t3, domain, Sizing_field(criteria.edge_criteria_object()));
+    protect_edges(c3t3,
+                  domain,
+                  Sizing_field(criteria.edge_criteria_object()),
+                  typename Edge_criteria::FT(),
+                  maximal_number_of_vertices,
+                  pointer_to_error_code
+#ifndef CGAL_NO_ATOMIC
+                  , pointer_to_stop
+#endif
+                  );
   protect_edges.set_nonlinear_growth_of_balls(nonlinear);
 
   protect_edges(true);
@@ -222,12 +237,21 @@ struct C3t3_initializer_base
 
   // Not calling 'init_c3t3_with_features' directly to leave it as a free function
   // outside of the C3T3_initializer class
-  virtual void initialize_features(C3T3& c3t3,
-                                   const MeshDomain& domain,
-                                   const MeshCriteria& criteria,
-                                   bool nonlinear = false)
+  virtual void
+  initialize_features(C3T3& c3t3,
+                      const MeshDomain& domain,
+                      const MeshCriteria& criteria,
+                      const parameters::internal::Mesh_3_options& mesh_options)
   {
-    return Mesh_3::internal::init_c3t3_with_features(c3t3, domain, criteria, nonlinear);
+    return Mesh_3::internal::init_c3t3_with_features
+      (c3t3, domain, criteria,
+       mesh_options.nonlinear_growth_of_balls,
+       mesh_options.maximal_number_of_vertices,
+       mesh_options.pointer_to_error_code
+#ifndef CGAL_NO_ATOMIC
+       , mesh_options.pointer_to_stop_atomic_boolean
+#endif
+       );
   }
 };
 
@@ -244,12 +268,12 @@ struct C3t3_initializer { };
 template < typename C3T3, typename MD, typename MC, typename HasFeatures >
 struct C3t3_initializer < C3T3, MD, MC, false, HasFeatures >
 {
+  typedef parameters::internal::Mesh_3_options Mesh_3_options;
   void operator()(C3T3& c3t3,
                   const MD& domain,
                   const MC& criteria,
                   bool with_features,
-                  bool /* nonlinear */= false,
-                  const int nb_initial_points = -1)
+                  Mesh_3_options mesh_options = Mesh_3_options())
   {
     if ( with_features )
     {
@@ -257,7 +281,8 @@ struct C3t3_initializer < C3T3, MD, MC, false, HasFeatures >
                 << " without features !" << std::endl;
     }
 
-    init_c3t3(c3t3,domain,criteria,nb_initial_points);
+    init_c3t3(c3t3,domain,criteria,
+              mesh_options.number_of_initial_points);
   }
 };
 
@@ -266,15 +291,15 @@ struct C3t3_initializer < C3T3, MD, MC, false, HasFeatures >
 template < typename C3T3, typename MD, typename MC, typename HasFeatures >
 struct C3t3_initializer < C3T3, MD, MC, true, HasFeatures >
 {
+  typedef parameters::internal::Mesh_3_options Mesh_3_options;
   void operator()(C3T3& c3t3,
                   const MD& domain,
                   const MC& criteria,
                   bool with_features,
-                  bool nonlinear = false,
-                  const int nb_initial_points = -1)
+                  Mesh_3_options mesh_options = Mesh_3_options())
   {
     C3t3_initializer < C3T3, MD, MC, true, typename MD::Has_features >()
-      (c3t3,domain,criteria,with_features,nonlinear,nb_initial_points);
+      (c3t3,domain,criteria,with_features,mesh_options);
   }
 };
 
@@ -287,15 +312,15 @@ struct C3t3_initializer < C3T3, MD, MC, true, CGAL::Tag_true >
 {
   virtual ~C3t3_initializer() { }
 
+  typedef parameters::internal::Mesh_3_options Mesh_3_options;
   void operator()(C3T3& c3t3,
                   const MD& domain,
                   const MC& criteria,
                   bool with_features,
-                  bool nonlinear = false,
-                  const int nb_initial_points = -1)
+                  Mesh_3_options mesh_options = Mesh_3_options())
   {
     if ( with_features ) {
-      this->initialize_features(c3t3, domain, criteria, nonlinear);
+      this->initialize_features(c3t3, domain, criteria,mesh_options);
 
       // If c3t3 initialization is not sufficient (may happen if there is only
       // a planar curve as feature for example), add some surface points
@@ -310,10 +335,12 @@ struct C3t3_initializer < C3T3, MD, MC, true, CGAL::Tag_true >
         }
       }
       if(need_more_init) {
-        init_c3t3(c3t3, domain, criteria, nb_initial_points);
+        init_c3t3(c3t3, domain, criteria,
+                  mesh_options.number_of_initial_points);
       }
     }
-    else { init_c3t3(c3t3,domain,criteria,nb_initial_points); }
+    else { init_c3t3(c3t3,domain,criteria,
+                     mesh_options.number_of_initial_points); }
   }
 };
 
@@ -323,12 +350,12 @@ struct C3t3_initializer < C3T3, MD, MC, true, CGAL::Tag_true >
 template < typename C3T3, typename MD, typename MC >
 struct C3t3_initializer < C3T3, MD, MC, true, CGAL::Tag_false >
 {
+  typedef parameters::internal::Mesh_3_options Mesh_3_options;
   void operator()(C3T3& c3t3,
                   const MD& domain,
                   const MC& criteria,
                   bool with_features,
-                  bool /* nonlinear */ = false,
-                  const int nb_initial_points = -1)
+                  Mesh_3_options mesh_options = Mesh_3_options())
   {
     if ( with_features )
     {
@@ -336,7 +363,8 @@ struct C3t3_initializer < C3T3, MD, MC, true, CGAL::Tag_false >
                 << " without features !" << std::endl;
     }
 
-    init_c3t3(c3t3,domain,criteria,nb_initial_points);
+    init_c3t3(c3t3,domain,criteria,
+              mesh_options.number_of_initial_points);
   }
 };
 
@@ -438,8 +466,7 @@ void make_mesh_3_impl(C3T3& c3t3,
             domain,
             criteria,
             with_features,
-            mesh_options.nonlinear_growth_of_balls,
-            mesh_options.number_of_initial_points);
+            mesh_options);
 
   CGAL_assertion( c3t3.triangulation().dimension() == 3 );
 
diff --git a/Mesh_3/include/CGAL/refine_mesh_3.h b/Mesh_3/include/CGAL/refine_mesh_3.h
index 4f1196af40d..c8820c610ed 100644
--- a/Mesh_3/include/CGAL/refine_mesh_3.h
+++ b/Mesh_3/include/CGAL/refine_mesh_3.h
@@ -209,7 +209,10 @@ struct Mesh_3_options {
 #else
       typedef bool* Pointer_to_stop_atomic_boolean_t;
 #endif
-  Mesh_3_options()
+  Mesh_3_options(bool nonlinear = false)
+    // This parameter `nonlinear` adds a compatibility with previous
+    // API of the constructor of `C3t3_initializer`.
+    // -- Laurent Rineau, 2019/05/03
     : dump_after_init_prefix()
     , dump_after_refine_surface_prefix()
     , dump_after_refine_prefix()
@@ -217,7 +220,7 @@ struct Mesh_3_options {
     , dump_after_perturb_prefix()
     , dump_after_exude_prefix()
     , number_of_initial_points(-1)
-    , nonlinear_growth_of_balls(false)
+    , nonlinear_growth_of_balls(nonlinear)
     , maximal_number_of_vertices(0)
     , pointer_to_error_code(0)
 #ifndef CGAL_NO_ATOMIC
@@ -381,6 +384,7 @@ BOOST_PARAMETER_FUNCTION((internal::Mesh_3_options), mesh_3_options, tag,
                           (dump_after_exude_prefix_, (std::string), "" )
                           (number_of_initial_points_, (int), -1)
 			  (maximal_number_of_vertices_, (std::size_t), 0)
+                          (nonlinear_growth_of_balls_, (bool), false)
 			  (pointer_to_error_code_, (Mesh_error_code*), ((Mesh_error_code*)0))
 			  (pointer_to_stop_atomic_boolean_, (internal::Mesh_3_options::Pointer_to_stop_atomic_boolean_t), ((internal::Mesh_3_options::Pointer_to_stop_atomic_boolean_t)0))
                           )
@@ -395,6 +399,7 @@ BOOST_PARAMETER_FUNCTION((internal::Mesh_3_options), mesh_3_options, tag,
   options.dump_after_perturb_prefix=dump_after_perturb_prefix_;
   options.dump_after_exude_prefix=dump_after_exude_prefix_;
   options.number_of_initial_points=number_of_initial_points_;
+  options.nonlinear_growth_of_balls = nonlinear_growth_of_balls_;
   options.maximal_number_of_vertices=maximal_number_of_vertices_;
   options.pointer_to_error_code=pointer_to_error_code_;
 #ifndef CGAL_NO_ATOMIC
diff --git a/Periodic_3_mesh_3/include/CGAL/make_periodic_3_mesh_3.h b/Periodic_3_mesh_3/include/CGAL/make_periodic_3_mesh_3.h
index d10d458824a..e753f9634ea 100644
--- a/Periodic_3_mesh_3/include/CGAL/make_periodic_3_mesh_3.h
+++ b/Periodic_3_mesh_3/include/CGAL/make_periodic_3_mesh_3.h
@@ -93,8 +93,7 @@ struct C3t3_initializer_base
                   const MeshDomain& domain,
                   const MeshCriteria& criteria,
                   bool with_features,
-                  bool nonlinear = false,
-                  const int nb_initial_points = -1)
+                  const parameters::internal::Mesh_3_options& mesh_options)
   {
     c3t3.triangulation().set_domain(domain.bounding_box());
     c3t3.triangulation().insert_dummy_points();
@@ -102,8 +101,7 @@ struct C3t3_initializer_base
 
     // Call the basic initialization from c3t3, which handles features and
     // adds a bunch of points on the surface
-    Base::operator()(c3t3, domain, criteria, with_features,
-                     nonlinear, nb_initial_points);
+    Base::operator()(c3t3, domain, criteria, with_features, mesh_options);
   }
 };
 
@@ -119,9 +117,10 @@ struct C3t3_initializer
                                 MeshDomainHasHasFeatures, HasFeatures> Base;
 
   void operator()(C3T3& c3t3, const MeshDomain& domain, const MeshCriteria& criteria,
-                  bool with_features, bool nonlinear = false, const int nb_initial_points = -1)
+                  bool with_features,
+                  const parameters::internal::Mesh_3_options& mesh_options)
   {
-    return Base::operator()(c3t3, domain, criteria, with_features, nonlinear, nb_initial_points);
+    return Base::operator()(c3t3, domain, criteria, with_features, mesh_options);
   }
 };
 
@@ -133,10 +132,11 @@ template <typename C3T3,
 struct C3t3_initializer<C3T3, MeshDomain, MeshCriteria, true, HasFeatures>
 {
   void operator()(C3T3& c3t3, const MeshDomain& domain, const MeshCriteria& criteria,
-                  bool with_features, bool nonlinear = false, const int nb_initial_points = -1)
+                  bool with_features,
+                  const parameters::internal::Mesh_3_options& mesh_options)
   {
     C3t3_initializer<C3T3, MeshDomain, MeshCriteria, true, typename MeshDomain::Has_features>()
-        (c3t3, domain, criteria, with_features, nonlinear, nb_initial_points);
+        (c3t3, domain, criteria, with_features, mesh_options);
   }
 };
 
@@ -152,18 +152,21 @@ struct C3t3_initializer<C3T3, MeshDomain, MeshCriteria, true, CGAL::Tag_true>
   virtual ~C3t3_initializer() { }
 
   // this override will be used when initialize_features() is called, in make_mesh_3.h
-  virtual void initialize_features(C3T3& c3t3,
-                                   const MeshDomain& domain,
-                                   const MeshCriteria& criteria,
-                                   bool nonlinear = false)
+  virtual void
+  initialize_features(C3T3& c3t3,
+                      const MeshDomain& domain,
+                      const MeshCriteria& criteria,
+                      const parameters::internal::Mesh_3_options& mesh_options)
   {
-    return Periodic_3_mesh_3::internal::init_c3t3_with_features(c3t3, domain, criteria, nonlinear);
+    return Periodic_3_mesh_3::internal::init_c3t3_with_features
+      (c3t3, domain, criteria, mesh_options.nonlinear_growth_of_balls);
   }
 
   void operator()(C3T3& c3t3, const MeshDomain& domain, const MeshCriteria& criteria,
-                  bool with_features, bool nonlinear = false, const int nb_initial_points = -1)
+                  bool with_features,
+                  const parameters::internal::Mesh_3_options& mesh_options)
   {
-    return Base::operator()(c3t3, domain, criteria, with_features, nonlinear, nb_initial_points);
+    return Base::operator()(c3t3, domain, criteria, with_features, mesh_options);
   }
 };
 
@@ -257,8 +260,7 @@ void make_periodic_3_mesh_3_impl(C3T3& c3t3,
                                                              domain,
                                                              criteria,
                                                              with_features,
-                                                             mesh_options.nonlinear_growth_of_balls,
-                                                             mesh_options.number_of_initial_points);
+                                                             mesh_options);
 
   // Build mesher and launch refinement process
   refine_periodic_3_mesh_3(c3t3, domain, criteria,
diff --git a/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Mesh_function.h b/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Mesh_function.h
index 0408113e335..0188d438c2b 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Mesh_function.h
+++ b/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Mesh_function.h
@@ -136,8 +136,8 @@ private:
 private:
   boost::any object_to_destroy;
   C3t3& c3t3_;
-  Domain* domain_;
-  Mesh_parameters p_;
+  Domain* const domain_;
+  Mesh_parameters const p_;
   std::atomic<bool> stop_;
   Mesher* mesher_;
 #ifdef CGAL_MESH_3_MESHER_STATUS_ACTIVATED
@@ -237,6 +237,7 @@ Mesh_function<D_,Tag>::
 initialize(const Mesh_criteria& criteria, Mesh_fnt::Domain_tag)
 // for the other domain types
 {
+  namespace p = CGAL::parameters;
   // Initialization of the mesh, either with the protection of sharp
   // features, or with the initial points (or both).
   // If `detect_connected_components==true`, the initialization is
@@ -250,7 +251,9 @@ initialize(const Mesh_criteria& criteria, Mesh_fnt::Domain_tag)
      *domain_,
      criteria,
      p_.protect_features,
-     p_.use_sizing_field_with_aabb_tree);
+     p::mesh_3_options(p::pointer_to_stop_atomic_boolean = &stop_,
+                       p::nonlinear_growth_of_balls =
+                       p_.use_sizing_field_with_aabb_tree));
 }
 
 template < typename D_, typename Tag >