diff --git a/BGL/include/CGAL/draw_face_graph.h b/BGL/include/CGAL/draw_face_graph.h
index e78016a56f1..f5784dc2a79 100644
--- a/BGL/include/CGAL/draw_face_graph.h
+++ b/BGL/include/CGAL/draw_face_graph.h
@@ -16,41 +16,40 @@
 
 #include <CGAL/Graphic_buffer.h>
 #include <CGAL/Drawing_functor.h>
-#include <CGAL/Qt/Basic_viewer_qt.h>
-
-#ifdef CGAL_USE_BASIC_VIEWER
-
 #include <CGAL/Dynamic_property_map.h>
 #include <CGAL/Random.h>
 #include <CGAL/boost/graph/helpers.h>
 
 namespace CGAL {
 
-namespace draw_function_for_SM {
+namespace draw_function_for_FG {
 
-template <typename BufferType = float, typename SM, typename DrawingFunctor>
-void compute_elements(const SM &sm,
+template <typename BufferType=float, typename FG, typename DrawingFunctor>
+void compute_elements(const FG &fg,
                       CGAL::Graphic_buffer<BufferType> &graphic_buffer,
-                      const DrawingFunctor &m_drawing_functor, bool anofaces = false) {
-
-  using Point =
-      typename boost::property_map_value<SM, CGAL::vertex_point_t>::type;
+                      const DrawingFunctor &m_drawing_functor)
+{
+  using Point=typename boost::property_map_value<FG, CGAL::vertex_point_t>::type;
   using Kernel = typename CGAL::Kernel_traits<Point>::Kernel;
   using Vector = typename Kernel::Vector_3;
 
-  auto vnormals = get(CGAL::dynamic_vertex_property_t<Vector>(), sm);
-  auto point_pmap = get(CGAL::vertex_point, sm);
-  for (auto v : vertices(sm)) {
+  auto vnormals = get(CGAL::dynamic_vertex_property_t<Vector>(), fg);
+  auto point_pmap = get(CGAL::vertex_point, fg);
+  for (auto v : vertices(fg))
+  {
     Vector n(NULL_VECTOR);
     int i = 0;
-    for (auto h : halfedges_around_target(halfedge(v, sm), sm)) {
-      if (!is_border(h, sm)) {
+    for (auto h : halfedges_around_target(halfedge(v, fg), fg))
+    {
+      if (!is_border(h, fg))
+      {
         Vector ni = CGAL::cross_product(
-            Vector(get(point_pmap, source(h, sm)),
-                    get(point_pmap, target(h, sm))),
-            Vector(get(point_pmap, target(h, sm)),
-                    get(point_pmap, target(next(h, sm), sm))));
-        if (ni != NULL_VECTOR) {
+            Vector(get(point_pmap, source(h, fg)),
+                    get(point_pmap, target(h, fg))),
+            Vector(get(point_pmap, target(h, fg)),
+                    get(point_pmap, target(next(h, fg), fg))));
+        if (ni != NULL_VECTOR)
+        {
           n += ni;
           ++i;
         }
@@ -59,70 +58,104 @@ void compute_elements(const SM &sm,
     put(vnormals, v, n / i);
   }
 
-  if (!anofaces) {
-    for (auto fh : faces(sm)) {
-      if (fh != boost::graph_traits<SM>::null_face() && m_drawing_functor.colored_face(sm, fh)) {
-        CGAL::IO::Color c = m_drawing_functor.face_color(sm, fh);
-        graphic_buffer.face_begin(c);
-        auto hd = halfedge(fh, sm);
+  if (m_drawing_functor.are_faces_enabled())
+  {
+    for (auto fh : faces(fg))
+    {
+      if (fh != boost::graph_traits<FG>::null_face() && // face exists
+          m_drawing_functor.colored_face && // std::function is not null
+          m_drawing_functor.colored_face(fg, fh)) // and face is colored
+      {
+        graphic_buffer.face_begin(m_drawing_functor.face_color(fg, fh));
+        auto hd = halfedge(fh, fg);
         const auto first_hd = hd;
-        do {
-          auto v = source(hd, sm);
+        do
+        {
+          auto v = source(hd, fg);
           graphic_buffer.add_point_in_face(get(point_pmap, v), get(vnormals, v));
-          hd = next(hd, sm);
-        } while (hd != first_hd);
+          hd = next(hd, fg);
+        }
+        while (hd != first_hd);
         graphic_buffer.face_end();
       }
     }
   }
 
-  for (auto e : edges(sm)) {
-    graphic_buffer.add_segment(get(point_pmap, source(halfedge(e, sm), sm)),
-                get(point_pmap, target(halfedge(e, sm), sm)));
+  if(m_drawing_functor.are_edges_enabled())
+  {
+    for (auto e : edges(fg))
+    {
+      if(m_drawing_functor.colored_edge && // std::function is not null
+         m_drawing_functor.colored_edge(fg, e)) // and edge is colored
+      { 
+        graphic_buffer.add_segment(get(point_pmap, source(halfedge(e, fg), fg)),
+                                   get(point_pmap, target(halfedge(e, fg), fg)),
+                                   m_drawing_functor.edge_color(fg, e));
+      }
+      else
+      {
+        graphic_buffer.add_segment(get(point_pmap, source(halfedge(e, fg), fg)),
+                                   get(point_pmap, target(halfedge(e, fg), fg)));
+      }
+    }
   }
 
-  for (auto v : vertices(sm)) {
-    graphic_buffer.add_point(get(point_pmap, v));
+  if(m_drawing_functor.are_vertices_enabled())
+  {
+    for (auto v : vertices(fg))
+    {
+      if(m_drawing_functor.colored_vertex && // std::function is not null
+         m_drawing_functor.colored_vertex(fg, v)) // and vertex is colored
+      { 
+        graphic_buffer.add_point(get(point_pmap, v),
+                                 m_drawing_functor.vertex_color(fg, v));
+      }
+      else
+      { 
+        graphic_buffer.add_point(get(point_pmap, v));
+      }
+    }
   }
 }
 
-} // draw_function_for_SM
+} // draw_function_for_FG
 
-template <typename BufferType = float, class SM, class DrawingFunctor>
-void add_in_graphic_buffer(const SM &sm, CGAL::Graphic_buffer<BufferType> &graphic_buffer,
-                             const DrawingFunctor &m_drawing_functor) {
-  draw_function_for_SM::compute_elements(sm, graphic_buffer, m_drawing_functor);
+template <typename BufferType=float, class FG, class DrawingFunctor>
+void add_in_graphic_buffer_for_fg(const FG &fg,
+                                  CGAL::Graphic_buffer<BufferType> &graphic_buffer,
+                                  const DrawingFunctor &drawing_functor)
+{
+  draw_function_for_FG::compute_elements(fg, graphic_buffer, drawing_functor);
 }
 
-template <typename BufferType = float, class SM>
-void add_in_graphic_buffer(const SM &sm, CGAL::Graphic_buffer<BufferType> &graphic_buffer) {
-
-  // Default functor; user can add his own functor.
-  Drawing_functor<SM, typename boost::graph_traits<SM>::face_descriptor,
-                  typename boost::graph_traits<SM>::face_descriptor,
-                  typename boost::graph_traits<SM>::face_descriptor>
+template <typename BufferType=float, class FG>
+void add_in_graphic_buffer_for_fg(const FG &fg,
+                                  CGAL::Graphic_buffer<BufferType> &graphic_buffer)
+{
+  Drawing_functor<FG,
+                  typename boost::graph_traits<FG>::vertex_descriptor,
+                  typename boost::graph_traits<FG>::edge_descriptor,
+                  typename boost::graph_traits<FG>::face_descriptor>
       drawing_functor;
 
-  drawing_functor.colored_face = [](const SM &,
-             typename boost::graph_traits<SM>::face_descriptor fh) -> bool
+  drawing_functor.colored_face = [](const FG&,
+             typename boost::graph_traits<FG>::face_descriptor) -> bool
   { return true; };
 
 
-  drawing_functor.face_color =  [] (const SM &,
-             typename boost::graph_traits<SM>::face_descriptor fh) -> CGAL::IO::Color
+  drawing_functor.face_color =  [] (const FG&,
+             typename boost::graph_traits<FG>::face_descriptor fh) -> CGAL::IO::Color
   {
-    if (fh ==
-        boost::graph_traits<SM>::null_face()) // use to get the mono color
-      return CGAL::IO::Color(100, 125, 200);     // R G B between 0-255
+    if (fh==boost::graph_traits<FG>::null_face())
+    { return CGAL::IO::Color(100, 125, 200); }
 
+    // TODO (?) use a seed given fh (cannot directly cast because FG is either a polyhedron or a surface mesh)
     return get_random_color(CGAL::get_default_random());
   };
 
-  add_in_graphic_buffer(sm, graphic_buffer, drawing_functor);
+  add_in_graphic_buffer_for_fg(fg, graphic_buffer, drawing_functor);
 }
 
 } // End namespace CGAL
 
-#endif // CGAL_USE_BASIC_VIEWER
-
 #endif // CGAL_DRAW_SURFACE_MESH_H
diff --git a/Polyhedron/include/CGAL/draw_polyhedron.h b/Polyhedron/include/CGAL/draw_polyhedron.h
index b6d92c56b3a..826a2b7a6e3 100644
--- a/Polyhedron/include/CGAL/draw_polyhedron.h
+++ b/Polyhedron/include/CGAL/draw_polyhedron.h
@@ -13,57 +13,81 @@
 #ifndef CGAL_DRAW_POLYHEDRON_H
 #define CGAL_DRAW_POLYHEDRON_H
 
+#include <CGAL/license/Polyhedron.h>
 #include <CGAL/Graphic_buffer.h>
 #include <CGAL/Drawing_functor.h>
-#include <CGAL/license/Polyhedron.h>
-#include <CGAL/Qt/Basic_viewer_qt.h>
-
-#ifdef CGAL_USE_BASIC_VIEWER
-#include <CGAL/Qt/init_ogl_context.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/draw_face_graph.h>
-#include <CGAL/Random.h>
+
+#ifdef CGAL_USE_BASIC_VIEWER
+#include <CGAL/Qt/Basic_viewer_qt.h>
+#endif
 
 namespace CGAL
 {
 
-// Specialization of draw function.
 #define CGAL_POLY_TYPE CGAL::Polyhedron_3 \
   <PolyhedronTraits_3, PolyhedronItems_3, T_HDS, Alloc>
 
+// Specialization of add_in_graphic_buffer function.
 template<class PolyhedronTraits_3,
          class PolyhedronItems_3,
          template < class T, class I, class A>
          class T_HDS,
-         class Alloc, typename BufferType = float>
+         class Alloc,
+         typename BufferType=float,
+         class DrawingFunctor>
+void add_in_graphic_buffer(const CGAL_POLY_TYPE& apoly,
+                           CGAL::Graphic_buffer<BufferType> &graphic_buffer,
+                           const DrawingFunctor &drawing_functor)
+{ add_in_graphic_buffer_for_fg(apoly, graphic_buffer, drawing_functor); }
+
+template<class PolyhedronTraits_3,
+         class PolyhedronItems_3,
+         template < class T, class I, class A>
+         class T_HDS,
+         class Alloc,
+         typename BufferType=float>
+void add_in_graphic_buffer(const CGAL_POLY_TYPE& apoly,
+                           CGAL::Graphic_buffer<BufferType> &graphic_buffer)
+{ add_in_graphic_buffer_for_fg(apoly, graphic_buffer); }
+
+// Specialization of draw function: require Qt and the CGAL basic viewer.
+#ifdef CGAL_USE_BASIC_VIEWER
+  
+template<class PolyhedronTraits_3,
+         class PolyhedronItems_3,
+         template < class T, class I, class A>
+         class T_HDS,
+         class Alloc,
+         typename BufferType=float>
 void draw(const CGAL_POLY_TYPE& apoly,
-          const char* title="Polyhedron Basic Viewer",
-          bool nofill=false)
+          const char* title="Polyhedron Basic Viewer")
 {
   CGAL::Graphic_buffer<BufferType> buffer;
-  add_in_graphic_buffer(apoly, buffer);
-  draw_buffer(buffer);
+  add_in_graphic_buffer_for_fg(apoly, buffer);
+  draw_buffer(buffer, title);
 }
 
 template<class PolyhedronTraits_3,
          class PolyhedronItems_3,
          template < class T, class I, class A>
          class T_HDS,
-         class Alloc, typename BufferType = float, class DrawingFunctor>
+         class Alloc,
+         typename BufferType=float,
+         class DrawingFunctor>
 void draw(const CGAL_POLY_TYPE& apoly,
           const DrawingFunctor &drawing_functor,
-          const char* title="Polyhedron Basic Viewer",
-          bool nofill=false)
+          const char* title="Polyhedron Basic Viewer")
 {
   CGAL::Graphic_buffer<BufferType> buffer;
-  add_in_graphic_buffer(apoly, buffer, drawing_functor);
-  draw_buffer(buffer);
+  add_in_graphic_buffer_for_fg(apoly, buffer, drawing_functor);
+  draw_buffer(buffer, title);
 }
-
+#endif // CGAL_USE_BASIC_VIEWER
+  
 #undef CGAL_POLY_TYPE
 
 } // End namespace CGAL
 
-#endif // CGAL_USE_BASIC_VIEWER
-
 #endif // CGAL_DRAW_POLYHEDRON_H
diff --git a/Surface_mesh/include/CGAL/draw_surface_mesh.h b/Surface_mesh/include/CGAL/draw_surface_mesh.h
index 184d80c5a83..c6a545a5bf8 100644
--- a/Surface_mesh/include/CGAL/draw_surface_mesh.h
+++ b/Surface_mesh/include/CGAL/draw_surface_mesh.h
@@ -29,46 +29,56 @@ void draw(const SM& asm);
 
 #else // DOXYGEN_RUNNING
 
+#include <CGAL/license/Surface_mesh.h>
 #include <CGAL/Graphic_buffer.h>
 #include <CGAL/Drawing_functor.h>
-#include <CGAL/license/Surface_mesh.h>
-#include <CGAL/Qt/Basic_viewer_qt.h>
-
-#ifdef CGAL_USE_BASIC_VIEWER
-
-#include <CGAL/Qt/init_ogl_context.h>
 #include <CGAL/Surface_mesh.h>
 #include <CGAL/draw_face_graph.h>
 
+#ifdef CGAL_USE_BASIC_VIEWER
+#include <CGAL/Qt/Basic_viewer_qt.h>
+#endif
+
 namespace CGAL
 {
 
-// Specialization of draw function.
-template<class K, typename BufferType = float>
+template<class K, typename BufferType=float,  class DrawingFunctor>
+void add_in_graphic_buffer(const Surface_mesh<K>& amesh,
+                           CGAL::Graphic_buffer<BufferType> &graphic_buffer,
+                           const DrawingFunctor &drawing_functor)
+{ add_in_graphic_buffer_for_fg(amesh, graphic_buffer, drawing_functor); }
+ 
+template<class K, typename BufferType=float>
+void add_in_graphic_buffer(const Surface_mesh<K>& amesh,
+                           CGAL::Graphic_buffer<BufferType> &graphic_buffer)
+{ add_in_graphic_buffer_for_fg(amesh, graphic_buffer); }
+ 
+#ifdef CGAL_USE_BASIC_VIEWER
+
+  // Specialization of draw function.
+template<class K, typename BufferType=float>
 void draw(const Surface_mesh<K>& amesh,
-          const char* title="Surface_mesh Basic Viewer",
-          bool nofill=false)
+          const char* title="Surface_mesh Basic Viewer")
 {
   CGAL::Graphic_buffer<BufferType> buffer;
-  add_in_graphic_buffer(amesh, buffer);
-  draw_buffer(buffer);
+  add_in_graphic_buffer_for_fg(amesh, buffer);
+  draw_buffer(buffer, title);
 }
 
-template<class K, typename BufferType = float, class DrawingFunctor>
+template<class K, typename BufferType=float, class DrawingFunctor>
 void draw(const Surface_mesh<K>& amesh,
           const DrawingFunctor &drawing_functor,
-          const char* title="Surface_mesh Basic Viewer",
-          bool nofill=false)
+          const char* title="Surface_mesh Basic Viewer")
 {
   CGAL::Graphic_buffer<BufferType> buffer;
-  add_in_graphic_buffer(amesh, buffer, drawing_functor);
-  draw_buffer(buffer);
+  add_in_graphic_buffer_for_fg(amesh, buffer, drawing_functor);
+  draw_buffer(buffer, title);
 }
 
-} // End namespace CGAL
-
 #endif // CGAL_USE_BASIC_VIEWER
 
+} // End namespace CGAL
+
 #endif // DOXYGEN_RUNNING
 
 #endif // CGAL_DRAW_SURFACE_MESH_H