diff --git a/Polyhedron/demo/Polyhedron/Scene.cpp b/Polyhedron/demo/Polyhedron/Scene.cpp
index ece211e9e31..f5edd194a9c 100644
--- a/Polyhedron/demo/Polyhedron/Scene.cpp
+++ b/Polyhedron/demo/Polyhedron/Scene.cpp
@@ -311,27 +311,28 @@ Scene::keyPressEvent(QKeyEvent* e){
     return res;
 }
 
-void
-Scene::draw()
-{
-    draw_aux(false, 0);
-}
 void
 Scene::draw(CGAL::Three::Viewer_interface* viewer)
 {
     draw_aux(false, viewer);
 }
 void
-Scene::drawWithNames()
-{
-    draw_aux(true, 0);
-}
-void
 Scene::drawWithNames(CGAL::Three::Viewer_interface* viewer)
 {
     draw_aux(true, viewer);
 }
 
+bool item_should_be_skipped_in_draw(Scene_item* item) {
+  if(!item->visible()) return true;
+  if(item->has_group == 0) return false;
+  Scene_group_item* group = item->parentGroup();
+  while(group != 0) {
+    if(!group->visible()) return false;
+    group = group->parentGroup();
+  }
+  return true;
+}
+
 void 
 Scene::draw_aux(bool with_names, CGAL::Three::Viewer_interface* viewer)
 {
@@ -342,10 +343,12 @@ Scene::draw_aux(bool with_names, CGAL::Three::Viewer_interface* viewer)
     // Flat/Gouraud OpenGL drawing
     for(int index = 0; index < m_entries.size(); ++index)
     {
+        CGAL::Three::Scene_item& item = *m_entries[index];
         if(with_names) {
             viewer->glPushName(index);
+        } else {
+          if(item_should_be_skipped_in_draw(&item)) continue;
         }
-        CGAL::Three::Scene_item& item = *m_entries[index];
         if(item.visible())
         {
             if(item.renderingMode() == Flat || item.renderingMode() == FlatPlusEdges || item.renderingMode() == Gouraud)
@@ -378,14 +381,17 @@ Scene::draw_aux(bool with_names, CGAL::Three::Viewer_interface* viewer)
             viewer->glPopName();
         }
     }
-glDepthFunc(GL_LEQUAL);
+    glDepthFunc(GL_LEQUAL);
     // Wireframe OpenGL drawing
     for(int index = 0; index < m_entries.size(); ++index)
     {
+        CGAL::Three::Scene_item& item = *m_entries[index];
         if(with_names) {
             viewer->glPushName(index);
         }
-        CGAL::Three::Scene_item& item = *m_entries[index];
+        else {
+            if(item_should_be_skipped_in_draw(&item)) continue;
+        }
         if(item.visible())
         {
             if(item.renderingMode() == FlatPlusEdges || item.renderingMode() == Wireframe)
@@ -442,10 +448,12 @@ glDepthFunc(GL_LEQUAL);
     // Points OpenGL drawing
     for(int index = 0; index < m_entries.size(); ++index)
     {
+        CGAL::Three::Scene_item& item = *m_entries[index];
         if(with_names) {
             viewer->glPushName(index);
+        } else {
+          if(item_should_be_skipped_in_draw(&item)) continue;
         }
-        CGAL::Three::Scene_item& item = *m_entries[index];
         if(item.visible())
         {
             if(item.renderingMode() == Points  || item.renderingMode() == PointsPlusNormals)
@@ -474,6 +482,7 @@ glDepthFunc(GL_LEQUAL);
         for(int index = 0; index < m_entries.size(); ++index)
         {
             CGAL::Three::Scene_item& item = *m_entries[index];
+            if(item_should_be_skipped_in_draw(&item)) continue;
             if(item.visible() && item.renderingMode() == Splatting)
             {
 
@@ -486,9 +495,11 @@ glDepthFunc(GL_LEQUAL);
             }
 
         }
-       ms_splatting->beginAttributePass();
-         for(int index = 0; index < m_entries.size(); ++index)
-        {  CGAL::Three::Scene_item& item = *m_entries[index];
+        ms_splatting->beginAttributePass();
+        for(int index = 0; index < m_entries.size(); ++index)
+        {
+            CGAL::Three::Scene_item& item = *m_entries[index];
+            if(item_should_be_skipped_in_draw(&item)) continue;
             if(item.visible() && item.renderingMode() == Splatting)
             {
                 viewer->glColor4d(item.color().redF(), item.color().greenF(), item.color().blueF(), item.color().alphaF());
@@ -1077,7 +1088,7 @@ void Scene::changeGroup(Scene_item *item, CGAL::Three::Scene_group_item *target_
   }
  //add the item to the target group
  target_group->addChild(item);
- item->has_group = target_group->has_group +1;
+ item->moveToGroup(target_group);
 }
 
 float Scene::get_bbox_length() const
diff --git a/Polyhedron/demo/Polyhedron/Scene.h b/Polyhedron/demo/Polyhedron/Scene.h
index 7e938d163fb..9e747154651 100644
--- a/Polyhedron/demo/Polyhedron/Scene.h
+++ b/Polyhedron/demo/Polyhedron/Scene.h
@@ -110,10 +110,6 @@ public:
    * of OpenGL code that needs a context.
    */
   void initializeGL();
-  /*! Is called by Viewer::draw(). Is deprecated and does nothing.*/
-  void draw();
-  /*! Is deprecated and does nothing.*/
-  void drawWithNames();
   /*! Is called by Viewer::draw(Viewer_interface*). Calls draw_aux(false, viewer).
    * @see draw_aux(bool with_names, Viewer_interface).*/
   void draw(CGAL::Three::Viewer_interface*);
diff --git a/Polyhedron/demo/Polyhedron/Scene_group_item.cpp b/Polyhedron/demo/Polyhedron/Scene_group_item.cpp
index 86d2b2269e5..56a597e29ac 100644
--- a/Polyhedron/demo/Polyhedron/Scene_group_item.cpp
+++ b/Polyhedron/demo/Polyhedron/Scene_group_item.cpp
@@ -1,5 +1,5 @@
-
 #include <CGAL/Three/Scene_group_item.h>
+#include <CGAL/Three/Viewer_interface.h>
 #include <QDebug>
 
 using namespace CGAL::Three;
@@ -114,3 +114,55 @@ void Scene_group_item::moveUp(int i)
 {
     children.move(i, i-1);
 }
+
+void Scene_group_item::draw(CGAL::Three::Viewer_interface* viewer) const {
+  if(viewer->inDrawWithNames()) return;
+  Q_FOREACH(Scene_item* child, children) {
+    if(!child->visible()) continue;
+    switch(child->renderingMode()) {
+    case Flat:
+    case FlatPlusEdges:
+    case Gouraud:
+      child->draw(viewer); break;
+    default: break;
+    }
+  }
+}
+
+void Scene_group_item::draw_edges(CGAL::Three::Viewer_interface* viewer) const
+{
+  if(viewer->inDrawWithNames()) return;
+  Q_FOREACH(Scene_item* child, children) {
+    if(!child->visible()) continue;
+    switch(child->renderingMode()) {
+    case FlatPlusEdges:
+    case Wireframe:
+    case PointsPlusNormals:
+      child->draw_edges(viewer); break;
+    default: break;
+    }
+  }
+}
+
+void Scene_group_item::draw_points(CGAL::Three::Viewer_interface* viewer) const
+{
+  if(viewer->inDrawWithNames()) return;
+  Q_FOREACH(Scene_item* child, children) {
+    if(!child->visible()) continue;
+    switch(child->renderingMode()) {
+    case Points:
+    case PointsPlusNormals:
+      child->draw_points(viewer); break;
+    default: break;
+    }
+  }
+}
+
+void Scene_group_item::draw_splats(CGAL::Three::Viewer_interface* viewer) const
+{
+  if(viewer->inDrawWithNames()) return;
+  Q_FOREACH(Scene_item* child, children) {
+    if(child->visible() && child->renderingMode() == Splatting)
+      child->draw_splats(viewer);
+  }
+}
diff --git a/Polyhedron/demo/Polyhedron/Scene_item.cpp b/Polyhedron/demo/Polyhedron/Scene_item.cpp
index c4ba9a84db7..ee89e41f305 100644
--- a/Polyhedron/demo/Polyhedron/Scene_item.cpp
+++ b/Polyhedron/demo/Polyhedron/Scene_item.cpp
@@ -1,4 +1,5 @@
 #include <CGAL/Three/Scene_item.h>
+#include <CGAL/Three/Scene_group_item.h>
 #include <CGAL/Three/Scene_interface.h>
 #include <QMenu>
 #include <iostream>
@@ -6,6 +7,37 @@
 #include <CGAL/Three/Viewer_interface.h>
 const QColor CGAL::Three::Scene_item::defaultColor = QColor(100, 100, 255);
 
+CGAL::Three::Scene_item::Scene_item(int buffers_size, int vaos_size)
+  : name_("unamed"),
+    color_(defaultColor),
+    visible_(true),
+    are_buffers_filled(false),
+    rendering_mode(FlatPlusEdges),
+    defaultContextMenu(0),
+    buffersSize(buffers_size),
+    vaosSize(vaos_size),
+    vaos(vaos_size)
+{
+  is_bbox_computed = false;
+  is_monochrome = true;
+  for(int i=0; i<vaosSize; i++)
+  {
+    addVaos(i);
+    vaos[i]->create();
+  }
+
+  buffers.reserve(buffersSize);
+  for(int i=0; i<buffersSize; i++)
+  {
+    QOpenGLBuffer n_buf;
+    buffers.push_back(n_buf);
+    buffers[i].create();
+  }
+  nb_isolated_vertices = 0;
+  has_group = 0;
+  parent_group = 0;
+}
+
 CGAL::Three::Scene_item::~Scene_item() {
   delete defaultContextMenu;
   for(int i=0; i<buffersSize; i++)
@@ -101,6 +133,19 @@ QMenu* CGAL::Three::Scene_item::contextMenu()
     return defaultContextMenu;
 }
 
+CGAL::Three::Scene_group_item* CGAL::Three::Scene_item::parentGroup() const {
+  return parent_group;
+}
+
+void CGAL::Three::Scene_item::
+moveToGroup(CGAL::Three::Scene_group_item* group) {
+  parent_group = group;
+  if(group)
+    has_group = group->has_group + 1;
+  else
+    has_group = 0;
+}
+
 void CGAL::Three::Scene_item::invalidateOpenGLBuffers() {}
 
 void CGAL::Three::Scene_item::selection_changed(bool) {}
diff --git a/Polyhedron/demo/Polyhedron/Viewer.cpp b/Polyhedron/demo/Polyhedron/Viewer.cpp
index 48f80eea8b0..9b50f0e33ba 100644
--- a/Polyhedron/demo/Polyhedron/Viewer.cpp
+++ b/Polyhedron/demo/Polyhedron/Viewer.cpp
@@ -16,6 +16,7 @@ public:
   bool twosides;
   bool macro_mode;
   bool inFastDrawing;
+  bool inDrawWithNames;
   
   void draw_aux(bool with_names, Viewer*);
 
@@ -31,6 +32,7 @@ Viewer::Viewer(QWidget* parent, bool antialiasing)
   d->twosides = false;
   d->macro_mode = false;
   d->inFastDrawing = true;
+  d->inDrawWithNames = false;
   d->shader_programs.resize(NB_OF_PROGRAMS);
   setShortcut(EXIT_VIEWER, 0);
   setShortcut(DRAW_AXIS, 0);
@@ -321,6 +323,7 @@ void Viewer_impl::draw_aux(bool with_names, Viewer* viewer)
     viewer->glHint(GL_LINE_SMOOTH_HINT, GL_FASTEST);
     viewer->glBlendFunc(GL_ONE, GL_ZERO);
   }
+  inDrawWithNames = with_names;
   if(with_names)
     scene->drawWithNames(viewer);
   else
@@ -329,6 +332,10 @@ void Viewer_impl::draw_aux(bool with_names, Viewer* viewer)
   viewer->glPolygonMode(GL_FRONT_AND_BACK,GL_FILL);
 }
 
+bool Viewer::inDrawWithNames() const {
+  return d->inDrawWithNames;
+}
+
 void Viewer::drawWithNames()
 {
   QGLViewer::draw();
diff --git a/Polyhedron/demo/Polyhedron/Viewer.h b/Polyhedron/demo/Polyhedron/Viewer.h
index 3435ebe047d..2f81d77dab6 100644
--- a/Polyhedron/demo/Polyhedron/Viewer.h
+++ b/Polyhedron/demo/Polyhedron/Viewer.h
@@ -59,6 +59,8 @@ public:
   bool antiAliasing() const;
   //! @returns the fastDrawing state.
   bool inFastDrawing() const;
+  //! Implementation of `Viewer_interface::inDrawWithNames()`
+  bool inDrawWithNames() const;
   //! Implementation of `Viewer_interface::attrib_buffers()`
   void attrib_buffers(int program_name) const;
   //! Implementation of `Viewer_interface::getShaderProgram()`
diff --git a/Three/include/CGAL/Three/Scene_draw_interface.h b/Three/include/CGAL/Three/Scene_draw_interface.h
index c9fa3f0844b..cbc562a8c30 100644
--- a/Three/include/CGAL/Three/Scene_draw_interface.h
+++ b/Three/include/CGAL/Three/Scene_draw_interface.h
@@ -33,10 +33,8 @@ class Scene_draw_interface {
 public:
   virtual ~Scene_draw_interface(){}
   virtual void initializeGL() = 0;
-  virtual void draw() = 0;
-  virtual void draw(CGAL::Three::Viewer_interface*) { draw(); };
-  virtual void drawWithNames() = 0;
-  virtual void drawWithNames(CGAL::Three::Viewer_interface*) { drawWithNames(); }
+  virtual void draw(CGAL::Three::Viewer_interface*) = 0;
+  virtual void drawWithNames(CGAL::Three::Viewer_interface*) = 0;
   virtual bool keyPressEvent(QKeyEvent* e) = 0;
   virtual float get_bbox_length() const = 0;
 };
diff --git a/Three/include/CGAL/Three/Scene_group_item.h b/Three/include/CGAL/Three/Scene_group_item.h
index bc4db1cc511..4d0a8c0e776 100644
--- a/Three/include/CGAL/Three/Scene_group_item.h
+++ b/Three/include/CGAL/Three/Scene_group_item.h
@@ -62,6 +62,15 @@ public :
     bool supportsRenderingMode(RenderingMode m) const;
     //!Prints the number of children.
     QString toolTip() const;
+
+    /// Draw functions
+    ///@{
+    virtual void draw(CGAL::Three::Viewer_interface*) const;
+    virtual void draw_edges(CGAL::Three::Viewer_interface*) const;
+    virtual void draw_points(CGAL::Three::Viewer_interface*) const;
+    virtual void draw_splats(CGAL::Three::Viewer_interface*) const;
+    ///@}
+
     //!Adds a Scene_item* to the list of children.
     //!@see getChildren. @see removeChild.
     void addChild(Scene_item* new_item);
diff --git a/Three/include/CGAL/Three/Scene_item.h b/Three/include/CGAL/Three/Scene_item.h
index 37eafaae201..24a8349ae6b 100644
--- a/Three/include/CGAL/Three/Scene_item.h
+++ b/Three/include/CGAL/Three/Scene_item.h
@@ -43,6 +43,7 @@ class QKeyEvent;
 namespace CGAL {
 namespace Three {
 
+class Scene_group_item;
 class Viewer_interface;
 //! This class represents an object in the OpenGL scene
 class SCENE_ITEM_EXPORT Scene_item : public QObject {
@@ -78,72 +79,12 @@ public:
   //! The default color of a scene_item.
   static const QColor defaultColor; // defined in Scene_item.cpp
 
-  //!The default Constructor.
-  /*!
-   * Initializes the number of VBOs to 20 and VAOs to 10 and creates them.
-   */
-  Scene_item()
-    : name_("unamed"),
-      color_(defaultColor),
-      visible_(true),
-      are_buffers_filled(false),
-      rendering_mode(FlatPlusEdges),
-      defaultContextMenu(0),
-      buffersSize(20),
-      vaosSize(10),
-      vaos(10)
-  {
-      is_bbox_computed = false;
-      is_monochrome = true;
-      for(int i=0; i<vaosSize; i++)
-      {
-          addVaos(i);
-          vaos[i]->create();
-      }
-
-      buffers.reserve(buffersSize);
-      for(int i=0; i<buffersSize; i++)
-      {
-          QOpenGLBuffer n_buf;
-          buffers.push_back(n_buf);
-          buffers[i].create();
-      }
-      nb_isolated_vertices = 0;
-      has_group = 0;
-  }
   //!The Constructor.
   /*!
    * Initializes the number of VBOs and VAOs and creates them.
    */
-  Scene_item(int buffers_size, int vaos_size)
-    : name_("unamed"),
-      color_(defaultColor),
-      visible_(true),
-      are_buffers_filled(false),
-      rendering_mode(FlatPlusEdges),
-      defaultContextMenu(0),
-      buffersSize(buffers_size),
-      vaosSize(vaos_size),
-      vaos(vaos_size)
-  {
-      is_bbox_computed = false;
-      is_monochrome = true;
-      for(int i=0; i<vaosSize; i++)
-      {
-          addVaos(i);
-          vaos[i]->create();
-      }
+  Scene_item(int buffers_size = 20, int vaos_size = 10);
 
-      buffers.reserve(buffersSize);
-      for(int i=0; i<buffersSize; i++)
-      {
-          QOpenGLBuffer n_buf;
-          buffers.push_back(n_buf);
-          buffers[i].create();
-      }
-      nb_isolated_vertices = 0;
-      has_group = 0;
-  }
   //! Setter for the number of isolated vertices.
   void setNbIsolatedvertices(std::size_t nb) { nb_isolated_vertices = nb;}
   //! Getter for the number of isolated vertices.
@@ -243,6 +184,9 @@ public:
   //!Handles key press events.
   virtual bool keyPressEvent(QKeyEvent*){return false;}
 
+  //!The parent group, or 0 if the item is not in a group.
+  Scene_group_item* parentGroup() const;
+
   //!Contains the header for the table in the statistics dialog
   /*!
    * A header data is composed of 2 columns : the Categories and the titles.
@@ -306,6 +250,10 @@ public Q_SLOTS:
   virtual void setName(QString n) { name_ = n; }
   //!Setter for the visibility of the item.
   virtual void setVisible(bool b) { visible_ = b; }
+  //!Set the parent group. If `group==0`, then the item has no parent.
+  //!This function is called by `Scene::changeGroup` and should not be
+  //!called manually.
+  virtual void moveToGroup(Scene_group_item* group);
   //!Setter for the rendering mode of the item.
   //!@see RenderingMode
   virtual void setRenderingMode(RenderingMode m) { 
@@ -378,6 +326,8 @@ protected:
   QColor color_;
   //!The visibility of the item.
   bool visible_;
+  //!The parent group, or 0 if the item is not in a group.
+  Scene_group_item* parent_group;
   //!Specifies if the item is currently selected.
   bool is_selected;
   //! Specifies if the item is monochrome and uses uniform attribute for its color
diff --git a/Three/include/CGAL/Three/Viewer_interface.h b/Three/include/CGAL/Three/Viewer_interface.h
index e99b5bbd785..27c1d08cd25 100644
--- a/Three/include/CGAL/Three/Viewer_interface.h
+++ b/Three/include/CGAL/Three/Viewer_interface.h
@@ -80,6 +80,8 @@ public:
   static QString dumpFrame(const qglviewer::Frame&);
   //! @returns the fastDrawing state.
   virtual bool inFastDrawing() const = 0;
+  //! @returns if the viewer is in `drawWithNames()`
+  virtual bool inDrawWithNames() const = 0;
 
   /*! Passes all the uniform data to the shaders.
    * According to program_name, this data may change.