diff --git a/AABB_tree/include/CGAL/AABB_triangle_primitive_2.h b/AABB_tree/include/CGAL/AABB_triangle_primitive_2.h
new file mode 100644
index 00000000000..393d8517cff
--- /dev/null
+++ b/AABB_tree/include/CGAL/AABB_triangle_primitive_2.h
@@ -0,0 +1,101 @@
+// Copyright (c) 2012 INRIA Sophia-Antipolis (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
+//
+//
+// Author(s)     : Sebastien Loriot
+//
+
+
+#ifndef CGAL_AABB_TRIANGLE_PRIMITIVE_2_H_
+#define CGAL_AABB_TRIANGLE_PRIMITIVE_2_H_
+
+#include <CGAL/license/AABB_tree.h>
+
+#include <CGAL/disable_warnings.h>
+
+#include <CGAL/AABB_primitive.h>
+#include <iterator>
+
+namespace CGAL {
+
+namespace internal {
+  template <class GeomTraits, class Iterator>
+  struct Point_from_triangle_2_iterator_property_map{
+    //classical typedefs
+    typedef Iterator key_type;
+    typedef typename GeomTraits::Point_2 value_type;
+    // typedef decltype(
+    //   std::declval<typename GeomTraits::Construct_vertex_2>()(
+    //     std::declval<typename GeomTraits::Triangle_2>(),
+    //     std::declval<int>())) reference;
+    typedef decltype(
+      typename GeomTraits::Construct_vertex_2()(
+        *std::declval<key_type&>(), 0)) reference;
+    typedef boost::readable_property_map_tag category;
+    typedef Point_from_triangle_2_iterator_property_map<GeomTraits, Iterator> Self;
+
+    inline friend reference
+    get(Self, key_type it)
+    {
+      return typename GeomTraits::Construct_vertex_2()( *it, 0 );
+    }
+  };
+}//namespace internal
+
+
+/*!
+ * \ingroup PkgAABBTreeRef
+ * Primitive type that uses as identifier an iterator with a 3D triangle as `value_type`.
+ * The iterator from which the primitive is built should not be invalided
+ * while the AABB tree holding the primitive is in use.
+ *
+ * \cgalModels{AABBPrimitive}
+ *
+ * \tparam GeomTraits is a traits class providing the nested type `Point_2` and `Triangle_2`.
+ *         It also provides the functor `Construct_vertex_2` that has an operator taking a `Triangle_2`
+ *         and an integer as parameters and returning a triangle point as a type convertible to `Point_2`.
+ * \tparam Iterator is a model of `ForwardIterator` with its value type convertible to `GeomTraits::Triangle_2`
+ * \tparam CacheDatum is either `CGAL::Tag_true` or `CGAL::Tag_false`. In the former case,
+ *           the datum is stored in the primitive, while in the latter it is
+ *           constructed on the fly to reduce the memory footprint.
+ *           The default is `CGAL::Tag_false` (datum is not stored).
+ *
+ * \sa `AABBPrimitive`
+ * \sa `AABB_primitive<Id,ObjectPropertyMap,PointPropertyMapPolyhedron,ExternalPropertyMaps,CacheDatum>`
+ * \sa `AABB_segment_primitive_2<Iterator,CacheDatum>`
+ * \sa `AABB_halfedge_graph_segment_primitive<HalfedgeGraph,OneHalfedgeGraphPerTree,CacheDatum>`
+ * \sa `AABB_face_graph_triangle_primitive<FaceGraph,OneFaceGraphPerTree,CacheDatum>`
+ */
+template < class GeomTraits,
+           class Iterator,
+           class CacheDatum=Tag_false>
+class AABB_triangle_primitive_2
+#ifndef DOXYGEN_RUNNING
+  : public AABB_primitive<  Iterator,
+                            Input_iterator_property_map<Iterator>,
+                            internal::Point_from_triangle_2_iterator_property_map<GeomTraits, Iterator>,
+                            Tag_false,
+                            CacheDatum >
+#endif
+{
+  typedef AABB_primitive< Iterator,
+                          Input_iterator_property_map<Iterator>,
+                          internal::Point_from_triangle_2_iterator_property_map<GeomTraits, Iterator>,
+                          Tag_false,
+                          CacheDatum > Base;
+public:
+  ///constructor from an iterator
+  AABB_triangle_primitive_2(Iterator it) : Base(it){}
+};
+
+}  // end namespace CGAL
+
+#include <CGAL/enable_warnings.h>
+
+#endif // CGAL_AABB_TRIANGLE_PRIMITIVE_2_H_
diff --git a/AABB_tree/include/CGAL/AABB_triangle_primitive_3.h b/AABB_tree/include/CGAL/AABB_triangle_primitive_3.h
index 569e579f12b..8c1116f4510 100644
--- a/AABB_tree/include/CGAL/AABB_triangle_primitive_3.h
+++ b/AABB_tree/include/CGAL/AABB_triangle_primitive_3.h
@@ -68,7 +68,7 @@ namespace internal {
  *
  * \sa `AABBPrimitive`
  * \sa `AABB_primitive<Id,ObjectPropertyMap,PointPropertyMapPolyhedron,ExternalPropertyMaps,CacheDatum>`
- * \sa `AABB_segment_primitive<Iterator,CacheDatum>`
+ * \sa `AABB_segment_primitive_3<Iterator,CacheDatum>`
  * \sa `AABB_halfedge_graph_segment_primitive<HalfedgeGraph,OneHalfedgeGraphPerTree,CacheDatum>`
  * \sa `AABB_face_graph_triangle_primitive<FaceGraph,OneFaceGraphPerTree,CacheDatum>`
  */
@@ -99,4 +99,3 @@ public:
 #include <CGAL/enable_warnings.h>
 
 #endif // CGAL_AABB_TRIANGLE_PRIMITIVE_3_H_
-
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
index 6da8fab4046..f0b5b7fa5ff 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
@@ -3279,6 +3279,7 @@ namespace CartesianKernelFunctors {
     typedef typename K::Point_2    Point_2;
     typedef typename K::Line_2     Line_2;
     typedef typename K::Segment_2  Segment_2;
+    typedef typename K::Triangle_2 Triangle_2;
   public:
     typedef Point_2                result_type;
 
@@ -3299,6 +3300,12 @@ namespace CartesianKernelFunctors {
       // CommonKernelFunctors::Construct_projected_point_3<K>()(s,p,K());
     }
 
+    Point_2
+    operator()( const Triangle_2& t, const Point_2& p ) const
+    {
+      assert(false);
+      return p;
+    }
   };