diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
index 22a6be53523..85d4ff65c29 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
@@ -17,14 +17,13 @@
 // SPDX-License-Identifier: GPL-3.0+
 //
 //
-// Author(s)     : Maxime Gimeno and Sebastien Loriot
+// Author(s)     : Maxime Gimeno, Sebastien Loriot, Martin Skrodzki
 
 #ifndef CGAL_POLYGON_MESH_PROCESSING_DISTANCE_H
 #define CGAL_POLYGON_MESH_PROCESSING_DISTANCE_H
 
 #include <CGAL/license/Polygon_mesh_processing/distance.h>
 
-
 #include <algorithm>
 #include <cmath>
 #include <CGAL/AABB_tree.h>
@@ -41,6 +40,8 @@
 #include <CGAL/Polygon_mesh_processing/measure.h>
 
 #include <CGAL/Polygon_mesh_processing/internal/mesh_to_point_set_hausdorff_distance.h>
+#include <CGAL/Polygon_mesh_processing/internal/AABB_traversal_traits_with_Hausdorff_distance.h>
+
 #ifdef CGAL_LINKED_WITH_TBB
 #include <tbb/parallel_for.h>
 #include <tbb/blocked_range.h>
@@ -874,8 +875,12 @@ double bounded_error_Hausdorff_impl(
   CGAL_assertion_msg (is_triangle,
         "One of the meshes is not triangulated. Distance computing impossible.");
 
+  typedef AABB_face_graph_triangle_primitive<TriangleMesh, VPM1> TM1_primitive;
   typedef AABB_face_graph_triangle_primitive<TriangleMesh, VPM2> TM2_primitive;
+  typedef AABB_tree< AABB_traits<Kernel, TM1_primitive> > TM1_tree;
   typedef AABB_tree< AABB_traits<Kernel, TM2_primitive> > TM2_tree;
+  typedef typename AABB_tree< AABB_traits<Kernel, TM2_primitive> >::AABB_traits Tree_traits;
+
   typedef typename Kernel::Point_3 Point_3;
 
   typedef typename boost::graph_traits<TriangleMesh>::vertex_descriptor vertex_descriptor;
@@ -904,6 +909,15 @@ double bounded_error_Hausdorff_impl(
                 tm1_vertices.end(),
                 Search_traits_3(vpm1) );
 
+  // Build an AABB tree on tm1
+  TM1_tree tm1_tree( faces(tm1).begin(), faces(tm1).end(), tm1, vpm1 );
+  tm1_tree.build();
+  tm1_tree.accelerate_distance_queries();
+
+  // Build traversal traits for tm1_tree
+  Hausdorff_primitive_traits<Tree_traits, Point_3> traversal_traits( tm1_tree.traits() );
+  tm1_tree.traversal( Point_3(0,0,0), traversal_traits );
+
   // Build an AABB tree on tm2
   TM2_tree tm2_tree( faces(tm2).begin(), faces(tm2).end(), tm2, vpm2 );
   tm2_tree.build();
@@ -1026,6 +1040,8 @@ double bounded_error_Hausdorff_impl(
       }
     }
 
+
+
     // TODO Iterate over candidate_triangles and kill those which cannot contribute anymore
 
     // TODO Send the remaining triangles to the Subdivision
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/AABB_traversal_traits_with_Hausdorff_distance.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/AABB_traversal_traits_with_Hausdorff_distance.h
new file mode 100644
index 00000000000..58bf1d85805
--- /dev/null
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/AABB_traversal_traits_with_Hausdorff_distance.h
@@ -0,0 +1,80 @@
+// Copyright (c) 2019 GeometryFactory (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) : Sebastien Loriot, Martin Skrodzki
+//
+
+#ifndef CGAL_PMP_INTERNAL_AABB_TRAVERSAL_TRAITS_WITH_HAUSDORFF_DISTANCE
+#define CGAL_PMP_INTERNAL_AABB_TRAVERSAL_TRAITS_WITH_HAUSDORFF_DISTANCE
+
+#include <iostream>
+
+namespace CGAL {
+
+  /**
+   * @class Hausdorff_primitive_traits
+   */
+  template<typename AABBTraits, typename Query>
+  class Hausdorff_primitive_traits
+  {
+    typedef typename AABBTraits::Primitive Primitive;
+    typedef ::CGAL::AABB_node<AABBTraits> Node;
+
+  public:
+    Hausdorff_primitive_traits(const AABBTraits& traits)
+      : m_traits(traits) {}
+
+    // Explore the whole tree, i.e. always enter children if the methods
+    // do_intersect() below determines that it is worthwhile.
+    bool go_further() const { return true; }
+
+    // Compute the explicit Hausdorff distance to the given primitive
+    void intersection(const Query& query, const Primitive& primitive)
+    {
+      // Have reached a single triangle
+      std::cout << "Reached Triangle " << primitive.id() << '\n';
+
+      /* TODO implement handling of a single triangle
+      /  - Call Culling on B (First maybe don't cull, but only consider closest
+      /    triangle), obtain local bounds for the triangle
+      /  - Update global Hausdorff bounds according to the obtained local bounds
+      /  - return the current best known global bounds
+      */
+    }
+
+    bool do_intersect(const Query& query, const Node& node) const
+    {
+      // Have reached a node, determine whether or not to enter it
+
+      /* TODO implement processing of an AABB node
+      /  - Determine distance of the node's bounding box (node.bbox()) to the
+      /    closest point in B (First maybe any point)
+      /  - If the distance is larger than the global lower bound, enter the
+      /    node, i.e. return true.
+      */
+      return true;
+      //return m_traits.do_intersect_object()(query, node.bbox());
+    }
+
+  private:
+    const AABBTraits& m_traits;
+  };
+}
+
+#endif //CGAL_PMP_INTERNAL_AABB_TRAVERSAL_TRAITS_WITH_HAUSDORFF_DISTANCE