diff --git a/Kernel_23/include/CGAL/internal/Projection_traits_3.h b/Kernel_23/include/CGAL/internal/Projection_traits_3.h
index 67e2760cfe2..0f15a7e084f 100644
--- a/Kernel_23/include/CGAL/internal/Projection_traits_3.h
+++ b/Kernel_23/include/CGAL/internal/Projection_traits_3.h
@@ -248,6 +248,8 @@ public:
   typedef typename R::Point_2   Point_2; 
   typedef typename R::Line_3    Line_3; 
   typedef typename R::Line_2    Line_2;
+  typedef typename R::Segment_3 Segment_3;
+  typedef typename R::Segment_2 Segment_2;
   typedef typename R::FT        RT;
   typename R::FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
   typename R::FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
@@ -270,6 +272,13 @@ public:
     Line_2 l2(project(l.point(0)), project(l.point(1)));
     return squared_distance(p2, l2);
   }
+  
+  RT operator()(const Segment_3& s, const Point_3& p) const
+  {
+    Point_2 p2(project(p));
+    Segment_2 s2(project(s.source()), project(s.target()));
+    return squared_distance(p2, s2);
+  }
 };
 
 template <class R,int dim>
diff --git a/Polyline_simplification_2/doc/Polyline_simplification_2/Polyline_simplification_2.txt b/Polyline_simplification_2/doc/Polyline_simplification_2/Polyline_simplification_2.txt
index 04d89c86104..d094507e9e2 100644
--- a/Polyline_simplification_2/doc/Polyline_simplification_2/Polyline_simplification_2.txt
+++ b/Polyline_simplification_2/doc/Polyline_simplification_2/Polyline_simplification_2.txt
@@ -196,6 +196,12 @@ At the end we remove the points that were kept from the constraints.
 
 \cgalExample{Polyline_simplification_2/points_and_vertices.cpp}
 
+\subsection Subsection_PolylineSimplification_Terrain Simplification of a Terrain
+
+It is possible to use the class `Projection_traits_xy_3` in order to simplify polylines in space.
+Note that the segment length is computed in the xy-plane, and the polyline must not have any vertical segment.
+
+\cgalExample{Polyline_simplification_2/simplify_terrain.cpp}
 
 \section Section_PolylineSimplification_History Design and Implementation History
 
diff --git a/Polyline_simplification_2/doc/Polyline_simplification_2/examples.txt b/Polyline_simplification_2/doc/Polyline_simplification_2/examples.txt
index de187d52b28..a0713d4fd20 100644
--- a/Polyline_simplification_2/doc/Polyline_simplification_2/examples.txt
+++ b/Polyline_simplification_2/doc/Polyline_simplification_2/examples.txt
@@ -1,5 +1,6 @@
 /*!
 \example Polyline_simplification_2/simplify_polygon.cpp
 \example Polyline_simplification_2/simplify.cpp
+\example Polyline_simplification_2/simplify_terrain.cpp
 \example Polyline_simplification_2/points_and_vertices.cpp
 */
diff --git a/Polyline_simplification_2/examples/Polyline_simplification_2/simplify_terrain.cin b/Polyline_simplification_2/examples/Polyline_simplification_2/simplify_terrain.cin
new file mode 100644
index 00000000000..37ac2bedd1c
--- /dev/null
+++ b/Polyline_simplification_2/examples/Polyline_simplification_2/simplify_terrain.cin
@@ -0,0 +1 @@
+4 0 0 0 1 0 0 2 4 0 3 10 0
diff --git a/Polyline_simplification_2/examples/Polyline_simplification_2/simplify_terrain.cpp b/Polyline_simplification_2/examples/Polyline_simplification_2/simplify_terrain.cpp
new file mode 100644
index 00000000000..4ba1a4d41d7
--- /dev/null
+++ b/Polyline_simplification_2/examples/Polyline_simplification_2/simplify_terrain.cpp
@@ -0,0 +1,50 @@
+#include <iostream>
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Projection_traits_xy_3.h>
+#include <CGAL/Polygon_2.h>
+#include <CGAL/Constrained_Delaunay_triangulation_2.h>
+#include <CGAL/Constrained_triangulation_plus_2.h>
+#include <CGAL/Polyline_simplification_2/simplify.h>
+#include <CGAL/Polyline_simplification_2/Squared_distance_cost.h>
+
+namespace PS = CGAL::Polyline_simplification_2;
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel Epic;
+typedef CGAL::Projection_traits_xy_3<Epic>  K;
+typedef CGAL::Polygon_2<K>                                  Polygon_2;
+
+typedef PS::Vertex_base_2<K> Vb;
+typedef CGAL::Constrained_triangulation_face_base_2<K> Fb;
+typedef CGAL::Triangulation_data_structure_2<Vb, Fb> TDS;
+typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS, CGAL::Exact_predicates_tag> CDT;
+typedef CGAL::Constrained_triangulation_plus_2<CDT>     CT;
+typedef CT::Point                           Point;
+typedef CT::Constraint_iterator             Constraint_iterator;
+typedef CT::Vertices_in_constraint_iterator Vertices_in_constraint_iterator;
+typedef CT::Points_in_constraint_iterator   Points_in_constraint_iterator;
+typedef PS::Stop_below_count_ratio_threshold Stop;
+typedef PS::Squared_distance_cost Cost;
+
+int main()
+{
+  CT ct;
+  Polygon_2 P;
+  while(std::cin >> P){
+    ct.insert_constraint(P);
+  }
+  PS::simplify(ct, Cost(), Stop(0.5));
+
+  for(Constraint_iterator cit = ct.constraints_begin();
+      cit != ct.constraints_end();
+      ++cit) {
+    std::cout << "simplified polyline" << std::endl;
+    for(Points_in_constraint_iterator vit = 
+          ct.points_in_constraint_begin(*cit);
+        vit != ct.points_in_constraint_end(*cit);
+        ++vit)
+      std::cout << *vit << std::endl;
+  }
+  return 0;
+}
+
+