diff --git a/Polyline_simplification_2/examples/Polyline_simplification_2/simplify_polyline.cpp b/Polyline_simplification_2/examples/Polyline_simplification_2/simplify_polyline.cpp
new file mode 100644
index 00000000000..2190354efa5
--- /dev/null
+++ b/Polyline_simplification_2/examples/Polyline_simplification_2/simplify_polyline.cpp
@@ -0,0 +1,35 @@
+#include <iostream>
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Polyline_simplification_2/simplify.h>
+#include <list>
+#include <vector>
+
+namespace PS = CGAL::Polyline_simplification_2;
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
+typedef K::Point_2 Point_2;
+typedef std::list<Point_2> Polyline;
+typedef PS::Stop_above_cost_threshold Stop;
+typedef PS::Squared_distance_cost Cost;
+
+int main( )
+{
+  Polyline polyline;
+  int n;
+  Point_2 p;
+  std::cin >> n;
+  while(std::cin >> p){
+    polyline.push_back(p);
+  }
+  Cost cost;
+  std::vector<Point_2> result;
+  PS::simplify(polyline.begin(), polyline.end(), cost, Stop(0.5), std::back_inserter(result));
+  
+  std::cout.precision(12);
+  for(int i=0; i < result.size(); ++i){
+    std::cout << result[i] << std::endl;
+  }
+  return 0;
+}
+
+
diff --git a/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h b/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h
index 210366cf284..ec89294c2c2 100644
--- a/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h
+++ b/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h
@@ -353,6 +353,55 @@ template <class PolygonTraits_2, class Container, class CostFunction, class Stop
   return result;
 }
 
+/*!
+\ingroup  PkgPolylineSimplification2Functions
+
+Simplifies an open or closed polyline given as an iterator range of 2D \cgal points.
+
+\tparam PointIterator must be an iterator with value type `CGAL::Kernel::Point_2`.
+\tparam CostFunction must be a model of `PolylineSimplificationCostFunction`
+\tparam StopFunction must be a model of `PolylineSimplificationStopPredicate`
+\tparam OutputIterator must be an output iterator to which `CGAL::Kernel::Point_2` can be assigned.
+*/
+  template <class PointIterator, class CostFunction, class StopFunction, class OutputIterator>
+  OutputIterator
+  simplify(PointIterator b, PointIterator e,
+           CostFunction cost,
+           StopFunction stop,
+           OutputIterator out,
+           bool close = false)
+{
+  typedef typename std::iterator_traits<PointIterator>::value_type Point_2;
+  typedef typename CGAL::Kernel_traits<Point_2>::type K;
+  typedef 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>       PCT;
+  typedef typename PCT::Constraint_id Constraint_id;
+  typedef typename PCT::Vertices_in_constraint_iterator Vertices_in_constraint_iterator;
+
+  PCT pct;
+
+  Constraint_id cid = pct.insert_constraint(b,e, close);
+
+  bool keep_points = false;
+  Polyline_simplification_2<PCT, CostFunction, StopFunction> simplifier(pct, cost, stop);
+  while(simplifier()){}
+
+  Vertices_in_constraint_iterator beg = pct.vertices_in_constraint_begin(cid);
+  Vertices_in_constraint_iterator end = pct.vertices_in_constraint_end(cid);
+  for(; beg!=end;){
+    Point_2 p = (*beg)->point();
+    ++beg;
+    if((!close) || (beg!=end)){
+      *out++ = p;
+    }
+  }
+  return out;
+}
+
+
 /*!
 \ingroup  PkgPolylineSimplification2Functions