Make the example more interesting.

Fix const correctness.
Fix the Subconstraint_iterator.
Improve the manual.

Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h

@@ -291,13 +291,7 @@ template <class PolygonTraits_2, class Container, class CostFunction, class Stop
                            CostFunction cost,
                            StopFunction stop)
 {
-  typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
+  typedef CGAL::Polyline_constrained_triangulation_2<>       PCT;
-  typedef CGAL::Triangulation_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::Exact_predicates_tag                        Itag;
-  typedef CGAL::Constrained_Delaunay_triangulation_2<K,TDS, Itag> CDT;
-  typedef CGAL::Polyline_constrained_triangulation_2<CDT>       PCT;
   typedef PCT::Constraint_id Constraint_id;
   typedef PCT::Vertices_in_constraint_iterator Vertices_in_constraint_iterator;
 

Triangulation_2/doc/Triangulation_2/CGAL/Constrained_triangulation_2.h

@@ -283,7 +283,7 @@ void insert_constraint(InputIterator begin, InputIterator end);
 
 /*!
 Inserts the polyline defined by the iterator range `range`. 
-\tparam InputIterator must be an input iterator with value type `Point`.
+\tparam IteratorRange must be an iterator range with value type `Point`.
 */
 template <typename IteratorRange>
 void insert_constraint(IteratorRange range);

Triangulation_2/doc/Triangulation_2/CGAL/Constrained_triangulation_plus_2.h

@@ -208,7 +208,7 @@ void insert_constraint(Point a, Point b);
 /*! 
 Inserts the constraint `c`. 
 */ 
-void push_back(const Constraint& c); 
+  void push_back(const std::pair<Point,Point>& c); 
 
 /*! 
 Inserts a constraint whose endpoints are the vertices 
@@ -216,6 +216,21 @@ pointed by `va` and `vb` in the triangulation.
 */ 
 void insert_constraint(Vertex_handle va, Vertex_handle vb); 
 
+/*!
+Inserts a polyline defined by the points in the range `[first,last)`.
+
+\tparam InputIterator must be an input iterator with the value type `Point`. 
+*/
+template < class InputIterator>
+insert_constraint(InputIterator first, InputIterator last)
+
+/*!
+Inserts the polyline defined by the iterator range `range`. 
+\tparam IteratorRange must be an iterator range with value type `Point`.
+*/
+template <typename IteratorRange>
+void insert_constraint(IteratorRange range);
+
 /*! 
 Removes the constraint joining the vertices pointed by `va` and `vb`. 
 \pre `va` and `vb` have to refer to the endpoint vertices of an input constraint. 

Triangulation_2/doc/Triangulation_2/CGAL/Polyline_constrained_triangulation_2.h

@@ -222,6 +222,22 @@ pointed by `va` and `vb` in the triangulation.
 */ 
 void insert_constraint(Vertex_handle va, Vertex_handle vb); 
 
+/*!
+Inserts a polyline defined by the points in the range `[first,last)`.
+Returns the constraint id.
+
+\tparam InputIterator must be an input iterator with the value type `Point`. 
+*/
+template < class InputIterator>
+Constraint_id insert_constraint(InputIterator first, InputIterator last);
+
+/*!
+Inserts the polyline defined by the iterator range `range`. 
+\tparam IteratorRange must be an iterator range with value type `Point`.
+*/
+template <typename IteratorRange>
+void insert_constraint(IteratorRange range);
+
 /*! 
 Removes the constraint `cid`, without removing the points from the triangulation.
 */ 
@@ -303,10 +319,19 @@ vertices_in_constraint_end(Constraint_id cid) const;
 
 /// @}
 
-/// \name Polyline Simplification
+/*! \name Polyline Simplification
-/// The polyline simplification algorithm described in Chapter
+ The polyline simplification algorithm described in Chapter
-/// \ref Chapter_2D_Polyline_simplification uses the following types and 
+\ref Chapter_2D_Polyline_simplification 
-/// functions.
+operates on polyline constraints. The algorithm removes
+vertices of a constraint and at the same time  from the triangulation.
+The points of removed vertices are nevertheless kept
+in the the polyline constraint.
+This allows the simplification algorithm to compute the error
+introduced by the simplification process by comparing the 
+current sequence (vertices) to the original sequence (points).
+
+The simplification algorithm uses the following types and functions.
+*/
 
 /// @{
 
@@ -321,9 +346,11 @@ typedef Hidden_type Points_in_constraint_iterator;
 /*! 
 Removes vertex at `viq` from the constraint and the triangulation.
 Only the vertex but not the point is removed from the constraint `cid`.
-\pre The vertex at `viq` must not be the first or last vertex, 
+\pre The vertices `vip`, `viq`, and `vir` must be three successive 
-must not be fixed, and the line segment between the predecessor `vip` and 
+vertices in a constraint.
-the successor `vir` of `viq` must not intersect any constraint.
+\pre No other constraint must pass through `viq`.
+\pre The line segment between `vip` and `vir` must not intersect any constraint.
+\pre All vertices of the triangulation are vertex of a constaint.
  */
 
 void

Triangulation_2/doc/Triangulation_2/Triangulation_2.txt

@@ -1027,12 +1027,12 @@ constrained edge, the set of input constraints that overlap it.
 The class `Polyline_constrained_triangulation_2<Tr>`
 is especially useful when the base constrained triangulation class
 handles intersections of constraints and uses an exact number type,
-i.e. when its intersection tag is `Exact_intersections_tag`.
+i.e.\ when its intersection tag is `Exact_intersections_tag`.
 Indeed in this case, the `Polyline_constrained_triangulation_2<Tr>`
 is specially designed to avoid cascading in the computations of
 intersection points.
 
-\subsection Triangulation_2ExampleBuildingaTriangulated Example: Building a Triangulated Arrangement of Segments
+\subsection Triangulation_2ExampleBuildingaTriangulated Example: Building a Triangulated Arrangement of Polylines
 
 The following code inserts a set of intersecting constraint segments
 into a triangulation 

Triangulation_2/examples/Triangulation_2/polylines.cpp

@@ -17,12 +17,13 @@ typedef CGAL::Polyline_constrained_triangulation_2<CDT>          PCT;
 
 typedef PCT::Point                                               Point;
 typedef PCT::Constraint_id                                       Cid;
-typedef PCT::Vertices_in_constraint                              Vertices_in_constraint;
 typedef PCT::Vertex_handle                                       Vertex_handle;
 
 void 
 print(const PCT& cdt, Cid cid)
 {
+  typedef PCT::Vertices_in_constraint                              Vertices_in_constraint;
+
   std::cout << "Polyline constraint:" << std::endl;
   for(Vertices_in_constraint it = cdt.vertices_in_constraint_begin(cid);
       it != cdt.vertices_in_constraint_end(cid);
@@ -32,6 +33,30 @@ print(const PCT& cdt, Cid cid)
   }
 }
 
+
+void 
+contexts(const PCT& pct)
+{
+  PCT::Subconstraint_iterator beg, end;
+  beg = pct.subconstraints_begin();
+  end = pct.subconstraints_end();
+
+  for(; beg!=end; ++beg){
+    Vertex_handle vp = beg->first, vq = beg->second;
+
+    if(pct.number_of_enclosing_constraints(vp, vq) == 2){
+      PCT::Context_iterator cbeg = pct.contexts_begin(vp,vq);
+      PCT::Context_iterator cend = pct.contexts_end(vp,vq);
+      std::cout << "subconstraint " << vp->point() << " " << vq->point() 
+                << " is on constraints starting at:\n";
+      for(; cbeg !=  cend; ++cbeg){
+        PCT::Context c = *cbeg;
+        std::cout << (*(c.vertices_begin()))->point() << std::endl;
+      }
+    }
+  }
+}
+
 int
 main( )
 {
@@ -59,5 +84,7 @@ main( )
   print(pct, id1);
   print(pct, id2);
 
+  contexts(pct);
+
   return 0;
 }

Triangulation_2/include/CGAL/Polyline_constrained_triangulation_2.h

@@ -39,7 +39,7 @@ namespace CGAL {
 template < class Tr_ = Default >
 class Polyline_constrained_triangulation_2  
   : public  
-      Default::Get< Constrained_Delaunay_triangulation_2< 
+Default::Get< Tr_, Constrained_Delaunay_triangulation_2< 
                       Exact_predicates_inexact_constructions_kernel
                       , Triangulation_data_structure_2< 
                           Polyline_constrained_triangulation_vertex_base< 
@@ -48,11 +48,10 @@ class Polyline_constrained_triangulation_2
                           , Constrained_triangulation_face_base_2<Exact_predicates_inexact_constructions_kernel>
                           >
                       , CGAL::Exact_predicates_tag
-                      >
+                      > >::type
-                    , Tr_>::type
 {
   typedef typename 
-  Default::Get< Constrained_Delaunay_triangulation_2< 
+  Default::Get< Tr_, Constrained_Delaunay_triangulation_2< 
                   Exact_predicates_inexact_constructions_kernel
                   , Triangulation_data_structure_2< 
                       Polyline_constrained_triangulation_vertex_base< 
@@ -61,9 +60,7 @@ class Polyline_constrained_triangulation_2
                       , Constrained_triangulation_face_base_2<Exact_predicates_inexact_constructions_kernel>
                       >
                   , CGAL::Exact_predicates_tag
-                  >
+                  > >::type Tr;
-                , Tr_
-  >::type Tr;
 
 
   template<class CDT>
@@ -144,7 +141,7 @@ public:
   typedef typename Polyline_constraint_hierarchy::Context      Context;
   typedef typename Polyline_constraint_hierarchy::Context_iterator  Context_iterator;
   typedef typename Polyline_constraint_hierarchy::C_iterator   Constraint_iterator;
-  typedef typename Polyline_constraint_hierarchy::Sc_iterator  Subconstraint_iterator;
+  typedef typename Polyline_constraint_hierarchy::Subconstraint_iterator  Subconstraint_iterator;
  
   typedef typename Polyline_constraint_hierarchy::Constraint_id Constraint_id;   
                                             
@@ -501,7 +498,7 @@ private:
       vertices.push_back(vertices.front());
     }
 
-    int n = vertices.size();
+    std::size_t n = vertices.size();
     if(n == 1){
       return NULL;
     }
@@ -625,16 +622,16 @@ public:
   Constraint_iterator constraints_end()   const;
   Subconstraint_iterator subconstraints_begin() const;
   Subconstraint_iterator subconstraints_end() const;
-  Context   context(Vertex_handle va, Vertex_handle vb); 
+  Context   context(Vertex_handle va, Vertex_handle vb) const; 
 
   bool is_subconstraint(Vertex_handle va, 
 			Vertex_handle vb);
   size_type number_of_enclosing_constraints(Vertex_handle va, 
-                                            Vertex_handle vb);
+                                            Vertex_handle vb) const;
   Context_iterator   contexts_begin(Vertex_handle va, 
-				    Vertex_handle vb);
+				    Vertex_handle vb) const;
   Context_iterator   contexts_end(Vertex_handle va, 
-				  Vertex_handle vb);
+				  Vertex_handle vb) const;
 
   Vertices_in_constraint_iterator vertices_in_constraint_begin(Constraint_id cid) const;
   Vertices_in_constraint_iterator vertices_in_constraint_end(Constraint_id cid) const ;
@@ -1013,7 +1010,7 @@ Polyline_constrained_triangulation_2<Tr>::Subconstraint_iterator
 Polyline_constrained_triangulation_2<Tr>::
 subconstraints_begin() const
 {
-  return hierarchy.sc_begin();
+  return hierarchy.subconstraint_begin();
 }
 
 template <class Tr>
@@ -1023,7 +1020,7 @@ Polyline_constrained_triangulation_2<Tr>::Subconstraint_iterator
 Polyline_constrained_triangulation_2<Tr>::
 subconstraints_end() const
 {
-  return hierarchy.sc_end();
+  return hierarchy.subconstraint_end();
 }
 
 
@@ -1031,7 +1028,7 @@ template <class Tr>
 inline
 typename Polyline_constrained_triangulation_2<Tr>::Context
 Polyline_constrained_triangulation_2<Tr>::
-context(Vertex_handle va, Vertex_handle vb)
+context(Vertex_handle va, Vertex_handle vb) const
 {
   return hierarchy.context(va,vb);
 }
@@ -1041,7 +1038,7 @@ template <class Tr>
 inline 
 typename Polyline_constrained_triangulation_2<Tr>::size_type
 Polyline_constrained_triangulation_2<Tr>::
-number_of_enclosing_constraints(Vertex_handle va, Vertex_handle vb)
+number_of_enclosing_constraints(Vertex_handle va, Vertex_handle vb) const
 {
  return static_cast<size_type> 
    (hierarchy.number_of_enclosing_constraints(va,vb)); 
@@ -1060,7 +1057,7 @@ template <class Tr>
 inline
 typename Polyline_constrained_triangulation_2<Tr>::Context_iterator
 Polyline_constrained_triangulation_2<Tr>::
-contexts_begin(Vertex_handle va, Vertex_handle vb)
+contexts_begin(Vertex_handle va, Vertex_handle vb) const
 {
   return hierarchy.contexts_begin(va,vb);
 }
@@ -1069,7 +1066,7 @@ template <class Tr>
 inline
 typename Polyline_constrained_triangulation_2<Tr>::Context_iterator
 Polyline_constrained_triangulation_2<Tr>::
-contexts_end(Vertex_handle va, Vertex_handle vb)
+contexts_end(Vertex_handle va, Vertex_handle vb) const
 {
   return hierarchy.contexts_end(va,vb);
 }

Triangulation_2/include/CGAL/Polyline_constraint_hierarchy_2.h

@@ -29,6 +29,7 @@
 #include <CGAL/Skiplist.h>
 #include <CGAL/Iterator_project.h>
 #include <CGAL/triangulation_assertions.h>
+#include <boost/iterator/transform_iterator.hpp>
 
 namespace CGAL {
 
@@ -113,11 +114,11 @@ public:
       : enclosing(hc.enclosing), pos(hc.pos)
     {}
 
-    Vertex_it    vertices_begin() { return enclosing->begin();}
+    Vertex_it    vertices_begin() { return enclosing->skip_begin();}
     Vertex_it    current() {return pos;}
-    Vertex_it    vertices_end() {return enclosing->end();}
+    Vertex_it    vertices_end() {return enclosing->skip_end();}
     Constraint_id  id() { return enclosing; }
-    std::size_t    number_of_vertices() {return enclosing->size();}
+    std::size_t    number_of_vertices() const {return enclosing->size();}
   };                                           
 
   typedef std::list<Context>              Context_list;
@@ -128,6 +129,15 @@ public:
   typedef typename Constraint_set::const_iterator C_iterator;
   typedef typename Sc_to_c_map::const_iterator    Sc_iterator;
 
+  struct First
+    : public std::unary_function<std::pair<Edge, Context_list*>,Edge>  {
+    Edge operator()(const std::pair<Edge, Context_list*>& p) const
+    {
+      return p.first;
+    } 
+  };
+  typedef boost::transform_iterator<First,Sc_iterator> Subconstraint_iterator;
+  
 private:
   // data for the 1d hierarchy
   Constraint_set   constraint_set;
@@ -164,11 +174,11 @@ public:
   void oriented_end(T va, T vb, T& vc) const;
 
   Context context(T va, T vb);
-  std::size_t number_of_enclosing_constraints(T va, T vb);
+  std::size_t number_of_enclosing_constraints(T va, T vb) const;
-  Context_iterator contexts_begin(T va, T vb);
+  Context_iterator contexts_begin(T va, T vb) const;
-  Context_iterator contexts_end(T va, T vb);
+  Context_iterator contexts_end(T va, T vb) const;
-  std::size_t number_of_constraints() { return constraint_set.size();}
+  std::size_t number_of_constraints() const  { return constraint_set.size();}
-  std::size_t number_of_subconstraints() {return sc_to_c_map.size();}
+  std::size_t number_of_subconstraints()const {return sc_to_c_map.size();}
   
 
   // insert/remove
@@ -194,6 +204,18 @@ public:
   void remove_Steiner(T v, T va, T vb);
 
   // iterators
+
+  Subconstraint_iterator subconstraint_begin() const
+  { 
+    First f;
+    return boost::make_transform_iterator(sc_to_c_map.begin(),f); 
+  }
+
+  Subconstraint_iterator subconstraint_end() const
+  { 
+    First f;
+    return boost::make_transform_iterator(sc_to_c_map.end(),f);   }
+
   Sc_iterator sc_begin() const{ return sc_to_c_map.begin(); }
   Sc_iterator sc_end()   const{ return sc_to_c_map.end();   }
   C_iterator  c_begin()  const{ return constraint_set.begin(); }
@@ -389,7 +411,7 @@ context(T va, T vb)
 template <class T, class Data>
 std::size_t 
 Polyline_constraint_hierarchy_2<T,Data>::
-number_of_enclosing_constraints(T va, T vb)
+number_of_enclosing_constraints(T va, T vb) const
 {
   Context_list* hcl;
   if (! get_contexts(va,vb,hcl)) CGAL_triangulation_assertion(false);
@@ -399,7 +421,7 @@ number_of_enclosing_constraints(T va, T vb)
 template <class T, class Data>
 typename Polyline_constraint_hierarchy_2<T,Data>::Context_iterator
 Polyline_constraint_hierarchy_2<T,Data>::
-contexts_begin(T va, T vb)
+contexts_begin(T va, T vb) const
 {
    Context_iterator first, last;
    if( !get_contexts(va,vb,first,last))  CGAL_triangulation_assertion(false);
@@ -409,7 +431,7 @@ contexts_begin(T va, T vb)
 template <class T, class Data>
 typename Polyline_constraint_hierarchy_2<T,Data>::Context_iterator
 Polyline_constraint_hierarchy_2<T,Data>::
-contexts_end(T va, T vb)
+contexts_end(T va, T vb) const
 {   
    Context_iterator first, last;
    if( !get_contexts(va,vb,first,last))  CGAL_triangulation_assertion(false);