Fix the Polyline_constrained_triangulation for the Exact_constructions_tag

To avoid cascading the intersection is done with endpoints of segment constraints
For polyline constraints we cannot take the endpoints of the polyline
but must find input points of the polyline.

Triangulation_2/include/CGAL/Polyline_constraint_hierarchy_2.h

@@ -47,8 +47,8 @@ public:
 private:
   class Node {
   public:
-    explicit Node(Vertex_handle vh)
-    : vertex_(vh), point_(vh->point()), id(-1)
+    explicit Node(Vertex_handle vh, bool input = false)
+      : vertex_(vh), point_(vh->point()), id(-1), input(input)
     {}
     Point& point() { return point_; }
     const Point& point() const { return point_; }
@@ -58,6 +58,7 @@ private:
     Point point_;
   public:
     int id;
+    bool input;
   };
 
   typedef CGAL::Skiplist<Node>  Vertex_list;
@@ -93,6 +94,7 @@ public:
     Vertex_it() : Vertex_it::iterator_adaptor_() {}
     Vertex_it(typename Vertex_list::skip_iterator it) : Vertex_it::iterator_adaptor_(it) {}
     operator Point_it() const { return Point_it(this->base()); }
+    bool& input() { return this->base()->input; }
   private:
     friend class boost::iterator_core_access;
     Vertex_handle dereference() const { return this->base()->vertex(); }
@@ -379,8 +381,26 @@ enclosing_constraint(T  vaa, T  vbb, T& va, T& vb) const
 {
   Context_iterator hcit, past;
   if ( !get_contexts(vaa,vbb, hcit ,past)) return false;
-  va = hcit->enclosing->front().vertex();
-  vb = hcit->enclosing->back().vertex();
+  // va = hcit->enclosing->front().vertex();
+  // vb = hcit->enclosing->back().vertex();
+  Vertex_list* vl = hcit->enclosing;
+  Vertex_it pos = hcit->pos;
+  if(vaa != *pos){
+    std::swap(vaa,vbb);
+  }
+  while(!pos.input()){
+    std::cerr << "decrement\n";
+    --pos;
+  }
+  va = *pos;
+  pos = hcit->pos;
+  ++pos;
+  assert(vbb == *pos);
+  while(!pos.input()){
+    std::cerr << "increment\n";
+    ++pos;
+  }
+  vb = *pos;
   return true;
 }
 
@@ -551,6 +571,10 @@ void Polyline_constraint_hierarchy_2<T,Data>::simplify(Vertex_it uc,
     CGAL_assertion_msg(uv_hcl->size() == 1, "more than one constraint passing through the subconstraint" );
   }
   // now u,v, and w are ordered along the polyline constraint
+  if(vc.input()){
+    uc.input() = true;
+    wc.input() = true;
+  }
   typename Sc_to_c_map::iterator vw_sc_iter = sc_to_c_map.find(make_edge(v, w));
   CGAL_assertion_msg( vw_sc_iter != sc_to_c_map.end(), "not a subconstraint" );
   Context_list*  vw_hcl = vw_sc_iter->second;
@@ -716,6 +740,8 @@ Polyline_constraint_hierarchy_2<T,Data>::split(Constraint_id first, Vertex_it vc
   Vertex_list* second = new Vertex_list;
   second->splice(second->end(), *first, vcit, first->end());
   first->push_back(second->front()); // Duplicate the common vertex
+  second->front().input() = true;
+  first->back().input() = true;
   constraint_set.insert(first);
   constraint_set.insert(second);
  // We have to look at all subconstraints
@@ -746,6 +772,8 @@ Polyline_constraint_hierarchy_2<T,Data>::split2(Constraint_id first, Vertex_it v
   Vertex_list* second = new Vertex_list;
   second->splice(second->end(), *first, first->begin(), vcit);
   second->push_back(first->front()); // Duplicate the common vertex
+  second->back().input() = true;
+  first->front().input() = true;
   constraint_set.insert(first);
   constraint_set.insert(second);
  // We have to look at all subconstraints
@@ -787,8 +815,8 @@ insert_constraint(T va, T vb){
     fathers = scit->second;
   }
 
-  children->push_front(Node(va));  // was he.first
-  children->push_back(Node(vb));   // was he.second
+  children->push_front(Node(va, true));  // was he.first
+  children->push_back(Node(vb, true));   // was he.second
   constraint_set.insert(children);
   Context ctxt;
   ctxt.enclosing = children;
@@ -816,7 +844,7 @@ append_constraint(Vertex_list* vl, T va, T vb){
 
   typename Vertex_list::skip_iterator bit = vl->skip_end();
   --bit;
-  vl->push_back(Node(vb));
+  vl->push_back(Node(vb, true));
   Context ctxt;
   ctxt.enclosing = vl;
   ctxt.pos     = bit;