// Copyright (c) 2000  Max-Planck-Institute Saarbruecken (Germany).
// 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.
//
// $URL$
// $Id$
// 
//
// Author(s)     : Susan Hert <hert@mpi-sb.mpg.de>

/*
    A rotation tree for computing the vertex visibility graph of a set of
    non-intersecting segments in the plane (e.g. edges of a polygon).

    Let $V$ be the set of segment endpoints and
    let $p_{\infinity}$ ($p_{-\infinity}$) be a point with $y$ coordinate
    $\infinity$ ($-\infinity$) and $x$ coordinate larger than all points
    in $V$. The tree $G$ is a tree with node set
    $V \cup \{p_{\infinity}, p_{-\infinity}\}$.  Every node (except the one
    corresponding to $p_{\infinity}$) has exactly one outgoing edge to the
    point $q$ with the following property:  $q$ is the first point encountered
    when looking from $p$ in direction $d$ and rotating counterclockwise.
 */

#ifndef  CGAL_ROTATION_TREE_H
#define  CGAL_ROTATION_TREE_H

#include <CGAL/vector.h>
#include <CGAL/Partition_2/Rotation_tree_node_2.h>
#include <boost/bind.hpp>

namespace CGAL {

template <class Traits_>
class Rotation_tree_2 : public internal::vector< Rotation_tree_node_2<Traits_> >
{
public:
   typedef Traits_                                 Traits;
   typedef Rotation_tree_node_2<Traits>            Node;
   typedef typename internal::vector<Node>::iterator  Self_iterator;
   typedef typename Traits::Point_2                Point_2;

  using  internal::vector< Rotation_tree_node_2<Traits_> >::push_back;

   // constructor
   template<class ForwardIterator>
   Rotation_tree_2(ForwardIterator first, ForwardIterator beyond)
   {
      for (ForwardIterator it = first; it != beyond; it++)
         push_back(*it);
   
      std::sort(this->begin(), this->end(), 
                boost::bind(Traits().less_xy_2_object(), _2, _1));
      std::unique(this->begin(), this->end());
   
      // front() is the point with the largest x coordinate
   
      // push the point p_minus_infinity; the coordinates should never be used
      push_back(Point_2( 1, -1));

      // push the point p_infinity; the coordinates should never be used
      push_back(Point_2(1, 1));
   
      _p_inf = this->end();  // record the iterators to these extreme points
      _p_inf--;
      _p_minus_inf = _p_inf;
      _p_minus_inf--;
   
      Self_iterator child;
      // make p_minus_inf a child of p_inf
      set_rightmost_child(_p_minus_inf, _p_inf); 
      child = this->begin();               // now points to p_0
      while (child != _p_minus_inf)  // make all points children of p_minus_inf
      {
         set_rightmost_child(child, _p_minus_inf);
         child++;
      }
   }


   // the point that comes first in the right-to-left ordering is first
   // in the ordering, after the auxilliary points p_minus_inf and p_inf
   Self_iterator rightmost_point_ref() 
   {
      return this->begin();
   }

   Self_iterator right_sibling(Self_iterator p) 
   {
      if (!(*p).has_right_sibling()) return this->end();
      return (*p).right_sibling();
   }

   Self_iterator left_sibling(Self_iterator p) 
   {
      if (!(*p).has_left_sibling()) return this->end();
      return (*p).left_sibling();
   }

   Self_iterator rightmost_child(Self_iterator p) 
   {
      if (!(*p).has_children()) return this->end();
      return (*p).rightmost_child();
   }

   Self_iterator parent(Self_iterator p) 
   {
      if (!(*p).has_parent()) return this->end();
      return (*p).parent();
   }

   bool parent_is_p_infinity(Self_iterator p) 
   {
      return parent(p) == _p_inf;
   }

   bool parent_is_p_minus_infinity(Self_iterator p) 
   {
      return parent(p) == _p_minus_inf;
   }

   // makes *p the parent of *q
   void set_parent (Self_iterator p, Self_iterator q)
   {
      CGAL_assertion(q != this->end());
      if (p == this->end())
         (*q).clear_parent();
      else
         (*q).set_parent(p);
   }

   // makes *p the rightmost child of *q
   void set_rightmost_child(Self_iterator p, Self_iterator q);

   // makes *p the left sibling of *q
   void set_left_sibling(Self_iterator p, Self_iterator q);

   // makes *p the right sibling of *q
   void set_right_sibling(Self_iterator p, Self_iterator q);

   // NOTE:  this function does not actually remove the node p from the
   //        list; it only reorganizes the pointers so this node is not
   //        in the tree structure anymore
   void erase(Self_iterator p);

private:
   Self_iterator _p_inf;
   Self_iterator _p_minus_inf;
};

}

#include <CGAL/Partition_2/Rotation_tree_2_impl.h>

#endif // CGAL_ROTATION_TREE_H