// Copyright (c) 2000  Max-Planck-Institute Saarbruecken (Germany).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1.2/Partition_2/include/CGAL/Partition_2/Indirect_edge_compare.h $
// $Id: include/CGAL/Partition_2/Indirect_edge_compare.h 37e2b278910 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Susan Hert <hert@mpi-sb.mpg.de>

#ifndef CGAL_INDIRECT_EDGE_COMPARE_H
#define CGAL_INDIRECT_EDGE_COMPARE_H

#include <CGAL/license/Partition_2.h>


namespace CGAL {

//
// given circulators to endpoints of two edges, sorts the edges that come
// next (in the direction of circulator) from right to left. This ordering
// makes finding the edge directly left of a given edge (needed for the
// y-monotone decomposition algorithm) easy.
//
template <class ForwardCirculator, class Traits>
class Indirect_edge_compare
{
   public:
     typedef typename Traits::Orientation_2       Orientation_2;
     typedef typename Traits::Compare_y_2        Compare_y_2;
     typedef typename Traits::Compare_x_2        Compare_x_2;
     typedef typename Traits::Point_2            Point_2;

     Indirect_edge_compare(const Traits& traits) :
          _orientation_2(traits.orientation_2_object()),
          _compare_y_2(traits.compare_y_2_object()),
          _compare_x_2(traits.compare_x_2_object())
     { }

     // determines if the edge (edge_vtx_1, edge_vtx_1++) has a larger
     // x value than vertex.x at y-value vertex.y
     bool
     larger_x_at_vertex_y(ForwardCirculator edge_vtx_1,
                          ForwardCirculator vertex) const
     {
        ForwardCirculator edge_vtx_2 = edge_vtx_1;
        edge_vtx_2++;
        // check for horizontal edge
        if(_compare_y_2(Point_2(*edge_vtx_1), Point_2(*edge_vtx_2)) == EQUAL)
        {
            // compare the smaller x and vertex x
          if(_compare_x_2(Point_2(*edge_vtx_1), Point_2(*edge_vtx_2)) == SMALLER)
            return _compare_x_2(Point_2(*edge_vtx_1), Point_2(*vertex)) == LARGER;
           else
             return _compare_x_2(Point_2(*edge_vtx_2), Point_2(*vertex)) == LARGER;
        }
        else
        {
           // construct supporting line for edge
           return compare_x_at_y(Point_2(*vertex), Point_2(*edge_vtx_1), Point_2(*edge_vtx_2)) == SMALLER;
        }
     }

     Comparison_result compare_x_at_y(const Point_2& p, const Point_2& a, const Point_2& b) const
     {
       Orientation ori =  _orientation_2(a, b, p);
       if(ori == COLLINEAR){
         return EQUAL;
       }

       if(_compare_y_2(a, b) == SMALLER){ // a below b
         return (ori == RIGHT_TURN) ? LARGER : SMALLER;
       }else { // a above b
         return (ori == LEFT_TURN) ? LARGER : SMALLER;
       }
     }

     bool
     operator()(ForwardCirculator p, ForwardCirculator q) const
     {
        ForwardCirculator after_p = p;
        after_p++;
        ForwardCirculator after_q = q;
        after_q++;

        if (p == q && after_p == after_q) return false;

        if (p == after_q)
          return larger_x_at_vertex_y(p, q);

        if (after_p == q)
          return !larger_x_at_vertex_y(q, p);

        if (p == q)
          return larger_x_at_vertex_y(p, after_q);

        if (after_p == after_q)
          return larger_x_at_vertex_y(p, q);

        // else neither endpoint is shared
        // construct supporting line
        if(_compare_y_2(Point_2(*p), Point_2(*after_p)) == EQUAL)
        {
          if(_compare_y_2(Point_2(*q), Point_2(*after_q)) == EQUAL)
            {
                 Point_2 p_max;
                 Point_2 q_max;
                 if (_compare_x_2(Point_2(*p), Point_2(*after_p)) == SMALLER)
                    p_max = *after_p;
                 else
                    p_max = *p;
                 if (_compare_x_2(Point_2(*q), Point_2(*after_q)) == SMALLER)
                    q_max = *after_q;
                 else
                    q_max = *q;
                 return (_compare_x_2(p_max, q_max) == LARGER);
            }
            else  // p and after_p must both be on same side of l_q
            {
              return (compare_x_at_y(Point_2(*p), Point_2(*q), Point_2(*after_q)) == LARGER);
            }
        }

        // lp is not horizontal
        bool q_larger_x = compare_x_at_y(Point_2(*q), Point_2(*p), Point_2(*after_p)) == SMALLER;
        bool after_q_larger_x = compare_x_at_y(Point_2(*after_q), Point_2(*p), Point_2(*after_p)) == SMALLER;

        if (q_larger_x == after_q_larger_x)
            return q_larger_x;
        // else one smaller and one larger
        // construct the other line
        if(_compare_y_2(Point_2(*q), Point_2(*after_q)) == EQUAL)
        {
          return compare_x_at_y(Point_2(*q), Point_2(*p), Point_2(*after_p)) == LARGER;
        }
        return compare_x_at_y(Point_2(*p), Point_2(*q), Point_2(*after_q)) != SMALLER;
     }

   private:
     Orientation_2    _orientation_2;
     Compare_y_2      _compare_y_2;
     Compare_x_2      _compare_x_2;
};

}



#endif // CGAL_INDIRECT_EDGE_COMPARE_H
