// Copyright (c) 2013-2015  The University of Western Sydney, Australia.
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL$
// $Id$
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Authors: Weisheng Si, Quincy Tse

#ifndef CGAL_LESS_BY_DIRECTION_2_H
#define CGAL_LESS_BY_DIRECTION_2_H

#include <CGAL/license/Cone_spanners_2.h>


#include <iostream>
#include <cstdlib>
#include <utility>
#include <CGAL/Polynomial.h>
#include <CGAL/number_utils.h>
#include <CGAL/enum.h>
#include <CGAL/Exact_predicates_exact_constructions_kernel_with_sqrt.h>
#include <CGAL/Aff_transformation_2.h>

#include <boost/config.hpp>
#include <boost/graph/adjacency_list.hpp>

namespace CGAL {

/*  Function object that orders the vertex_descriptors in a 2D graph based on the order
 *  induced by the direction D described in the book:
 *
 *  Giri Narasimhan and Michiel Smid, Chapter 4: Spanners based on the Theta graph, Geometric Spanner Networks,
 *  Cambridge University Press, 2007.
 *
 *  In this implementation, the ties are broken according to the direction of cw90(D).
 *  This way of breaking ties will prevent the overlapping of cone boundaries when this functor
 *  is used to construct Theta and Yao graphs in `CGAL::Construct_theta_graph_2` and 
 *  `CGAL::Construct_yao_graph_2`. Resultantly, the cw boundary of a cone will be considered inside this cone,
 *  while the ccw boundary not. On the other hand, if your application requires that 
 *  the ccw boundary of a cone belongs to this cone while the cw boundary not, 
 *  you can modify the code below to use the direction of ccw90(D) to break the ties. 
 *
 *  This function object utilizes the existing function `CGAL::compare_signed_distance_to_line_2()`,
 *  which orders two points according to their signed distance to a base line.
 *
 */
template <typename Kernel_, typename Graph_>
class Less_by_direction_2
  : public CGAL::cpp98::binary_function <typename Graph_::vertex_descriptor,
                                         typename Graph_::vertex_descriptor, bool>
{
public:
    // typedef for C++11 - doesn't hurt to also have for C++98
    typedef typename Graph_::vertex_descriptor first_argument_type;
    typedef typename Graph_::vertex_descriptor second_argument_type;
    typedef bool     result_type;

    // typedef for Direction_2 and Line_2
    typedef typename Kernel_::Direction_2 Direction_2;
    typedef typename Kernel_::Line_2 Line_2;
    typedef typename Kernel_::Point_2 Point_2;
    typedef typename Kernel_::Aff_transformation_2 Transformation;

    // constructor
    Less_by_direction_2(const Graph_& g, const Direction_2& d)
        : graph(g), base_line(Point_2(0,0), d) {};

    bool operator() (const typename Graph_::vertex_descriptor& p,
                     const typename Graph_::vertex_descriptor& q) const {
        Comparison_result outcome;
        outcome = compare_signed_distance_to_line(base_line, graph[p], graph[q]);
        if (outcome == SMALLER)
            return true;
        else {
            if (outcome == LARGER)
                return false;
        }

        /* otherwise, outcome == CGAL::EQUAL, ties will be broken by a second order
         * according to the cw90(base_line) direction. 
         */
        // define a rotation of clockwise 90
        Transformation cw90(0, 1, -1,  0);
        // rotate
        Line_2 cw90_line = cw90(base_line);
        outcome = compare_signed_distance_to_line(cw90_line, graph[p], graph[q]);
        if (outcome == SMALLER)
            return true;
        else
            return false;
    }

private:
    const Graph_& graph;
    const Line_2 base_line;

};      // class Less_by_direction_2

}  // namespace CGAL


#endif
