// Copyright (c) 2003,2004,2005,2006,2007,2008,2009,2010,2011 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v5.6/Arrangement_on_surface_2/include/CGAL/Arr_circular_line_arc_traits_2.h $
// $Id: Arr_circular_line_arc_traits_2.h af94033 2021-01-07T16:39:03+01:00 Dmitry Anisimov
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s)     : Monique Teillaud, Sylvain Pion, Julien Hazebrouck

// Partially supported by the IST Programme of the EU as a Shared-cost
// RTD (FET Open) Project under Contract No  IST-2000-26473
// (ECG - Effective Computational Geometry for Curves and Surfaces)
// and a STREP (FET Open) Project under Contract No  IST-006413
// (ACS -- Algorithms for Complex Shapes)

#ifndef CGAL_CIRCULAR_KERNEL_VARIANT_TRAITS_2_H
#define CGAL_CIRCULAR_KERNEL_VARIANT_TRAITS_2_H

#include <CGAL/license/Arrangement_on_surface_2.h>

#include <CGAL/disable_warnings.h>

/*! \file
 * This file was developed at Inria, France, and copied over to the
 * Arrangement_2 package, which it is now part of. It contains a traits
 * class for the arrangement package that handles circular and linear curves.
 * It is based on the circular kernel.
 *
 * \todo Fix the circular-kernel make-x-monotone functor to use modern variant
 *       instead of the legacy CGAL::Object. Then, eliminate the special
 *       implementation here and directly use the kernel functor instead.
 */

#include <vector>

#include <boost/variant.hpp>

#include <CGAL/basic.h>
#include <CGAL/Arr_tags.h>

namespace CGAL {
  namespace VariantFunctors{

    // Takes an iterator range of Object(Line/Circular_arc/Point),
    // returns a variant of Line, Circular_arc, and Point_2.
    template <class CK, class Arc1, class Arc2, class OutputIterator>
    OutputIterator
    object_to_object_variant(const std::vector<CGAL::Object>& res1,
                             OutputIterator res2)
    {
      typedef typename CK::Circular_arc_point_2         Point_2;
      typedef boost::variant<Arc1, Arc2>                X_monotone_curve_2;
      typedef boost::variant<Point_2, X_monotone_curve_2>
        Make_x_monotone_result;

      for (auto it = res1.begin(); it != res1.end(); ++it) {
        if (const Arc1* arc = CGAL::object_cast<Arc1>(&*it)) {
          boost::variant<Arc1, Arc2> v =  *arc;
          *res2++ = Make_x_monotone_result(v);
        }
        else if (const Arc2* line = CGAL::object_cast<Arc2>(&*it)) {
          boost::variant<Arc1, Arc2> v =  *line;
          *res2++ = Make_x_monotone_result(v);
        }
        else if (const Point_2* p = CGAL::object_cast<Point_2>(&*it)) {
          *res2++ = Make_x_monotone_result(*p);
        }
        else CGAL_error();
      }
      return res2;
    }

    template <class CircularKernel, class Arc1, class Arc2>
    class Compare_y_to_right_2
    {
    public:
      typedef CGAL::Comparison_result result_type;
      typedef typename CircularKernel::Circular_arc_point_2
                                                  Circular_arc_point_2;

      result_type
        operator()(const boost::variant< Arc1, Arc2 > &a1,
                   const boost::variant< Arc1, Arc2 > &a2,
                   const Circular_arc_point_2 &p) const
      {
        if ( const Arc1* arc1 = boost::get<Arc1>( &a1 ) ){
          if ( const Arc1* arc2 = boost::get<Arc1>( &a2 ) ){
            return CircularKernel()
              .compare_y_to_right_2_object()(*arc1, *arc2, p);
          }
          else {
            const Arc2* arc2e = boost::get<Arc2>( &a2 );
            return CircularKernel()
              .compare_y_to_right_2_object()(*arc1, *arc2e, p);
          }
        }
        const Arc2* arc1 = boost::get<Arc2>( &a1 );
        if ( const Arc1* arc2 = boost::get<Arc1>( &a2 ) ){
          return CircularKernel()
            .compare_y_to_right_2_object()(*arc1, *arc2, p);
        }
        const Arc2* arc2e = boost::get<Arc2>( &a2 );
        return CircularKernel()
          .compare_y_to_right_2_object()(*arc1, *arc2e, p);
      }
    };


    template <class CircularKernel>
    class Variant_Equal_2
      : public boost::static_visitor<bool>
    {
    public :

      template < typename T >
      bool
      operator()(const T &a0, const T &a1) const
      {
        return CircularKernel().equal_2_object()(a0,a1);
      }

      template < typename T1, typename T2 >
      bool
      operator()(const T1 &, const T2 &) const
      {
        return false;
      }
    };



    template <class CircularKernel, class Arc1, class Arc2>
    class Equal_2
      : public CircularKernel::Equal_2
    {
    public:
      typedef boost::variant< Arc1, Arc2 >  Curve_2;
      typedef bool result_type;
      using CircularKernel::Equal_2::operator();
      typedef typename CircularKernel::Circular_arc_point_2
                                                  Circular_arc_point_2;
      typedef typename CircularKernel::Line_arc_2     Line_arc_2;
      typedef typename CircularKernel::Circular_arc_2 Circular_arc_2;
      typedef typename CircularKernel::Equal_2        CK_Equal_2;

    result_type
    operator() (const Circular_arc_point_2 &p0,
                const Circular_arc_point_2 &p1) const
    { return CK_Equal_2()(p0, p1); }

    result_type
    operator() (const Circular_arc_2 &a0, const Circular_arc_2 &a1) const
    { return CK_Equal_2()(a0, a1); }

    result_type
    operator() (const Line_arc_2 &a0, const Line_arc_2 &a1) const
    { return CK_Equal_2()(a0, a1); }

    result_type
    operator() ( const Line_arc_2 &/*a0*/, const Circular_arc_2 &/*a1*/) const
    { return false; }

    result_type
    operator() ( const Circular_arc_2 &/*a0*/, const Line_arc_2 &/*a1*/) const
    { return false; }

      result_type
      operator()(const Curve_2 &a0, const Curve_2 &a1) const
      {
        return boost::apply_visitor
          ( Variant_Equal_2<CircularKernel>(), a0, a1 );
      }

    };




    template <class CircularKernel, class Arc1, class Arc2>
    class Compare_y_at_x_2
    {
    public:
      typedef typename CircularKernel::Circular_arc_point_2
                                                  Circular_arc_point_2;
      typedef CGAL::Comparison_result result_type;

      result_type
      operator() (const Circular_arc_point_2 &p,
                  const boost::variant< Arc1, Arc2 > &A1) const
      {
        if ( const Arc1* arc1 = boost::get<Arc1>( &A1 ) ){
          return CircularKernel().compare_y_at_x_2_object()(p, *arc1);
        }
        else {
          const Arc2* arc2 = boost::get<Arc2>( &A1 );
          return CircularKernel().compare_y_at_x_2_object()(p, *arc2);
        }
      }
    };

    template <class CircularKernel>
    class Variant_Do_overlap_2 : public boost::static_visitor<bool>
    {
    public:
      template < typename T >
      bool
      operator()(const T &a0, const T &a1) const
      {
        return CircularKernel().do_overlap_2_object()(a0, a1);
      }

      template < typename T1, typename T2 >
      bool
      operator()(const T1 &, const T2 &) const
      {
        return false;
      }
    };


    template <class CircularKernel, class Arc1, class Arc2>
    class Do_overlap_2
    {
    public:
      typedef typename CircularKernel::Circular_arc_point_2
                                                  Circular_arc_point_2;
      typedef bool result_type;

      result_type
      operator()(const boost::variant< Arc1, Arc2 > &A0,
                 const boost::variant< Arc1, Arc2 > &A1) const
      {
        return boost::apply_visitor
          ( Variant_Do_overlap_2<CircularKernel>(), A0, A1 );
      }
    };


    //! A functor for subdividing curves into x-monotone curves.
    template <class CircularKernel, class Arc1, class Arc2>
    class Make_x_monotone_2
    {
    public:
      typedef typename CircularKernel::Circular_arc_point_2
                                                  Circular_arc_point_2;

      template < class OutputIterator,class Not_X_Monotone >
      OutputIterator
      operator()(const boost::variant<Arc1, Arc2, Not_X_Monotone> &A,
                 OutputIterator res) const
      {
        if ( const Arc1* arc1 = boost::get<Arc1>( &A ) ) {
          std::vector<CGAL::Object> container;
          CircularKernel().
            make_x_monotone_2_object()(*arc1,std::back_inserter(container));
          return object_to_object_variant<CircularKernel, Arc1, Arc2>
                                          (container, res);
        }
        else {
          const Arc2* arc2 = boost::get<Arc2>( &A );
          std::vector<CGAL::Object> container;
          CircularKernel().
            make_x_monotone_2_object()(*arc2,std::back_inserter(container));
          return object_to_object_variant<CircularKernel, Arc1, Arc2>
                                          (container, res);
        }
      }
    };

    template <class CircularKernel, class Arc1, class Arc2>
    class Intersect_2
    {
    public:
      typedef typename CircularKernel::Circular_arc_point_2
                                                        Circular_arc_point_2;

      template < class OutputIterator >
        OutputIterator
        operator()(const boost::variant< Arc1, Arc2 > &c1,
                   const boost::variant< Arc1, Arc2 > &c2,
                   OutputIterator oi) const
      {
        if ( const Arc1* arc1 = boost::get<Arc1>( &c1 ) ){
          if ( const Arc1* arc2 = boost::get<Arc1>( &c2 ) ){
            return CircularKernel().intersect_2_object()(*arc1, *arc2, oi);
          }
          const Arc2* arc2 = boost::get<Arc2>( &c2 );
          return CircularKernel().intersect_2_object()(*arc1, *arc2, oi);
        }

        const Arc2* arc1e = boost::get<Arc2>( &c1 );
        if ( const Arc1* arc2 = boost::get<Arc1>( &c2 ) ){
          return CircularKernel().intersect_2_object()(*arc1e, *arc2, oi);
        }
        const Arc2* arc2 = boost::get<Arc2>( &c2 );
        return CircularKernel().intersect_2_object()(*arc1e, *arc2, oi);
      }

    };

    template <class CircularKernel, class Arc1, class Arc2>
    class Split_2
    {

    public:
    typedef typename CircularKernel::Circular_arc_point_2
                                                Circular_arc_point_2;
      typedef void result_type;
      result_type
        operator()(const boost::variant< Arc1, Arc2 > &A,
                   const Circular_arc_point_2 &p,
                   boost::variant< Arc1, Arc2 > &ca1,
                   boost::variant< Arc1, Arc2 > &ca2) const
      {
        // TODO : optimize by extracting the references from the variants ?
        if ( const Arc1* arc1 = boost::get<Arc1>( &A ) ){
          Arc1 carc1;
          Arc1 carc2;
          CircularKernel().split_2_object()(*arc1, p, carc1, carc2);
          ca1 = carc1;
          ca2 = carc2;
          return ;

        }
        else{
          const Arc2* arc2 = boost::get<Arc2>( &A );
          Arc2 cline1;
          Arc2 cline2;
          CircularKernel().split_2_object()(*arc2, p, cline1, cline2);
          ca1 = cline1;
          ca2 = cline2;
          return ;

        }
      }
    };


     template <class CircularKernel>
    class Variant_Construct_min_vertex_2
      : public boost::static_visitor
      <const typename CircularKernel::Circular_arc_point_2&>
    {
      typedef typename CircularKernel::Circular_arc_point_2
                                                  Circular_arc_point_2;

    public :

      typedef Circular_arc_point_2  result_type;
      //typedef const result_type&       qualified_result_type;

      template < typename T >
      //typename boost::remove_reference<qualified_result_type>::type
        Circular_arc_point_2
      operator()(const T &a) const
      {
        //CGAL_kernel_precondition(CircularKernel().compare_xy_2_object()(a.left(), a.right())==CGAL::SMALLER);
        return CircularKernel().construct_circular_min_vertex_2_object()(a);
      }
    };

    template <class CircularKernel, class Arc1, class Arc2>
    class Construct_min_vertex_2//: public Has_qrt
    {
      typedef typename CircularKernel::Circular_arc_point_2      Point_2;
    public:

      typedef Point_2                  result_type;
      //typedef const result_type&       qualified_result_type;

      //typename boost::remove_reference<qualified_result_type>::type
      result_type
      operator() (const boost::variant< Arc1, Arc2 > & cv) const
      {
        return boost::apply_visitor
          ( Variant_Construct_min_vertex_2<CircularKernel>(), cv );
      }
    };





     template <class CircularKernel>
    class Variant_Construct_max_vertex_2
       : public boost::static_visitor<const typename
                                      CircularKernel::Circular_arc_point_2&>
    {
      typedef typename CircularKernel::Circular_arc_point_2
                                                  Circular_arc_point_2;

    public :

      typedef Circular_arc_point_2  result_type;
      //typedef const result_type&       qualified_result_type;

      template < typename T >
      //typename boost::remove_reference<qualified_result_type>::type
        Circular_arc_point_2
      operator()(const T &a) const
      {
        //CGAL_kernel_precondition(CircularKernel().compare_xy_2_object()(a.left(), a.right())==CGAL::SMALLER);
        return (CircularKernel().construct_circular_max_vertex_2_object()(a));
      }
    };


    template <class CircularKernel, class Arc1, class Arc2>
    class Construct_max_vertex_2//: public Has_qrt
    {
      typedef typename CircularKernel::Circular_arc_point_2      Point_2;
    public:
      /*!
       * Get the right endpoint of the x-monotone curve (segment).
       * \param cv The curve.
       * \return The right endpoint.
       */
      typedef Point_2                  result_type;
      //typedef const result_type&       qualified_result_type;

       //typename boost::remove_reference<qualified_result_type>::type
      result_type
       operator() (const boost::variant< Arc1, Arc2 > & cv) const
      {
        return boost::apply_visitor
          ( Variant_Construct_max_vertex_2<CircularKernel>(), cv );
      }
    };

      template <class CircularKernel>
    class Variant_Is_vertical_2
      : public boost::static_visitor<bool>
    {
    public :

      template < typename T >
      bool
      operator()(const T &a) const
      {
        return CircularKernel().is_vertical_2_object()(a);
      }
    };

    template <class CircularKernel, class Arc1, class Arc2>
    class Is_vertical_2
    {
    public:
      typedef bool result_type;

      bool operator() (const boost::variant< Arc1, Arc2 >& cv) const
      {
        return boost::apply_visitor
          ( Variant_Is_vertical_2<CircularKernel>(), cv );
      }
    };

  }


  // a empty class used to have different types between Curve_2 and X_monotone_curve_2
  // in Arr_circular_line_arc_traits_2.
  namespace internal_Argt_traits{
    struct Not_X_Monotone{};
    inline std::ostream& operator << (std::ostream& os, const Not_X_Monotone&)
    {return os;}
  }

  /// Traits class for CGAL::Arrangement_2 (and similar) based on a CircularKernel.

  template < typename CircularKernel>
  class Arr_circular_line_arc_traits_2 {

    typedef Arr_circular_line_arc_traits_2< CircularKernel >   Self;

    typedef typename CircularKernel::Line_arc_2                Arc1;
    typedef typename CircularKernel::Circular_arc_2            Arc2;

  public:

    typedef CircularKernel Kernel;
    typedef typename CircularKernel::Circular_arc_point_2
                                                Circular_arc_point_2;

    typedef typename CircularKernel::Circular_arc_point_2      Point;
    typedef typename CircularKernel::Circular_arc_point_2      Point_2;

    typedef unsigned int                           Multiplicity;

    typedef CGAL::Tag_false                        Has_left_category;
    typedef CGAL::Tag_false                        Has_merge_category;
    typedef CGAL::Tag_false                        Has_do_intersect_category;

    typedef Arr_oblivious_side_tag                 Left_side_category;
    typedef Arr_oblivious_side_tag                 Bottom_side_category;
    typedef Arr_oblivious_side_tag                 Top_side_category;
    typedef Arr_oblivious_side_tag                 Right_side_category;

    typedef internal_Argt_traits::Not_X_Monotone                Not_X_Monotone;

    typedef boost::variant< Arc1, Arc2, Not_X_Monotone >        Curve_2;
    typedef boost::variant< Arc1, Arc2 >                        X_monotone_curve_2;

  private:
    CircularKernel ck;
  public:

    Arr_circular_line_arc_traits_2(const CircularKernel &k = CircularKernel())
      : ck(k) {}

    typedef typename CircularKernel::Compare_x_2           Compare_x_2;
    typedef typename CircularKernel::Compare_xy_2          Compare_xy_2;
    typedef typename
    VariantFunctors::Construct_min_vertex_2<CircularKernel, Arc1, Arc2>
                                                  Construct_min_vertex_2;
    typedef
    VariantFunctors::Construct_max_vertex_2<CircularKernel, Arc1, Arc2>
                                                  Construct_max_vertex_2;
    typedef VariantFunctors::Is_vertical_2<CircularKernel, Arc1, Arc2>
                                                  Is_vertical_2;
    typedef VariantFunctors::Compare_y_at_x_2<CircularKernel, Arc1, Arc2>
                                                  Compare_y_at_x_2;
    typedef VariantFunctors::Compare_y_to_right_2<CircularKernel, Arc1, Arc2>
                                                  Compare_y_at_x_right_2;
    typedef VariantFunctors::Equal_2<CircularKernel, Arc1, Arc2>
                                                  Equal_2;
    typedef VariantFunctors::Make_x_monotone_2<CircularKernel, Arc1, Arc2>
                                                  Make_x_monotone_2;
    typedef VariantFunctors::Split_2<CircularKernel, Arc1, Arc2>
                                                  Split_2;
    typedef VariantFunctors::Intersect_2<CircularKernel, Arc1, Arc2>
                                                  Intersect_2;


 Compare_x_2 compare_x_2_object() const
  { return ck.compare_x_2_object(); }

  Compare_xy_2 compare_xy_2_object() const
  { return ck.compare_xy_2_object(); }

  Compare_y_at_x_2 compare_y_at_x_2_object() const
  { return Compare_y_at_x_2(); }

  Compare_y_at_x_right_2 compare_y_at_x_right_2_object() const
  { return Compare_y_at_x_right_2(); }

  Equal_2 equal_2_object() const
  { return Equal_2(); }

  Make_x_monotone_2 make_x_monotone_2_object() const
  { return Make_x_monotone_2(); }

  Split_2 split_2_object() const
  { return Split_2(); }

  Intersect_2 intersect_2_object() const
    { return Intersect_2(); }

  Construct_min_vertex_2 construct_min_vertex_2_object() const
    { return Construct_min_vertex_2(); }

  Construct_max_vertex_2 construct_max_vertex_2_object() const
    { return Construct_max_vertex_2(); }

  Is_vertical_2 is_vertical_2_object() const
    { return Is_vertical_2();}


};

} // namespace CGAL

#include <CGAL/enable_warnings.h>

#endif // CGAL_CIRCULAR_KERNEL_VARIANT_TRAITS_H

