File: function_objects_polynomial_circular.h

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// Copyright (c) 2003-2008  INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Circular_kernel_2/include/CGAL/Circular_kernel_2/function_objects_polynomial_circular.h $
// $Id: include/CGAL/Circular_kernel_2/function_objects_polynomial_circular.h b26b07a1242 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s)     : Monique Teillaud, Sylvain Pion, Pedro Machado

// 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_FUNCTION_OBJECTS_POLYNOMIAL_CIRCULAR_H
#define CGAL_CIRCULAR_KERNEL_FUNCTION_OBJECTS_POLYNOMIAL_CIRCULAR_H

#include <CGAL/license/Circular_kernel_2.h>


#include <CGAL/Circular_kernel_intersections.h>
#include <CGAL/Circular_kernel_2/internal_functions_on_circular_arc_2.h>
#include <CGAL/Circular_kernel_2/internal_functions_on_line_arc_2.h>
#include <CGAL/Circular_kernel_2/Intersection_traits.h>
#include <CGAL/Bbox_2.h>

namespace CGAL {
namespace CircularFunctors {

#define CGAL_CIRCULAR_KERNEL_MACRO_FUNCTOR_COMPARE_(V)\
template < class CK > \
  class Compare_ ##V## _2 {\
    /*: public CK::Linear_kernel::Compare_ ##V## _2{*/\
    typedef typename CK::Comparison_result Comparison_result;\
    typedef typename CK::Circular_arc_point_2 Circular_arc_point_2;\
    typedef typename CK::Linear_kernel::Compare_ ##V## _2 Linear_Compare_ ##V## _2;\
  public:\
    template <class... Args>\
    Comparison_result\
    operator()(const Args&... args) const\
    { return Linear_Compare_ ##V## _2()(args...); }\
    /*using CK::Linear_kernel::Compare_ ##V## _2::operator();*/\
    Comparison_result\
    operator() (const Circular_arc_point_2 &p0,\
                const Circular_arc_point_2 &p1) const\
    { return CircularFunctors::compare_ ##V <CK>(p0, p1); }\
  };\

  CGAL_CIRCULAR_KERNEL_MACRO_FUNCTOR_COMPARE_(x)
  CGAL_CIRCULAR_KERNEL_MACRO_FUNCTOR_COMPARE_(y)
  CGAL_CIRCULAR_KERNEL_MACRO_FUNCTOR_COMPARE_(xy)

#undef CGAL_CIRCULAR_KERNEL_MACRO_FUNCTOR_COMPARE_

  template < class CK >
  class In_x_range_2
  {
    typedef typename CK::Boolean                 Boolean;
    typedef typename CK::Circular_arc_2          Circular_arc_2;
    typedef typename CK::Circular_arc_point_2    Circular_arc_point_2;
    typedef typename CK::Line_arc_2              Line_arc_2;

  public:
    Boolean
    operator()(const Circular_arc_2 &a, const Circular_arc_point_2 &p) const
    { return CircularFunctors::point_in_x_range<CK>(a, p); }

    Boolean
    operator()(const Line_arc_2 &a, const Circular_arc_point_2 &p) const
    { return CircularFunctors::point_in_x_range<CK>(a, p); }
  };

  template < class CK >
  class Has_on_2
    // : public CK::Linear_kernel::Has_on_2
  {
    typedef typename CK::Boolean                 Boolean;
    typedef typename CK::Circular_arc_2          Circular_arc_2;
    typedef typename CK::Circular_arc_point_2    Circular_arc_point_2;
    typedef typename CK::Line_arc_2              Line_arc_2;
    typedef typename CK::Circle_2                Circle_2;
    typedef typename CK::Line_2                  Line_2;

    typedef typename CK::Linear_kernel::Has_on_2 Linear_Has_on_2;

  public:
    // using CK::Linear_kernel::Has_on_2::operator();

    template <typename A, typename B>
    Boolean
    operator()(const A& a, const B& b) const
    { return Linear_Has_on_2()(a, b); }

    Boolean
    operator()(const Circle_2 &a, const Circular_arc_point_2 &p) const
    { return CircularFunctors::has_on<CK>(a, p); }

    Boolean
    operator()(const Line_2 &a, const Circular_arc_point_2 &p) const
    { return LinearFunctors::has_on<CK>(a, p); }

    Boolean
    operator()(const Circular_arc_2 &a, const Circular_arc_point_2 &p) const
    { return CircularFunctors::has_on<CK>(a, p); }

    Boolean
    operator()(const Line_arc_2 &a, const Circular_arc_point_2 &p) const
    { return CircularFunctors::has_on<CK>(a, p); }
  };

  template < class CK >
  class Compare_y_to_right_2
  {
    typedef typename CK::Comparison_result        Comparison_result;
    typedef typename CK::Circular_arc_2           Circular_arc_2;
    typedef typename CK::Circular_arc_point_2     Circular_arc_point_2;
    typedef typename CK::Line_arc_2               Line_arc_2;

  public:
    Comparison_result
    operator()(const Circular_arc_2 &a1,
               const Circular_arc_2 &a2,
               const Circular_arc_point_2 &p) const
    { return CircularFunctors::compare_y_to_right<CK>(a1, a2, p); }

    Comparison_result
    operator()(const Line_arc_2 &a1,
               const Line_arc_2 &a2,
               const Circular_arc_point_2 &p) const
    { return CircularFunctors::compare_y_to_right<CK>(a1, a2, p); }

    Comparison_result
    operator()(const Line_arc_2 &a1,
               const Circular_arc_2 &a2,
               const Circular_arc_point_2 &p) const
    { return CircularFunctors::compare_y_to_right<CK>(a1, a2, p); }

    Comparison_result
    operator()(const Circular_arc_2 &a1,
               const Line_arc_2 &a2,
               const Circular_arc_point_2 &p) const
    { if (CircularFunctors::compare_y_to_right<CK>(a2, a1, p) == CGAL::LARGER)
        return CGAL::SMALLER;
      return CGAL::LARGER;
    }
  };

  template < class CK >
  class Equal_2
    // : public CK::Linear_kernel::Equal_2
  {
    typedef typename CK::Boolean                 Boolean;
    typedef typename CK::Circular_arc_point_2    Circular_arc_point_2;
    typedef typename CK::Circular_arc_2          Circular_arc_2;
    typedef typename CK::Line_arc_2              Line_arc_2;
    typedef typename CK::Point_2 Point_2;
    typedef typename CK::Vector_2 Vector_2;
    typedef typename CK::Direction_2 Direction_2;
    typedef typename CK::Segment_2 Segment_2;
    typedef typename CK::Ray_2 Ray_2;
    typedef typename CK::Line_2 Line_2;
    typedef typename CK::Triangle_2 Triangle_2;
    typedef typename CK::Iso_rectangle_2 Iso_rectangle_2;
    typedef typename CK::Circle_2 Circle_2;

    typedef typename  CK::Linear_kernel::Equal_2 Linear_Equal_2;

  public:
    // using CK::Linear_kernel::Equal_2::operator();

    template <typename A, typename B>
    Boolean
    operator()(const A& a, const B& b) const {
      return Linear_Equal_2()(a, b);
    }

    Boolean
    operator() (const Circular_arc_point_2 &p0,
                const Circular_arc_point_2 &p1) const
    { return CircularFunctors::equal<CK>(p0, p1); }

    Boolean
    operator() (const Circular_arc_2 &a0, const Circular_arc_2 &a1) const
    { return CircularFunctors::equal<CK>(a0, a1); }

    Boolean
    operator() (const Line_arc_2 &a0, const Line_arc_2 &a1) const
    { return CircularFunctors::equal<CK>(a0, a1); }
   };

  template < class CK >
  class Compare_y_at_x_2
    // : public CK::Linear_kernel::Compare_y_at_x_2
  {
    typedef typename CK::Comparison_result       Comparison_result;
    typedef typename CK::Circular_arc_2          Circular_arc_2;
    typedef typename CK::Circular_arc_point_2    Circular_arc_point_2;
    typedef typename CK::Line_arc_2              Line_arc_2;

    typedef typename CK::Linear_kernel::Compare_y_at_x_2 Linear_Compare_y_at_x_2;

  public:
    // using CK::Linear_kernel::Compare_y_at_x_2::operator();

    template <class... Args>
    Comparison_result
    operator()(const Args&... args) const
    { return Linear_Compare_y_at_x_2()(args...); }

    Comparison_result
    operator() (const Circular_arc_point_2 &p,
                const Circular_arc_2 &A1) const
    { return CircularFunctors::compare_y_at_x<CK>(p, A1); }

    Comparison_result
    operator() (const Circular_arc_point_2 &p,
                const Line_arc_2 &A1) const
    { return CircularFunctors::compare_y_at_x<CK>(p, A1); }
  };

  template < class CK >
  class Do_overlap_2
  {
    typedef typename CK::Boolean        Boolean;
    typedef typename CK::Circular_arc_2 Circular_arc_2;
    typedef typename CK::Line_arc_2     Line_arc_2;

  public:
    Boolean
    operator() (const Circular_arc_2 &A1, const Circular_arc_2 &A2) const
    { return CircularFunctors::do_overlap<CK>(A1, A2); }

    Boolean
    operator() (const Line_arc_2 &A1, const Line_arc_2 &A2) const
    { return CircularFunctors::do_overlap<CK>(A1, A2); }
  };

  template < class CK >
  class Make_x_monotone_2
  {
    typedef typename CK::Circular_arc_2 Circular_arc_2;
    typedef typename CK::Line_arc_2 Line_arc_2;

  public:
    template < class OutputIterator >
    OutputIterator
    operator()(const Circular_arc_2 &A, OutputIterator res) const
    {
      return    CircularFunctors::make_x_monotone<CK> (A, res);
    }

    template < class OutputIterator >
    OutputIterator
    operator()(const Line_arc_2 &A, OutputIterator res) const
    {
      return CircularFunctors::make_x_monotone<CK>(A,res);
    }
  };

 template < class CK >
  class Make_xy_monotone_2
  {
    typedef typename CK::Circular_arc_2 Circular_arc_2;
    typedef typename CK::Line_arc_2 Line_arc_2;

  public:
    template < class OutputIterator >
    OutputIterator
    operator()(const Circular_arc_2 &A, OutputIterator res) const
      {
        typedef std::pair<bool, bool>                  relat_pos;
        typedef std::pair< Circular_arc_2, relat_pos>    Obj_descr_2;
        std::vector<Obj_descr_2> vec;

        CircularFunctors::advanced_make_xy_monotone<CK> (A, std::back_inserter(vec));

        for(unsigned i=0;i<vec.size();++i)
          *res++=vec.at(i).first;

        return res;

      }

    template < class OutputIterator >
    OutputIterator
    operator()(const Line_arc_2 &A, OutputIterator res) const
    { *res++ = make_object(A);
      return res;
    }
  };

  template < class CK >
  class Do_intersect_2
    // : public CK::Linear_kernel::Do_intersect_2
  {
    typedef typename CK::Boolean                 Boolean;

    typedef typename CK::Linear_kernel::Do_intersect_2 Linear_Do_intersect_2;

  public:
    template <typename A, typename B>
    Boolean
    operator()(const A& a, const B& b) const
    { return Intersections::internal::do_intersect(a, b, CK()); }
  };

  template < class CK >
  class Intersect_2
  //The inheritance is commented as for some reason this does not work when
  //using the Lazy_kernel as linear kernel.
    //: public CK::Linear_kernel::Intersect_2
  {
    typedef typename CK::Circle_2                 Circle;
    typedef typename CK::Circular_arc_2           Circular_arc;
    typedef typename CK::Line_arc_2               Line_arc;
    typedef typename CK::Line_2                   Line;

    public:
    //using CK::Linear_kernel::Intersect_2::operator();

    template<class A, class B>
    decltype(auto)
    operator()(const A& a, const B& b) const{
      return typename CK::Linear_kernel::Intersect_2()(a,b);
    }

    template < class OutputIterator >
    OutputIterator
    operator()(const Line & c1, const Circle & c2,
               OutputIterator res) const
      { return CircularFunctors::intersect_2<CK> (c1,c2,res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Circle & c1, const Line & c2,
               OutputIterator res) const
      {        return CircularFunctors::intersect_2<CK> (c2,c1,res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Circle & c1, const Circle & c2, OutputIterator res) const
      { return CircularFunctors::intersect_2<CK> (c1,c2,res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Circle & c1, const Circular_arc & c2,
               OutputIterator res) const
    { return CircularFunctors::intersect_2<CK> (Circular_arc(c1),c2,res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Circular_arc & c1, const Circle & c2,
               OutputIterator res) const
    { return CircularFunctors::intersect_2<CK> (c1,Circular_arc(c2),res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Circular_arc & c1, const Circular_arc & c2,
               OutputIterator res) const
      { return CircularFunctors::intersect_2<CK> (c1,c2,res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Line_arc & c1, const Line_arc & c2,
               OutputIterator res) const
      {        return CircularFunctors::intersect_2<CK> (c1,c2,res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Line_arc & c1, const Circle & c2,
               OutputIterator res) const
    { return CircularFunctors::intersect_2<CK> (c1,c2,res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Circle & c1, const Line_arc & c2,
               OutputIterator res) const
    { return CircularFunctors::intersect_2<CK> (c2,c1,res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Line_arc & c1, const Circular_arc & c2,
               OutputIterator res) const
    { return CircularFunctors::intersect_2<CK> (c1,c2,res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Circular_arc & c1, const Line_arc & c2,
               OutputIterator res) const
    { return CircularFunctors::intersect_2<CK> (c2,c1,res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Line & l, const Circular_arc & c,
               OutputIterator res) const
    { return CircularFunctors::intersect_2<CK> (l,c,res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Line & l, const Line_arc & la,
               OutputIterator res) const
    { return CircularFunctors::intersect_2<CK> (l,la,res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Circular_arc & c, const Line & l,
               OutputIterator res) const
    { return CircularFunctors::intersect_2<CK> (l,c,res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Line_arc & la, const Line & l,
               OutputIterator res) const
    { return CircularFunctors::intersect_2<CK> (l,la,res); }

    template < class OutputIterator >
    OutputIterator
    operator()(const Line & l1, const Line & l2,
               OutputIterator res) const
    {
      *res++=typename CK::Linear_kernel::Intersect_2()(l1, l2);
      return res;
    }
  };

  template < class CK >
  class Get_equation
  {
    public:

    typename CK::Polynomial_1_2
    operator() ( const typename CK::Line_2 & l )
    {
      return LinearFunctors::get_equation<CK>(l);
    }

    typename CK::Polynomial_for_circles_2_2
    operator() ( const typename CK::Circle_2 & c )
    {
      return CircularFunctors::get_equation<CK>(c);
    }
  };

  template < class CK >
  class Split_2
  {
    typedef typename CK::Circular_arc_2          Circular_arc_2;
    typedef typename CK::Circular_arc_point_2    Circular_arc_point_2;
    typedef typename CK::Line_arc_2              Line_arc_2;

  public:
    void
    operator()(const Circular_arc_2 &A,
               const Circular_arc_point_2 &p,
               Circular_arc_2 &ca1, Circular_arc_2 &ca2) const
    { return CircularFunctors::split<CK>(A, p, ca1, ca2); }

    void
    operator()(const Line_arc_2 &A,
               const Circular_arc_point_2 &p,
               Line_arc_2 &ca1, Line_arc_2 &ca2) const
    { return CircularFunctors::split<CK>(A, p, ca1, ca2); }
  };

  template < class CK >
  class Is_vertical_2
    // : public CK::Linear_kernel::Is_vertical_2
  {
    typedef typename CK::Boolean                 Boolean;
    typedef typename CK::Circular_arc_2          Circular_arc_2;
    typedef typename CK::Line_arc_2              Line_arc_2;

    typedef typename CK::Linear_kernel::Is_vertical_2 Linear_Is_vertical_2;

  public:
    // using CK::Linear_kernel::Is_vertical_2::operator();

    template <typename A>
    Boolean
    operator()(const A& a) const
    { return Linear_Is_vertical_2()(a); }

    Boolean
    operator()(const Circular_arc_2 &A) const
    { return CircularFunctors::is_vertical<CK>(A); }

    Boolean
    operator()(const Line_arc_2 &A) const
    { return CircularFunctors::is_vertical<CK>(A); }

  };

  template < class CK >
  class Construct_circular_arc_2
  {
    typedef typename CK::FT                           FT;
    typedef typename CK::Point_2                      Point_2;
    typedef typename CK::Line_2                       Line_2;
    typedef typename CK::Circle_2                     Circle_2;
    typedef typename CK::Circular_arc_2               Circular_arc_2;
    typedef typename Circular_arc_2::Rep              Rep;
    typedef typename CK::Circular_arc_point_2         Circular_arc_point_2;

  public:
    Circular_arc_2
    operator()(void)
    { return Rep(); }

    Circular_arc_2
    operator()(const Circle_2 &c) const
    { return Rep(c); }

    Circular_arc_2
    operator()(const Circle_2 &support,
               const Circular_arc_point_2 &source,
               const Circular_arc_point_2 &target) const
    { return Rep(support,source,target); }

    // Not Documented
    Circular_arc_2
    operator()(const Circle_2 &support,
               const Line_2 &l1, bool b1,
               const Line_2 &l2, bool b2) const
    { return Rep(support,l1,b1,l2,b2); }

    // Not Documented
    Circular_arc_2
    operator()(const Circle_2 &c,
               const Circle_2 &c1, bool b_1,
               const Circle_2 &c2, bool b_2) const
    { return Rep(c,c1,b_1,c2,b_2); }

    Circular_arc_2
    operator()(const Point_2 &begin,
               const Point_2 &middle,
               const Point_2 &end) const
    { return Rep(begin,middle,end); }

    // Not Documented
    Circular_arc_2
    operator()(const Point_2 &begin,
               const Point_2 &end,
               const FT& bulge) const
    { return Rep(begin,end,bulge); }

  };

  template < class CK >
  class Construct_line_arc_2
  {

    typedef typename CK::Point_2                   Point_2;
    typedef typename CK::Line_2                    Line_2;
    typedef typename CK::Circle_2                  Circle_2;
    typedef typename CK::Circular_arc_point_2      Circular_arc_point_2;
    typedef typename CK::Segment_2                 Segment_2;
    typedef typename CK::Line_arc_2                Line_arc_2;
    typedef typename Line_arc_2::Rep               Rep;

  public:
    Line_arc_2
    operator()(void)
    { return Rep(); }

    // Not Documented
    Line_arc_2
    operator()(const Line_2 &support,
               const Circle_2 &c1,const bool b1,
               const Circle_2 &c2,const bool b2) const
    { return Rep(support,c1,b1,c2,b2); }

    // Not Documented
    Line_arc_2
    operator()(const Line_2 &support,
               const Line_2 &l1,
               const Line_2 &l2) const
    { return Rep(support,l1,l2); }

    Line_arc_2
    operator()(const Line_2 &support,
               const Circular_arc_point_2 &p1,
               const Circular_arc_point_2 &p2) const
    { return Rep(support,p1,p2); }

//     Line_arc_2
//     operator()(const Line_2 &support,
//                const Point_2 &p1,
//                const Point_2 &p2) const
//     { return Rep(support,p1,p2); }

    Line_arc_2
    operator()(const Segment_2 &s) const
    { return Rep(s); }

    Line_arc_2
    operator()(const Point_2 &p1,
               const Point_2 &p2) const
    { return Rep(p1,p2); }

  };

  template < class CK >
  class Construct_circular_arc_point_2
  {
    typedef typename CK::Point_2               Point_2;
    typedef typename CK::Circular_arc_point_2  Circular_arc_point_2;
    typedef typename Circular_arc_point_2::Rep Rep;
    typedef typename Circular_arc_point_2::Root_for_circles_2_2
                                               Root_for_circles_2_2;

  public:
    Circular_arc_point_2
    operator()(void)
    { return Rep(); }

    Circular_arc_point_2
    operator()(const Root_for_circles_2_2 & np) const
    { return Rep(np); }

    Circular_arc_point_2
    operator()(const Point_2 & p) const
    { return Rep(p); }

  };

  template <class CK>
  class Compute_circular_x_2
  {
    typedef typename CK::Circular_arc_point_2   Circular_arc_point_2;

  public:
    decltype(auto) operator() (const Circular_arc_point_2 & a) const
    {
      return (a.rep().x());
    }
  };


  template <class CK>
  class Compute_circular_y_2
  {
    typedef typename CK::Circular_arc_point_2   Circular_arc_point_2;

  public:
    decltype(auto) operator() (const Circular_arc_point_2 & a) const
    {
      return (a.rep().y());
    }
  };


  template <class CK>
  class Construct_circular_min_vertex_2
  {
    typedef typename CK::Circular_arc_2            Circular_arc_2;
    typedef typename CK::Line_arc_2                Line_arc_2;

  public:
    decltype(auto) operator() (const Circular_arc_2& a) const
    {
      return (a.rep().left());
    }

    decltype(auto) operator() (const Line_arc_2& a) const
    {
      return (a.rep().left());
    }

  };

  template <class CK>
  class Construct_circular_max_vertex_2
  {
    typedef typename CK::Circular_arc_2            Circular_arc_2;
    typedef typename CK::Line_arc_2                Line_arc_2;

  public:
    decltype(auto) operator() (const Circular_arc_2& a) const
    {
      return (a.rep().right());
    }

    decltype(auto) operator() (const Line_arc_2& a) const
    {
      return (a.rep().right());
    }

  };

  template <class CK>
  class Construct_circular_source_vertex_2
  {
    typedef typename CK::Circular_arc_2            Circular_arc_2;
    typedef typename CK::Line_arc_2                Line_arc_2;

  public:
    decltype(auto) operator() (const Circular_arc_2& a) const
    { return a.rep().source(); }

    decltype(auto) operator() (const Line_arc_2& a) const
    { return a.rep().source();}

  };


  template <class CK>
  class Construct_circular_target_vertex_2
  {
    typedef typename CK::Circular_arc_2            Circular_arc_2;
    typedef typename CK::Line_arc_2                Line_arc_2;

  public:
    decltype(auto) operator() (const Circular_arc_2& a) const
    { return a.rep().target();}

    decltype(auto) operator() (const Line_arc_2& a) const
    { return a.rep().target();}

  };

  template <class CK>
  class Is_x_monotone_2
  {
    typedef typename CK::Boolean                   Boolean;
    typedef typename CK::Circular_arc_2            Circular_arc_2;
    typedef typename CK::Line_arc_2                Line_arc_2;

  public:
    Boolean operator() (const Circular_arc_2 & a) const
    {
      return (a.rep().is_x_monotone());
    }

    Boolean operator() (const Line_arc_2 & a) const
    {
      return (a.rep().is_x_monotone());
    }

  };

  template <class CK>
  class Is_y_monotone_2
  {
    typedef typename CK::Boolean                   Boolean;
    typedef typename CK::Circular_arc_2            Circular_arc_2;
    typedef typename CK::Line_arc_2                Line_arc_2;

  public:
    Boolean operator() (const Circular_arc_2& a) const
    {
      return (a.rep().is_y_monotone());
    }

    Boolean operator() (const Line_arc_2& a) const
    {
      return (a.rep().is_y_monotone());
    }

  };

  template <class CK>
  class Construct_bbox_2
    // : public CK::Linear_kernel::Construct_bbox_2
  {
    typedef typename CK::Circular_arc_2            Circular_arc_2;
    typedef typename CK::Circular_arc_point_2      Circular_arc_point_2;
    typedef typename CK::Line_arc_2                Line_arc_2;
    typedef typename CK::Circle_2                  Circle_2;

    typedef typename CK::Linear_kernel::Construct_bbox_2 Linear_Construct_bbox_2;

  public:
    // using CK::Linear_kernel::Construct_bbox_2::operator();

    template <typename A>
    decltype(auto)
    operator()(const A& a) const
    { return Linear_Construct_bbox_2()(a); }

    decltype(auto) operator() (const Circular_arc_point_2& a) const
    {
      return a.rep().bbox();
    }

    decltype(auto) operator() (const Circular_arc_2& a) const
    {
      return a.rep().bbox();
    }

    decltype(auto) operator() (const Line_arc_2& a) const
    {
      return a.rep().bbox();
    }
  };

  template <class CK>
  class Bounded_side_2
    // : public CK::Linear_kernel::Bounded_side_2
  {
    typedef typename CK::Bounded_side          Bounded_side;
    typedef typename CK::Circle_2              Circle_2;
    typedef typename CK::Circular_arc_point_2  Circular_arc_point_2;

    typedef typename CK::Linear_kernel::Bounded_side_2 Linear_Bounded_side_2;

  public:
    // using CK::Linear_kernel::Bounded_side_2::operator();

    template <typename A, typename B>
    Bounded_side
    operator()(const A& a, const B& b) const
    { return Linear_Bounded_side_2()(a, b); }

    Bounded_side
    operator()(const Circle_2& c, const Circular_arc_point_2& p) const
    { return CircularFunctors::bounded_side<CK>(c,p); }

  };

  template <class CK>
  class Has_on_bounded_side_2
    // : public CK::Linear_kernel::Has_on_bounded_side_2
  {
    typedef typename CK::Boolean               Boolean;
    typedef typename CK::Circle_2              Circle_2;
    typedef typename CK::Circular_arc_point_2  Circular_arc_point_2;

    typedef typename CK::Linear_kernel::Has_on_bounded_side_2 Linear_Has_on_bounded_side_2;

  public:
    // using CK::Linear_kernel::Has_on_bounded_side_2::operator();

    template <typename A, typename B>
    Boolean
    operator()(const A& a, const B& b) const
    { return Linear_Has_on_bounded_side_2()(a, b); }

    Boolean
    operator()(const Circle_2& c, const Circular_arc_point_2& p) const
    { return CK().bounded_side_2_object()(c,p) == ON_BOUNDED_SIDE; }

  };

  template <class CK>
  class Has_on_unbounded_side_2
    // : public CK::Linear_kernel::Has_on_unbounded_side_2
  {
    typedef typename CK::Boolean               Boolean;
    typedef typename CK::Circle_2              Circle_2;
    typedef typename CK::Circular_arc_point_2  Circular_arc_point_2;

    typedef typename CK::Linear_kernel::Has_on_unbounded_side_2 Linear_Has_on_unbounded_side_2;

  public:
    // using CK::Linear_kernel::Has_on_unbounded_side_2::operator();

    template <typename A, typename B>
    Boolean
    operator()(const A& a, const B& b) const
    { return Linear_Has_on_unbounded_side_2()(a, b); }

    Boolean
    operator()(const Circle_2& c, const Circular_arc_point_2& p) const
    { return CK().bounded_side_2_object()(c,p) == ON_UNBOUNDED_SIDE; }
  };

#ifndef CGAL_NO_DEPRECATED_CODE
  template <class CK>
  class Construct_supporting_circle_2
  {
    typedef typename CK::Circular_arc_2            Circular_arc_2;

  public:
    CGAL_DEPRECATED decltype(auto) operator() (const Circular_arc_2 & a) const
    {
      return a.rep().supporting_circle();
    }
  };

  template <class CK>
  class Construct_supporting_line_2
  {
    typedef typename CK::Line_arc_2            Line_arc_2;

  public:
    CGAL_DEPRECATED decltype(auto) operator() (const Line_arc_2 & a) const
    {
      return a.rep().supporting_line();
    }
  };
#endif

  template <typename CK>
  class Construct_center_2
    // : public CK::Linear_kernel::Construct_center_2
  {
    typedef typename CK::Circular_arc_2  Circular_arc_2;

    typedef typename CK::Linear_kernel::Construct_center_2 Linear_Construct_center_2;

  public:
    // using CK::Linear_kernel::Construct_center_2::operator();

    template <typename A>
    decltype(auto)
    operator()(const A& a) const
    { return Linear_Construct_center_2()(a); }

    decltype(auto)
    operator()(const Circular_arc_2& c) const
    { return c.rep().center(); }
  };

  template <typename CK>
  class Compute_squared_radius_2
  {
    typedef typename CK::Circular_arc_2  Circular_arc_2;
    typedef typename CK::Linear_kernel LK;
    typedef typename LK::Compute_squared_radius_2 LK_Compute_squared_radius_2;
    typedef typename CK::FT          FT;
    typedef typename CK::Point_2     Point_2;
    typedef typename CK::Circle_2    Circle_2;
  public:

    decltype(auto)
    operator()( const Circle_2& c) const
    { return LK_Compute_squared_radius_2()(c); }

    FT operator()( const Point_2& p) const
    { return LK_Compute_squared_radius_2()(p); }

    FT operator()( const Point_2& p, const Point_2& q) const
    { return LK_Compute_squared_radius_2()(p, q); }

    FT operator()( const Point_2& p, const Point_2& q, const Point_2& r) const
    { return LK_Compute_squared_radius_2()(p, q, r); }

    decltype(auto)
    operator()(const Circular_arc_2& c) const
    { return c.rep().squared_radius(); }

  };

} // namespace CircularFunctors
} // namespace CGAL

#endif // CGAL_CIRCULAR_KERNEL_FUNCTION_OBJECTS_POLYNOMIAL_CIRCULAR_H