// Copyright (c) 2012, 2017  INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.0.2/Alpha_shapes_2/include/CGAL/Alpha_shapes_2/internal/Lazy_alpha_nt_2.h $
// $Id: include/CGAL/Alpha_shapes_2/internal/Lazy_alpha_nt_2.h e13ef800cb7 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s)     : Sébastien Loriot <sebastien.loriot@geometryfactory.com>
//                 Mael Rouxel-Labbé

#ifndef CGAL_INTERNAL_LAZY_ALPHA_NT_2_H
#define CGAL_INTERNAL_LAZY_ALPHA_NT_2_H

#include <CGAL/license/Alpha_shapes_2.h>

#include <CGAL/assertions.h>
#include <CGAL/Number_types/internal/Exact_type_selector.h>
#include <CGAL/number_type_basic.h>
#include <CGAL/Cartesian_converter.h>
#include <CGAL/Has_conversion.h>

#include <boost/mpl/has_xxx.hpp>
#include <boost/type_traits.hpp>

#include <iostream>

namespace CGAL {

namespace internal {

// check whether Cartesian_converter can do the following conversions
//  -- Input_traits::(Weighted_)Point_2 to K2::(Weighted_)Point_2
//  -- Input_traits::(Weighted_)Point_2 to K3::(Weighted_)Point_2
//
template < class Input_traits, class Kernel_approx, class Kernel_exact,
           class Weighted_tag >
class Is_traits_point_convertible_2
{
  typedef typename Kernel_traits<typename Input_traits::Point_2>::Kernel   Kernel_input;

  typedef typename Input_traits::Point_2                                   K1P;
  typedef typename Kernel_approx::Point_2                                  K2P;
  typedef typename Kernel_exact::Point_2                                   K3P;

public:
  static const bool value
    = (Has_conversion<Kernel_input, Kernel_approx, K1P, K2P>::value &&
       Has_conversion<Kernel_input, Kernel_exact, K1P, K3P>::value);
};

template < class Input_traits, class Kernel_approx, class Kernel_exact >
class Is_traits_point_convertible_2<Input_traits, Kernel_approx, Kernel_exact,
                                  ::CGAL::Tag_true /* Weighted_tag */>
{
  typedef typename Kernel_traits<typename Input_traits::Point_2>::Kernel   Kernel_input;

  typedef typename Input_traits::Weighted_point_2                          K1WP;
  typedef typename Kernel_approx::Weighted_point_2                         K2WP;
  typedef typename Kernel_exact::Weighted_point_2                          K3WP;

public:
  static const bool value
    = (Has_conversion<Kernel_input, Kernel_approx, K1WP, K2WP>::value &&
       Has_conversion<Kernel_input, Kernel_exact, K1WP, K3WP>::value);
};

template <class T>
struct Input_points_for_lazy_alpha_nt_2
{
  int nbpts;
  const T* p0;
  const T* p1;
  const T* p2;
};

//non-weighted case
template <class Weighted_tag, class Input_traits, class Kernel_input,
          class Kernel_approx, class Kernel_exact>
struct Types_for_alpha_nt_2
{
  //Converter types
  typedef CGAL::Cartesian_converter<Kernel_input, Kernel_approx> To_approx;
  typedef CGAL::Cartesian_converter<Kernel_input, Kernel_exact>  To_exact;

  //Point types
  typedef typename Kernel_approx::Point_2                        Approx_point;
  typedef typename Kernel_exact::Point_2                         Exact_point;
  typedef typename Input_traits::Point_2                         Input_point;

  //Constructions
  typedef typename Kernel_approx::Compute_squared_radius_2       Approx_squared_radius;
  typedef typename Kernel_exact::Compute_squared_radius_2        Exact_squared_radius;
};

//weighted case
template <class Input_traits, class Kernel_input,
          class Kernel_approx, class Kernel_exact>
struct Types_for_alpha_nt_2< ::CGAL::Tag_true /* Weighted_tag */,
                             Input_traits, Kernel_input,
                             Kernel_approx, Kernel_exact >
{
  //Converter types
  typedef CGAL::Cartesian_converter<Kernel_input, Kernel_approx> To_approx;
  typedef CGAL::Cartesian_converter<Kernel_input, Kernel_exact>  To_exact;

  //Point types
  typedef typename Kernel_approx::Weighted_point_2               Approx_point;
  typedef typename Kernel_exact::Weighted_point_2                Exact_point;
  typedef typename Input_traits::Weighted_point_2                Input_point;

  //Constructions
  typedef typename Kernel_approx::Compute_squared_radius_smallest_orthogonal_circle_2  Approx_squared_radius;
  typedef typename Kernel_exact::Compute_squared_radius_smallest_orthogonal_circle_2   Exact_squared_radius;
};

template<class Input_traits, bool mode, class Weighted_tag>
class Lazy_alpha_nt_2
{
  //NT & kernels
  typedef CGAL::Interval_nt<mode>                                          NT_approx;

  //Gmpq or Quotient<MP_float>
  typedef Exact_field_selector<double>::Type                               NT_exact;
  typedef CGAL::Simple_cartesian<NT_approx>                                Kernel_approx;
  typedef CGAL::Simple_cartesian<NT_exact>                                 Kernel_exact;
  typedef typename Kernel_traits<typename Input_traits::Point_2>::Kernel   Kernel_input;

  //Helper class for weighted and non-weighted case
  typedef Types_for_alpha_nt_2<Weighted_tag, Input_traits, Kernel_input,
                               Kernel_approx, Kernel_exact>                Types;

  //Converters
  typedef typename Types::To_approx                                        To_approx;
  typedef typename Types::To_exact                                         To_exact;

  //Constructions class
  typedef typename Types::Approx_squared_radius                            Approx_squared_radius;
  typedef typename Types::Exact_squared_radius                             Exact_squared_radius;

  //Point
  typedef typename Types::Approx_point                                     Approx_point;
  typedef typename Types::Exact_point                                      Exact_point;
  typedef typename Types::Input_point                                      Input_point;

  //Conversion functions
  Approx_point to_approx(const Input_point& wp) const
  {
    // The traits class' Point_2 must be convertible using the Cartesian converter
    static_assert(Is_traits_point_convertible_2<
                            Input_traits, Kernel_approx, Kernel_exact, Weighted_tag>::value);

    To_approx converter;
    return converter(wp);
  }

  Exact_point to_exact(const Input_point& wp) const
  {
    // The traits class' Point_2 must be convertible using the Cartesian converter
    static_assert(Is_traits_point_convertible_2<
                            Input_traits, Kernel_approx, Kernel_exact, Weighted_tag>::value);

    To_exact converter;
    return converter(wp);
  }

  //members
  //the members can be updated when calling method exact()
  mutable std::optional<NT_exact> exact_;
  mutable NT_approx approx_;

  //private functions
  typedef Input_points_for_lazy_alpha_nt_2<Input_point> Data_vector;
  Data_vector input_points;

  const Data_vector& data() const{ return input_points;}
  Data_vector& data(){ return input_points;}

  static double & relative_precision_of_to_double_internal()
  {
    CGAL_STATIC_THREAD_LOCAL_VARIABLE(double, relative_precision_of_to_double, 0.00001);
      return relative_precision_of_to_double;
  }

public:

  static const double & get_relative_precision_of_to_double()
  {
    return relative_precision_of_to_double_internal();
  }

  static void set_relative_precision_of_to_double(double d)
  {
      CGAL_assertion((0 < d) & (d < 1));
      relative_precision_of_to_double_internal() = d;
  }

  typedef NT_exact               Exact_nt;
  typedef NT_approx              Approximate_nt;

  void update_exact() const
  {
    switch(data().nbpts) {
      case 1:
        exact_ = Exact_squared_radius()( to_exact(*data().p0) );
        break;
      case 2:
        exact_ = Exact_squared_radius()( to_exact(*data().p0),to_exact(*data().p1) );
        break;
      case 3:
        exact_ = Exact_squared_radius()( to_exact(*data().p0),to_exact(*data().p1),to_exact(*data().p2) );
        break;
      default:
        CGAL_assertion(false);
    }
  }

  void set_approx()
  {
    switch(data().nbpts) {
      case 1:
        approx_ = Approx_squared_radius()( to_approx(*data().p0) );
        break;
      case 2:
        approx_ = Approx_squared_radius()( to_approx(*data().p0),to_approx(*data().p1) );
        break;
      case 3:
        approx_ = Approx_squared_radius()( to_approx(*data().p0),to_approx(*data().p1),to_approx(*data().p2) );
        break;
      default:
        CGAL_assertion(false);
    }
  }

  const NT_exact& exact() const
  {
    if (exact_ == std::nullopt) {
      update_exact();
      approx_=to_interval(*exact_);
    }
    return *exact_;
  }

  const NT_approx& approx() const {
    return approx_;
  }

  //Constructors
  Lazy_alpha_nt_2()
    : exact_(Exact_nt(0)), approx_(0)
  {
    data().nbpts=0;
    data().p0=nullptr;
    data().p1=nullptr;
    data().p2=nullptr;
  }

  Lazy_alpha_nt_2(double d)
   : exact_(Exact_nt(d)), approx_(d)
  {
    data().nbpts=0;
    data().p0=nullptr;
    data().p1=nullptr;
    data().p2=nullptr;
  }

  Lazy_alpha_nt_2(const Input_point& wp0)
  {
    data().nbpts=1;
    data().p0=&wp0;
    data().p1=nullptr;
    data().p2=nullptr;
    set_approx();
  }

  Lazy_alpha_nt_2(const Input_point& wp0,
                  const Input_point& wp1)
  {
    data().nbpts=2;
    data().p0=&wp0;
    data().p1=&wp1;
    data().p2=nullptr;
    set_approx();
  }

  Lazy_alpha_nt_2(const Input_point& wp0,
                  const Input_point& wp1,
                  const Input_point& wp2)
  {
    data().nbpts=3;
    data().p0=&wp0;
    data().p1=&wp1;
    data().p2=&wp2;
    set_approx();
  }

#define CGAL_LANT_COMPARE_FUNCTIONS(CMP) \
  bool \
  operator CMP (const Lazy_alpha_nt_2<Input_traits,mode,Weighted_tag> &other) const \
  { \
    Uncertain<bool> res = this->approx() CMP other.approx(); \
    if (res.is_certain()) \
      return res; \
    else \
      return this->exact() CMP other.exact(); \
  } \

  CGAL_LANT_COMPARE_FUNCTIONS(<)
  CGAL_LANT_COMPARE_FUNCTIONS(>)
  CGAL_LANT_COMPARE_FUNCTIONS(>=)
  CGAL_LANT_COMPARE_FUNCTIONS(<=)
  CGAL_LANT_COMPARE_FUNCTIONS(==)
  CGAL_LANT_COMPARE_FUNCTIONS(!=)

#undef CGAL_LANT_COMPARE_FUNCTIONS
};

template<class Input_traits, bool mode, class Weighted_tag>
std::ostream&
operator<< (std::ostream& os,
            const Lazy_alpha_nt_2<Input_traits, mode, Weighted_tag>& a){
  return os << ::CGAL::to_double(a.approx());
}

// small classes to select the functors in weighted or unweighted cases
template <class GeomTraits, class Weighted_tag>
struct iCompute_squared_radius_2;

template <class GeomTraits>
struct iCompute_squared_radius_2<GeomTraits, Tag_false /* Weighted_tag*/>
{
  template <class As>
  typename GeomTraits::Compute_squared_radius_2
  operator()(const As& as) const {
    return static_cast<const typename As::Triangulation&>(as).geom_traits().
        compute_squared_radius_2_object();
  }
};

template <class GeomTraits>
struct iCompute_squared_radius_2<GeomTraits, Tag_true /* Weighted_tag*/>
{
  template <class As>
  typename GeomTraits::Compute_squared_radius_smallest_orthogonal_circle_2
  operator()(const As& as) const {
    return static_cast<const typename As::Triangulation&>(as).geom_traits().
        compute_squared_radius_smallest_orthogonal_circle_2_object();
  }
};

template <class GeomTraits, class Weighted_tag>
struct iSide_of_bounded_circle_2;

template <class GeomTraits>
struct iSide_of_bounded_circle_2<GeomTraits, Tag_false /* Weighted_tag*/>
{
  template <class As>
  typename GeomTraits::Side_of_bounded_circle_2
  operator()(const As& as) const {
    return static_cast<const typename As::Triangulation&>(as).geom_traits().
        side_of_bounded_circle_2_object();
  }
};

template <class GeomTraits>
struct iSide_of_bounded_circle_2<GeomTraits, Tag_true /* Weighted_tag*/>
{
  template <class As>
  typename GeomTraits::Power_side_of_bounded_power_circle_2
  operator()(const As& as) const {
    return static_cast<const typename As::Triangulation&>(as).geom_traits().
        power_side_of_bounded_power_circle_2_object();
  }
};

template <class Type_of_alpha, class Point>
struct Lazy_compute_squared_radius_2
{
  Type_of_alpha operator()(const Point& p,
                           const Point& q,
                           const Point& r)
  { return Type_of_alpha(p,q,r); }

  Type_of_alpha operator()(const Point& p,
                           const Point& q)
  { return Type_of_alpha(p,q); }

  Type_of_alpha operator()(const Point& p)
  { return Type_of_alpha(p); }
};

template <class GeomTraits, class ExactAlphaComparisonTag, class Weighted_tag>
struct Alpha_nt_selector_impl_2;

template <class GeomTraits, class Weighted_tag>
struct Alpha_nt_selector_impl_2<GeomTraits,
                                Tag_false /* ExactAlphaComparisonTag */,
                                Weighted_tag>
{
  typedef typename GeomTraits::FT Type_of_alpha;
  typedef iCompute_squared_radius_2<GeomTraits, Weighted_tag> Compute_squared_radius_2;
  typedef iSide_of_bounded_circle_2<GeomTraits, Weighted_tag> Side_of_bounded_circle_2;
};

template <class GeomTraits, class Weighted_tag>
struct Alpha_nt_selector_impl_2<GeomTraits,
                                Tag_true /* ExactAlphaComparisonTag */,
                                Weighted_tag>
{
  typedef Lazy_alpha_nt_2<
    GeomTraits, true /* mode */, Tag_false /* Weighted_tag */> Type_of_alpha;
  typedef Lazy_compute_squared_radius_2<
    Type_of_alpha, typename GeomTraits::Point_2>               Functor;

  struct Compute_squared_radius_2
  {
    template<class As>
    Functor operator()(const As&){return Functor();}
  };

  typedef iSide_of_bounded_circle_2<GeomTraits, Weighted_tag> Side_of_bounded_circle_2;
};

template <class GeomTraits>
struct Alpha_nt_selector_impl_2<GeomTraits,
                                Tag_true /* ExactAlphaComparisonTag */,
                                Tag_true /* Weighted_tag */ >
{
  typedef Lazy_alpha_nt_2<
    GeomTraits, true /* mode */, Tag_true /* Weighted_tag */>   Type_of_alpha;

  typedef Lazy_compute_squared_radius_2<
    Type_of_alpha, typename GeomTraits::Weighted_point_2>       Functor;

  struct Compute_squared_radius_2
  {
    template<class As>
    Functor operator()(const As&){return Functor();}
  };

  typedef iSide_of_bounded_circle_2<GeomTraits, Tag_true> Side_of_bounded_circle_2;
};

template <class GeomTraits, class ExactAlphaComparisonTag, class Weighted_tag>
struct Alpha_nt_selector_2
  : public Alpha_nt_selector_impl_2<
             GeomTraits,
             // If the base traits is already exact then we don't need to do anything,
             // and we can simply directly use the traits class
             Boolean_tag<std::is_floating_point<typename GeomTraits::FT>::value &&
                         ExactAlphaComparisonTag::value >,
             Weighted_tag>
{ };

} // namespace internal

template<class Input_traits, bool mode, class Weighted_tag>
double to_double(const internal::Lazy_alpha_nt_2<Input_traits, mode, Weighted_tag>& a)
{
  double r;
  if (fit_in_double(a.approx(), r))
    return r;

  // If it isn't precise enough,
  // we trigger the exact computation first,
  // which will refine the approximation.
  if (!has_smaller_relative_precision(a.approx(), a.get_relative_precision_of_to_double()))
    a.exact();

  return CGAL_NTS to_double(a.approx());
}

} // namespace CGAL

#endif // CGAL_INTERNAL_LAZY_ALPHA_NT_2_H

