// Copyright (c) 2003, 2017  INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.2-beta1/Interpolation/include/CGAL/Voronoi_intersection_2_traits_3.h $
// $Id: include/CGAL/Voronoi_intersection_2_traits_3.h 431cfb5357d $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s)     : Julia Floetotto, Mael Rouxel-Labbé

#ifndef CGAL_VORONOI_INTERSECTION_2_TRAITS_3_H
#define CGAL_VORONOI_INTERSECTION_2_TRAITS_3_H

#include <CGAL/license/Interpolation.h>

#include <CGAL/Origin.h>
#include <CGAL/tags.h>
#include <CGAL/number_utils.h>
#include <CGAL/double.h>
#include <CGAL/number_utils_classes.h>
#include <CGAL/Algebraic_structure_traits.h>
#include <CGAL/predicates/predicates_for_voronoi_intersection_cartesian_2_3.h>
#include <CGAL/constructions/constructions_for_voronoi_intersection_cartesian_2_3.h>
#include <CGAL/function_objects.h>
#include <CGAL/representation_tags.h>

namespace CGAL {

template <class Traits>
class Orientation_with_normal_plane_2_3
{
public:
  typedef typename Traits::Point_3     Point;
  typedef typename Traits::Vector_3    Vector;

  typedef Orientation                  result_type;

  Orientation_with_normal_plane_2_3(const Vector& _normal, const Traits& _traits)
    : normal(_normal), traits(_traits)
  { }

  Orientation operator()(const Point& p, const Point& q, const Point& r) const
  {
    return traits.orientation_3_object()(p,q,q+normal,r);
  }

public:
  const Vector& normal;
  const Traits& traits;
};

template < typename K >
class Side_of_plane_centered_sphere_2_3
{
public:
  typedef typename K::Point_3               Point;
  typedef typename K::Weighted_point_3      Weighted_point;
  typedef typename K::Vector_3              Vector;
  typedef typename K::Plane_3               Plane;
  typedef typename K::Direction_3           Direction;

  typedef Oriented_side                     result_type;

  Side_of_plane_centered_sphere_2_3(const Point& _a, const Vector& _normal)
    : a(_a), normal(_normal)
  { }

  Oriented_side operator()(const Weighted_point& p, const Weighted_point& q,
                           const Weighted_point& r, const Weighted_point& t) const
  {
    return side_of_plane_centered_sphere(a,normal,p,q,r,t);
  }

  Oriented_side operator()(const Weighted_point& p, const Weighted_point& q,
                           const Weighted_point& r) const
  {
    return side_of_plane_centered_sphere(a,normal,p,q,r);
  }

  Oriented_side operator()(const Weighted_point& p, const Weighted_point& q) const
  {
    return side_of_plane_centered_sphere(a,normal,p,q);
  }

private:
  const Point&   a;
  const Vector&  normal;
};

template < typename K >
class Construct_plane_centered_circumcenter_3
{
public:
  typedef typename K::Point_3               Point;
  typedef typename K::Weighted_point_3      Weighted_point;
  typedef typename K::Vector_3              Vector;

  typedef Point                             result_type;

  Construct_plane_centered_circumcenter_3(const Point& _a, const Vector& _normal)
    : a(_a), normal(_normal)
  { }

  Point operator()(const Weighted_point& p, const Weighted_point& q,
                   const Weighted_point& r) const
  {
    return plane_centered_circumcenter_3(a,normal,p,q,r);
  }

private:
  const Point&  a;
  const Vector& normal;
};

template < typename K >
class Construct_plane_intersected_bisector_3
{
public:
  typedef typename K::Point_3             Point;
  typedef typename K::Weighted_point_3    Weighted_point;
  typedef typename K::Vector_3            Vector;
  typedef typename K::Line_3              Line;

  typedef Line                            result_type;

  Construct_plane_intersected_bisector_3(const Point& _a, const Vector& _normal)
    : a(_a), normal(_normal)
  { }

  Line operator()(const Weighted_point& p, const Weighted_point& q) const
  {
    return plane_intersected_bisector_3(a, normal, p, q);
  }

private:
  const Point&  a;
  const Vector& normal;
};

template < typename K >
class Compare_first_projection_3
{
  //compares the projection of two points onto a second (non-trivial)
  // vector in the projection plane:
public:
  typedef typename K::Point_3      Point;
  typedef typename K::Vector_3     Vector;
  typedef typename K::FT           Coord_type;

  typedef Comparison_result        result_type;

  Compare_first_projection_3(const Vector& _normal) : normal(_normal) { }

  Comparison_result operator()(const Point& p, const Point& q) const
  {
    if(normal.x() != Coord_type(0))
      return (Comparison_result) CGAL_NTS
          sign(Vector(normal.y(), -normal.x(), Coord_type(0))*(p-q));
    if(normal.y() != Coord_type(0))
      return (Comparison_result) CGAL_NTS
          sign(Vector(-normal.y(), normal.x(), Coord_type(0))*(p-q));

    CGAL_assertion(normal.z() != Coord_type(0));
    return (Comparison_result) CGAL_NTS
        sign(Vector(-normal.z(), Coord_type(0), normal.x())*(p-q));
  }

private:
  const Vector& normal;
};

template < typename K >
class Compare_second_projection_3
{
  //compares the projection of two points onto a second (non-trivial)
  // vector in the projection plane:
public:
  typedef typename K::FT           Coord_type;
  typedef typename K::Vector_3     Vector;
  typedef typename K::Point_3      Point;

  typedef Comparison_result        result_type;

  Compare_second_projection_3(const Vector& _normal) : normal(_normal) { }

  Comparison_result operator()(const Point& p, const Point& q) const
  {
    if(normal.x() != Coord_type(0))
      return (Comparison_result) CGAL_NTS
          sign(Vector(normal.z(), Coord_type(0), -normal.x())*(p-q));
    if(normal.y() != Coord_type(0))
      return (Comparison_result) CGAL_NTS
          sign(Vector(Coord_type(0), normal.z(), -normal.y())*(p-q));

    CGAL_assertion(normal.z() != Coord_type(0));
    return (Comparison_result) CGAL_NTS
        sign(Vector(Coord_type(0), -normal.z(), normal.y())*(p-q));
  }

private:
  const Vector& normal;
};

namespace Interpolation {

template < typename K >
class Compute_area_3
{
  //squareroot of compute_squared_area_3:
  //-> if no sqrt is supported, cast to double
public:
  typedef typename K::FT                       FT;
  typedef typename K::Point_3                  Point;
  typedef typename K::Compute_squared_area_3   Compute_squared_area;

  typedef FT                                   result_type;

  FT operator()(const Point& p, const Point& q, const Point& r) const
  {
    typedef typename CGAL::Algebraic_structure_traits<FT> AST;
    FT squared_area = Compute_squared_area()(p,q,r);
    return cast_sqrt_to_double(squared_area, typename AST::Algebraic_category());
  }

private:
  FT cast_sqrt_to_double(const FT& squared_area, Field_with_sqrt_tag) const
  {
    return CGAL_NTS sqrt(squared_area);
  }

  FT cast_sqrt_to_double(const FT& squared_area, Integral_domain_without_division_tag) const
  {
    double approx = CGAL_NTS to_double(squared_area);
    return CGAL_NTS sqrt(approx);
  }
};

} // namespace Interpolation

template < class K_ >
class Voronoi_intersection_2_traits_3
  : public K_
{
  typedef K_                                        Base;

public:
  typedef K_                                        Rep;

  //the regular triangulation traits model:
  //Traits::Point_2 is a 3D point!!
  typedef typename Rep::Point_3                     Point_2;
  typedef typename Rep::Weighted_point_3            Weighted_point_2;

  //other types needed:
  typedef typename Rep::Segment_3                   Segment_2;
  typedef typename Rep::Triangle_3                  Triangle_2;
  typedef typename Rep::Line_3                      Line_2;
  typedef typename Rep::Ray_3                       Ray_2;
  typedef typename Rep::Vector_3                    Vector_2;
  typedef typename Rep::Circle_3                    Circle_2;

  typedef typename Rep::Construct_point_3           Construct_point_2;
  typedef typename Rep::Construct_weighted_point_3  Construct_weighted_point_2;
  typedef typename Rep::Construct_segment_3         Construct_segment_2;
  typedef typename Rep::Construct_vector_3          Construct_vector_2;
  typedef typename Rep::Construct_ray_3             Construct_ray_2;
  typedef typename Rep::Construct_triangle_3        Construct_triangle_2;

  typedef typename Rep::Equal_3                     Equal_2;
  typedef typename Rep::Construct_circumcenter_3    Construct_circumcenter_2;

  typedef typename Rep::Compare_distance_3          Compare_distance_2;
  //if no sqrt is supported, it casts to double:
  typedef Interpolation::Compute_area_3<Rep>        Compute_area_2;

  //specific tests:
  typedef Orientation_with_normal_plane_2_3<Rep>    Orientation_2;
  typedef Side_of_plane_centered_sphere_2_3<Rep>    Power_side_of_oriented_power_circle_2;

  typedef Construct_plane_centered_circumcenter_3<Rep> Construct_weighted_circumcenter_2;
  typedef Construct_plane_intersected_bisector_3<Rep>  Construct_radical_axis_2;

  typedef Compare_first_projection_3<Rep>           Compare_x_2;
  typedef Compare_second_projection_3<Rep>          Compare_y_2;

  typedef Compare_to_less<Compare_x_2>              Less_x_2;
  typedef Compare_to_less<Compare_y_2>              Less_y_2;

  //for certificated coordinate/neighbor computation:
  typedef typename Rep::Less_distance_to_point_3    Less_distance_to_point_2;
  typedef typename Rep::Compute_squared_distance_3  Compute_squared_distance_2;

  struct Compare_xy_2 {
    Compare_x_2 cx_2;
    Compare_y_2 cy_2;

    Compare_xy_2(const Compare_x_2& cx_2, const Compare_y_2& cy_2)
      : cx_2(cx_2), cy_2(cy_2)
    {}

    Comparison_result operator()(const Point_2& p, const Point_2& q) const
    {
       Comparison_result res = cx_2(p, q);
       if (res == EQUAL) {
         return cy_2(p, q);
       }
       return res;
    }
  };

  //instantiations and creation of functors:
  //for the triangulation:
  Orientation_2
  orientation_2_object() const
  { return Orientation_2(normal, static_cast<const Base&>(*this)); }

  Power_side_of_oriented_power_circle_2
  power_side_of_oriented_power_circle_2_object() const
  { return Power_side_of_oriented_power_circle_2(a, normal); }

  Compare_distance_2 compare_distance_2_object() const
  { return this->K_::compare_distance_3_object(); }

  Compare_x_2
  compare_x_2_object() const
  { return Compare_x_2(normal); }

  Compare_y_2
  compare_y_2_object() const
  { return Compare_y_2(normal); }

  Compare_xy_2
  compare_xy_2_object() const
  { return Compare_xy_2(compare_x_2_object(), compare_y_2_object()); }

  Less_x_2
  less_x_2_object() const
  { return compare_to_less(compare_x_2_object()); }

  Less_y_2
  less_y_2_object() const
  { return compare_to_less(compare_y_2_object()); }

  //for the coordinate computation:
  Compute_area_2 compute_area_2_object() const
  { return Compute_area_2(); }

  //for constructions of dual:
  Construct_weighted_circumcenter_2
  construct_weighted_circumcenter_2_object() const
  { return Construct_weighted_circumcenter_2(a, normal); }

  Construct_radical_axis_2 construct_radical_axis_2_object() const
  { return Construct_radical_axis_2(a, normal); }

  Construct_ray_2 construct_ray_2_object() const
  { return this->Base::construct_ray_3_object(); }

  Construct_segment_2 construct_segment_2_object() const
  { return this->Base::construct_segment_3_object(); }

  Construct_triangle_2 construct_triangle_2_object() const
  { return this->Base::construct_triangle_3_object(); }

  //for certification of coordinate/neighbor computation:
  Less_distance_to_point_2 less_distance_to_point_2_object() const
  { return this->Base::less_distance_to_point_3_object(); }

  Compute_squared_distance_2 compute_squared_distance_2_object() const
  { return this->Base::compute_squared_distance_3_object(); }

  //for compilation
  Construct_point_2 construct_point_2_object() const
  { return this->Base::construct_point_3_object(); }

  Construct_weighted_point_2 construct_weighted_point_2_object() const
  { return this->Base::construct_weighted_point_3_object(); }

  Equal_2 equal_2_object() const
  { return this->Base::equal_3_object(); }

  Construct_vector_2 construct_vector_2_object() const
  { return this->Base::construct_vector_3_object(); }

  Construct_circumcenter_2 construct_circumcenter_2_object() const
  { return this->Base::construct_circumcenter_3_object(); }

  //construction
  Voronoi_intersection_2_traits_3(const Point_2& _a = Point_2(),
                                  const Vector_2& _normal = NULL_VECTOR,
                                  const K_& k = K_())
    : Base(k), a(_a), normal(_normal)
  { }

  const Vector_2& get_normal() const { return normal; }
  const Point_2& get_point() const { return a; }

public:
  //defining the intersection plane:
  const Point_2 a;
  const Vector_2 normal;
};

//put the homogeneous or cartesian tag
template < class Point, class Weighted_point, class Vector >
inline
Oriented_side
side_of_plane_centered_sphere(const Point& a, const Vector& n, /*defines the plane*/
                              const Weighted_point& p, const Weighted_point& q,
                              const Weighted_point& r, const Weighted_point& t)
{
  typedef typename Point::R::Rep_tag Tag;
  return side_of_plane_centered_sphere(a,n,p,q,r,t, Tag());
}

template < class Point, class Weighted_point, class Vector >
inline
Oriented_side
side_of_plane_centered_sphere(const Point& a, const Vector& n, /*defines the plane*/
                              const Weighted_point& p, const Weighted_point& q,
                              const Weighted_point& r)
{
  typedef typename Point::R::Rep_tag Tag;
  return side_of_plane_centered_sphere(a,n,p,q,r,Tag());
}

template < class Point, class Weighted_point, class Vector >
inline
Oriented_side
side_of_plane_centered_sphere(const Point& a, const Vector& n, /*defines the plane*/
                              const Weighted_point& p, const Weighted_point& q)
{
  typedef typename Point::R::RT    RT;

  Comparison_result r =
    Compare<RT>()(-CGAL_NTS square(  (p.x() - a.x()) * n.x() // Vector(a,p) * n
                                   + (p.y() - a.y()) * n.y()
                                   + (p.z() - a.z()) * n.z()),
                  -CGAL_NTS square(  (q.x() - a.x()) * n.x() // Vector(a,q) * n
                                   + (q.y() - a.y()) * n.y()
                                   + (q.z() - a.z()) * n.z()));

  if(r == LARGER)
    return ON_NEGATIVE_SIDE;
  else if(r == SMALLER)
    return ON_POSITIVE_SIDE;
  return ON_ORIENTED_BOUNDARY;
}

template < class Point, class Weighted_point, class Vector >
inline
Point
plane_centered_circumcenter_3(const Point& a, const Vector& n, /*defines the plane*/
                              const Weighted_point& p, const Weighted_point& q,
                              const Weighted_point& r)
{
  typedef typename Point::R::Rep_tag Tag;
  return plane_centered_circumcenter_3(a,n,p,q,r, Tag());
}

template < class Point, class Weighted_point, class Vector >
inline
typename Point::R::Line_3
plane_intersected_bisector_3(const Point& a, const Vector& n, /*defines the plane*/
                             const Weighted_point& p, const Weighted_point& q)
{
  typedef typename Point::R::Rep_tag Tag;
  return plane_intersected_bisector_3(a,n,p,q, Tag());
}

///-----------------------------------------------------------
// Cartesian variants:
//
template < class Point, class Weighted_point, class Vector>
inline
Oriented_side
side_of_plane_centered_sphere(const Point& a, const Vector& n, /*defines the plane*/
                              const Weighted_point& p, const Weighted_point& q,
                              const Weighted_point& r, const Weighted_point& t,
                              Cartesian_tag)
{
  return side_of_plane_centered_sphereC3(a.x(), a.y(), a.z(),
                                         n.x(), n.y(), n.z(),
                                         p.x(), p.y(), p.z(),
                                         q.x(), q.y(), q.z(),
                                         r.x(), r.y(), r.z(),
                                         t.x(), t.y(), t.z());
}

template < class Point, class Weighted_point, class Vector >
inline
Oriented_side
side_of_plane_centered_sphere(const Point& a, const Vector& n, /*defines the plane*/
                              const Weighted_point& p, const Weighted_point& q,
                              const Weighted_point& r,
                              Cartesian_tag)
{
  return side_of_plane_centered_sphereC3(a.x(), a.y(), a.z(),
                                         n.x(), n.y(), n.z(),
                                         p.x(), p.y(), p.z(),
                                         q.x(), q.y(), q.z(),
                                         r.x(), r.y(), r.z());
}

template < class Point, class Weighted_point, class Vector >
inline
Point
plane_centered_circumcenter_3(const Point& a, const Vector& n, /*defines the plane*/
                              const Weighted_point& p, const Weighted_point& q,
                              const Weighted_point& r,
                              Cartesian_tag)
{
  typename Point::R::RT x,y,z;
  plane_centered_circumcenterC3(a.x(), a.y(), a.z(),
                                n.x(), n.y(), n.z(),
                                p.x(), p.y(), p.z(),
                                q.x(), q.y(), q.z(),
                                r.x(), r.y(), r.z(),x,y,z);
  return Point(x,y,z);
}

template < class Point, class Weighted_point, class Vector>
inline
typename Point::R::Line_3
plane_intersected_bisector_3(const Point& a, const Vector& n, /*defines the plane*/
                             const Weighted_point& p, const Weighted_point& q,
                             Cartesian_tag)
{
  typename Point::R::RT x1,y1,z1, x2,y2,z2;
  typedef typename Point::R::Line_3 Line;
  bisector_plane_intersectionC3(a.x(), a.y(), a.z(),
                                n.x(), n.y(), n.z(),
                                p.x(), p.y(), p.z(),
                                q.x(), q.y(), q.z(), x1,y1,z1,x2,y2,z2);

  return Line(Point(x1,y1,z1), Point(x2,y2,z2));
}

// Homogeneous variants.

// The 3 following call the cartesian version over FT, because an
// homogeneous special version has not yet been written.

template <class Point, class Weighted_point, class Vector >
inline
Oriented_side
side_of_plane_centered_sphere(const Point& a, const Vector& n, /*defines the plane*/
                              const Weighted_point& p, const Weighted_point& q,
                              const Weighted_point& r, const Weighted_point& t,
                              Homogeneous_tag)
{
  return side_of_plane_centered_sphereC3(a.x(), a.y(), a.z(),
                                         n.x(), n.y(), n.z(),
                                         p.x(), p.y(), p.z(),
                                         q.x(), q.y(), q.z(),
                                         r.x(), r.y(), r.z(),
                                         t.x(), t.y(), t.z());
}

template < class Point, class Weighted_point, class Vector >
inline
Oriented_side
side_of_plane_centered_sphere(const Point& a, const Vector& n, /*defines the plane*/
                              const Weighted_point& p, const Weighted_point& q,
                              const Weighted_point& r,
                              Homogeneous_tag)
{
  return side_of_plane_centered_sphereC3(a.x(), a.y(), a.z(),
                                         n.x(), n.y(), n.z(),
                                         p.x(), p.y(), p.z(),
                                         q.x(), q.y(), q.z(),
                                         r.x(), r.y(), r.z());
}

template < class Point, class Weighted_point, class Vector >
inline
Point
plane_centered_circumcenter_3(const Point& a, const Vector& n, /*defines the plane*/
                              const Weighted_point& p, const Weighted_point& q,
                              const Weighted_point& r,
                              Homogeneous_tag)
{
  typename Point::R::RT x,y,z;
  plane_centered_circumcenterC3(a.x(), a.y(), a.z(),
                                n.x(), n.y(), n.z(),
                                p.x(), p.y(), p.z(),
                                q.x(), q.y(), q.z(),
                                r.x(), r.y(), r.z(),x,y,z);
  return Point(x,y,z);
}

template < class Point, class Weighted_point, class Vector >
inline
typename Point::R::Line_3
plane_intersected_bisector_3(const Point& a, const Vector& n, /*defines the plane*/
                             const Weighted_point& p, const Weighted_point& q,
                             Homogeneous_tag)
{
  typename Point::R::RT x1,y1,z1, x2,y2,z2;
  typedef typename Point::R::Line_3 Line;
  bisector_plane_intersectionC3(a.x(), a.y(), a.z(),
                                n.x(), n.y(), n.z(),
                                p.x(), p.y(), p.z(),
                                q.x(), q.y(), q.z(),x1,y1,z1,x2,y2,z2);

  return Line(Point(x1,y1,z1), Point(x2,y2,z2));
}

} //namespace CGAL

#endif // CGAL_VORONOI_INTERSECTION_2_TRAITS_3_H
