// Copyright (c) 2008  INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v5.6.1/Circular_kernel_3/include/CGAL/Circular_kernel_3/internal_function_has_on_spherical_kernel.h $
// $Id: internal_function_has_on_spherical_kernel.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s) : Monique Teillaud, Sylvain Pion, Pedro Machado,
//             Sebastien Loriot

// Partially supported by the IST Programme of the EU as a
// STREP (FET Open) Project under Contract No  IST-006413
// (ACS -- Algorithms for Complex Shapes)

#ifndef CGAL_SPHERICAL_KERNEL_PREDICATES_HAS_ON_3_H
#define CGAL_SPHERICAL_KERNEL_PREDICATES_HAS_ON_3_H

#include <CGAL/license/Circular_kernel_3.h>


#include <CGAL/Circular_kernel_3/internal_functions_on_sphere_3.h>
#include <CGAL/number_utils.h>
#include <CGAL/int.h>

namespace CGAL {
  namespace SphericalFunctors {

    template <class SK>
    inline
    bool
    has_on(const typename SK::Sphere_3 &a,
           const typename SK::Circular_arc_point_3 &p)
    {
      typedef typename SK::Algebraic_kernel Algebraic_kernel;
      typedef typename SK::Polynomial_for_spheres_2_3 Equation;
      Equation equation = get_equation<SK>(a);
      return (Algebraic_kernel().sign_at_object()(equation,p.rep().coordinates()) == ZERO);
    }

    template <class SK>
    inline
    bool
    has_on(const typename SK::Plane_3 &a,
           const typename SK::Circular_arc_point_3 &p)
    {
      typedef typename SK::Algebraic_kernel Algebraic_kernel;
      typedef typename SK::Polynomial_1_3 Equation;
      Equation equation = get_equation<SK>(a);
      return (Algebraic_kernel().sign_at_object()(equation,p.rep().coordinates()) == ZERO);
    }

    template <class SK>
    inline
    bool
    has_on(const typename SK::Line_3 &a,
           const typename SK::Circular_arc_point_3 &p)
    {
      typedef typename SK::Polynomials_for_line_3 Equation;
      Equation equation = get_equation<SK>(a);
      return p.rep().coordinates().is_on_line(equation);
    }

    template <class SK>
    inline
    bool
    has_on(const typename SK::Circle_3 &a,
           const typename SK::Circular_arc_point_3 &p)
    {
      return has_on<SK>(a.diametral_sphere(),p) &&
             has_on<SK>(a.supporting_plane(),p);
    }

    //duplicated code
    template <class SK>
    inline
    bool
    has_on(const typename SK::Circle_on_reference_sphere_3 &a,
           const typename SK::Point_3 &p)
    {
      return has_on<SK>(a.diametral_sphere(),p) &&
             has_on<SK>(a.supporting_plane(),p);
    }

    template <class SK>
    inline
    bool
    has_on(const typename SK::Circle_on_reference_sphere_3 &a,
           const typename SK::Circular_arc_point_on_reference_sphere_3 &p)
    {
      return has_on<SK>(a.diametral_sphere(),p) &&
             has_on<SK>(a.supporting_plane(),p);
    }

    template <class SK>
    inline
    bool
    has_on(const typename SK::Line_arc_3 &l,
           const typename SK::Circular_arc_point_3 &p,
           const bool has_on_supporting_line = false)
    {
      if(!has_on_supporting_line) {
        if(!has_on<SK>(l.supporting_line(), p)) {
          return false;
        }
      }
      return SK().compare_xyz_3_object()(l.lower_xyz_extremity(),p) <= ZERO &&
             SK().compare_xyz_3_object()(p,l.higher_xyz_extremity()) <= ZERO;
    }

    template <class SK>
    inline
    bool
    has_on(const typename SK::Line_arc_3 &l,
           const typename SK::Point_3 &p,
           const bool has_on_supporting_line = false)
    {
      if(!has_on_supporting_line) {
        if(!has_on<SK>(l.supporting_line(), p)) {
          return false;
        }
      }
      return SK().compare_xyz_3_object()(l.lower_xyz_extremity(),p) <= ZERO &&
             SK().compare_xyz_3_object()(p,l.higher_xyz_extremity()) <= ZERO;
    }

    template <class SK>
    inline
    bool
    has_on(const typename SK::Plane_3 &p,
           const typename SK::Line_arc_3 &l)
    {
      return SK().has_on_3_object()(p, l.supporting_line());
    }

    template <class SK>
    inline
    bool
    has_on(const typename SK::Line_3 &l,
           const typename SK::Line_arc_3 &la)
    {
      return non_oriented_equal<SK>(l, la.supporting_line());
    }

    template< class SK>
    inline Sign element_cross_product_sign(const typename SK::Root_of_2 & y1,
                                           const typename SK::Root_of_2 &z2,
                                           const typename SK::Root_of_2 &z1,
                                           const typename SK::Root_of_2 &y2)
    {
      int s1=CGAL_NTS sign(z1);
      int s2=CGAL_NTS sign(z2);
      if (s1==0){
        if (s2==0)
          return CGAL_NTS sign(0);
        else
          return CGAL_NTS sign(y1) * CGAL_NTS sign(z2);
      }
      else{
        if (s2==0)
          return CGAL_NTS sign(- z1) * CGAL_NTS sign(y2);
        else
          return CGAL_NTS sign((s1*s2)*compare(y1/z1,y2/z2));
      }
    }

    template< class SK>
    inline
    Sign
    compute_sign_of_cross_product(const typename SK::Root_of_2 &x1,
                                  const typename SK::Root_of_2 &y1,
                                  const typename SK::Root_of_2 &z1,
                                  const typename SK::Root_of_2 &x2,
                                  const typename SK::Root_of_2 &y2,
                                  const typename SK::Root_of_2 &z2)
    {
      Sign s = element_cross_product_sign<SK>(y1,z2,z1,y2);
      if(s!=0) return s;
      s = element_cross_product_sign<SK>(z1,x2,x1,z2);
      if(s!=0) return s;
      s = element_cross_product_sign<SK>(x1,y2,y1,x2);
      return s;
    }

    template< class SK>
    inline
    Sign
    compute_sign_of_cross_product(const typename SK::Circular_arc_point_3 &p1,
                                  const typename SK::Circular_arc_point_3 &p2,
                                  const typename SK::Circular_arc_point_3 &c) {
      return compute_sign_of_cross_product<SK>(p1.x()-c.x(),
                                               p1.y()-c.y(),
                                               p1.z()-c.z(),
                                               p2.x()-c.x(),
                                               p2.y()-c.y(),
                                               p2.z()-c.z());
    }

    template <class SK>
    inline
    bool
    has_on(const typename SK::Circular_arc_3 &a,
           const typename SK::Point_3 &p,
           const bool has_on_supporting_circle = false)
    {
      if(!has_on_supporting_circle) {
        if(!SK().has_on_3_object()(a.supporting_circle(),p))
          return false;
      }
      if(a.rep().is_full()) return true;
      const Sign s_x_t = a.sign_cross_product();
      const Sign s_x_p =
        compute_sign_of_cross_product<SK>(a.source(),p,a.center());
      const Sign p_x_t =
        compute_sign_of_cross_product<SK>(p,a.target(),a.center());
      if(s_x_t == ZERO) return (s_x_p != NEGATIVE);
      if(a.source() == p) return true;
      if(a.target() == p) return true;
      if(s_x_t == POSITIVE) {
        if(s_x_p == POSITIVE) return p_x_t == POSITIVE;
        else return false;
      } else {
        if(s_x_p == NEGATIVE) return p_x_t == POSITIVE;
        else return true;
      }
    }

    template <class SK>
    inline
    bool
    has_on(const typename SK::Circular_arc_3 &a,
           const typename SK::Circular_arc_point_3 &p,
           const bool has_on_supporting_circle = false)
    {
      if(!has_on_supporting_circle) {
        if(!has_on<SK>(a.supporting_circle(),p))
          return false;
      }
      if(a.rep().is_full()) return true;
      const Sign s_x_t = a.sign_cross_product();
      const Sign s_x_p =
        compute_sign_of_cross_product<SK>(a.source(),p,a.center());
      const Sign p_x_t =
        compute_sign_of_cross_product<SK>(p,a.target(),a.center());
      if(s_x_t == ZERO) return (s_x_p != NEGATIVE);
      if(a.source() == p) return true;
      if(p == a.target()) return true;
      if(s_x_t == POSITIVE) {
        if(s_x_p == POSITIVE) return p_x_t == POSITIVE;
        else return false;
      } else {
        if(s_x_p == NEGATIVE) return p_x_t == POSITIVE;
        else return true;
      }
    }

    template <class SK>
    inline
    bool
    has_on(const typename SK::Sphere_3 &a,
           const typename SK::Circular_arc_3 &p)
    {
      return a.has_on(p.supporting_circle());
    }

    template <class SK>
    inline
    bool
    has_on(const typename SK::Plane_3 &a,
           const typename SK::Circular_arc_3 &p)
    {
      return a.has_on(p.supporting_circle());
    }

    template <class SK>
    inline
    bool
    has_on(const typename SK::Circle_3 &c,
           const typename SK::Circular_arc_3 &ca)
    {
      return non_oriented_equal<SK>(c,ca.supporting_circle());
    }

    template <class SK>
    inline
    bool
    has_on(const typename SK::Circular_arc_3 &ca,
           const typename SK::Circle_3 &c)
    {
       if(!non_oriented_equal<SK>(c,ca.supporting_circle())) return false;
       return ca.rep().is_full();
    }



  }//SphericalFunctors
}//CGAL

#endif //CGAL_SPHERICAL_KERNEL_PREDICATES_HAS_ON_3_H

