// Copyright (c) 1998-2021
// Utrecht University (The Netherlands),
// ETH Zurich (Switzerland),
// INRIA Sophia-Antipolis (France),
// Max-Planck-Institute Saarbruecken (Germany),
// and Tel-Aviv University (Israel).  All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1.2/Distance_3/include/CGAL/Distance_3/Ray_3_Ray_3.h $
// $Id: include/CGAL/Distance_3/Ray_3_Ray_3.h 37e2b278910 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Geert-Jan Giezeman, Andreas Fabri

#ifndef CGAL_DISTANCE_3_RAY_3_RAY_3_H
#define CGAL_DISTANCE_3_RAY_3_RAY_3_H

#include <CGAL/Distance_3/internal/squared_distance_utils_3.h>

#include <CGAL/Ray_3.h>
#include <CGAL/Vector_3.h>

namespace CGAL {
namespace internal {

template <class K>
typename K::FT
ray_ray_squared_distance_parallel(const typename K::Vector_3& ray1dir,
                                  const typename K::Vector_3& ray2dir,
                                  const typename K::Vector_3& s1_min_s2,
                                  const K& k)
{
  if(!is_acute_angle(ray2dir, s1_min_s2, k))
    if(!same_direction(ray1dir, ray2dir, k))
      return typename K::FT(s1_min_s2*s1_min_s2);

  return squared_distance_to_line(ray1dir, s1_min_s2, k);
}

template <class K>
typename K::FT
squared_distance(const typename K::Ray_3& ray1,
                 const typename K::Ray_3& ray2,
                 const K& k)
{
  typedef typename K::RT RT;
  typedef typename K::FT FT;
  typedef typename K::Point_3 Point_3;
  typedef typename K::Vector_3 Vector_3;

  typename K::Construct_vector_3 construct_vector = k.construct_vector_3_object();
  typename K::Compute_squared_distance_3 sq_dist = k.compute_squared_distance_3_object();

  const Point_3& s1 = ray1.source();
  const Point_3& s2 = ray2.source();
  const Vector_3 dir1 = ray1.direction().vector();
  const Vector_3 dir2 = ray2.direction().vector();
  const Vector_3 normal = wcross(dir1, dir2, k);
  const Vector_3 s1_min_s2 = construct_vector(s2, s1);

  if(is_null(normal, k))
    return ray_ray_squared_distance_parallel(dir1, dir2, s1_min_s2, k);

  bool crossing1, crossing2;

  const Vector_3 perpend1 = wcross(dir1, normal, k);
  const Vector_3 perpend2 = wcross(dir2, normal, k);

  const RT sdm_s1_2 = wdot(perpend2, s1_min_s2, k);
  if(sdm_s1_2 < RT(0))
  {
    crossing1 = (wdot(perpend2, dir1, k) >= RT(0));
  }
  else
  {
    if(RT(wdot(perpend2, dir1, k)) <= RT(0))
      crossing1 = true;
    else
      crossing1 = (sdm_s1_2 == RT(0));
  }

  const RT sdm_s2_1 = - wdot(perpend1, s1_min_s2, k);
  if(sdm_s2_1 < RT(0))
  {
    crossing2 = (wdot(perpend1, dir2, k) >= RT(0));
  }
  else
  {
    if(wdot(perpend1, dir2, k) <= RT(0))
      crossing2 = true;
    else
      crossing2 = (sdm_s2_1 == RT(0));
  }

  if(crossing1)
  {
    if(crossing2)
      return squared_distance_to_plane(normal, s1_min_s2, k);

    return sq_dist(s2, ray1);
  }
  else
  {
    if(crossing2)
    {
      return sq_dist(s1, ray2);
    }
    else
    {
      FT min1, min2;
      min1 = sq_dist(s1, ray2);
      min2 = sq_dist(s2, ray1);
      return (min1 < min2) ? min1 : min2;
    }
  }
}

template <class K>
typename K::Comparison_result
compare_squared_distance(const typename K::Ray_3& ray1,
                         const typename K::Ray_3& ray2,
                         const K& k,
                         const typename K::FT& d2)
{
  return ::CGAL::compare(squared_distance(ray1, ray2, k), d2);
}

} // namespace internal

template <class K>
inline
typename K::FT
ray_ray_squared_distance_parallel(const Vector_3<K>& ray1dir,
                                  const Vector_3<K>& ray2dir,
                                  const Vector_3<K>& s1_min_s2)
{
  return internal::ray_ray_squared_distance_parallel(ray1dir, ray2dir, s1_min_s2, K());
}

} // namespace CGAL

#endif // CGAL_DISTANCE_3_RAY_3_RAY_3_H
