// Copyright (c) 2008  INRIA Sophia-Antipolis (France), ETH Zurich (Switzerland).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v6.2/Intersections_3/include/CGAL/Intersections_3/internal/Iso_cuboid_3_Sphere_3_do_intersect.h $
// $Id: include/CGAL/Intersections_3/internal/Iso_cuboid_3_Sphere_3_do_intersect.h cac3e9d75e2 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Camille Wormser, Jane Tournois, Pierre Alliez

#ifndef CGAL_INTERNAL_INTERSECTIONS_3_ISO_CUBOID_3_SPHERE_3_DO_INTERSECT_H
#define CGAL_INTERNAL_INTERSECTIONS_3_ISO_CUBOID_3_SPHERE_3_DO_INTERSECT_H

#include <CGAL/Coercion_traits.h>
#include <CGAL/number_utils.h>
#include <CGAL/Uncertain.h>

namespace CGAL {
namespace Intersections {
namespace internal {

template <class K, class BFT> // Iso_cuboid_3 or Bbox_3
typename K::Boolean
do_intersect_sphere_box_3(const typename K::Sphere_3& sphere,
                          const BFT bxmin, const BFT bymin, const BFT bzmin,
                          const BFT bxmax, const BFT bymax, const BFT bzmax,
                          const K&)
{
  typedef typename K::FT SFT;
  typedef typename Coercion_traits<SFT, BFT>::Type FT;
  typedef typename K::Point_3 Point;

  typename Coercion_traits<SFT, BFT>::Cast to_FT;

  FT d = FT(0);
  FT distance = FT(0);
  FT sr = sphere.squared_radius();

  const Point& center = sphere.center();

  if(compare(center.x(), bxmin) == SMALLER)
  {
    d = to_FT(bxmin) - to_FT(center.x());
    d = square(d);
    if(certainly(d > sr))
      return false;

    distance = d;
  }
  else if(compare(center.x(), bxmax) == LARGER)
  {
    d = to_FT(center.x()) - to_FT(bxmax);
    d = square(d);
    if(certainly(d > sr))
      return false;

    distance = d;
  }

  if(compare(center.y(), bymin) == SMALLER)
  {
    d = to_FT(bymin) - to_FT(center.y());
    d = square(d);
    if(certainly(d > sr))
      return false;

    distance += d;
  }
  else if(compare(center.y(), bymax) == LARGER)
  {
    d = to_FT(center.y()) - to_FT(bymax);
    d = square(d);
    if(certainly(d > sr))
      return false;

    distance += d;
  }

  if(compare(center.z(), bzmin) == SMALLER)
  {
    d = to_FT(bzmin) - to_FT(center.z());
    d = square(d);
    if (certainly(d > sr))
      return false;

    distance += d;
  }
  else if(compare(center.z(), bzmax) == LARGER)
  {
    d = to_FT(center.z()) - to_FT(bzmax);
    d = square(d);
    if (certainly(d > sr))
      return false;

    distance += d;
  }
  // Note that with the way the distance above is computed, the distance is '0'
  // if the box contains the center of the sphere. But since we use '>', we don't exit
  if (distance > sr)
    return false;

  distance = FT(0);
  if (compare(center.x(), (bxmin + bxmax) * FT(0.5)) == SMALLER)
  {
    FT d = bxmax - center.x();
    distance += d * d;
  }
  else
  {
    FT d = center.x() - bxmin;
    distance += d * d;
  }

  if (compare(center.y(), (bymin + bymax) * FT(0.5)) == SMALLER)
  {
    FT d = bymax - center.y();
    distance += d * d;
  }
  else
  {
    FT d = center.y() - bymin;
    distance += d * d;
  }

  if (compare(center.z(), (bzmin + bzmax) * FT(0.5)) == SMALLER)
  {
    FT d = bzmax - center.z();
    distance += d * d;
  }
  else
  {
    FT d = center.z() - bzmin;
    distance += d * d;
  }

  return (distance >= sr);
}

template <class K>
typename K::Boolean
do_intersect(const typename K::Sphere_3& sphere,
             const typename K::Iso_cuboid_3& ic,
             const K& k)
{
  return do_intersect_sphere_box_3(sphere,
                                   (ic.min)().x(), (ic.min)().y(), (ic.min)().z(),
                                   (ic.max)().x(), (ic.max)().y(), (ic.max)().z(),
                                   k);
}

template <class K>
typename K::Boolean
do_intersect(const typename K::Iso_cuboid_3& ic,
             const typename K::Sphere_3& sphere,
             const K& k)
{
  return do_intersect(sphere, ic, k);
}

} // namespace internal
} // namespace Intersections
} // namespace CGAL

#endif // CGAL_INTERNAL_INTERSECTIONS_3_ISO_CUBOID_3_SPHERE_3_DO_INTERSECT_H
