namespace CGAL {

/*!
\ingroup RangeQueryItemClasses

The class `Fuzzy_sphere` implements fuzzy `d`-dimensional spheres.
A fuzzy sphere with radius \f$ r\f$ and fuzziness value \f$ \epsilon\f$ has
as inner approximation a sphere with radius \f$ r-\epsilon\f$ and
as outer approximation a sphere with radius \f$ r+\epsilon\f$.
Points are returned depending on their location respective to the approximations,
as follows:
- points in the inner approximation (boundary included) are always returned.
- points in the outer approximation (boundary included) and not in the previous
  category may or may not be returned.
- points that do not fit in the two previous categories are never returned.

Note that if the fuzziness value is strictly greater than the radius, there is no
inner approximation.

\tparam Traits must be a model of the concept
`SearchTraits`, for example `CGAL::Cartesian_d<double>`.

\cgalModels `FuzzyQueryItem`
*/
template< typename Traits >
class Fuzzy_sphere {
public:

/// \name Types
/// @{

/*!
Dimension Tag.
*/
typedef unspecified_type D;

/*!
Point type.
*/
typedef Traits::Point_d Point_d;

/*!
Number type.
*/
typedef Traits::FT FT;

/// @}

/// \name Creation
///
/// @{

/*!
Construct a fuzzy sphere
centered at `center` with radius `radius` and fuzziness value `epsilon`.
*/
Fuzzy_sphere(Point_d center, FT radius, FT epsilon=FT(0),Traits t=Traits());

/*!
Construct a fuzzy sphere centered at `center` with radius `radius` and fuzziness value `epsilon`.
\attention Only available in case `Traits` is `Search_traits_adapter<Key,PointPropertyMap,BaseTraits>`.
*/
Fuzzy_sphere(Traits::Base::Point_d center, FT radius, FT epsilon=FT(0), Traits t=Traits());

/// @}

/// \name Operations
/// @{

/*!
Test whether the fuzzy sphere contains `p`.

That is, whether the distance between the center of the fuzzy sphere and `p` is
less than \f$ r\f$.
*/
bool contains(const Point_d& p) const;

/*!
Test whether the inner sphere intersects the rectangle
associated with a node of a tree.

That is, whether the minimal distance between the center of the fuzzy sphere and
`rectangle` is less than \f$ r-\epsilon\f$.
*/
bool inner_range_intersects(const Kd_tree_rectangle<FT,D>& rectangle) const;

/*!
Test whether the outer sphere encloses the rectangle associated with a node of a tree.

That is, whether the maximal distance between the center of the fuzzy sphere and
`rectangle` is less than \f$ r+\epsilon\f$.
*/
bool outer_range_contains(const Kd_tree_rectangle<FT,D>& rectangle) const;

/// @}

}; /* end Fuzzy_sphere */
} /* end namespace CGAL */
