\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - dD Spatial Searching

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CGAL::Fuzzy_sphere< Traits > Class Template Reference
Range Query Item Classes

`#include <CGAL/Fuzzy_sphere.h>`

## Definition

The class `Fuzzy_sphere` implements fuzzy `d`-dimensional spheres.

A fuzzy sphere with radius \( r\) and fuzziness value \( \epsilon\) has as outer approximation a sphere with radius \( r+\epsilon\) and as inner approximation a sphere with radius \( r-\epsilon\).

Template Parameters

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

Is Model Of:
  `FuzzyQueryItem`

See Also
  `FuzzyQueryItem`

Examples:
  Spatial_searching/circular_query.cpp, Spatial_searching/fuzzy_range_query.cpp, and Spatial_searching/searching_with_circular_query.cpp.

## Types
typedef unspecified_type | D
| Dimension Tag.
typedef Traits::Point_d | Point_d
| Point type.
typedef Traits::FT | FT
| Number type.

## Creation
| Fuzzy_sphere (Point_d center, FT radius, FT epsilon=FT(0), Traits t=Traits())
| Constructs a fuzzy sphere centered at `center` with radius `radius` and fuzziness value `epsilon`.
| Fuzzy_sphere (Traits::Base::Point_d center, FT radius, FT epsilon=FT(0), Traits t=Traits())
| Constructs a fuzzy sphere centered at `center` with radius `radius` and fuzziness value `epsilon`. More...

## Operations
bool | contains (const Point_d &p) const
| test whether the fuzzy sphere contains `p`.
bool | inner_range_intersects (const Kd_tree_rectangle< FT, D > &rectangle) const
| test whether the inner sphere intersects the rectangle associated with a node of a tree.
bool | outer_range_contains (const Kd_tree_rectangle< FT, D > &rectangle) const
| test whether the outer sphere encloses the rectangle associated with a node of a tree.

## Constructor & Destructor Documentation

template<typename Traits >

CGAL::Fuzzy_sphere< Traits >::Fuzzy_sphere | ( | Traits::Base::Point_d | center,
|  | FT | radius,
|  | FT | epsilon = `FT(0)`,
|  | Traits | t = `Traits()`
| ) |  |

Constructs 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>`.