CGAL::Fuzzy_sphere< Traits > Class Template Reference

#include <CGAL/Fuzzy_sphere.h>

Definition

template<typename Traits>
class CGAL::Fuzzy_sphere< Traits >

The class Fuzzy_sphere implements fuzzy d-dimensional spheres. A fuzzy sphere with radius \( r\) and fuzziness value \( \epsilon\) has as inner approximation a sphere with radius \( r-\epsilon\) and as outer approximation a sphere with radius \( r+\epsilon\). 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.

Template Parameters

Traits

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

Is Model Of:

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. More...
typedef Traits::Point_d	Point_d
	Point type. More...
typedef Traits::FT	FT
	Number type. More...

Creation
	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. More...
	Fuzzy_sphere (Traits::Base::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. More...

Operations
bool	contains (const Point_d &p) const
	Test whether the fuzzy sphere contains p. More...
template<typename Coord_iterator >
bool	contains_point_given_as_coordinates (Coord_iterator begin, Coord_iterator end) const
	Test whether the fuzzy sphere contains the point whose Cartesian coordinates are contained in the range [begin, end). More...
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. More...
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. More...

Member Typedef Documentation

D

template<typename Traits >

typedef unspecified_type CGAL::Fuzzy_sphere< Traits >::D

Dimension Tag.

FT

template<typename Traits >

typedef Traits::FT CGAL::Fuzzy_sphere< Traits >::FT

Number type.

Point_d

template<typename Traits >

typedef Traits::Point_d CGAL::Fuzzy_sphere< Traits >::Point_d

Point type.

Constructor & Destructor Documentation

Fuzzy_sphere() [1/2]

template<typename Traits >

CGAL::Fuzzy_sphere< Traits >::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.

Fuzzy_sphere() [2/2]

template<typename Traits >

CGAL::Fuzzy_sphere< Traits >::Fuzzy_sphere	(	Traits::Base::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>.

Member Function Documentation

contains()

template<typename Traits >

bool CGAL::Fuzzy_sphere< Traits >::contains

(

const Point_d &

p

)

const

Test whether the fuzzy sphere contains p.

That is, whether the distance between the center of the fuzzy sphere and p is less than \( r\).

contains_point_given_as_coordinates()

template<typename Traits >

template<typename Coord_iterator >

bool CGAL::Fuzzy_sphere< Traits >::contains_point_given_as_coordinates	(	Coord_iterator	begin,
		Coord_iterator	end
	)		const

Test whether the fuzzy sphere contains the point whose Cartesian coordinates are contained in the range [begin, end).

inner_range_intersects()

template<typename Traits >

bool CGAL::Fuzzy_sphere< Traits >::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.

That is, whether the minimal distance between the center of the fuzzy sphere and rectangle is less than \( r-\epsilon\).

outer_range_contains()

template<typename Traits >

bool CGAL::Fuzzy_sphere< Traits >::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.

That is, whether the maximal distance between the center of the fuzzy sphere and rectangle is less than \( r+\epsilon\).