CGAL::Euclidean_distance< Traits > Class Template Reference

#include <CGAL/Euclidean_distance.h>

Definition

The class Euclidean_distance provides an implementation of the concept OrthogonalDistance, with the Euclidean distance ( \( l_2\) metric).

To optimize distance computations squared distances are used.

Template Parameters

Traits

must be a model of the concept SearchTraits, for example Search_traits_2<Simple_cartesian<double> >.

Is Model Of:

OrthogonalDistance

See also

OrthogonalDistance

CGAL::Weighted_Minkowski_distance<Traits>

Examples:

Spatial_searching/searching_sphere_orthogonally.cpp, Spatial_searching/splitter_worst_cases.cpp, and Spatial_searching/using_fair_splitting_rule.cpp.

Types
typedef Traits::Dimension	D
	Dimension Tag. More...
typedef Traits::FT	FT
	Number type. More...
typedef Traits::Point_d	Point_d
	Point type. More...
typedef Point_d	Query_item
	Query item type. More...

Creation
	Euclidean_distance (Traits t=Traits())
	Default constructor. More...

Operations
FT	transformed_distance (Query_item q, Point_d p) const
	Returns the squared Euclidean distance between q and p. More...
FT	min_distance_to_rectangle (Query_item q, Kd_tree_rectangle< FT, D > r) const
	Returns the squared Euclidean distance between q and the point on the boundary of r closest to q. More...
FT	min_distance_to_rectangle (Query_item q, Kd_tree_rectangle< FT, D > r, vector< FT > &dists)
	Returns the squared Euclidean distance between q and the point on the boundary of r closest to q. More...
FT	max_distance_to_rectangle (Query_item q, Kd_tree_rectangle< FT, D > r) const
	Returns the squared Euclidean distance, where \( d\) denotes the distance between q and the point on the boundary of r farthest to q. More...
FT	max_distance_to_rectangle (Query_item q, Kd_tree_rectangle< FT, D > r, vector< FT > &dists)
	Returns the squared Euclidean distance, where \( d\) denotes the distance between q and the point on the boundary of r farthest to q. More...
FT	new_distance (FT dist, FT old_off, FT new_off, int cutting_dimension) const
	Updates the squared dist incrementally and returns the updated squared distance. More...
FT	transformed_distance (FT d) const
	Returns \( d^2\). More...
FT	inverse_of_transformed_distance (FT d) const
	Returns \( d^{1/2}\). More...

Member Typedef Documentation

template<typename Traits >

typedef Traits::Dimension CGAL::Euclidean_distance< Traits >::D

Dimension Tag.

template<typename Traits >

typedef Traits::FT CGAL::Euclidean_distance< Traits >::FT

Number type.

template<typename Traits >

typedef Traits::Point_d CGAL::Euclidean_distance< Traits >::Point_d

Point type.

template<typename Traits >

typedef Point_d CGAL::Euclidean_distance< Traits >::Query_item

Query item type.

Constructor & Destructor Documentation

template<typename Traits >

CGAL::Euclidean_distance< Traits >::Euclidean_distance

(

Traits

t = Traits()

)

Default constructor.

Member Function Documentation

template<typename Traits >

FT CGAL::Euclidean_distance< Traits >::inverse_of_transformed_distance

(

FT

d

)

const

Returns \( d^{1/2}\).

template<typename Traits >

FT CGAL::Euclidean_distance< Traits >::max_distance_to_rectangle	(	Query_item	q,
		Kd_tree_rectangle< FT, D >	r
	)		const

Returns the squared Euclidean distance, where \( d\) denotes the distance between q and the point on the boundary of r farthest to q.

template<typename Traits >

FT CGAL::Euclidean_distance< Traits >::max_distance_to_rectangle	(	Query_item	q,
		Kd_tree_rectangle< FT, D >	r,
		vector< FT > &	dists
	)

Returns the squared Euclidean distance, where \( d\) denotes the distance between q and the point on the boundary of r farthest to q.

Stores the distances in each dimension in dists.

template<typename Traits >

FT CGAL::Euclidean_distance< Traits >::min_distance_to_rectangle	(	Query_item	q,
		Kd_tree_rectangle< FT, D >	r
	)		const

Returns the squared Euclidean distance between q and the point on the boundary of r closest to q.

template<typename Traits >

FT CGAL::Euclidean_distance< Traits >::min_distance_to_rectangle	(	Query_item	q,
		Kd_tree_rectangle< FT, D >	r,
		vector< FT > &	dists
	)

Returns the squared Euclidean distance between q and the point on the boundary of r closest to q.

Stores the distances in each dimension in dists.

template<typename Traits >

FT CGAL::Euclidean_distance< Traits >::new_distance	(	FT	dist,
		FT	old_off,
		FT	new_off,
		int	cutting_dimension
	)		const

Updates the squared dist incrementally and returns the updated squared distance.

template<typename Traits >

FT CGAL::Euclidean_distance< Traits >::transformed_distance	(	Query_item	q,
		Point_d	p
	)		const

Returns the squared Euclidean distance between q and p.

template<typename Traits >

FT CGAL::Euclidean_distance< Traits >::transformed_distance

(

FT

d

)

const

Returns \( d^2\).