CGAL::Euclidean_distance_sphere_point< Traits > Class Template Reference

#include <CGAL/Euclidean_distance_sphere_point.h>

Definition

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

The class Euclidean_distance_sphere_point provides an implementation of the GeneralDistance concept for the Euclidean distance ( \( l_2\) metric) between a \( d\)-dimensional sphere and a point, and the Euclidean distance between a \( d\)-dimensional sphere and a \( d\)-dimensional iso-rectangle defined as a \(k\)- \(d\) tree rectangle.

Template Parameters

Traits

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

Is Model Of:

GeneralDistance

See also

GeneralDistance

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

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

Operations
NT	transformed_distance (Query_item s, Point_d p) const
	Returns the distance between s and p. More...
NT	min_distance_to_rectangle (Query_item s, Kd_tree_rectangle< FT, D > r) const
	Returns the minimal distance between a point from the sphere s and a point from r. More...
NT	max_distance_to_rectangle (Query_item s, Kd_tree_rectangle< FT, D > r) const
	Returns the maximal distance between the sphere s and a point from r furthest to s. More...
NT	transformed_distance (NT d) const
	Returns \( d^2\). More...
NT	inverse_of_transformed_distance (NT d) const
	Returns \( d^{1/2}\). More...

Member Typedef Documentation

D

template<typename Traits >

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

Dimension Tag.

FT

template<typename Traits >

typedef Traits::FT CGAL::Euclidean_distance_sphere_point< Traits >::FT

Number type.

Point_d

template<typename Traits >

typedef Traits::Point_d CGAL::Euclidean_distance_sphere_point< Traits >::Point_d

Point type.

Sphere_d

template<typename Traits >

typedef Traits::Sphere_d CGAL::Euclidean_distance_sphere_point< Traits >::Sphere_d

Query item type.

Constructor & Destructor Documentation

Euclidean_distance_sphere_point()

template<typename Traits >

CGAL::Euclidean_distance_sphere_point< Traits >::Euclidean_distance_sphere_point

(

Traits

t = Traits()

)

Default constructor.

Member Function Documentation

inverse_of_transformed_distance()

template<typename Traits >

NT CGAL::Euclidean_distance_sphere_point< Traits >::inverse_of_transformed_distance

(

NT

d

)

const

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

max_distance_to_rectangle()

template<typename Traits >

NT CGAL::Euclidean_distance_sphere_point< Traits >::max_distance_to_rectangle	(	Query_item	s,
		Kd_tree_rectangle< FT, D >	r
	)		const

Returns the maximal distance between the sphere s and a point from r furthest to s.

min_distance_to_rectangle()

template<typename Traits >

NT CGAL::Euclidean_distance_sphere_point< Traits >::min_distance_to_rectangle	(	Query_item	s,
		Kd_tree_rectangle< FT, D >	r
	)		const

Returns the minimal distance between a point from the sphere s and a point from r.

transformed_distance() [1/2]

template<typename Traits >

NT CGAL::Euclidean_distance_sphere_point< Traits >::transformed_distance

(

NT

d

)

const

Returns \( d^2\).

transformed_distance() [2/2]

template<typename Traits >

NT CGAL::Euclidean_distance_sphere_point< Traits >::transformed_distance	(	Query_item	s,
		Point_d	p
	)		const

Returns the distance between s and p.