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.
typedef Traits::FT	FT
	Number type.
typedef Traits::Point_d	Point_d
	Point type.
typedef Point_d	Query_item
	Query item type.

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

Operations
FT	transformed_distance (Query_item q, Point_d p) const
	Returns the squared Euclidean distance between q and p.
template<typename Coord_iterator >
FT	transformed_distance_from_coordinates (Query_item q, Coord_iterator begin, Coord_iterator end) const
	Returns the transformed distance between q and the point whose Cartesian coordinates are contained in the range [begin, end).
template<typename Coord_iterator >
FT	interruptible_transformed_distance (Query_item q, Coord_iterator begin, Coord_iterator end, FT stop_if_geq_to_this) const
	Returns the transformed distance between q and the point whose Cartesian coordinates are contained in the range [begin, end), or any value \( \geq \) stop_if_geq_to_this if the transformed distance is \( \geq \) stop_if_geq_to_this.
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.
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.
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.
FT	transformed_distance (FT d) const
	Returns \( d^2\).
FT	inverse_of_transformed_distance (FT d) const
	Returns \( d^{1/2}\).

Member Function Documentation

max_distance_to_rectangle()

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.

min_distance_to_rectangle()

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.