Euclidean_distance<Traits>

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CGAL::Euclidean_distance<Traits>

Definition

The class Euclidean_distance<Traits> provides an implementation of the concept OrthogonalDistance, with the Euclidean distance (l₂ metric). To optimize distance computations squared distances are used.

#include <CGAL/Euclidean_distance.h>

Parameters

Expects for the first template argument a model of the concept SearchTraits, for example CGAL::Search_traits_2<CGAL::Cartesian<double> >.

Is Model for the Concepts

OrthogonalDistance

Types

Traits::FT	FT;	Number type.

Traits::Point_d	Point_d;	Point type.

Point_d	Query_item;	Query item type.

Creation

Euclidean_distance<Traits> ed;
	Default constructor.

Operations

FT	ed.transformed_distance ( Query_item q, Point_d p)
		Returns the squared Euclidean distance between q and p.

FT	ed.min_distance_to_rectangle ( Query_item q, Kd_tree_rectangle<FT> r)
		Returns the squared Euclidean distance between q and the point on the boundary of r closest to q.

FT	ed.max_distance_to_rectangle ( Query_item q, Kd_tree_rectangle<FT> r;)
		Returns the squared Euclidean distance, where d denotes the distance between q and the point on the boundary of r farthest to q.

FT	ed.new_distance ( FT dist, FT old_off, FT new_off, int cutting_dimension)
		Updates the squared dist incrementally and returns the updated squared distance.

FT	ed.transformed_distance ( FT d)	Returns d².

FT	ed.inverse_of_transformed_distance ( FT d)
		Returns d^1/2.