Weighted_Minkowski_distance<Traits>

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CGAL::Weighted_Minkowski_distance<Traits>

Definition

The class Weighted_Minkowski_distance<Traits> provides an implementation of the concept OrthogonalDistance, with a weighted Minkowski metric on d-dimensional points defined by l_p(w)(r,q)= (Σ_i=1^i=d w_i(r_i-q_i)^p)^1/p for 0 < p <∞ and defined by l_∞(w)(r,q)=max {w_i |r_i-q_i| | 1 ≤ i ≤ d}. For the purpose of the distance computations it is more efficient to compute the transformed distance σ_i=1^i=d w_i(r_i-q_i)^p instead of the actual distance.

#include <CGAL/Weighted_Minkowski_distance.h>

Parameters

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

Is Model for the Concepts

OrthogonalDistance

Types

Traits::FT	FT;	Number type.

Traits::Point_d	Point_d;	Point type.

Creation

Weighted_Minkowski_distance<Traits> wd ( int d);
	Constructor implementing l₂ metric for d-dimensional points.

template <class InputIterator>
Weighted_Minkowski_distance<Traits> wd ( FT power, int dim, InputIterator wb, InputIterator we);
	Constructor implementing the l_power(weights) metric. power ≤ 0 denotes the l_∞(weights) metric. The values in the iterator range [wb,we) are the weight.

Operations

FT	wd.transformed_distance ( Point_d q, Point_d r)
		Returns d^power, where d denotes the distance between q and r.

FT	wd.min_distance_to_rectangle ( Point_d q, Kd_tree_rectangle<Traits> r;)
		Returns d^power, where d denotes the distance between the query item q and the point on the boundary of r closest to q.

FT	wd.max_distance_to_rectangle ( Point_d q, Kd_tree_rectangle<Traits> r;)
		Returns d^power, where d denotes the distance between the query item q and the point on the boundary of r farthest to q.

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

FT	wd.transformed_distance ( FT d)	Returns d^p for 0 < p <∞ . Returns d for p=∞ .

FT	wd.inverse_of_transformed_distance ( FT d)
		Returns d^1/p for 0 < p <∞. Returns d for p=∞.