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 lp(w)(r,q)= (Σi=1i=d wi(ri-qi)p)1/p for 0 < p <∞ and defined by l(w)(r,q)=max {wi |ri-qi| | 1 i d}. For the purpose of the distance computations it is more efficient to compute the transformed distance σi=1i=d wi(ri-qi)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, Traits t=Traits());
Constructor implementing l2 metric for d-dimensional points.


template <class InputIterator>
Weighted_Minkowski_distance<Traits> wd ( FT power, int dim, InputIterator wb, InputIterator we, Traits t=Traits());
Constructor implementing the lpower(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 dpower, where d denotes the distance between q and r.

FT wd.min_distance_to_rectangle ( Point_d q, Kd_tree_rectangle<FT> r;)
Returns dpower, 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<FT> r;)
Returns dpower, 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 dp for 0 < p <∞ . Returns d for p=∞ .

FT wd.inverse_of_transformed_distance ( FT d)
Returns d1/p for 0 < p <∞. Returns d for p=∞.

See Also

OrthogonalDistance
CGAL::Euclidean_distance<Traits>