CGAL 4.8.2 - dD Spatial Searching
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CGAL::Weighted_Minkowski_distance< Traits > Class Template Reference

#include <CGAL/Weighted_Minkowski_distance.h>

Definition

The class Weighted_Minkowski_distance provides an implementation of the concept OrthogonalDistance, with a weighted Minkowski metric on d-dimensional points defined by lp(w)(r,q)=(Σi=di=1wi(riqi)p)1/p for 0<p< and defined by l(w)(r,q)=max{wi|riqi|1id}.

For the purpose of the distance computations it is more efficient to compute the transformed distance σi=di=1wi(riqi)p instead of the actual distance.

Template Parameters
Traitsmust be a model of the concept SearchTraits, for example Search_traits_2.
Is Model Of:
OrthogonalDistance
See Also
OrthogonalDistance
CGAL::Euclidean_distance<Traits>
Examples:
Spatial_searching/weighted_Minkowski_distance.cpp.

Types

typedef Traits::Dimension D
 Dimension tag.
 
typedef Traits::FT FT
 Number type.
 
typedef Traits::Point_d Point_d
 Point type.
 

Creation

 Weighted_Minkowski_distance (int d, Traits t=Traits())
 Constructor implementing l2 metric for d-dimensional points.
 
template<class InputIterator >
 Weighted_Minkowski_distance (FT power, int dim, InputIterator wb, InputIterator we, Traits t=Traits())
 Constructor implementing the lpower(weights) metric. More...
 

Operations

FT transformed_distance (Point_d q, Point_d r) const
 Returns dpower, where d denotes the distance between q and r.
 
FT min_distance_to_rectangle (Point_d q, Kd_tree_rectangle< FT, D > r) const
 Returns dpower, where d denotes the distance between the query item q and the point on the boundary of r closest to q.
 
FT min_distance_to_rectangle (Point_d q, Kd_tree_rectangle< FT, D > r, vector< FT > &dists)
 Returns dpower, where d denotes the distance between the query item q and the point on the boundary of r closest to q. More...
 
FT max_distance_to_rectangle (Point_d q, Kd_tree_rectangle< FT, D > r) const
 Returns dpower, where d denotes the distance between the query item q and the point on the boundary of r farthest to q.
 
FT max_distance_to_rectangle (Point_d q, Kd_tree_rectangle< FT, D > r, vector< FT > &dists)
 Returns dpower, where d denotes the distance between the query item 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 dist incrementally and returns the updated distance.
 
FT transformed_distance (FT d) const
 Returns dp for 0<p< . More...
 
FT inverse_of_transformed_distance (FT d) const
 Returns d1/p for 0<p<. More...
 

Constructor & Destructor Documentation

template<typename Traits >
template<class InputIterator >
CGAL::Weighted_Minkowski_distance< Traits >::Weighted_Minkowski_distance ( FT  power,
int  dim,
InputIterator  wb,
InputIterator  we,
Traits  t = Traits() 
)

Constructor implementing the lpower(weights) metric.

power0 denotes the l(weights) metric. The values in the iterator range [wb,we) are the weight.

Member Function Documentation

template<typename Traits >
FT CGAL::Weighted_Minkowski_distance< Traits >::inverse_of_transformed_distance ( FT  d) const

Returns d1/p for 0<p<.

Returns d for p=.

template<typename Traits >
FT CGAL::Weighted_Minkowski_distance< Traits >::max_distance_to_rectangle ( Point_d  q,
Kd_tree_rectangle< FT, D r,
vector< FT > &  dists 
)

Returns dpower, where d denotes the distance between the query item q and the point on the boundary of r farthest to q.

Stores the distances in each dimension in dists.

template<typename Traits >
FT CGAL::Weighted_Minkowski_distance< Traits >::min_distance_to_rectangle ( Point_d  q,
Kd_tree_rectangle< FT, D r,
vector< FT > &  dists 
)

Returns dpower, where d denotes the distance between the query item q and the point on the boundary of r closest to q.

Stores the distances in each dimension in dists.

template<typename Traits >
FT CGAL::Weighted_Minkowski_distance< Traits >::transformed_distance ( FT  d) const

Returns dp for 0<p< .

Returns d for p= .