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 \( l_p(w)(r,q)= ({\Sigma_{i=1}^{i=d} \, w_i(r_i-q_i)^p})^{1/p}\) for \( 0 < p <\infty\) and defined by \( l_{\infty}(w)(r,q)=max \{w_i |r_i-q_i| \mid 1 \leq i \leq d\}\).

For the purpose of the distance computations it is more efficient to compute the transformed distance \( {\sigma_{i=1}^{i=d} \, w_i(r_i-q_i)^p}\) instead of the actual distance.

Note

As this distance involves the computation of a power it is not done exact but with floating point arithmetic.

Template Parameters

Traits

must 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 \( l_2\) 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 \( l_{power}(weights)\) metric. More...

Operations
FT	transformed_distance (Point_d q, Point_d r) const
	Returns \( d^{power}\), 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 \( d^{power}\), 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 \( d^{power}\), 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 \( d^{power}\), 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 \( d^{power}\), 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 \( d^p\) for \( 0 < p <\infty\) . More...
FT	inverse_of_transformed_distance (FT d) const
	Returns \( d^{1/p}\) for \( 0 < p <\infty\). More...

Constructor & Destructor Documentation

Weighted_Minkowski_distance()

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 \( l_{power}(weights)\) metric.

power=0 denotes the \( l_{\infty}(weights)\) metric. The values in the iterator range [wb,we) are the weight.

Member Function Documentation

inverse_of_transformed_distance()

template<typename Traits >

FT CGAL::Weighted_Minkowski_distance< Traits >::inverse_of_transformed_distance

(

FT

d

)

const

Returns \( d^{1/p}\) for \( 0 < p <\infty\).

Returns \( d\) for \( p=\infty\).

max_distance_to_rectangle()

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 \( d^{power}\), 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.

min_distance_to_rectangle()

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 \( d^{power}\), 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.

transformed_distance()

template<typename Traits >

FT CGAL::Weighted_Minkowski_distance< Traits >::transformed_distance

(

FT

d

)

const

Returns \( d^p\) for \( 0 < p <\infty\) .

Returns \( d\) for \( p=\infty\) .