\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
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CGAL::Euclidean_distance_sphere_point< Traits > Class Template Reference
Distance Classes

#include <CGAL/Euclidean_distance_sphere_point.h>

Definition

The class Euclidean_distance_sphere_point provides an implementation of the GeneralDistance concept for the Euclidean distance ( \( l_2\) metric) between a \( d\)-dimensional sphere and a point, and the Euclidean distance between a \( d\)-dimensional sphere and a \( d\)-dimensional iso-rectangle defined as a \(k\)- \(d\) tree rectangle.

Parameters

Expects for the template argument a model of the concept SearchTraits, for example Simple_cartesian_d<double>.

Is Model Of:
GeneralDistance
See Also
GeneralDistance

Types

typedef Traits::FT FT
 Number type.
 
typedef Traits::Point_d Point_d
 Point type.
 
typedef Traits::Sphere_d Sphere_d
 Query item type.
 

Creation

 Euclidean_distance_sphere_point (Traits t=Traits())
 Default constructor.
 

Operations

NT transformed_distance (Query_item s, Point_d p) const
 Returns the distance between s and p.
 
NT min_distance_to_rectangle (Query_item s, Kd_tree_rectangle< FT > r) const
 Returns the minimal distance between a point from the sphere s and a point from r.
 
NT max_distance_to_rectangle (Query_item s, Kd_tree_rectangle< FT > r) const
 Returns the maximal distance between the sphere s and a point from r furthest to s.
 
NT transformed_distance (NT d) const
 Returns \( d^2\).
 
NT inverse_of_transformed_distance (NT d) const
 Returns \( d^{1/2}\).