\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - dD Spatial Searching

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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.

Template Parameters

  Traits | must be a model of the concept `SearchTraits`, for example `Simple_cartesian_d<double>`.

Is Model Of:
  `GeneralDistance`

See Also
  `GeneralDistance`

## Types
typedef unspecified_type | D
| Dimension Tag.
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, D > 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, D > 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 \( d^{1/2}\).