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

CGAL 4.8 - dD Spatial Searching

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CGAL::Manhattan_distance_iso_box_point< Traits > Class Template Reference
Distance Classes

`#include <CGAL/Manhattan_distance_iso_box_point.h>`

## Definition

The class `Manhattan_distance_iso_box_point` provides an implementation of the `GeneralDistance` concept for the Manhattan distance ( \( l_1\) metric) between a `d`-dimensional iso-box and a `d`-dimensional point and the Manhattan distance between a `d`-dimensional iso-box and a `d`-dimensional iso-box defined as a `k-d` tree rectangle.

Template Parameters

  Traits | must be a model for the concept `SearchTraits`, for example `Search_traits_3<Simple_cartesian<double> >`.

Is Model Of:
  `GeneralDistance`

See Also
  `GeneralDistance`

Examples:
  Spatial_searching/general_neighbor_searching.cpp.

## Types
typedef unspecified_type | D
| Dimension Tag.
typedef Traits::FT | FT
| Number type.
typedef Traits::Point_d | Point_d
| Point type.
typedef Traits::Iso_box_d | Query_item
| Query item type.

## Creation
| Manhattan_distance_iso_box_point (Traits t=Traits())
| Default constructor.

## Operations
FT | transformed_distance (Query_item b, Point_d p) const
| Returns the transformed distance between `b` and `p`.
FT | transformed_distance (FT d) const
| Returns the transformed value of of `d`.
FT | inverse_of_transformed_distance (FT d) const
| Returns the value of the inverse of the transform function applied to `d`.
FT | min_distance_to_rectangle (Query_item b, Kd_tree_rectangle< FT, D > r) const
| Returns the minimal distance between a point from `b` and a point from `r`.
FT | max_distance_to_rectangle (Query_item b, Kd_tree_rectangle< FT, D > r) const
| Returns the maximal distance between the iso-box `b` and a point from `r` furthest to `b`.