## CGAL::Manhattan_distance_iso_box_point<Traits>

### Definition

The class Manhattan_distance_iso_box_point<Traits> provides an implementation of the GeneralDistance concept for the Manhattan distance (l1 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.

#include <CGAL/Manhattan_distance_iso_box_point.h>

### Parameters

Expects for the template argument a model for the concept SearchTraits, for example CGAL::Search_traits_3<CGAL::Cartesian<double> >.

### Is Model for the Concept

GeneralDistance

### Types

Traits::FT | FT; | Number type.
Traits::Point_d | Point_d; | Point type.
Traits::Iso_box_d | Query_item; | Query item type.

### Creation

Manhattan_distance_iso_box_point<Traits> md;
| Default constructor.

### Operations

FT | md.transformed_distance ( Query_item b, Point_d p)
|  | Returns the transformed distance between b and p.
FT | md.transformed_distance ( FT d)
|  | Returns the transformed value of of d.
FT | md.inverse_of_transformed_distance ( FT d)
|  | Returns the value of the inverse of the transform function applied to d.

FT

md.min_distance_to_rectangle ( | Query_item b, Kd_tree_rectangle<Traits> r)

|  | Returns the minimal distance between a point from b and a point from r.

FT

md.max_distance_to_rectangle ( | Query_item b, Kd_tree_rectangle<Traits> r)

|  | Returns the maximal distance between the iso-box b and a point from r furthest to b.

### See Also

GeneralDistance.