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

CGAL 4.8 - Optimal Distances

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PolytopeDistanceDTraits Concept Reference
Concepts

## Definition

This concept defines the requirements for traits classes of \( d\)-dimensional optimisation algorithms.

Has Models:

  `CGAL::Polytope_distance_d_traits_2<K,ET,NT>`

  `CGAL::Polytope_distance_d_traits_3<K,ET,NT>`

  `CGAL::Polytope_distance_d_traits_d<K,ET,NT>`

See Also
  `CGAL::Polytope_distance_d<Traits>`

## Types
typedef unspecified_type | Point_d
| point type used to represent the input points.
typedef unspecified_type | Rep_tag
| compile time tag to distinguish between Cartesian and homogeneous representation of the input points. More...
typedef unspecified_type | RT
| number type used to represent the coordinates of the input points. More...
typedef unspecified_type | FT
| number type used to return either the squared radius of the smallest enclosing sphere or annulus, or the squared distance of the polytopes. More...
typedef unspecified_type | Access_dimension_d
| data accessor object used to access the dimension of the input points.
typedef unspecified_type | Access_coordinates_begin_d
| data accessor object used to access the coordinates of the input points.
typedef unspecified_type | Construct_point_d
| constructor object used to construct either the center of the smallest enclosing sphere or annulus, or the points realizing the distance between the two polytopes.

## Special types
The following two number types are only needed for `CGAL::Min_annulus_d<Traits>` and `CGAL::Polytope_distance_d<Traits>`.
typedef unspecified_type | ET
| exact number type used to do the exact computations in the underlying solver for linear programs. More...
typedef unspecified_type | NT
| fast (possibly inexact) number type used to speed up the pricing step in the underlying solver for linear programs. More...

## Creation
Only default and copy constructor are required.
| PolytopeDistanceDTraits ()
| PolytopeDistanceDTraits (const PolytopeDistanceDTraits &)

## Operations
The following functions just return the corresponding function class object.
Access_dimension_d | access_dimension_d_object () const
Access_coordinates_begin_d | access_coordinates_begin_d_object () const
Construct_point_d | construct_point_d_object () const

## Member Typedef Documentation

typedef unspecified_type PolytopeDistanceDTraits::ET

exact number type used to do the exact computations in the underlying solver for linear programs.

It has to to be a model for `RingNumberType`. There must be an implicit conversion from `RT` to `ET` available.

typedef unspecified_type PolytopeDistanceDTraits::FT

number type used to return either the squared radius of the smallest enclosing sphere or annulus, or the squared distance of the polytopes.

`FT` has to be either `RT` or `CGAL::``Quotient<RT>` if the input points have Cartesian or homogeneous representation, respectively (cf. `Rep_tag`).

typedef unspecified_type PolytopeDistanceDTraits::NT

fast (possibly inexact) number type used to speed up the pricing step in the underlying solver for linear programs.

It has to be a model for `RingNumberType`. There must be implicit conversions from `RT` to `NT` and from `NT` to `ET` available.

typedef unspecified_type PolytopeDistanceDTraits::Rep_tag

compile time tag to distinguish between Cartesian and homogeneous representation of the input points.

`Rep_tag` has to be either `CGAL::``Cartesian_tag` or `CGAL::``Homogeneous_tag`.

typedef unspecified_type PolytopeDistanceDTraits::RT

number type used to represent the coordinates of the input points.

It has to be a model for `RingNumberType`.