CGAL 5.5.2 - Bounding Volumes
MinSphereAnnulusDTraits Concept Reference

## Definition

This concept defines the requirements for traits classes of $$d$$-dimensional min sphere and min annulus algorithms.

Has Models:

CGAL::Min_sphere_annulus_d_traits_2<K,ET,NT>

CGAL::Min_sphere_annulus_d_traits_3<K,ET,NT>

CGAL::Min_sphere_annulus_d_traits_d<K,ET,NT>

CGAL::Min_sphere_d<Traits>
CGAL::Min_annulus_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 Number 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.

MinSphereAnnulusDTraits ()

MinSphereAnnulusDTraits (const MinSphereAnnulusDTraits &)

## 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

## ◆ 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.

## ◆ 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).

## ◆ 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.

## ◆ 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.

## ◆ RT

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

It has to be a model for RingNumberType.