PolytopeDistanceDTraits Concept Reference

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

ET

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.

FT

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).

NT

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.

Rep_tag

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.

RT

typedef unspecified_type PolytopeDistanceDTraits::RT

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

It has to be a model for RingNumberType.