CGAL 5.3  Optimal Distances

This concept defines the requirements for traits classes of \( d\)dimensional optimisation algorithms.
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>
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  
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  
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 
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.
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
).
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.
number type used to represent the coordinates of the input points.
It has to be a model for RingNumberType
.