\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5.1 - dD Convex Hulls and Delaunay Triangulations
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DelaunayTraits_d Concept Reference

Definition

Requirements of the first traits class to be used with the class CGAL::Delaunay_d.

Has Models:

CGAL::Cartesian_d<FT,LA>

CGAL::Homogeneous_d<RT,LA>

Public Member Functions

 DelaunayTraits_d ()
 A default constructor and copy constructor is required.
 

Types

typedef unspecified_type Point_d
 the dD point type on which the Delaunay algorithm operates
 
typedef unspecified_type Sphere_d
 a dD sphere
 
typedef unspecified_type FT
 an arithmetic field type
 
typedef unspecified_type Point_of_sphere_d
 Predicate object type that provides Point_d operator()(Sphere_d s, int i), which returns the \( i\)th point defining sphere s.
 
typedef unspecified_type Construct_sphere_d
 Predicate object type that provides Sphere_d operator()(int d, ForwardIterator first, ForwardIterator last), which returns a dD sphere through the points in tuple[first,last).
 
typedef unspecified_type Contained_in_simplex_d
 Predicate object type that provides bool operator()(ForwardIterator first, ForwardIterator last, Point_d p), which determines if p is contained in the closed simplex defined by the points in tuple[first,last).
 
typedef unspecified_type Squared_distance_d
 Predicate object type that provides FT operator()(Point_d p,Point_d q), which determines the squared distance from p to q.
 
typedef unspecified_type Affinely_independent_d
 Predicate object type that provides bool operator()(ForwardIterator first, ForwardIterator last), which determines if the points in tuple[first,last) are affinely independent.
 

Operations

For each of the above function and predicate object types, Func_obj_type, a function must exist with the name func_obj_type_object that creates an instance of the function or predicate object type.

For example:

Construct_sphere_d construct_sphere_d_object ()