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

CGAL 4.8 - dD Convex Hulls and Delaunay Triangulations

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DelaunayTraits_d Concept Reference
Concepts

## Definition

Deprecated:
  This package is deprecated since the version 4.6 of CGAL. The package dD Triangulations should be used instead.

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 ()