DelaunayLiftedTraits_d Concept Reference

Definition

Deprecated:

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

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

Has Models:

CGAL::Cartesian_d<FT,LA>

CGAL::Homogeneous_d<RT,LA>

Types
typedef unspecified_type	Point_d
	the dD point type on which the Delaunay algorithm operates
typedef unspecified_type	Hyperplane_d
	a dD plane
typedef unspecified_type	Vector_d
	a dD vector
typedef unspecified_type	Ray_d
	a dD ray
typedef unspecified_type	RT
	a arithmetic ring type
typedef unspecified_type	Construct_vector_d
	Function object type that provides Vector_d operator()(int d, CGAL::Null_vector), which constructs and returns the null vector.
typedef unspecified_type	Construct_hyperplane_d
	Function object type that provides Hyperplane_d operator()(ForwardIterator first, ForwardIterator last, Point_d p, CGAL::Oriented_side side), which constructs and returns a hyperplane passing through the points in tuple[first,last) and oriented such that p is on the side side of the returned hyperplane.
typedef unspecified_type	Vector_to_point_d
	Function object type that provides Point_d operator()(Vector_d v), which constructs and returns the point defined by \( 0+v\).
typedef unspecified_type	Point_to_vector_d
	Function object type that provides Vector_d operator()(Point_d v), which constructs and returns the vector defined by \( p-0\).
typedef unspecified_type	Orientation_d
	Function object type that provides Orientation operator()(ForwardIterator first, ForwardIterator last), which determines the orientation of the points tuple[first,last).
typedef unspecified_type	Orthogonal_vector_d
	Function object type that provides Vector_d operator()(Hyperplane_d h), which constructs and returns a vector orthogonal to h and pointing from the boundary into its positive halfspace.
typedef unspecified_type	Oriented_side_d
	Predicate object type that provides Oriented_side operator()(Hyperplane_d h, Point_d p), which determines the oriented side of p with respect to h.
typedef unspecified_type	Has_on_positive_side_d
	Predicate object type that provides bool operator()(Hyperplane_d h, Point_d p), which return true iff p lies in the positive halfspace determined by h.
typedef unspecified_type	Affinely_independent_d
	Predicate object type that provides bool operator()(ForwardIterator first, ForwardIterator last), which determines if the points tuple[first,last) are affinely independent.
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	Contained_in_affined_hull_d
	Predicate object type that provides bool operator()(ForwardIterator first, ForwardIterator last, Point_d p), which determines if p is contained in the affine hull of the points in tuple[first,last).
typedef unspecified_type	Intersect_d
	Predicate object type that provides Object operator()(Ray_d r, Hyperplane_d h), which determines if r and h intersect and returns the corresponding polymorphic object.
The previous requirements are all identical to the requirements of concept ConvexHullTraits_d. The Delaunay class adds the following requirements.
typedef unspecified_type	Project_along_d_axis_d
	Predicate object type that provides DelaunayTraits_d::Point_d operator()(Point_d p), which determines the \( d-1\)-dimensional point from the \( d\)-dimensional point \( p\) while discarding the last coordinate.
typedef unspecified_type	Lift_to_paraboloid_d
	Predicate object type that provides Point_d operator()(DelaunayTraits_d::Point_d p), which determines the \( d\)-dimensional point from the \( d-1\)-dimensional point \( p\) while lifting it to the paraboloid of revolution.
typedef unspecified_type	Component_accessor_d
	Predicate object type that provides RT homogeneous(Vector_d v,int i) and int dimension(Vector_d v), where the former determines the \( i\)th coordinate of \( v\) and the latter the dimension of \( v\).

Creation
	DelaunayLiftedTraits_d ()
	A default constructor and copy constructor is required.

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_vector_d	construct_vector_d_object ()

Member Typedef Documentation

Construct_hyperplane_d

typedef unspecified_type DelaunayLiftedTraits_d::Construct_hyperplane_d

Function object type that provides Hyperplane_d operator()(ForwardIterator first, ForwardIterator last, Point_d p, CGAL::Oriented_side side), which constructs and returns a hyperplane passing through the points in tuple[first,last) and oriented such that p is on the side side of the returned hyperplane.

When side==ON_ORIENTED_BOUNDARY then any hyperplane containing the tuple is returned.