\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.12.2 - 2D Triangulation
DelaunayTriangulationTraits_2 Concept Reference

Definition

In addition to the requirements of the concept TriangulationTraits_2 the concept DelaunayTriangulationTraits_2 requires a predicate to check the empty circle property. The corresponding predicate type is called type Side_of_oriented_circle_2.

The additional types Line_2, Ray_2 and the constructor objects Construct_ray_2, Construct_circumcenter_2, Construct_bisector_2, Construct_midpoint are used to build the dual Voronoi diagram and are required only if the dual functions are called. The additional predicate type Compare_distance_2 is required if the method nearest_vertex() is used.

Refines:
TriangulationTraits_2
Has Models:

CGAL kernels

CGAL::Projection_traits_xy_3<K> (not for dual Voronoi functions)

CGAL::Projection_traits_yz_3<K> (not for dual Voronoi functions)

CGAL::Projection_traits_xz_3<K> (not for dual Voronoi functions)

See also
TriangulationTraits_2

Types

typedef unspecified_type Line_2
 The line type. More...
 
typedef unspecified_type Ray_2
 The type for ray. More...
 
typedef unspecified_type Side_of_oriented_circle_2
 A function object to perform an incircle test for a point and three other points. More...
 
typedef unspecified_type Compare_distance_2
 A function object to compare two distances for three points. More...
 
typedef unspecified_type Construct_circumcenter_2
 A function object to construct the circumcenter of three points. More...
 
typedef unspecified_type Construct_bisector_2
 A function object to construct the bisector of two points. More...
 
typedef unspecified_type Construct_ray_2
 A function object to build a ray from a point and a line. More...
 

Creation

 DelaunayTriangulationTraits_2 ()
 default constructor.
 
 DelaunayTriangulationTraits_2 (DelaunayTriangulationTraits_2 dtt)
 copy constructor
 
DelaunayTriangulationTraits_2 operator= (traits2)
 Assignment operator.
 

Access to Predicate and Constructor Objects

Side_of_oriented_circle_2 side_of_oriented_circle_2_object ()
 

The following functions are required only if member functions of the Delaunay triangulation relative to the dual Voronoi diagram are called.

Compare_distance_2 compare_distance_2_object ()
 
Construct_circumcenter_2 construct_circumcenter_2_object ()
 
Construct_bisector_2 construct_bisector_2_object ()
 
Construct_ray_2 construct_ray_2_object ()
 

Member Typedef Documentation

◆ Compare_distance_2

A function object to compare two distances for three points.

Provides the operator:

Comparison_result operator()(Point_2 p, Point_2 q, Point_2 r) which returns SMALLER, EQUAL or LARGER according to the distance between p and q being smaller, equal or larger than the distance between p and r. This type is only require if nearest_vertex queries are issued.

◆ Construct_bisector_2

A function object to construct the bisector of two points.

Provides the operator:

Line_2 operator()(Point_2 p, Point_2 q) which constructs the bisector line of points p and q. This type is required only if functions relative to the dual Voronoi diagram are called.

◆ Construct_circumcenter_2

A function object to construct the circumcenter of three points.

Provides the operator:

Point_2 operator()(Point_2 p, Point_2 q, Point_2 r) which returns the circumcenter of the three points p, q and r. This type is required only if functions relative to the dual Voronoi diagram are called.

◆ Construct_ray_2

A function object to build a ray from a point and a line.

Provides the operator:

Ray_2 operator() ( Point_2 p, Line_2 l);

◆ Line_2

The line type.

This type is required only if some dual functions are called.

◆ Ray_2

The type for ray.

This type is required only if some dual functions are called.

◆ Side_of_oriented_circle_2

A function object to perform an incircle test for a point and three other points.

Provides the operator:

Oriented_side operator()(Point p, Point q, Point r, Point s) which takes four points p, q, r, s as arguments and returns ON_POSITIVE_SIDE, ON_NEGATIVE_SIDE or, ON_ORIENTED_BOUNDARY according to the position of points s with respect to the oriented circle through p, q and r.