CGAL 5.6.3 - 2D Triangulations on the Sphere

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DelaunayTriangulationOnSphereTraits_2 Concept Reference
2D Triangulation on the Sphere Reference » Concepts

## Definition

Refines
  `TriangulationOnSphereTraits_2`

The concept `DelaunayTriangulationOnSphereTraits_2` describes the set of requirements to be fulfilled by any class used to instantiate the first template parameter of the class `CGAL::Delaunay_triangulation_on_sphere_2<Traits, Tds>`.

To the requirements listed within the concept `TriangulationOnSphereTraits_2`, this concept adds types and functors requirements related to build the dual on the sphere.

Has Models:

  `CGAL::Delaunay_triangulation_on_sphere_traits_2`

  `CGAL::Projection_on_sphere_traits_3`

## Constructions
typedef unspecified_type | Construct_circumcenter_on_sphere_2
| Construction object type.
typedef unspecified_type | Construct_circumcenter_3
| Construction object type.

## Operations
The following functions give access to the predicate and constructor objects.
Construct_circumcenter_on_sphere_2 | construct_circumcenter_on_sphere_2_object ()
Construct_circumcenter_3 | construct_circumcenter_3_object ()

## Member Typedef Documentation

## ◆ Construct_circumcenter_3

typedef unspecified_type DelaunayTriangulationOnSphereTraits_2::Construct_circumcenter_3

Construction object type.

Must provide the operator:

`Point_3 operator()(Point_3 p, Point_3 q, Point_3 r)`

which returns the center of the circle circumscribed to the face with vertices `p`, `q`, and `r`.

Note
  This type is only required for the computation of dual objects (Voronoi vertices and edges) and a dummy type can be used otherwise.

## ◆ Construct_circumcenter_on_sphere_2

typedef unspecified_type DelaunayTriangulationOnSphereTraits_2::Construct_circumcenter_on_sphere_2

Construction object type.

Must provide the operator:

`Point_on_sphere_2 operator()(Point_on_sphere_2 p, Point_on_sphere_2 q, Point_on_sphere_2 r)`

which returns the intersection of the dual of the face defined by the three points `p`, `q`, and `r`, and the sphere, on the positive side of the plane defined by `p`, `q`, and `r`. The dual of the face is the line orthogonal to the face, passing through the center of the smallest circumscribing sphere of the face.

Precondition
  the center of the sphere is on the negative side of the plane defined by `p`, `q`, and `r`.

Note
  This type is only required for the computation of dual objects (Voronoi vertices and edges) and a dummy type can be used otherwise.