CGAL 5.3 - 2D Triangulations on the Sphere
DelaunayTriangulationOnSphereTraits_2 Concept Reference

## 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. More...

typedef unspecified_type Construct_circumcenter_3
Construction object type. More...

## Operations

Construct_circumcenter_on_sphere_2 construct_circumcenter_on_sphere_2_object ()

Construct_circumcenter_3 construct_circumcenter_3_object ()

## ◆ 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

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.