CGAL 5.4.4  2D Triangulations on the Sphere

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.
Constructions  
typedef unspecified_type  Construct_circumcenter_on_sphere_2 
Construction object type. More...  
typedef unspecified_type  Construct_circumcenter_3 
Construction object type. More...  
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 () 
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
.
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.
p
, q
, and r
.