Delaunay simplexes

An example of Delaunay triangulation in two-dimensions

A Delaunay simplex is the dual of the Voronoi diagram. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions $({\mathbb {R} }^{2})$ it is more commonly known as Delaunay triangulation, and in three-dimensions $({\mathbb {R} }^{3})$, as Delaunay tetrahedralisation.

The Delaunay triangulation fulfills the empty circle property: the circumscribing circle of each facet of such a triangulation does not contain any other vertex of the triangulation in its interior (a similar property holds for the tetrahedralisation).

References

1. Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.

External links

1. The CGAL project on computational geometry