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.

A Delaunay triangulation fulfills the empty circle property (also called Delaunay property): the circumscribing circle of any facet of the triangulation contains no data point in its interior. For a point set with no subset of four co-circular points the Delaunay triangulation is unique. A similar property holds for tetrahedralisation in three dimensions.

External links

• The CGAL project on computational geometry

References

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