Delaunay simplexes: Difference between revisions

From SklogWiki
Jump to navigation Jump to search
m (Fixed DOI)
m (Placed external links at foot of page.)
Line 3: Line 3:


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.
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==
*[http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/packages.html#part_VIII The CGAL project on computational geometry]
==References==
==References==
#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.
#Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.
#[http://dx.doi.org/10.1007/11424758_84 A. V. Anikeenko, M. L. Gavrilova and N. N. Medvedev "A Novel Delaunay Simplex Technique for Detection of Crystalline Nuclei in Dense Packings of Spheres", Lecture Notes in Computer Science '''3480''' pp. 816-826 (2005)]
#[http://dx.doi.org/10.1007/11424758_84 A. V. Anikeenko, M. L. Gavrilova and N. N. Medvedev "A Novel Delaunay Simplex Technique for Detection of Crystalline Nuclei in Dense Packings of Spheres", Lecture Notes in Computer Science '''3480''' pp. 816-826 (2005)]
==External links==
*[http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/packages.html#part_VIII The CGAL project on computational geometry]
[[category: mathematics]]
[[category: mathematics]]

Revision as of 19:28, 11 December 2008

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 it is more commonly known as Delaunay triangulation, and in three-dimensions , 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.

References

  1. Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.
  2. A. V. Anikeenko, M. L. Gavrilova and N. N. Medvedev "A Novel Delaunay Simplex Technique for Detection of Crystalline Nuclei in Dense Packings of Spheres", Lecture Notes in Computer Science 3480 pp. 816-826 (2005)

External links