Delaunay simplexes: Difference between revisions
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[[Image:Delaunay.png|thumb|An example of Delaunay triangulation in two-dimensions]] | [[Image:Delaunay.png|thumb|An example of Delaunay triangulation in two-dimensions]] | ||
A '''Delaunay simplex''' is the dual of the [[Voronoi cells |Voronoi diagram]]. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions <math>({\mathbb R}^2)</math> it is more commonly known as ''Delaunay triangulation'', and in three-dimensions <math>({\mathbb R}^3)</math>, as ''Delaunay tetrahedralisation''. | A '''Delaunay simplex''' is the dual of the [[Voronoi cells |Voronoi diagram]]. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions <math>({\mathbb R}^2)</math> it is more commonly known as ''Delaunay triangulation'', and in three-dimensions <math>({\mathbb R}^3)</math>, as ''Delaunay tetrahedralisation''. Delaunay triangulation fulfils the so called '''empty circle property''', i.e. | ||
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 tetrahedralisation in three dimensions. | |||
==External links== | |||
the circumscribing circle of each facet of such a triangulation does not contain any other vertex of the triangulation in its interior | *[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. | ||
[[category: mathematics]] | |||
Revision as of 15:55, 13 September 2007
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. Delaunay triangulation fulfils the so called empty circle property, i.e. 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 tetrahedralisation in three dimensions.
External links
References
- Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.