Editing Delaunay simplexes
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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 | 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 triangulation fulfils 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 fulfils 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. | ||