Difference between revisions of "Dirichlet tesselation"
From Encyclopedia of Mathematics
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''Voronoi tesselation, Dirichlet–Voronoi tesselation, Dirichlet–Voronoi decomposition, Thiessen tesselation'' | ''Voronoi tesselation, Dirichlet–Voronoi tesselation, Dirichlet–Voronoi decomposition, Thiessen tesselation'' | ||
| − | The Dirichlet tesselation defined by a set | + | The Dirichlet tesselation defined by a set $S$ of points in $\mathbf R^n$ is the same as the [[Voronoi diagram|Voronoi diagram]] of that set $S$. If $S$ is a [[Lattice|lattice]], it is also called the Dirichlet–Voronoi tiling. The straight-line dual of the Dirichlet tesselation is the [[Delaunay triangulation|Delaunay triangulation]]. |
See also [[Decomposition|Decomposition]]. | See also [[Decomposition|Decomposition]]. | ||
Latest revision as of 19:53, 29 April 2014
Voronoi tesselation, Dirichlet–Voronoi tesselation, Dirichlet–Voronoi decomposition, Thiessen tesselation
The Dirichlet tesselation defined by a set $S$ of points in $\mathbf R^n$ is the same as the Voronoi diagram of that set $S$. If $S$ is a lattice, it is also called the Dirichlet–Voronoi tiling. The straight-line dual of the Dirichlet tesselation is the Delaunay triangulation.
See also Decomposition.
How to Cite This Entry:
Dirichlet tesselation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dirichlet_tesselation&oldid=31996
Dirichlet tesselation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dirichlet_tesselation&oldid=31996