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Difference between revisions of "Dirichlet tesselation"

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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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d120/d120210/d1202101.png" /> of points in <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d120/d120210/d1202102.png" /> is the same as the [[Voronoi diagram|Voronoi diagram]] of that set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d120/d120210/d1202103.png" />. If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d120/d120210/d1202104.png" /> 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]].
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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=12620