Editing Delaunay triangulation (section)

==Relationship with the Voronoi diagram==
{{multiple image
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 | image1    = Delaunay_circumcircles_centers.svg
 | alt1      = Circumcircles in the Delaunay triangulation.
 | caption1  = The Delaunay triangulation with all the circumcircles and their centers (in red).

 | image2    = Delaunay_Voronoi.svg
 | alt2      = Connecting the triangulation's circumcenters gives the Voronoi diagram.
 | caption2  = Connecting the centers of the circumcircles produces the [[Voronoi diagram]] (in red).
}}
The Delaunay [[triangulation (geometry)|triangulation]] of a [[discrete space|discrete]] point set {{math|'''P'''}} in general position corresponds to the [[dual graph]] of the [[Voronoi diagram]] for {{math|'''P'''}}.
The [[circumscribed circle|circumcenter]]s of Delaunay triangles are the vertices of the Voronoi diagram.
In the 2D case, the Voronoi vertices are connected via edges, that can be derived from adjacency-relationships of the Delaunay triangles: If two triangles share an edge in the Delaunay triangulation, their circumcenters are to be connected with an edge in the Voronoi tesselation.

Special cases where this relationship does not hold, or is ambiguous, include cases like:
* Three or more [[Collinearity|collinear]] points, where the circumcircles are of infinite [[Radius|radii]].
* Four or more points on a perfect circle, where the triangulation is ambiguous and all circumcenters are trivially identical. In this case the Voronoi diagram contains vertices of degree four or greater and its dual graph contains polygonal faces with four or more sides. The various triangulations of these faces complete the various possible Delaunay triangulations.
*Edges of the Voronoi diagram going to infinity are not defined by this relation in case of a finite set {{math|'''P'''}}. If the Delaunay [[triangulation (geometry)|triangulation]] is calculated using the [[Bowyer–Watson algorithm]] then the circumcenters of triangles having a common vertex with the "super" triangle should be ignored. Edges going to infinity start from a circumcenter and they are perpendicular to the common edge between the kept and ignored triangle.