Delaunay triangulation
From Encyclopedia of Mathematics
Delone triangulation
A very important geometric structure in computational geometry, named after B.N. Delaunay.
Let 
be a generic set of 
points in 
. The straight-line dual of the Voronoi diagram generated by 
is a triangulation of 
, called the Delaunay triangulation and usually denoted by 
. The Delaunay triangulation of 
is triangulation of the convex hull of 
in 
and the set of vertices of 
is 
.
One of the equivalent definitions for 
is as follows: 
is a triangulation of 
satisfying the "empty sphere propertyempty sphere property" , i.e. no 
-simplex of the triangulation of its circumsphere has a point of 
in its interior.
References
| [a1] | F.P. Preparata, M.I. Shamos, "Computational geometry: an introduction" , Springer (1985) |
| [a2] | H. Edelsbrunner, "Algorithms in combinatorial geometry" , Springer (1987) |
| [a3] | A. Okabe, B. Boots, K. Sugihara, "Spatial tessellations: concepts and applications of Voronoi diagrams" , Wiley (1992) |
How to Cite This Entry:
Delaunay triangulation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Delaunay_triangulation&oldid=12570
Delaunay triangulation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Delaunay_triangulation&oldid=12570
This article was adapted from an original article by O.R. Musin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article