# delaunay

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##### Delaunay Triangulation of Point Pattern

Computes the Delaunay triangulation of a spatial point pattern.

Keywords
manip, spatial
##### Usage
delaunay(X)
##### Arguments
X

Spatial point pattern (object of class "ppp").

##### Details

The Delaunay triangulation of a spatial point pattern X is defined as follows. First the Dirichlet/Voronoi tessellation of X computed; see dirichlet. Then two points of X are defined to be Delaunay neighbours if their Dirichlet/Voronoi tiles share a common boundary. Every pair of Delaunay neighbours is joined by a straight line. The result is a tessellation, consisting of disjoint triangles. The union of these triangles is the convex hull of X.

##### Value

A tessellation (object of class "tess"). The window of the tessellation is the convex hull of X, not the original window of X.

tess, dirichlet, convexhull.xy, ppp, delaunayDistance, delaunayNetwork

• delaunay
##### Examples
# NOT RUN {
X <- runifpoint(42)
plot(delaunay(X))