# delaunay

##### Delaunay Triangulation of Point Pattern

Computes the Delaunay triangulation of a spatial point pattern.

##### 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`

.

##### See Also

`tess`

,
`dirichlet`

,
`convexhull.xy`

,
`ppp`

,
`delaunayDistance`

,
`delaunayNetwork`

##### Examples

```
# NOT RUN {
X <- runifpoint(42)
plot(delaunay(X))
plot(X, add=TRUE)
# }
```

*Documentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)*