# delaunay

From spatstat v1.41-1
by Adrian Baddeley

##### 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`

,
`delaunay.distance`

,
`delaunay.network`

##### Examples

```
X <- runifpoint(42)
plot(delaunay(X))
plot(X, add=TRUE)
```

*Documentation reproduced from package spatstat, version 1.41-1, License: GPL (>= 2)*

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