# dirichlet

##### Dirichlet Tessellation of Point Pattern

Computes the Dirichlet tessellation of a spatial point pattern. Also known as the Voronoi or Thiessen tessellation.

##### Usage

`dirichlet(X)`

##### Arguments

- X
- Spatial point pattern (object of class
`"ppp"`

).

##### Details

In a spatial point pattern `X`

, the Dirichlet tile associated
with a particular point `X[i]`

is the region of space that is
closer to `X[i]`

than to any other point in `X`

. The
Dirichlet tiles divide the two-dimensional plane into disjoint
regions, forming a tessellation.

The Dirichlet tessellation is also known as the Voronoi or Thiessen tessellation.

This function computes the Dirichlet tessellation (within the original
window of `X`

) using the function `deldir`

in the package

To ensure that there is a one-to-one correspondence between the
points of `X`

and the tiles of `dirichlet(X)`

,
duplicated points in `X`

should first be removed by
`X <- unique(X, rule="deldir")`

.
The tiles of the tessellation will be computed as polygons
if the original window is a rectangle or a polygon.
Otherwise the tiles will be computed as binary masks.

##### Value

- A tessellation (object of class
`"tess"`

).

##### See Also

##### Examples

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

*Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)*