# lineardirichlet

##### Dirichlet Tessellation on a Linear Network

Given a point pattern on a linear network, compute the Dirichlet (or Voronoi or Thiessen) tessellation induced by the points.

##### Usage

`lineardirichlet(X)`

##### Arguments

- X
Point pattern on a linear network (object of class

`"lpp"`

).

##### Details

The Dirichlet tessellation induced by a point pattern `X`

on a linear network `L`

is a partition of `L`

into subsets. The subset `L[i]`

associated with the data point `X[i]`

is the part of `L`

lying closer to `X[i]`

than to any other data point `X[j]`

,
where distance is measured by the shortest path.

##### Value

A tessellation on a linear network
(object of class `"lintess"`

).

##### Missing tiles

If the linear network is not connected, and if one of the connected
components contains no data points, then the Dirichlet tessellation
is mathematically undefined inside this component.
The resulting tessellation object includes
a tile with label `NA`

, which contains this component of the network.
A plot of the tessellation will not show this tile.

##### See Also

##### Examples

```
# NOT RUN {
X <- runiflpp(5, simplenet)
plot(lineardirichlet(X), lwd=3)
points(X)
# }
```

*Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)*