# dirichletVertices

##### Vertices and Edges of Dirichlet Tessellation

Computes the Dirichlet-Voronoi tessellation of a point pattern and extracts the vertices or edges of the tiles.

##### Usage

`dirichletVertices(X)`dirichletEdges(X)

##### Arguments

- X
- Point pattern (object of class
`"ppp"`

).

##### Details

These function compute the Dirichlet-Voronoi tessellation of `X`

(see `dirichlet`

)
and extract the vertices or edges of the tiles of the tessellation.

The Dirichlet vertices are the spatial locations which are locally
farthest away from `X`

, that is, where the distance function
of `X`

reaches a local maximum.

The Dirichlet edges are the dividing lines equally distant between
a pair of points of `X`

.

The Dirichlet tessellation of `X`

is computed
using `dirichlet`

. The vertices or edges of all
tiles of the tessellation are extracted.

For `dirichletVertices`

, any vertex which
lies on the boundary of the window of `X`

is deleted.
The remaining vertices are returned, as a point pattern,
without duplicated entries.

##### Value

`dirichletVertices`

returns a point pattern (object of class`"ppp"`

) in the same window as`X`

.`dirichletEdges`

returns a line segment pattern (object of class`"psp"`

).

##### See Also

##### Examples

```
plot(dirichlet(cells))
plot(dirichletVertices(cells), add=TRUE)
ed <- dirichletEdges(cells)
```

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