R: Dirichlet Tessellation of Point Pattern

dirichlet {spatstat.geom} | R Documentation

## Dirichlet Tessellation of Point Pattern

### Description

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 deldir.

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"`).

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### See Also

`tess`, `delaunay`, `ppp`, `dirichletVertices`

### Examples

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

[Package spatstat.geom version 2.3-2 Index]