R: Vertices and Edges of Dirichlet Tessellation

dirichletVertices {spatstat} | R Documentation

## Vertices and Edges of Dirichlet Tessellation

### Description

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"`).

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

Rolf Turner r.turner@auckland.ac.nz

and Ege Rubak rubak@math.aau.dk

### See Also

`dirichlet`, `dirichletAreas`

### Examples

      plot(dirichlet(cells))

      plot(dirichletVertices(cells), add=TRUE)

      ed <- dirichletEdges(cells)

[Package spatstat version 1.63-3 Index]