R: Delaunay Triangulation of Point Pattern

delaunay {spatstat.geom} | R Documentation

## Delaunay Triangulation of Point Pattern

### Description

Computes the Delaunay triangulation of a spatial point pattern.

### Usage

    delaunay(X)

### Arguments

`X` | Spatial point pattern (object of class `"ppp"`).

### Details

The Delaunay triangulation of a spatial point pattern `X` is defined as follows. First the Dirichlet/Voronoi tessellation of `X` computed; see `dirichlet`. Then two points of `X` are defined to be Delaunay neighbours if their Dirichlet/Voronoi tiles share a common boundary. Every pair of Delaunay neighbours is joined by a straight line. The result is a tessellation, consisting of disjoint triangles. The union of these triangles is the convex hull of `X`.

### Value

A tessellation (object of class `"tess"`). The window of the tessellation is the convex hull of `X`, not the original window of `X`.

### 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

`tess`, `dirichlet`, `convexhull.xy`, `ppp`, `delaunayDistance`, `delaunayNetwork`.

### Examples

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

[Package spatstat.geom version 2.3-2 Index]