R: Distance on Delaunay Triangulation

delaunayDistance {spatstat} | R Documentation

## Distance on Delaunay Triangulation

### Description

Computes the graph distance in the Delaunay triangulation of a point pattern.

### Usage

    delaunayDistance(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 graph distance in the Delaunay triangulation between two points `X[i]` and `X[j]` is the minimum number of edges of the Delaunay triangulation that must be traversed to go from `X[i]` to `X[j]`.

This command returns a matrix `D` such that `D[i,j]` is the graph distance between `X[i]` and `X[j]`.

### Value

A symmetric square matrix with integer entries.

### 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

`delaunay`, `delaunayNetwork`

### Examples

      X <- runifpoint(20)
      M <- delaunayDistance(X)
      plot(delaunay(X), lty=3)
      text(X, labels=M[1, ], cex=2)

[Package spatstat version 1.54-0 Index]