# delaunayDistance: Distance on Delaunay Triangulation In spatstat: Spatial Point Pattern Analysis, Model-Fitting, Simulation, Tests

## Description

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

## Usage

 `1` ```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)

and \ege

`delaunay`, `delaunayNetwork`

## Examples

 ```1 2 3 4``` ``` X <- runifpoint(20) M <- delaunayDistance(X) plot(delaunay(X), lty=3) text(X, labels=M[1, ], cex=2) ```

### Example output

```Loading required package: nlme

spatstat 1.52-1       (nickname: 'Apophenia')
For an introduction to spatstat, type 'beginner'

Note: R version 3.4.1 (2017-06-30) is more than 9 months old; we strongly recommend upgrading to the latest version

PLEASE NOTE:  The components "delsgs" and "summary" of the
object returned by deldir() are now DATA FRAMES rather than
matrices (as they were prior to release 0.0-18).
See help("deldir").

PLEASE NOTE: The process that deldir() uses for determining
duplicated points has changed from that used in version
0.0-9 of this package (and previously). See help("deldir").
```

spatstat documentation built on Jan. 10, 2019, 5:04 p.m.