# delaunay.distance

From spatstat v1.31-2
by Adrian Baddeley

##### Distance on Delaunay Triangulation

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

##### Usage

`delaunay.distance(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.

##### See Also

##### Examples

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

*Documentation reproduced from package spatstat, version 1.31-2, License: GPL (>= 2)*

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