Description Usage Arguments Details Value Author(s) See Also Examples

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

1 |

`X` |
Spatial point pattern (object of class |

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]`

.

A symmetric square matrix with integer entries.

and \ege

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

```
Loading required package: nlme
Loading required package: rpart
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").
```

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