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

`delaunayDistance(X)`

X

Spatial point pattern (object of class `"ppp"`

).

A symmetric square matrix with integer entries.

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]`

.

`delaunay`

,
`delaunayNetwork`

.

# NOT RUN { X <- runifrect(20) M <- delaunayDistance(X) plot(delaunay(X), lty=3) text(X, labels=M[1, ], cex=2) # }