# delaunayDistance

0th

Percentile

##### Distance on Delaunay Triangulation

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

Keywords
manip, spatial
##### 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.

delaunay, delaunayNetwork

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

Documentation reproduced from package spatstat, version 1.57-1, License: GPL (>= 2)

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