Distance on Delaunay Triangulation

Description

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

Usage

delaunayDistance(X)

Arguments

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)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

See Also

delaunay, delaunayNetwork.

Examples

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