Distance on Delaunay Triangulation
Computes the graph distance in the Delaunay triangulation of a point pattern.
delaunayDistance(X)
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.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
delaunay,
delaunayNetwork.
X <- runifrect(20) M <- delaunayDistance(X) plot(delaunay(X), lty=3) text(X, labels=M[1, ], cex=2)
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