Distance on Delaunay Triangulation
Computes the graph distance in the Delaunay triangulation of a point pattern.
- Spatial point pattern (object of class
The Delaunay triangulation of a spatial point pattern
is defined as follows. First the Dirichlet/Voronoi tessellation of
dirichlet. Then two points of
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
is the minimum number of edges of the Delaunay triangulation
that must be traversed to go from
This command returns a matrix
D such that
D[i,j] is the graph distance
- A symmetric square matrix with integer entries.
X <- runifpoint(20) M <- delaunay.distance(X) plot(delaunay(X), lty=3) text(X, labels=M[1, ], cex=2)