Dirichlet Tessellation of Point Pattern
Computes the Dirichlet tessellation of a spatial point pattern. Also known as the Voronoi or Thiessen tessellation.
dirichlet(X)
X |
Spatial point pattern (object of class |
In a spatial point pattern X, the Dirichlet tile associated
with a particular point X[i] is the region of space that is
closer to X[i] than to any other point in X. The
Dirichlet tiles divide the two-dimensional plane into disjoint
regions, forming a tessellation.
The Dirichlet tessellation is also known as the Voronoi or Thiessen tessellation.
This function computes the Dirichlet tessellation (within the original
window of X) using the function deldir
in the package deldir.
To ensure that there is a one-to-one correspondence between the
points of X and the tiles of dirichlet(X),
duplicated points in X should first be removed by
X <- unique(X, rule="deldir").
The tiles of the tessellation will be computed as polygons if the original window is a rectangle or a polygon. Otherwise the tiles will be computed as binary masks.
A tessellation (object of class "tess").
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
X <- runifrect(42) plot(dirichlet(X)) plot(X, add=TRUE)
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