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Computes the Delaunay triangulation of a spatial point pattern.
delaunay(X)A tessellation (object of class "tess"). The window of the
tessellation is the convex hull of X, not the original window
of X.
Spatial point pattern (object of class "ppp").
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner rolfturner@posteo.net and Ege Rubak rubak@math.aau.dk.
The Delaunay triangulation of a spatial point pattern X
is defined as follows. First the Dirichlet/Voronoi tessellation
based on X is computed; see dirichlet. This
tessellation is extended to cover the entire two-dimensional plane.
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 to make the Delaunay triangulation.
The result is a tessellation, consisting of
disjoint triangles. The union of these triangles is the convex hull of
X.
tess,
dirichlet,
convexhull.xy,
ppp,
delaunayDistance,
delaunayNetwork.
X <- runifrect(42)
plot(delaunay(X))
plot(X, add=TRUE)
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