Delaunay Triangulation of Point Pattern
Computes the Delaunay triangulation of a spatial point pattern.
delaunay(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 result is a tessellation, consisting of
disjoint triangles. The union of these triangles is the convex hull of
X.
A tessellation (object of class "tess"). The window of the
tessellation is the convex hull of X, not the original window
of X.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
tess,
dirichlet,
convexhull.xy,
ppp,
delaunayDistance,
delaunayNetwork.
X <- runifrect(42) plot(delaunay(X)) plot(X, add=TRUE)
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