| delaunay {spatstat.geom} | R Documentation |
Delaunay Triangulation of Point Pattern
Description
Computes the Delaunay triangulation of a spatial point pattern.
Usage
delaunay(X)
Arguments
X |
Spatial point pattern (object of class |
Details
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.
Value
A tessellation (object of class "tess"). The window of the
tessellation is the convex hull of X, not the original window
of X.
Author(s)
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner rolfturner@posteo.net and Ege Rubak rubak@math.aau.dk.
See Also
tess,
dirichlet,
convexhull.xy,
ppp,
delaunayDistance,
delaunayNetwork.
Examples
X <- runifrect(42)
plot(delaunay(X))
plot(X, add=TRUE)