spatstat.geom (version 3.2-9)

delaunay: Delaunay Triangulation of Point Pattern

Description

Computes the Delaunay triangulation of a spatial point pattern.

Usage

delaunay(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.

Arguments

X

Spatial point pattern (object of class "ppp").

Author

Adrian Baddeley , Rolf Turner and Ege Rubak .

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.

See Also

tess, dirichlet, convexhull.xy, ppp, delaunayDistance, delaunayNetwork.

Examples

  X <- runifrect(42)
  plot(delaunay(X))
  plot(X, add=TRUE)