spatstat (version 1.31-3)

delaunay: 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 "ppp").

Value

• A tessellation (object of class "tess"). The window of the tessellation is the convex hull of X, not the original window of X.

Details

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.

See Also

tess, dirichlet, convexhull.xy, ppp

Examples

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