rpoisDirichletTess: Poisson Dirichlet Tessellation

In spatstat.random: Random Generation Functionality for the 'spatstat' Family

Poisson Dirichlet Tessellation

Description

Generate a random tessellation of a given spatial region, using the Dirichlet tessellation defined by a Poisson point process on the infinite plane.

Usage

rpoisDirichletTess(lambda, win = owin())

Arguments

lambda	Intensity of the Poisson point process. Either a single positive number, or a function which can be evaluated at any spatial location.
win	Window to be divided into tiles. An object of class "owin" or something acceptable to as.owin.

Details

This algorithm computes the Dirichlet-Voronoi tessellation of the window win induced by a Poisson point process on the infinite two-dimensional plane, avoiding edge effects.

The argument lambda is the intensity of the Poisson process. It should be either a single positive number, or a function(x,y) which can be evaluated at any spatial location (x,y).

The algorithm is a modification of Algorithm C_2 of Hinde and Miles (1980). It first generates a realisation of the Poisson process inside win, and computes the Dirichlet-Voronoi tessellation of this point pattern. Then in order to avoid edge effects, the algorithm calculates the maximum possible distance d outside the window such that a random point outside w could affect the outcome inside w. The window is expanded by this distance d; the realisation of the Poisson process in the expanded region is generated; and the Dirichlet-Voronoi tessellation of the augmented point pattern is computed, then restricted to the original window.

If lambda is a single number, the result is a realisation of a stationary random tessellation (restricted to win).

Value

A tessellation (object of class "tess").

Also has an attribute "X" containing the realisation of the Poisson point process (restricted to those points which affected the result).

Author(s)

\adrian

.

References

Hinde, A.L. and Miles, R.E. (1980) Monte Carlo estimates of the distribution of the random polygons of the Voronoi tessellation with respect to a Poisson process. J. Statist. Comput. Simul. 10, 205–223.

See Also

rpoislinetess

Examples

 A <- rpoisDirichletTess(10)
 X <- attr(A, "X")
 plot(Frame(X), type="n", main="rpoisDirichletTess(10)")
 plot(A, add=TRUE)
 plot(X, add=TRUE, pch=16)

spatstat.random documentation built on July 27, 2026, 9:09 a.m.