spatstat (version 1.16-1)

# rcell: Simulate Baddeley-Silverman Cell Process

## Description

Generates a random point pattern, a simulated realisation of the Baddeley-Silverman cell process model.

## Usage

`rcell(win=square(1), nx, ny=nx, dx=NULL, dy=NULL)`

## Arguments

win
A window. An object of class `owin`, or data in any format acceptable to `as.owin()`.
dx
Width of the cells. Incompatible with `nx`.
dy
Height of the cells. Incompatible with `ny`.
nx
Number of columns of cells in the window. Incompatible with `dx`.
ny
Number of rows of cells in the window. Incompatible with `dy`.

## Value

• A point pattern (object of class `"ppp"`).

## Details

This function generates a simulated realisation of the cell process (Baddeley and Silverman, 1984), a random point process with the same second-order properties as the uniform Poisson process. In particular, the \$K\$ function of this process is identical to the \$K\$ function of the uniform Poisson process (aka Complete Spatial Randomness). The same holds for the pair correlation function and all other second-order properties. The cell process is a counterexample to the claim that the \$K\$ function completely characterises a point pattern. A cell process is generated by dividing space into equal rectangular tiles. In each tile, a random number \$N\$ of points is placed, where \$N\$ takes the values \$0\$, \$1\$ and \$10\$ with probabilities \$1/10\$, \$8/9\$ and \$1/90\$ respectively. The points within a tile are independent and uniformly distributed in that tile, and the numbers of points in different tiles are independent random integers.

In the function `rcell` the tile dimensions are determined by the quantities `dx, dy` if they are present. If they are absent, then the grid spacing is determined so that there will be `nx` columns and `ny` rows of tiles in the bounding rectangle of `win`. The cell process is then generated in these tiles.

Some of the resulting random points may lie outside the window `win`: if they do, they are deleted. The result is a point pattern inside the window `win`.

## References

Baddeley, A.J. and Silverman, B.W. (1984) A cautionary example on the use of second-order methods for analyzing point patterns. Biometrics 40, 1089-1094.

`rstrat`, `rsyst`, `runifpoint`, `Kest`
``````X <- rcell(nx=15)