R: Simulate Baddeley-Silverman Cell Process

rcell {spatstat} | R Documentation

## 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=NULL, ny=nx, ..., dx=NULL, dy=dx,
           N=10, nsim=1, drop=TRUE)

### Arguments

`win` | A window. An object of class `owin`, or data in any format acceptable to `as.owin()`.
`nx` | Number of columns of cells in the window. Incompatible with `dx`.
`ny` | Number of rows of cells in the window. Incompatible with `dy`.
`...` | Ignored.
`dx` | Width of the cells. Incompatible with `nx`.
`dy` | Height of the cells. Incompatible with `ny`.
`N` | Integer. Distributional parameter: the maximum number of random points in each cell. Passed to `rcellnumber`.
`nsim` | Number of simulated realisations to be generated.
`drop` | Logical. If `nsim=1` and `drop=TRUE` (the default), the result will be a point pattern, rather than a list containing a point pattern.

### 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 of random points is placed. By default, there are either 0, 1 or 10 points, 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.

The tile width is determined either by the number of columns `nx` or by the horizontal spacing `dx`. The tile height is determined either by the number of rows `ny` or by the vertical spacing `dy`. The cell process is then generated in these tiles. The random numbers of points are generated by `rcellnumber`.

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`.

### Value

A point pattern (an object of class `"ppp"`) if `nsim=1`, or a list of point patterns if `nsim > 1`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### 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.

### See Also

`rcellnumber`, `rstrat`, `rsyst`, `runifpoint`, `Kest`

### Examples

      X <- rcell(nx=15)
      plot(X)
      plot(Kest(X))

[Package spatstat version 1.54-0 Index]