# default.expand

##### Default Expansion Rule for Simulation of Model

Defines the default expansion window or expansion rule for simulation of a fitted point process model.

##### Usage

`default.expand(object, m=2, epsilon=1e-6)`

##### Arguments

- object
- A point process model (object of class
`"ppm"`

or`"rmhmodel"`

). - m
- A single numeric value.
The window will be expanded by a distance
`m * reach(object)`

along each side. - epsilon
- Threshold argument passed to
`reach`

to determine`reach(object)`

.

##### Details

This function computes a default value for the
expansion rule (the argument `expand`

in `rmhcontrol`

)
given a fitted point process model `object`

.
This default is used by `envelope`

,
`qqplot.ppm`

, `simulate.ppm`

and other functions.

Suppose we wish to generate simulated realisations
of a fitted point process model inside a window `w`

.
It is advisable to first simulate
the pattern on a larger window, and then clip it to the original
window `w`

. This avoids edge effects in the simulation.
It is called *expansion* of the simulation window.
Accordingly, for the Metropolis-Hastings simulation algorithm
`rmh`

, the algorithm control parameters specified by
`rmhcontrol`

include an argument `expand`

that
determines the expansion of the simulation window.

The function `default.expand`

determines the default expansion
rule for a fitted point process model `object`

.
If the model is Poisson, then no expansion is necessary.
No expansion is performed by default,
and `default.expand`

returns a rule representing no expansion.
The simulation window is the original window `w = as.owin(object)`

.
If the model depends on external covariates (i.e. covariates other than
the Cartesian covariates `x`

and `y`

and the `marks`

)
then no expansion is feasible, in general, because the spatial domain
of the covariates is not guaranteed to be large enough.
`default.expand`

returns a rule representing no expansion.
The simulation window is the original window `w = as.owin(object)`

.

If the model depends on the Cartesian covariates `x`

and `y`

,
it would be feasible to expand the simulation window, and this was the
default for *not* to expand if the model depends
on `x`

or `y`

.
Again `default.expand`

returns a rule representing no expansion.
Otherwise, expansion will occur.
The original window `w = as.owin(object)`

is expanded by
a distance `m * rr`

, where
`rr`

is the interaction range of the model, computed by
`reach`

. If `w`

is a rectangle then
each edge of `w`

is displaced outward by distance `m * rr`

.
If `w`

is not a rectangle then `w`

is dilated by
distance `m * rr`

using `dilation`

.

##### Value

- A window expansion rule (object of class
`"rmhexpand"`

).

##### See Also

##### Examples

```
data(cells)
fit <- ppm(cells, ~1, Strauss(0.07))
default.expand(fit)
mod <- rmhmodel(cif="strauss", par=list(beta=100, gamma=0.5, r=0.07))
default.expand(fit)
```

*Documentation reproduced from package spatstat, version 1.27-0, License: GPL (>= 2)*