Generate a random point pattern, a simulated realisation of the Matern Model II inhibition process.

```
rMaternII(kappa, r, win = owin(c(0,1),c(0,1)), stationary=TRUE, ...,
nsim=1, drop=TRUE)
```

kappa

Intensity of the Poisson process of proposal points. A single positive number.

r

Inhibition distance.

win

Window in which to simulate the pattern.
An object of class `"owin"`

or something acceptable to `as.owin`

.
Alternatively a higher-dimensional box of class
`"box3"`

or `"boxx"`

.

stationary

Logical. Whether to start with a stationary process of proposal points
(`stationary=TRUE`

) or to generate the
proposal points only inside the window (`stationary=FALSE`

).

…

Ignored.

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.

A point pattern
if `nsim=1`

, or a list of point patterns if `nsim > 1`

.
Each point pattern is normally an object of class `"ppp"`

,
but may be of class `"pp3"`

or `"ppx"`

depending on the window.

This algorithm generates one or more realisations
of Matern's Model II
inhibition process inside the window `win`

.

The process is constructed by first
generating a uniform Poisson point process of ``proposal'' points
with intensity `kappa`

. If `stationary = TRUE`

(the
default), the proposal points are generated in a window larger than
`win`

that effectively means the proposals are stationary.
If `stationary=FALSE`

then the proposal points are
only generated inside the window `win`

.

Then each proposal point is marked by an ``arrival time'', a number uniformly distributed in \([0,1]\) independently of other variables.

A proposal point is deleted if it lies within `r`

units' distance
of another proposal point *that has an earlier arrival time*.
Otherwise it is retained.
The retained points constitute Matern's Model II.

The difference between Matern's Model I and II is the italicised statement above. Model II has a higher intensity for the same parameter values.

# NOT RUN { X <- rMaternII(20, 0.05) Y <- rMaternII(20, 0.05, stationary=FALSE) # }