# rMaternII

##### Simulate Matern Model II

Generate a random point pattern, a simulated realisation of the

##### Usage

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

##### Arguments

- 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`

. - 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`

).

##### Details

This algorithm generates a realisation of `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

The difference between

##### Value

- The simulated point pattern (an object of class
`"ppp"`

).

##### See Also

##### Examples

```
X <- rMaternII(20, 0.05)
Y <- rMaternII(20, 0.05, stationary=FALSE)
```

*Documentation reproduced from package spatstat, version 1.31-2, License: GPL (>= 2)*