# rHardcore

##### Perfect Simulation of the Hardcore Process

Generate a random pattern of points, a simulated realisation of the Hardcore process, using a perfect simulation algorithm.

##### Usage

`rHardcore(beta, R = 0, W = owin())`

##### Arguments

- beta
- intensity parameter (a positive number).
- R
- hard core distance (a non-negative number).
- W
- window (object of class
`"owin"`

) in which to generate the random pattern. Currently this must be a rectangular window.

##### Details

This function generates a realisation of the
Hardcore point process in the window `W`

using a

The Hardcore process is a model for strong spatial inhibition.
Two points of the process are forbidden to lie closer than
`R`

units apart.
The Hardcore process is the special case of the Strauss process
(see `rStrauss`

)
with interaction parameter $\gamma$ equal to zero.
The simulation algorithm used to generate the point pattern
is `rmh`

, whose output
is only approximately correct).

There is a tiny chance that the algorithm will run out of space before it has terminated. If this occurs, an error message will be generated.

##### Value

- A point pattern (object of class
`"ppp"`

).

##### References

Berthelsen, K.K. and Moller, J. (2002)
A primer on perfect simulation for spatial point processes.
*Bulletin of the Brazilian Mathematical Society* 33, 351-367.

Berthelsen, K.K. and Moller, J. (2003)
Likelihood and non-parametric Bayesian MCMC inference
for spatial point processes based on perfect simulation and
path sampling.
*Scandinavian Journal of Statistics* 30, 549-564.

Moller, J. and Waagepetersen, R. (2003).
*Statistical Inference and Simulation for Spatial Point Processes.*
Chapman and Hall/CRC.

##### See Also

##### Examples

```
X <- rHardcore(0.05,1.5,square(141.4))
Z <- rHardcore(100,0.05)
```

*Documentation reproduced from package spatstat, version 1.25-1, License: GPL (>= 2)*