# rMaternI

0th

Percentile

##### Simulate Matern Model I

Generate a random point pattern, a simulated realisation of the latex{Mat'ern}{Matern} Model I inhibition process model.

Keywords
spatial, datagen
##### Usage
rMaternI(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 latex{Mat'ern}{Matern}'s Model I 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.

A proposal point is then deleted if it lies within r units' distance of another proposal point. Otherwise it is retained. The retained points constitute latex{Mat'ern}{Matern}'s Model I.

##### Value

• The simulated point pattern (an object of class "ppp").

rpoispp, rMatClust
X <- rMaternI(20, 0.05)
Y <- rMaternI(20, 0.05, stationary=FALSE)