\name{rMatClust}
\alias{rMatClust}
\title{Simulate Matern Cluster Process}
\description{
Generate a random point pattern using the
Mat\'ern Cluster Process.
}
\usage{
rMatClust(kappa, r, mu, win = owin(c(0,1),c(0,1)))
}
\arguments{
\item{kappa}{
Intensity of the Poisson process of cluster centres.
A single positive number, a function, or a pixel image.
}
\item{r}{
Radius parameter of the clusters.
}
\item{mu}{
Mean number of points per cluster.
}
\item{win}{
Window in which to simulate the pattern.
An object of class \code{"owin"}
or something acceptable to \code{\link{as.owin}}.
}
}
\value{
The simulated point pattern (an object of class \code{"ppp"}).
Additionally, some intermediate results of the simulation are
returned as attributes of this point pattern.
See \code{\link{rNeymanScott}}.
}
\details{
This algorithm generates a realisation of Mat\'ern's cluster process
inside the window \code{win}. The process is constructed by first
generating a Poisson point process of ``parent'' points
with intensity \code{kappa}. Then each parent point is
replaced by a random cluster of points, the number of points in each
cluster being random with a Poisson (\code{mu}) distribution,
and the points being placed independently and uniformly inside
a disc of radius \code{r} centred on the parent point.
In this implementation, parent points are not restricted to lie in the
window; the parent process is effectively the uniform
Poisson process on the infinite plane.
}
\seealso{
\code{\link{rpoispp}},
\code{\link{rNeymanScott}}
}
\examples{
pp <- rMatClust(10, 0.05, 4)
}
\author{Adrian Baddeley
\email{adrian@maths.uwa.edu.au}
\url{http://www.maths.uwa.edu.au/~adrian/}
and Rolf Turner
\email{rolf@math.unb.ca}
\url{http://www.math.unb.ca/~rolf}
}
\keyword{spatial}
\keyword{datagen}