https://github.com/cran/spatstat
Tip revision: 266eff5f191cc8b0835e6d7323f680723aebab99 authored by Adrian Baddeley on 06 December 2011, 07:00:35 UTC
version 1.25-0
version 1.25-0
Tip revision: 266eff5
rcell.Rd
\name{rcell}
\alias{rcell}
\title{Simulate Baddeley-Silverman Cell Process}
\description{
Generates a random point pattern, a simulated realisation of the
Baddeley-Silverman cell process model.
}
\usage{
rcell(win=square(1), nx, ny=nx, dx=NULL, dy=NULL)
}
\arguments{
\item{win}{
A window.
An object of class \code{\link{owin}},
or data in any format acceptable to \code{\link{as.owin}()}.
}
\item{dx}{Width of the cells. Incompatible with \code{nx}.
}
\item{dy}{Height of the cells.
Incompatible with \code{ny}.
}
\item{nx}{Number of columns of cells in the window.
Incompatible with \code{dx}.
}
\item{ny}{Number of rows of cells in the window.
Incompatible with \code{dy}.
}
}
\value{
A point pattern (object of class \code{"ppp"}).
}
\details{
This function generates a simulated realisation of the \dQuote{cell process}
(Baddeley and Silverman, 1984), a random point process
with the same second-order properties as the uniform Poisson process.
In particular, the \eqn{K} function of this process is identical to
the \eqn{K} function of the uniform Poisson process (aka Complete
Spatial Randomness). The same holds for the pair correlation function
and all other second-order properties.
The cell process is a counterexample to the claim that the
\eqn{K} function completely characterises a point pattern.
A cell process is generated by dividing space into equal rectangular
tiles. In each tile, a random number \eqn{N} of points is placed,
where \eqn{N} takes the values \eqn{0}, \eqn{1} and \eqn{10}
with probabilities \eqn{1/10}, \eqn{8/9} and \eqn{1/90} respectively.
The points within a tile are independent and uniformly distributed in
that tile, and the numbers of points in different tiles are
independent random integers.
In the function \code{rcell} the tile dimensions are determined
by the quantities \code{dx, dy}
if they are present. If they are absent, then the grid spacing is
determined so that there will be \code{nx} columns and \code{ny} rows
of tiles in the bounding rectangle of \code{win}.
The cell process is then generated in these tiles.
Some of the resulting random points may lie outside the window \code{win}:
if they do, they are deleted.
The result is a point pattern inside the window \code{win}.
}
\seealso{
\code{\link{rstrat}},
\code{\link{rsyst}},
\code{\link{runifpoint}},
\code{\link{Kest}}
}
\examples{
X <- rcell(nx=15)
plot(X)
plot(Kest(X))
}
\references{
Baddeley, A.J. and Silverman, B.W. (1984)
A cautionary example on the use of second-order methods for analyzing
point patterns. \emph{Biometrics} \bold{40}, 1089-1094.
}
\author{Adrian Baddeley
\email{Adrian.Baddeley@csiro.au}
\url{http://www.maths.uwa.edu.au/~adrian/}
and Rolf Turner
\email{r.turner@auckland.ac.nz}
}
\keyword{spatial}
\keyword{datagen}