\name{rsyst}
\alias{rsyst}
\title{Simulate systematic random point pattern}
\description{
Generates a ``systematic random'' pattern of points in a window,
consisting of a grid of equally-spaced points with a random common
displacement.
}
\usage{
rsyst(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}{Spacing of grid points in \eqn{x} direction.
Incompatible with \code{nx}.
}
\item{dy}{Spacing of grid points in \eqn{y} direction.
Incompatible with \code{ny}.
}
\item{nx}{Number of columns of grid points in the window.
Incompatible with \code{dx}.
}
\item{ny}{Number of rows of grid points in the window.
Incompatible with \code{dy}.
}
}
\value{
A point pattern (object of class \code{"ppp"}).
}
\details{
This function generates a \dQuote{systematic random} pattern of points
in the window \code{win}. The pattern consists of a rectangular grid
of points with a random common displacement.
The grid spacing is determined by the distances \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 grid points in the bounding rectangle of \code{win}.
The grid is then given a random displacement (the common displacement
of the grid points is a uniformly distributed random vector in the
tile of dimensions \code{dx, dy}).
Some of the resulting grid 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}.
This function is useful in creating dummy points for quadrature
schemes (see \code{\link{quadscheme}}) as well as in simulating
random point patterns.
}
\seealso{
\code{\link{rstrat}},
\code{\link{runifpoint}},
\code{\link{quadscheme}}
}
\examples{
X <- rsyst(nx=10)
plot(X)
# polygonal boundary
data(letterR)
X <- rsyst(letterR, 5, 10)
plot(X)
}
\author{Adrian Baddeley
\email{adrian@maths.uwa.edu.au}
\url{http://www.maths.uwa.edu.au/~adrian/}
and Rolf Turner
\email{r.turner@auckland.ac.nz}
}
\keyword{spatial}
\keyword{datagen}