areaGain.Rd
\name{areaGain}
\alias{areaGain}
\title{Difference of Disc Areas}
\description{
Computes the area of that part of a disc
that is not covered by other discs.
}
\usage{
areaGain(u, X, r, ..., W=as.owin(X), exact=FALSE,
ngrid=spatstat.options("ngrid.disc"))
}
\arguments{
\item{u}{
Coordinates of the centre of the disc of interest.
A vector of length 2.
Alternatively, a point pattern (object of class \code{"ppp"}).
}
\item{X}{
Locations of the centres of other discs.
A point pattern (object of class \code{"ppp"}).
}
\item{r}{
Disc radius, or vector of disc radii.
}
\item{\dots}{Ignored.}
\item{W}{
Window (object of class \code{"owin"})
in which the area should be computed.
}
\item{exact}{
Choice of algorithm.
If \code{exact=TRUE}, areas are computed exactly using
analytic geometry. If \code{exact=FALSE} then a faster algorithm
is used to compute a discrete approximation to the areas.
}
\item{ngrid}{
Integer. Number of points in the square grid used to compute
the discrete approximation, when \code{exact=FALSE}.
}
}
\value{
A matrix with one row for each point in \code{u}
and one column for each value in \code{r}.
}
\details{
This function computes the area of that part of
the disc of radius \code{r} centred at the location \code{u}
that is \emph{not} covered by any of the discs of radius \code{r}
centred at the points of the pattern \code{X}.
This area is important in some calculations related to
the area-interaction model \code{\link{AreaInter}}.
If \code{u} is a point pattern and \code{r} is a vector,
the result is a matrix, with one row for each point in \code{u}
and one column for each entry of \code{r}. The \code{[i,j]} entry
in the matrix is the area of that part of the disc of radius
\code{r[j]} centred at the location \code{u[i]} that is
\emph{not} covered by any of the discs of radius \code{r[j]}
centred at the points of the pattern \code{X}.
If \code{W} is not \code{NULL}, then the areas are computed only
inside the window \code{W}.
}
\seealso{
\code{\link{AreaInter}},
\code{\link{areaLoss}}
}
\examples{
data(cells)
u <- c(0.5,0.5)
areaGain(u, cells, 0.1)
}
\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{math}