\name{discpartarea}
\Rdversion{1.1}
\alias{discpartarea}
\title{
Area of Part of Disc
}
\description{
Compute area of intersection between a disc and a window
}
\usage{
discpartarea(X, r, W=as.owin(X))
}
\arguments{
\item{X}{
Point pattern (object of class \code{"ppp"})
specifying the centres of the discs.
Alternatively, \code{X} may be in any format
acceptable to \code{\link{as.ppp}}.
}
\item{r}{
Matrix, vector or numeric value specifying the
radii of the discs.
}
\item{W}{
Window (object of class \code{"owin"}) with which the
discs should be intersected.
}
}
\details{
This algorithm computes the exact area of the intersection between
a window \code{W} and a disc (or each of several discs).
The centres of the discs are specified by the point pattern
\code{X}, and their radii are specified by \code{r}.
If \code{r} is a single numeric value, then the algorithm computes the
area of intersection between \code{W} and the disc of radius \code{r} centred
at each point of \code{X}, and returns a one-column matrix
containing one entry for each point of \code{X}.
If \code{r} is a vector of length \code{m}, then the algorithm
returns an \code{n * m} matrix in which the entry on row \code{i},
column \code{j} is the area of the
intersection between \code{W} and the disc centred at \code{X[i]}
with radius \code{r[j]}.
If \code{r} is a matrix, it should have one row for each point in
\code{X}. The algorithm
returns a matrix in which the entry on row \code{i},
column \code{j} is the area of the
intersection between \code{W} and the disc centred at \code{X[i]}
with radius \code{r[i,j]}.
Areas are computed by analytic geometry.
}
\value{
Numeric matrix, with one row for each point of \code{X}.
}
\seealso{
\code{\link{owin}},
\code{\link{disc}}
}
\examples{
data(letterR)
X <- runifpoint(3, letterR)
discpartarea(X, 0.2)
}
\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{math}