dilated.areas.Rd
\name{dilated.areas}
\Rdversion{1.1}
\alias{dilated.areas}
\title{
Areas of Morphological Dilations
}
\description{
Computes the areas of successive morphological dilations.
}
\usage{
dilated.areas(X, r, W=as.owin(X), ..., constrained=TRUE, exact = FALSE)
}
\arguments{
\item{X}{
Object to be dilated.
A point pattern (object of class \code{"ppp"}),
a line segment pattern (object of class \code{"psp"}),
or a window (object of class \code{"owin"}).
}
\item{r}{
Numeric vector of radii for the dilations.
}
\item{W}{
Window (object of class \code{"owin"}) inside which the areas
will be computed, if \code{constrained=TRUE}.
}
\item{\dots}{Ignored.}
\item{constrained}{
Logical flag indicating whether areas should be restricted
to the window \code{W}.
}
\item{exact}{
Logical flag indicating whether areas should be computed
using analytic geometry (which is slower but more accurate).
Currently available only when \code{X} is a point pattern.
}
}
\details{
This function computes the areas of the dilations of \code{X}
by each of the radii \code{r[i]}. Areas may also be computed
inside a specified window \code{W}.
The morphological dilation of a set \eqn{X} by a distance \eqn{r > 0}
is the subset
consisting of all points \eqn{x}{x} such that the
distance from \eqn{x} to \eqn{X} is less than
or equal to \eqn{r}.
When \code{X} is a point pattern, the dilation by a distance
\eqn{r} is the union of
discs of radius \eqn{r} centred at the points of \code{X}.
The argument \code{r} should be a vector of nonnegative numbers.
If \code{exact=TRUE} and if \code{X} is a point pattern,
then the areas are computed using analytic geometry, which is
slower but much more accurate. Otherwise the computation is performed
using \code{\link{distmap}}.
To compute the dilated object itself, use \code{\link{dilation}}.
}
\seealso{
\code{\link{owin}},
\code{\link{as.owin}},
\code{\link{dilation}},
\code{\link{eroded.areas}}
}
\examples{
X <- runifpoint(10)
a <- dilated.areas(X, c(0.1,0.2), W=square(1), exact=TRUE)
}
\author{\adrian
and \rolf
}
\keyword{spatial}
\keyword{math}