dirichletWeights.Rd
\name{dirichletWeights}
\alias{dirichletWeights}
\title{Compute Quadrature Weights Based on Dirichlet Tessellation}
\description{
Computes quadrature weights for a given set of points,
using the areas of tiles in the Dirichlet tessellation.
}
\usage{
dirichletWeights(X, window=NULL, exact=TRUE, \dots)
}
\arguments{
\item{X}{Data defining a point pattern.}
\item{window}{Default window for the point pattern}
\item{exact}{Logical value. If \code{TRUE}, compute exact areas
using the package \code{deldir}. If \code{FALSE}, compute
approximate areas using a pixel raster.
}
\item{\dots}{
Ignored.
}
}
\value{
Vector of nonnegative weights for each point in \code{X}.
}
\details{
This function computes a set of quadrature weights
for a given pattern of points
(typically comprising both ``data'' and `dummy'' points).
See \code{\link{quad.object}} for an explanation of quadrature
weights and quadrature schemes.
The weights are computed using the Dirichlet tessellation.
First \code{X} and (optionally) \code{window} are converted into a
point pattern object. Then the Dirichlet tessellation of the points
of \code{X} is computed.
The weight attached to a point of \code{X} is the area of
its Dirichlet tile (inside the window \code{Window(X)}).
If \code{exact=TRUE} the Dirichlet tessellation is computed exactly
by the Lee-Schachter algorithm using the package \code{deldir}.
Otherwise a pixel raster approximation is constructed and the areas
are approximations to the true weights. In all cases the sum of the
weights is equal to the area of the window.
}
\seealso{
\code{\link{quad.object}},
\code{\link{gridweights}}
}
\examples{
Q <- quadscheme(runifpoispp(10))
X <- as.ppp(Q) # data and dummy points together
w <- dirichletWeights(X, exact=FALSE)
}
\author{\adrian
and \rolf
}
\keyword{spatial}
\keyword{utilities}