Computes quadrature weights for a given set of points, using the areas of tiles in the Dirichlet tessellation.

`dirichletWeights(X, window=NULL, exact=TRUE, …)`

X

Data defining a point pattern.

window

Default window for the point pattern

exact

Logical value. If `TRUE`

, compute exact areas
using the package `deldir`

. If `FALSE`

, compute
approximate areas using a pixel raster.

…

Ignored.

Vector of nonnegative weights for each point in `X`

.

This function computes a set of quadrature weights
for a given pattern of points
(typically comprising both ``data'' and `dummy'' points).
See `quad.object`

for an explanation of quadrature
weights and quadrature schemes.

The weights are computed using the Dirichlet tessellation.
First `X`

and (optionally) `window`

are converted into a
point pattern object. Then the Dirichlet tessellation of the points
of `X`

is computed.
The weight attached to a point of `X`

is the area of
its Dirichlet tile (inside the window `Window(X)`

).

If `exact=TRUE`

the Dirichlet tessellation is computed exactly
by the Lee-Schachter algorithm using the package `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.

# NOT RUN { Q <- quadscheme(runifrect(10)) X <- as.ppp(Q) # data and dummy points together w <- dirichletWeights(X, exact=FALSE) # }