dirichletWeights: 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, ...)
Arguments
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.
Value
Vector of nonnegative weights for each point in X.
Details
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.