Compute Quadrature Weights Based on Dirichlet Tessellation
Computes quadrature weights for a given set of points, using the areas of tiles in the Dirichlet tessellation.
dirichlet.weights(X, window=NULL, exact=TRUE, ...)
- Data defining a point pattern.
- Default window for the point pattern
- Logical value. If
TRUE, compute exact areas using the package
FALSE, compute approximate areas using a pixel raster.
This function computes a set of quadrature weights
for a given pattern of points
(typically comprising both ``data'' and `dummy'' points).
quad.object for an explanation of quadrature
weights and quadrature schemes.
The weights are computed using the Dirichlet tessellation.
X and (optionally)
window are converted into a
point pattern object. Then the Dirichlet tessellation of the points
X is computed.
The weight attached to a point of
X is the area of
its Dirichlet tile (inside the window
exact=TRUE the Dirichlet tessellation is computed exactly
by the Lee-Schachter algorithm using the package
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.
- Vector of nonnegative weights for each point in
Q <- quadscheme(runifpoispp(10)) X <- as.ppp(Q) # data and dummy points together w <- dirichlet.weights(X, exact=FALSE)