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.
dirichletWeights(X, window=NULL, exact=TRUE, ...)
X |
Data defining a point pattern. |
window |
Default window for the point pattern |
exact |
Logical value. If |
... |
Ignored. |
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.
Vector of nonnegative weights for each point in X.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
Q <- quadscheme(runifrect(10)) X <- as.ppp(Q) # data and dummy points together w <- dirichletWeights(X, exact=FALSE)
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