gridweights: Compute Quadrature Weights Based on Grid Counts
Description
Computes quadrature weights for a given set of points,
using the ``counting weights'' for a grid of rectangular tiles.
Usage
gridweights(X, nx, ny, window=NULL)
Arguments
X
Data defining a point pattern.
nx
Number of tiles
in each row of the rectangular grid.
ny
Number of tiles
in each column of the rectangular grid.
window
Default window for the point pattern
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 by the ``counting weights'' rule
based on a regular grid of rectangular tiles.
First X and (optionally) window are converted into a
point pattern object. Then the bounding rectangle of the window of
the point pattern is
divided into a regular $nx \times ny$ grid of rectangular tiles.
The weight attached to a point of X is the area of the tile
in which it lies, divided by the number of points of X lying in
that tile.