spatstat.geom (version 2.1-0)

# 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, ntile, …, window=NULL, verbose=FALSE, npix=NULL, areas=NULL)`

## Arguments

X

Data defining a point pattern.

ntile

Number of tiles in each row and column of the rectangular grid. An integer vector of length 1 or 2.

Ignored.

window

Default window for the point pattern

verbose

Logical flag. If `TRUE`, information will be printed about the computation of the grid weights.

npix

Dimensions of pixel grid to use when computing a digital approximation to the tile areas.

areas

Vector of areas of the tiles, if they are already known.

## 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 `ntile[1] * ntile[2]` 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.

For non-rectangular windows the tile areas are currently calculated by approximating the window as a binary mask. The accuracy of this approximation is controlled by `npix`, which becomes the argument `dimyx` of `as.mask`.

`quad.object`, `dirichletWeights`
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