spatstat (version 1.3-2)

# dirichlet.weights: 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

`dirichlet.weights(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.

## 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 `X\$window`).

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.

## See Also

`quad.object`, `gridweights`

## Examples

```library(spatstat)
Q <- quadscheme(runifpoispp(10))
X <- as.ppp(Q) # data and dummy points together
w <- dirichlet.weights(X, exact=FALSE)```