# dirichletWeights: Compute Quadrature Weights Based on Dirichlet Tessellation In spatstat.geom: Geometrical Functionality of the 'spatstat' Family

## Description

Computes quadrature weights for a given set of points, using the areas of tiles in the Dirichlet tessellation.

## Usage

 `1` ``` dirichletWeights(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. `...` Ignored.

## 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 `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.

## Value

Vector of nonnegative weights for each point in `X`.

## Author(s)

and \rolf

`quad.object`, `gridweights`
 ```1 2 3``` ``` Q <- quadscheme(runifrect(10)) X <- as.ppp(Q) # data and dummy points together w <- dirichletWeights(X, exact=FALSE) ```