R: Compute Quadrature Weights Based on Dirichlet Tessellation

dirichletWeights {spatstat.geom} | R Documentation

## 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

     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)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### See Also

`quad.object`, `gridweights`

### Examples

      Q <- quadscheme(runifrect(10))
      X <- as.ppp(Q) # data and dummy points together
      w <- dirichletWeights(X, exact=FALSE)

[Package spatstat.geom version 2.3-2 Index]