# dirichletWeights

##### Compute Quadrature Weights Based on Dirichlet Tessellation

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`

.

##### See Also

##### Examples

```
# NOT RUN {
Q <- quadscheme(runifpoispp(10))
X <- as.ppp(Q) # data and dummy points together
w <- dirichletWeights(X, exact=FALSE)
# }
```

*Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)*