# dirichlet.weights

##### 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

`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. - ...
- 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 `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.

##### Value

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

.

##### See Also

##### Examples

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

*Documentation reproduced from package spatstat, version 1.10-3, License: GPL version 2 or newer*