# areaGain

##### Difference of Disc Areas

Computes the area of that part of a disc that is not covered by other discs.

##### Usage

`areaGain(u, X, r, W=NULL, ngrid=spatstat.options("ngrid.disc"))`

##### Arguments

- u
- Coordinates of the centre of the disc of interest.
A vector of length 2.
Alternatively, a point pattern (object of class
`"ppp"`

). - X
- Locations of the centres of other discs.
A point pattern (object of class
`"ppp"`

). - r
- Disc radius, or vector of disc radii.
- W
- Optional. Window (object of class
`"owin"`

) in which the area should be computed. - ngrid
- Dimensions of the
`ngrid * ngrid`

array of test points that will be used to estimate the uncovered area.

##### Details

This function computes the area of that part of
the disc of radius `r`

centred at the location `u`

that is *not* covered by any of the discs of radius `r`

centred at the points of the pattern `X`

.
This area is important in some calculations related to
the area-interaction model `AreaInter`

.

If `u`

is a point pattern and `r`

is a vector,
the result is a matrix, with one row for each point in `u`

and one column for each entry of `r`

. The `[i,j]`

entry
in the matrix is the area of that part of the disc of radius
`r[j]`

centred at the location `u[i]`

that is
*not* covered by any of the discs of radius `r[j]`

centred at the points of the pattern `X`

.

If `W`

is not `NULL`

, then the areas are computed only
inside the window `W`

. Currently this is implemented only for
rectangular windows.

The area is calculated by discrete approximation, using an
`ngrid * ngrid`

grid of test points.

##### Value

- A matrix with one row for each point in
`u`

and one column for each value in`r`

.

##### See Also

##### Examples

```
data(cells)
u <- c(0.5,0.5)
areaGain(u, cells, 0.1)
```

*Documentation reproduced from package spatstat, version 1.17-1, License: GPL (>= 2)*