# areaGain: Difference of Disc Areas In spatstat.geom: Geometrical Functionality of the 'spatstat' Family

## Description

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

## Usage

 ```1 2``` ``` areaGain(u, X, r, ..., W=as.owin(X), exact=FALSE, 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. `...` Arguments passed to `distmap` to determine the pixel resolution, when `exact=FALSE`. `W` Window (object of class `"owin"`) in which the area should be computed. `exact` Choice of algorithm. If `exact=TRUE`, areas are computed exactly using analytic geometry. If `exact=FALSE` then a faster algorithm is used to compute a discrete approximation to the areas. `ngrid` Integer. Number of points in the square grid used to compute the discrete approximation, when `exact=FALSE`.

## 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`.

## Value

A matrix with one row for each point in `u` and one column for each value in `r`.

## Author(s)

and \rolf

`AreaInter`, `areaLoss`
 ```1 2``` ``` u <- c(0.5,0.5) areaGain(u, cells, 0.1) ```