# areaLoss: 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 3``` ``` areaLoss(X, r, ..., W=as.owin(X), subset=NULL, exact=FALSE, ngrid=spatstat.options("ngrid.disc")) ```

## Arguments

 `X` Locations of the centres of discs. A point pattern (object of class `"ppp"`). `r` Disc radius, or vector of disc radii. `...` Ignored. `W` Optional. Window (object of class `"owin"`) inside which the area should be calculated. `subset` Optional. Index identifying a subset of the points of `X` for which the area difference 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, for each point `X[i]` in `X` and for each radius `r`, the area of that part of the disc of radius `r` centred at the location `X[i]` that is not covered by any of the other discs of radius `r` centred at the points `X[j]` for `j` not equal to `i`. This area is important in some calculations related to the area-interaction model `AreaInter`.

The result is a matrix, with one row for each point in `X` and one column for each entry of `r`.

## Value

A matrix with one row for each point in `X` (or `X[subset]`) and one column for each value in `r`.

## Author(s)

and \rolf

`AreaInter`, `areaGain`, `dilated.areas`
 `1` ``` areaLoss(cells, 0.1) ```