# discpartarea: Area of Part of Disc

### Description

Compute area of intersection between a disc and a window

### Usage

 `1` ```discpartarea(X, r, W=as.owin(X)) ```

### Arguments

 `X` Point pattern (object of class `"ppp"`) specifying the centres of the discs. Alternatively, `X` may be in any format acceptable to `as.ppp`. `r` Matrix, vector or numeric value specifying the radii of the discs. `W` Window (object of class `"owin"`) with which the discs should be intersected.

### Details

This algorithm computes the exact area of the intersection between a window `W` and a disc (or each of several discs). The centres of the discs are specified by the point pattern `X`, and their radii are specified by `r`.

If `r` is a single numeric value, then the algorithm computes the area of intersection between `W` and the disc of radius `r` centred at each point of `X`, and returns a one-column matrix containing one entry for each point of `X`.

If `r` is a vector of length `m`, then the algorithm returns an `n * m` matrix in which the entry on row `i`, column `j` is the area of the intersection between `W` and the disc centred at `X[i]` with radius `r[j]`.

If `r` is a matrix, it should have one row for each point in `X`. The algorithm returns a matrix in which the entry on row `i`, column `j` is the area of the intersection between `W` and the disc centred at `X[i]` with radius `r[i,j]`.

Areas are computed by analytic geometry.

### Value

Numeric matrix, with one row for each point of `X`.

### Author(s)

and \rolf

`owin`, `disc`

### Examples

 ```1 2 3``` ``` data(letterR) X <- runifpoint(3, letterR) discpartarea(X, 0.2) ```

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