# dilated.areas

##### Areas of Morphological Dilations

Computes the areas of successive morphological dilations.

##### Usage

`dilated.areas(X, r, W=as.owin(X), ..., constrained=TRUE, exact = FALSE)`

##### Arguments

- X
Object to be dilated. A point pattern (object of class

`"ppp"`

), a line segment pattern (object of class`"psp"`

), or a window (object of class`"owin"`

).- r
Numeric vector of radii for the dilations.

- W
Window (object of class

`"owin"`

) inside which the areas will be computed, if`constrained=TRUE`

.- …
Arguments passed to

`distmap`

to control the pixel resolution, if`exact=FALSE`

.- constrained
Logical flag indicating whether areas should be restricted to the window

`W`

.- exact
Logical flag indicating whether areas should be computed using analytic geometry (which is slower but more accurate). Currently available only when

`X`

is a point pattern.

##### Details

This function computes the areas of the dilations of `X`

by each of the radii `r[i]`

. Areas may also be computed
inside a specified window `W`

.

The morphological dilation of a set \(X\) by a distance \(r > 0\) is the subset consisting of all points \(x\) such that the distance from \(x\) to \(X\) is less than or equal to \(r\).

When `X`

is a point pattern, the dilation by a distance
\(r\) is the union of
discs of radius \(r\) centred at the points of `X`

.

The argument `r`

should be a vector of nonnegative numbers.

If `exact=TRUE`

and if `X`

is a point pattern,
then the areas are computed using analytic geometry, which is
slower but much more accurate. Otherwise the computation is performed
using `distmap`

.

To compute the dilated object itself, use `dilation`

.

##### See Also

##### Examples

```
# NOT RUN {
X <- runifpoint(10)
a <- dilated.areas(X, c(0.1,0.2), W=square(1), exact=TRUE)
# }
```

*Documentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)*