# 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`

. - ...
- Ignored.
- 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

```
X <- runifpoint(10)
a <- dilated.areas(X, c(0.1,0.2), W=square(1), exact=TRUE)
```

*Documentation reproduced from package spatstat, version 1.23-2, License: GPL (>= 2)*