# volume_ashape3d

##### Volume computation

This function calculates the volume of the \(\alpha\)-shape of a given sample of points in the three-dimensional space.

##### Usage

`volume_ashape3d(as3d, byComponents = FALSE, indexAlpha = 1)`

##### Arguments

- as3d
An object of class

`"ashape3d"`

that represents the \(\alpha\)-shape of a given sample of points in the three-dimensional space, see`ashape3d`

.- byComponents
Logical, if FALSE (default)

`volume_ashape3d`

computes the volume of the whole \(\alpha\)-shape. If TRUE,`volume_ashape3d`

computes the volume of each connected component of the \(\alpha\)-shape separately.- indexAlpha
A single value or vector with the indexes of

`as3d$alpha`

that should be used for the computation, see Details.

##### Details

The function `volume_ashape3d`

computes the volume of the
\(\alpha\)-shape for each value of \(\alpha\) in
`as3d$alpha[indexAlpha]`

when `indexAlpha`

is numeric.

If `indexAlpha="all"`

or `indexAlpha="ALL"`

then the function
computes the volume of the \(\alpha\)-shape for all values of \(\alpha\)
in `as3d$alpha`

.

##### Value

If `indexAlpha`

is a single value then the function returns the
volume of the \(\alpha\)-shape (if the argument `byComponents`

is set
to FALSE) or a vector with the volumes of each connected component of the
\(\alpha\)-shape (if the argument `byComponents`

is set to TRUE).

Otherwise `volume_ashape3d`

returns a list (each object in the list as
described above).

##### See Also

##### Examples

```
# NOT RUN {
C1 <- matrix(runif(6000), nc = 3)
C2 <- matrix(runif(6000), nc = 3) + 2
x <- rbind(C1, C2)
ashape3d.obj <- ashape3d(x, alpha = 0.75)
plot(ashape3d.obj, byComponents = TRUE)
# Compute the volume of the alpha-shape
volume_ashape3d(ashape3d.obj)
# Compute the volumes of the connected components of the alpha-shape
volume_ashape3d(ashape3d.obj, byComponents = TRUE)
# }
```

*Documentation reproduced from package alphashape3d, version 1.3, License: GPL-2*