# volume_ashape3d: Volume computation In alphashape3d: Implementation of the 3D Alpha-Shape for the Reconstruction of 3D Sets from a Point Cloud

## Description

This function calculates the volume of the α-shape of a given sample of points in the three-dimensional space.

## Usage

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

## Arguments

 `as3d` An object of class `"ashape3d"` that represents the α-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 α-shape. If TRUE, `volume_ashape3d` computes the volume of each connected component of the α-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 α-shape for each value of α in `as3d\$alpha[indexAlpha]` when `indexAlpha` is numeric.

If `indexAlpha="all"` or `indexAlpha="ALL"` then the function computes the volume of the α-shape for all values of α in `as3d\$alpha`.

## Value

If `indexAlpha` is a single value then the function returns the volume of the α-shape (if the argument `byComponents` is set to FALSE) or a vector with the volumes of each connected component of the α-shape (if the argument `byComponents` is set to TRUE).

Otherwise `volume_ashape3d` returns a list (each object in the list as described above).

`ashape3d`, `components_ashape3d`
 ``` 1 2 3 4 5 6 7 8 9 10``` ```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) ```