# Volume computation

### 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 |

`byComponents` |
Logical, if FALSE (default) |

`indexAlpha` |
A single value or vector with the indexes of |

### 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).

### See Also

`ashape3d`

, `components_ashape3d`

### Examples

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)
``` |

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