volume_ashape3d: Volume computation

Description

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)

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).

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.

Examples

Run this code


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)