spherize: spherize a zonotope

In zonohedra: Compute and Plot Zonohedra from Vector Generators

spherize a zonotope

Description

The input is a zonotope with a best-fit ellipsoid (or ellipse for a zonogon) with axes that may have very different lengths. The function computes a spherizing matrix W, and then transforms the zonotope so its boundary is close to a sphere.

Usage

## S3 method for class 'zonotope'
spherize( x, method='ZCA', ... )

Arguments

x	a zonotope object - a zonohedron, a zonogon, or a zonoseg.
method	for computing the matrix W, either 'ZCA' or 'PCA-COR'. Matching is partial and case-insensitive.
...	not used

Details

The 2 methods are taken from Kessy, et. al..

Value

After computing the matrix W, the function return lintransform(x,W). The "sphering" attribute is set to W.
If x is a 1D zonoseg, sphering is not really possible, so the function prints a warning message and returns x. In case of error, the function returns NULL.

References

Agnan Kessy, Alex Lewin, Korbinian Strimmer. Optimal whitening and decorrelation.
https://arxiv.org/abs/1512.00809 v4 2016.

See Also

lintransform()

zonohedra documentation built on April 3, 2025, 8:11 p.m.