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polarzonoid

This is the git repository for the package polarzonoid on CRAN.

Overview

In each odd dimension is a convex body - the polar zonoid - whose generating functions are trigonometric polynomials. The polar zonoid is a straightforward generalization of the polar zonohedron in dimension 3, as defined by Chilton and Coxeter (1963). The package has some applications of the polar zonoid, including the properties of configuration spaces of arcs on the circle and 3x3 rotation matrices. There is also a root solver for trigonometric polynomials.

In other contexts, i.e. the theory of convex bodies, the term "polar zonoid" is short for "polar of a zonoid", which is an entirely different concept.

Installation

install.packages("polarzonoid")

Getting help

If you encounter a bug, please file an issue with a minimal reproducible example on GitHub. Or, write me using my email address on the CRAN page for the package.

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Install

install.packages('polarzonoid')

Monthly Downloads

245

Version

0.2-0

License

GPL (>= 2)

Issues

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Maintainer

Glenn Davis

Last Published

August 26th, 2025

Functions in polarzonoid (0.2-0)

rotation

The homeomorphism between balanced configurations and rotation matrices
arcs and sphere

The Homeomorphism between the Space of \(n\) or fewer arcs, and the sphere \(\mathbb{S}^{2n}\)
support

The Support Function for the Polar Zonoid in \(\mathbb{R}^{2n+1}\)
boundary and sphere

The Homeomorphism between the Boundary of the Polar Zonoid in \(\mathbb{R}^{2n+1}\) and the sphere \(\mathbb{S}^{2n}\)
plotarcs

plot a collection of arcs
arc disjointness

arc disjointness
slerp

Spherical Linear Interpolation (slerp) on the Unit Sphere
polarzonoid-package

The Polar Zonoid \(Z_n \) in \(\mathbb{R}^{2n+1}\)
arcs and boundary

The Homeomorphism between the Space of \(n\) or fewer arcs, and the boundary of the Polar Zonoid
arc operations

Boolean arc operations, and also the distance between two collections of arcs.
trigpolyroot

compute roots of a trigonometric polynomial