Factorization of Motion Polynomials

TL;DR

This paper investigates the factorization of monic, bounded motion polynomials, providing algorithms to compute such factorizations, including one that guarantees an optimal degree, advancing the mathematical tools for motion analysis.

Contribution

The paper introduces two algorithms for factorizing monic, bounded motion polynomials, one simpler and one optimal in degree, expanding the methods for polynomial factorization in motion analysis.

Findings

Existence of factorizations after multiplication with a real polynomial.

Two algorithms for polynomial factorization, one simpler and one with optimal degree.

Algorithms applicable to motion polynomial analysis and synthesis.

Abstract

In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real polynomial and provide algorithms for computing polynomial factor and factorizations. The first algorithm is conceptually simpler but may require a high degree of the polynomial factor. The second algorithm gives an optimal degree.