A geometric algorithm for the factorization of rational motions in conformal three space

Abstract

Rational motions in conformal three space can be parametrized by polynomials with coefficients in a suitable Clifford algebra. We call them “spinor polynomials.” In this text we present a new algorithm to decompose generic spinor polynomials into linear factors. The factorization algorithm is based on the “kinematics at infinity”. Factorizations exist generically but not generally and are typically not unique. We prove that generic multiples of non-factorizable spinor polynomials admit factorizations and we demonstrate at hand of an example how our ideas can be used to tackle the hitherto unsolved problem of “factorizing” algebraic motions.