12 citations · 30 across the 12 of their papers we have counts for
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Quadratic Motion Polynomials With Irregular Factorizations
Daren A. Thimm, Zijia Li, Hans-Peter Schröcker +1
Motion polynomials are a specific type of polynomial over a Clifford algebra that can conveniently describe rational motions. There exists an algorithm for the factorization of mot…
Quadratic Spinor Polynomials with Infinitely Many Factorizations
Zijia Li, Hans-Peter Schröcker, Johannes Siegele +1
Spinor polynomials are polynomials with coefficients in the even sub-algebra of conformal geometric algebra whose norm polynomial is real. They describe rational conformal motions.…
A Geometric Algorithm for the Factorization of Spinor Polynomials
Zijia Li, Hans-Peter Schröcker, Johannes Siegele
We present a new algorithm to decompose generic spinor polynomials into linear factors. Spinor polynomials are certain polynomials with coefficients in the geometric algebra of dim…
The Study Variety of Conformal Kinematics
Bahar Kalkan, Zijia Li, Hans-Peter Schröcker +1
We introduce the Study variety of conformal kinematics and investigate some of its properties. The Study variety is a projective variety of dimension ten and degree twelve in real…
Factorization of Quaternionic Polynomials of Bi-Degree (n,1)
Johanna Lercher, Daniel F. Scharler, Hans-Peter Schröcker +1
We consider polynomials of bi-degree over the skew field of quaternions where the indeterminates commute with each other and with all coefficients. Polynomials of this type…
Factorization of Dual Quaternion Polynomials Without Study's Condition
Johannes Siegele, Martin Pfurner, Hans-Peter Schröcker
In this paper we investigate factorizations of polynomials over the ring of dual quaternions into linear factors. While earlier results assume that the norm polynomial is real ("mo…
Quadratic Split Quaternion Polynomials: Factorization and Geometry
Daniel F. Scharler, Johannes Siegele, Hans-Peter Schröcker
We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric inte…
Rational Motions with Generic Trajectories of Low Degree
Johannes Siegele, Daniel F. Scharler, Hans-Peter Schröcker
The trajectories of a rational motion given by a polynomial of degree n in the dual quaternion model of rigid body displacements are generically of degree 2n. In this article we st…