12 citations · 13 across the 6 of their papers we have counts for
7 papers
Uniqueness of Maximal Inscribed Parabolas and Minimal Circumscribing Horocycles
Martin Lukarevski, Hans-Peter Schröcker
We prove existence of three unique ``max-exparabolas'' to a triangle. Each of these parabolas is internally tangent to one edge and the two other sides. Among all like parabolas, i…
Rational Motions of Minimal Quaternionic Degree with Prescribed Plane Trajectories
Zülal Derin Yaqub, Hans-Peter Schröcker
This paper investigates the construction of rational motions of a minimal quaternionic degree that generate a prescribed plane trajectory (a ``rational torse''). Using the algebrai…
A Multiplication Technique for the Factorization of Bivariate Quaternionic Polynomials
Johanna Lercher, Hans-Peter Schröcker
We consider bivariate polynomials over the skew field of quaternions, where the indeterminates commute with all coefficients and with each other. We analyze existence of univariate…
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…
Factorization Results for Left Polynomials in Some Associative Real Algebras: State of the Art, Applications, and Open Questions
Zijia Li, Daniel F. Scharler, Hans-Peter Schröcker
We discuss existence of factorizations with linear factors for (left) polynomials over certain associative real involutive algebras, most notably over Clifford algebras. Because of…
Optimal Synthesis of Overconstrained 6R Linkages by Curve Evolution
Tudor-Dan Rad, Hans-Peter Schröcker
The paper presents an optimal synthesis of overconstrained linkages, based on the factorization of rational curves (representing one parametric motions) contained in Study's quadri…