4 citations · 8 across the 13 of their papers we have counts for
13 papers
Closed Bounded Rational Framing Motions
Hans-Peter Schröcker, Zbyněk Šír
We present a method for constructing all bounded rational motions that frame a space curve . This means that the motion guides an orthogonal frame along the curve su…
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…
Partial Fraction Decomposition for Rational Pythagorean Hodograph Curves
Hans-Peter Schröcker, Zbyněk Šír
All rational parametric curves with prescribed polynomial tangent direction form a vector space. Via tangent directions with rational norm, this includes the important case of rati…
Motion Polynomials Admitting a Factorization with Linear Factors
Zijia Li, Hans-Peter Schröcker, Mikhail Skopenkov +1
Motion polynomials (polynomials over the dual quaternions with nonzero real norm) describe rational motions. We present a necessary and sufficient condition for reduced bounded mot…
Space Kinematics and Projective Differential Geometry Over the Ring of Dual Numbers
Johannes Siegele, Hans-Peter Schröcker, Martin Pfurner
We study an isomorphism between the group of rigid body displacements and the group of dual quaternions modulo the dual number multiplicative group from the viewpoint of differenti…
From A to B: New Methods to Interpolate Two Poses
Hans-Peter Schröcker
We present two methods to interpolate between two given rigid body displacements. Both are based on linear interpolation in the ambient space of well-known curved point models for…
Singular Frégier Conics in Non-Euclidean Geometry
Hans-Peter Schröcker
The hypotenuses of all right triangles inscribed into a fixed conic with fixed right-angle vertex are incident with the Frégier point to and . As varies on t…
Discrete Laplace Cycles of Period Four
Hans-Peter Schröcker
We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different n…
The Bäcklund Transform of Principal Contact Element Nets
Hans-Peter Schröcker
We investigate geometric aspects of the the Bäcklund transform of principal contact element nets. A Bäcklund transform exists if and only if it the principal contact element net is…
Discrete Gliding Along Principal Curves
Hans-Peter Schröcker
We consider -dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation ("rotating motions"). In the Study quadric model of Euclidean di…
Contributions to Four-Position Theory with Relative Rotations
Hans-Peter Schröcker
We consider the geometry of four spatial displacements, arranged in cyclic order, such that the relative motion between neighbouring displacements is a pure rotation. We compute th…
Orthologic Tetrahedra with Intersecting Edges
Hans-Peter Schröcker
Two tetrahedra are called orthologic if the lines through vertices of one and perpendicular to corresponding faces of the other are intersecting. This is equivalent to the orthogon…