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The Geometry of Quadratic Quaternion Polynomials in Euclidean and Non-euclidean Planes
We propose a geometric explanation for the observation that generic quadratic polynomials over split quaternions may have up to six different factorizations while generic polynomials over HamiltonianExpand
From A to B: New Methods to Interpolate Two Poses
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 the group of rigidExpand
Davis' Convexity Theorem and Extremal Ellipsoids
We give a variety of uniqueness results for minimal ellipsoids circumscribing and maximal ellipsoids inscribed into a convex body. Uniqueness follows from a convexity or concavity criterion on theExpand
The B\"acklund Transform of Principal Contact Element Nets
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 of constantExpand
Singular Fr\'egier Conics in Non-Euclidean Geometry
The hypotenuses of all right triangles inscribed into a fixed conic C with fixed right-angle vertex p are incident with the Frégier point f to p and C. As p varies on the conic, the locus of theExpand
Contributions to Four-Position Theory with Relative Rotations
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 the locus of pointsExpand
Discrete Laplace Cycles of Period Four
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 net directions, thatExpand
A Multiplication Technique for the Factorization of Bivariate Quaternionic Polynomials
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 factorizations,Expand
Space Kinematics and Projective Differential Geometry Over the Ring of Dual Numbers
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 differential geometry in aExpand
Discrete Gliding Along Principal Curves
We consider n-dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation (“rotating motions”). In the Study quadric model of Euclidean displacements theseExpand