9 citations · 29 across the 9 of their papers we have counts for
13 papers
Bistable Quad-Nets Composed of Four-Bar Linkages
Gudrun Szewieczek, Daniel Huczala, Martin Pfurner +1
We study a novel type of mechanical structures, composed of spatial four-bar linkages, that are bistable, that is, they allow for two distinct configurations. These structures have…
A Bianchi-Calo method for Bryant type surfaces
F. E. Burstall, U. Hertrich-Jeromin, G. Szewieczek
We present a Bianchi-Calo type construction method for Bryant type linear Weingarten surfaces in hyperbolic space.
Discrete curve theory in space forms: planar elastic and area-constrained elastic curves
Tim Hoffmann, Jannik Steinmeier, Gudrun Szewieczek
We propose a notion of discrete elastic and area-constrained elastic curves in 2-dimensional space forms. Our definition extends the well-known discrete Euclidean curvature equatio…
Isothermic nets with spherical parameter lines from discrete holomorphic maps
Tim Hoffmann, Gudrun Szewieczek
We prove that all discrete isothermic nets with a family of planar or spherical lines of curvature can be obtained from special discrete holomorphic maps via lifted-folding. This n…
Differential geometry of space curves: Forgotten chapters
Dmitry Fuchs, Ivan Izmestiev, Matteo Raffaelli +2
We study evolutes and involutes of space curves. Although much of the material presented is not new and can be found in classic treatises, we believe that a modern and unified trea…
Dupin cyclidic systems geometrically revisited
Gudrun Szewieczek
The induced metrics of Dupin cyclidic systems, that is, orthogonal coordinate systems with Dupin cyclides and spheres as coordinate surfaces, were provided by Darboux. Here we take…
Notes on flat fronts in hyperbolic space
Juliette Dubois, Udo Hertrich-Jeromin, Gudrun Szewieczek
We give a short introduction to discrete flat fronts in hyperbolic space and prove that any discrete flat front in the mixed area sense admits a Weierstrass representation.
Discrete cyclic systems and circle congruences
Udo Hertrich-Jeromin, Gudrun Szewieczek
We discuss integrable discretizations of 3-dimensional cyclic systems, that is, orthogonal coordinate systems with one family of circular coordinate lines. In particular, the under…
Constrained elastic curves and surfaces with spherical curvature lines
Joseph Cho, Mason Pember, Gudrun Szewieczek
In this paper we consider surfaces with one or two families of spherical curvature lines. We show that every surface with a family of spherical curvature lines can locally be gener…
The Ribaucour families of discrete R-congruences
Thilo Rörig, Gudrun Szewieczek
While a generic smooth Ribaucour sphere congruence admits exactly two envelopes, a discrete R-congruence gives rise to a 2-parameter family of discrete enveloping surfaces. The mai…
A duality for Guichard nets
Gudrun Szewieczek
In this paper we study G-surfaces, a rather unknown surface class originally defined by Calapso, and show that the coordinate surfaces of a Guichard net are G-surfaces. Based on th…
Discrete channel surfaces
Udo Hertrich-Jeromin, Wayne Rossman, Gudrun Szewieczek
We present a definition of discrete channel surfaces in Lie sphere geometry, which reflects several properties for smooth channel surfaces. Various sets of data, defined at vertice…
Channel surfaces in Lie sphere geometry
Mason Pember, Gudrun Szewieczek
We discuss channel surfaces in the context of Lie sphere geometry and characterise them as certain -surfaces. Since -surfaces possess a rich transformation theory, we…