Publications (16)
Isometric Surfaces in Isotropic 3-Space
Christian Müller, Helmut Pottmann
While the notion of isometric deformations of surfaces is straightforward for surfaces with Euclidean metric, a corresponding notion in isotropic space has been missing. By making…
On Helical Surfaces with a Constant Ratio of Principal Curvatures
Yang Liu, Olimjoni Pirahmad, Hui Wang +2
We determine all helical surfaces in three-dimensional Euclidean space which possess a constant ratio of principal curvatures (CRPC surfaces), thus providing the fir…
Characterizing envelopes of moving rotational cones and applications in CNC machining
Mikhail Skopenkov, Pengbo Bo, Michael BartoÅ +1
Motivated by applications in CNC machining, we provide a characterization of surfaces which are enveloped by a one-parametric family of congruent rotational cones. As limit cases,…
Darboux cyclides and webs from circles
Helmut Pottmann, Ling Shi, Mikhail Skopenkov
Motivated by potential applications in architecture, we study Darboux cyclides. These algebraic surfaces of order a most 4 are a superset of Dupin cyclides and quadrics, and they c…
Smooth polyhedral surfaces
Felix Günther, Caigui Jiang, Helmut Pottmann
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for…
Non-Euclidean Laguerre geometry and incircular nets
Alexander I. Bobenko, Carl O. R. Lutz, Helmut Pottmann +1
Classical (Euclidean) Laguerre geometry studies oriented hyperplanes, oriented hyperspheres, and their oriented contact in Euclidean space. We describe how this can be generalized…