
Journal for Geometry and Graphics 20 (2016), No. 2, 225241 Copyright Heldermann Verlag 2016 Two Examples of Solids Constructed From Given Developments Hellmuth Stachel Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstr. 810 / 104, 1040 Vienna, Austria stachel@dmg.tuwien.ac.at The paper provides two examples, where the bending of a planar area Φ_{0} with boundary c_{0} generates a developable surface patch Φ bounded by a particular spatial curve c. There are various ways to restrict such bendings. In the first example the surface Φ is a cylinder with given rulings, and the spatial counterpart c of the boundary c_{0} is planar. In the second example the rulings are unknown. Instead of this constraint, the closed boundary c_{0} is subdivided into two subarcs which are glued together while Φ_{0} is bent. In both examples we obtain solids enclosed by torses with geodesic circles c as curved edges. Keywords: Surfaces of constant curvature, curved folding, developable surfaces, geodesic circle. MSC: 53A03; 51M04, 51N05, 68U07 [ Fulltextpdf (448 KB)] 