×

Two examples of solids constructed from given developments. (English) Zbl 1359.51015

Summary: The paper provides two examples, where the bending of a planar area \(\Phi_{0}\) with boundary \(c_{0}\) generates a developable surface patch \(\Phi\) bounded by a particular spatial curve \(c\). There are various ways to restrict such bendings. In the first example the surface \(\Phi\) 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 \(\Phi_{0}\) is bent. In both examples we obtain solids enclosed by torses with geodesic circles \(c\) as curved edges.

MSC:

51N05 Descriptive geometry
51M04 Elementary problems in Euclidean geometries
68U07 Computer science aspects of computer-aided design
PDFBibTeX XMLCite
Full Text: Link