Cyclides in computer aided geometric design
After noting the unsatisfactory state of solid modeling using planes, circular cylinders, cones and spheres, the author points out that most blending problems can be solved using cyclides, i.e., envelopes of one- parameter families of spheres tangent to three fixed spheres. (A good description of Dupin cyclides is in \textit{D. Hilbert} and \textit{S. Cohn- Vossen} [Geometry and the imagination (1952; Zbl 0047.388), pp. 217-219]. Since all curvature lines of cyclides are circles, patches are easily defined; the formulas are given by \textit{A. W. Nutbourne} and \textit{R. R. Martin} [Differential geometry applied to curve and surface design (1988; Zbl 0635.53002)]. The author gives some impressive examples of the ease with which Dupin cyclides solve blending problems.
scientific article; zbMATH DE number 4172235