Potential applications of Weingarten surfaces in CAGD, Part I: Weingarten surfaces and surface shape investigation Original Research Article

A certain class of surfaces arising in differential geometry, Weingarten surfaces, is discussed in this paper with a view towards potential applications in CAGD and specifically shape investigation. Weingarten surfaces include, among other important surface types, minimal and developable surfaces and surfaces of revolution. They have several features which make them attractive for use in CAGD where shape control is important. Such features include a substantial mitigation of computation for critical shape parameters such as principal curvatures and lines of constant curvature. A remarkable property of these surfaces is that the lines of curvature can be determined by quadratures.