Williams, C. J. K. Use of structural analogy in generation of smooth surfaces for engineering purposes. (English) Zbl 0655.65036 Comput.-Aided Des. 19, No. 6, 310-322 (1987). The use of the minimization of surface integrals of functions of the mean and Gaussian curvature to obtain smooth surfaces that satisfy given boundary and other conditions is discussed. A structural analogy based on the bending theory of shells is introduced to enable the designer to predict the effect of changing parameters in the integrals to be minimized. Surfaces of zero mean curvature (minimal or soap film surfaces), surfaces of constant mean curvature (inflated soap films, including the sphere) and the elastica (in two dimensions) are all special cases of the theory. Cited in 3 Documents MSC: 65D15 Algorithms for approximation of functions 51N05 Descriptive geometry 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 53A04 Curves in Euclidean and related spaces Keywords:minimal surfaces; computer-aided geometric design; surface; finite element method; finite difference method; Gaussian curvature; bending theory of shells; zero mean curvature; soap film surfaces PDFBibTeX XMLCite \textit{C. J. K. Williams}, Comput.-Aided Des. 19, No. 6, 310--322 (1987; Zbl 0655.65036) Full Text: DOI