Functionality in blend design
The last two authors [ibid. 21, No.3, 165-172 (1989; Zbl 0669.65006)] have proposed to model surfaces as vector solutions of a simple 4th order elliptic partial differential equation depending on one parameter and allowing the imposition of four sets of boundary conditions. While this uses incomparably more computer time to compute one example than Bézier or other splines, the lost time is more than made up in the study of optimizing problems since (apart from parameters appearing in the boundary conditions) only one parameter has to be varied and therefore exact optimizing studies are possible. The paper shows in outline how to treat four engineering problems (design of a wine cup of given volume, design of an optimal cooling fin, design of a blending surface between right circular cylinder and oblique plane that minimizes stresses in the linear elastic model). In the last two problems, the functions to be minimized are themselves results of integrations and the minimal number of parameters is a condition for the feasibility of automatic optimization.
scientific article; zbMATH DE number 4199448