Undefined freeform surfaces having deterministic structure: issues of their characterization for functionality and manufacture

Abstract

There is an increasing use of surfaces which have structure, an increase in the use of freeform surfaces, and most importantly an increase in the number of surfaces having both characteristics. These can be called multi-function surfaces, where more than one function is helped by the geometrical features: the structure can help one, the freeform another. Alternatively, they can be complementary to optimize a single function, but in all cases both geometries are involved. This paper examines some of the problems posed by having such disparate geometries on one surface; in particular, the methods of characterization needed to help understand the functionality and also to some extent their manufacture. This involves investigating ways of expressing how local and global geometric features of undefined freeform surfaces might influence function and how surface structure on top of or in series with the freeform affects the nature of the characterization. Some methods have been found of identifying possible strategies for tackling the characterization problem, based in part on the principles of least action and on the way that nature has solved the marriage of flexible freeform geometry and structure on surfaces.