Variable-Free Representation of Manifolds via Transfinite Blending with a Functional Language

Abstract

In this paper a variable-free parametric representation of manifolds is discussed, using transfinite interpolation or approximation, i.e. function blending in some functional space. This is a powerful approach to generation of curves, surfaces and solids (and even higher dimensional manifolds) by blending lower dimensional vector-valued functions. Transfinite blending, e.g. used in Gordon-Coons patches, is well known to mathematicians and CAD people. It is presented here in a very simple conceptual and computational framework, which leads such a powerful modeling to be easily handled even by the non mathematically sophisticated user of graphics techniques. In particular, transfinite blending is discussed in this paper by making use of a very powerful and simple functional language for geometric design.