Variable-free representation of manifolds via transfinite blending with a functional language

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 power ful appr oach to gener ion of cur es,sur aces and solids (and even higher dimensional manifolds) by blending lower dimensional vector -valued functions. Tr ansfinite blending, e.g. used in Gor don-Coons patches, is well known to mathematicians and CAD people. It is pr esented her e in a ver y simple conceptual and computational fr amewor k, which leads such a power ful modeling to be easily handled even by the non mathematically sophisticated user of gr aphics techniques. In particular, transfinite blending is discussed in this paper by making use of a very powerful and simple functional language for geometric design