Geometric Modelling in Functional Style

University of Caen, FranceAbstract. Modelling of 3D objects is a venerable subdomain of the applied geometry, too often coded in acrude way, with elegance sacrificed for the sake of efficiency. We propose to exploit the modern lazy func-tional programming to generate 3D surfaces, insisting upon the genericity of the underlying mathematics.We show how to generate easily the generalized sweeps thanks to the algorithmic differentiation proce-dures. The interest of this paper is mainly methodologic, but all solutions are practical, although they areextremely short. We show a simple but decent technique of parametrizing curves through their chord-length,using lazy series development. The relation between functional programming methods and the computergraphics world is concisely reviewed.