Geometric Modelling in Functional Style

Modelling of 3D objects is a venerable subdomain of the applied geometry, too often coded in a crude way, with elegance sacrificed for the sake of efficiency. We propose to exploit the modern lazy functional 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 procedures. The interest of this paper is mainly methodologic, but all solutions are practical, although they are extremely 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 computer graphics world is concisely reviewed.