S-power series: an alternative to Poisson expansions for representing analytic functions

Abstract

Morin and Goldman [Computer Aided Geometric Design 17 (2000) 813] have recently presented a remarkable new framework, based on employing Poisson series, for describing analytic functions in CAD. We compare this Poisson formulation with s-power series, modified Newton series that can be regarded as the two-point analogue of Taylor expansions. Such s-power series yield, over finite intervals, better approximations for CAD purposes, as they are polynomial and hence expressible in the Bernstein–Bézier standard, can be pieced together in a smooth Hermitian spline and, in general, display better convergence.