Polynomial approximation to clothoids via s-power series

Given an arbitrary segment of a clothoid over a finite interval, we propose a novel method for generating polynomial approximation, based on employing s-power series, the two-point analogue of Taylor expansions. Truncating at the kth term the s-power series furnishes the order-k Hermite interpolant, i.e. the degree-(2k + 1) polynomial curve that reproduces up to the kth derivative of the original curve at the endpoints of a given interval. By piecing these approximations we obtain a Hermitian spline that exhibits C-k continuity at the joints and enjoys almost arc-length parameterization. This is a more suitable alternative than the truncated Taylor series or the blending of Taylor expansions advocated by Wang et al. [Computer-Aided Design 33 (2001) 1049] in a recent article. (C) 2003 Elsevier Ltd. All rights reserved.