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Polynomial approximation to clothoids via s-power series

✍ Scribed by J. Sánchez-Reyes; J.M. Chacón

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
196 KB
Volume
35
Category
Article
ISSN
0010-4485

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✦ Synopsis

Given an arbitrary segment of a clothoid over a finite interval, we propose a novel method for generating a 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-ð2k þ 1Þ 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.

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