A note on quintic polynomial approximation of generalized Cornu spiral segments

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:253

Article

Lu, Lizheng

关键词: Generalized Cornu spiral;    Quintic Bezier polynomial;    Approximation;    G(3) continuity;   

DOI  :  10.1016/j.cam.2013.04.010

来源: Elsevier

【 摘 要 】

In two recent papers Cripps et al. (2010) [3], and Cross and Cripps (2012) [2], quintic polynomial approximations of the generalized Cornu spirals have been studied by considering G(2) continuity and G(3) continuity at the end points respectively. The quintic curve is constructed so that the maximum curvature error is within the specified tolerance. In this paper, we provide corrections to the typing errors in Cross and Cripps (2012)[2], and propose a simpler and more efficient method for the G(2)-constrained quintic polynomial approximation where the G(2) conditions are always satisfied by four free variables. Also, we introduce a new error measure of the maximum curvature error, which can greatly reduce the computational time when looking for the solution. Numerical experiments demonstrate the effectiveness of the new measure. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free