G3 quintic polynomial approximation for Generalised Cornu Spiral segments

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Cross, Benjamin¹  Cripps, Robert J.¹ 

[1] Univ Birmingham, Sch Mech Engn, Geometr Modelling Grp, Birmingham B15 2TT, W Midlands, England

关键词: Quintic Bezier polynomial;    Approximation;    Generalised Cornu Spiral;   

DOI  :  10.1016/j.cam.2012.01.034

来源: Elsevier

【 摘 要 】

Within Computer Aided Design (CAD) there is a need to construct fair curves. The Generalised Cornu Spirals (GCSs) are a set of curves with a monotonic curvature profile and are hence considered fair but implementation in current CAD systems is not straightforward, partly due to not being in the usual polynomial form. A method to approximate a GCS using a quintic polynomial curve is presented. The method seeks to interpolate the GCS to satisfy the G(3) constraints at the end points with a quintic Bezier, leaving two degrees of freedom. An initial approximation is shown to be effective for the majority of GCS curves. Moreover, it is possible to determine when an initial approximation is likely to be poor. If this approximation does not meet the tolerance required, a search involving two parameters is performed. Characteristics of the search domain are used to establish a suitable starting value. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free