Quintic polynomial approximation of log-aesthetic curves by curvature deviation

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• 作者：Lizheng Lu ; ^{lulz99@163.com" class="auth_mail" title="E-mail the corresponding author} ; Xueyan Xiang
• 关键词：Log-aesthetic curve ; Monotone curvature ; Quintic Bé ; zier curve ; G2G2 interpolation ; Polynomial approximation
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：296
• 期：Complete
• 页码：389-396
• 全文大小：590 K

文摘

Log-aesthetic curves (LACs), possessing monotone curvature and including many classical curves, have been widely used to describe fair shapes in geometric modeling. However, they are generally represented in non-polynomial form and are thus not compatible with current CAD systems. In this paper we present quintic polynomial approximation of LAC segments. For a given LAC segment, a quintic G²$G^2$ interpolating Bézier curve is obtained by minimizing a curvature-based error metric, with the advantage of being more likely to preserve the monotone curvature property. Numerical experiments demonstrate that our method can usually generate better results than the previous methods in terms of the deviation in positions and curvatures.