Quintic polynomial approximation of log-aesthetic curves by curvature deviation
Quintic polynomial approximation of log-aesthetic curves by curvature deviation
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DOI：
10.1016/j.cam.2015.10.002
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发表时间：
2016-04
期刊：
影响因子：
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通讯作者：
Lizheng Lu;Xueyan Xiang
中科院分区：
文献类型：
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作者：
Lizheng Lu;Xueyan Xiang
摘要对数美学曲线（LACs）具有单调曲率，包含许多经典曲线，在几何建模中被广泛用于描述对称形状。然而，它们通常以非多项式形式表示，因此与当前的CAD系统不兼容。本文给出了LAC线段的五次多项式近似。对于给定的LAC线段，通过最小化基于曲率的误差度量，获得了五次g2插值bsamzier曲线，其优点是更有可能保持单调曲率特性。数值实验表明，该方法在位置偏差和曲率偏差方面通常比现有方法得到更好的结果。
Abstract 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 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.