对数螺线段的多项式逼近与C-Bézier逼近

Approximating logarithmic spiral segments by polynomial and C-Bézier

为了适合当前计算机辅助设计(CAD)系统中的曲线形式和工业设计中的美学需要,提出了对数螺线段的两种逼近方法:(1)利用s-Power级数,推导出s-Power系数的计算公式,给出了对数螺线段的快速多项式逼近算法、对数螺线的等距曲线的具体表达式及其s-Power逼近算法;(2)首先推导出两端点C-Bézier形式的G2Hermite插值公式,然后提出了对数螺线段的C-Bézie表示的G2Hermite插值逼近算法.实例运算结果表明,两种逼近方法是正确与有效的,完全适合CAD系统使用.

To fit the curve forms in current computer aided design （CAD） systems and aesthetic needs in industrial designs, two approximation algorithms for logarithmic spiral segments were proposed. In the first method, the calculation formula for s-Power series was derived and a fast polynomial approximation algorithm was presented, and then the calculation formula for the offset curves of the logarithmic spiral and the corresponding approximation algorithm by s Power series were presented. In the second method, the G^2 Hermite interpolation formula of two end points by C-Bézier form was firstly derived, and then a G^2 Hermite interpolation approximation algorithm by C-Bézier form was presented. The computing results of examples show that these two approximation methods are correct and effective, suitable for the use of CADsystems.