G^2连续的圆弧样条曲线插值

G^2 Circular Spline Interpolation Algorithm

该文提出了一种插值给定型值点及切向的G2连续的圆弧样条曲线构造方法,算法简单,连续阶高于G1连续的传统方法。进一步给出了该文方法构造的圆弧样条曲线整体细分生成算法,应用于数控加工中刀轨路径设计具有重要意义。

This paper presents a G2 circular spline interpolation algorithm in which the data points and their tangents are given.For each data point,we construct an initial circle with a common radius.And then we compute the tangent circles for each pair of adjacent initial circles.At last we select suitable circular arcs from these initial circles and tangent circles,which can generate a G2 circular spline curve.In addition,the whole circular spline curve can be reproduced by subdivision.This is important for designing NC milling tool path.