Abstract: A new method of constructing spatial C1 cubic PH curve is proposed to solve the arc-length preserving problem of parametric curve interpolation with given endpoint positions, tangent vectors and arc-length. Quaternion interpolation is adopted for describing the change of tangent vectors and two segment interpolations are joined together at the middle. By means of calculating the length of PH curve accurately, the interpolation curve of any given arc-length can be provided easily and quickly. The existence of solution of interpolation governing equation is also demonstrated. Numerical examples are given to show the effectiveness and practicability of this method.

摘要： 针对已知两端点处位矢和切矢的空间曲线定弧长插值问题，构造了C1连续的三次PH曲线。通过四元数运算描述空间曲线切矢的变化，将曲线分成两段进行插值。利用PH曲线可以精确计算弧长的优势，实现了给定曲线弧长，简单快速地插值出空间曲线，并且论证了所提曲线插值方法的控制方程解的存在性。最后，通过算例验证了该方法在实现空间曲线定弧长插值方面的有效性和实用性。

关键词: 三次毕达哥拉斯速端（PH）曲线, 定弧长, 四元数插值, 分段插值