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

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.