中文摘要：

讨论平面上三次PH曲线Hermite插值问题。当通过插入满足条件的中间数据来构造段数最少的C^1插值PH样条曲线时,对于固定的弦长,如果所给的切矢模长太大或夹角太小,符合C^1插值条件的解可能不存在,结合优化手段,给出了适当调整模长的大小,来求得符合G^1插值条件的解的方法。拓宽了PH曲线在机器人路径的设计、数控加工的计算等方面的应用范围。

英文摘要：

The problem of constructing planar cubic PH curve Hermite interpolation is discussed. When constructing C^1 interpolation PH spline curves with least segments by interpolating condition-satisfied middle data, for the fixed chord-length, the solution satisfying C^1 interpolation condition may not be found in the cases that the magnitudes of the tangent vectors are too long or the angles between the tangent vectors and are too small. By optimizing means being combined, the approach for adjusting properly the magnitudes of the tangent vectors to construct cubic PH spline curves meeting G^1 interpolation conditions is given, which expands the application scope of PH curve in the design of the locus of robots and CNC （Computerized Numerical Control） computing, etc.