Abstract: A subdivision and sphere approximation method was presented in order to improve the accuracy and efficiency of the evaluation. First of all, the surface patch containing the perpendicular foot of measuring point was determined by subdividing the surface. A sphere, approximating the surface patch, was constructed with four points on the surface patch and the approximate distance was then obtained based on the geometric properties of sphere. Finally, the surface patch was subdivided and the above process was iterated until the difference between adjacent results was less than the preset threshold. The evaluating of complex surface profile error was realized by using subdivision and sphere approximation method combined with improved simplex method. The calculating examples showed that the subdivision and sphere approximation method was rapid and accurate, which was suitable for the evaluating of complex surface profile error.

Key words: shortest distance, subdivision and sphere approximation, profile error, improved simplex method

摘要： 为进一步提高复杂曲面轮廓度误差评定的精度和效率，提出一种计算点到曲面最短距离的分割球面逼近方法。该方法首先分割曲面以确定测点垂足所在的曲面片；然后用曲面片上的四点构成球面去逼近该曲面片，利用球面的几何性质求得测点到曲面片的近似距离；最后再分割该曲面片，重复上述步骤，当相邻两次的结果之差小于设定阈值时停止分割。在分割球面逼近方法的基础上结合改进单纯形法对复杂曲面轮廓度误差进行了评定。计算实例表明，分割球面逼近方法快速、精确，适用于复杂曲面轮廓度误差评定。

关键词: 最短距离, 分割球面逼近, 轮廓度误差, 改进单纯形法