反求点在自由曲面上投影参数值的一种稳定算法

A Steady Algorithm of Reverse Calculating the Parameters of the Point’s Projection on the Surface

针对反求曲线曲面上点的参数值存在数值不稳定的问题,提出了一种稳定的算法。实际应用的曲面很多采用高阶次曲面并且由很多曲面片拼接而成,采用NURBS曲面形式记录曲面信息。针对这类复杂曲面,采用牛顿迭代法求解参数值,再采用单纯形法对参数值进行优化。通过上百个数据的试验,证明该算法是反求点在自由曲面上投影的参数值的一种稳定的并有效的算法。

The traditional algorithm of calculating the parameters of the point＇s projection on the surface or the curve leads the result unsteady. A new steady algorithm is proposed. Most actual surfaces are high degrees and are made up of many pieces. With these complicated surfaces, the Newton iterative algorithm is used to calculate the parameters of the projection of the point, and then the parameters are optimized with the Nelder-Meade algorithm. After testing more than one hundred data, it shows that the algorithm is steady and effective.