利用单纯形法优化点到曲面的最近距离  

Optimizing the Distance between Point and Surface with the Nelder-Meade Algorithm

作　　者：李淑萍[1] 闫坤[1] 李环[2] 张广岩[3] 

机构地区：[1]沈阳航空工业学院,辽宁沈阳110034 [2]沈阳飞机工业集团,辽宁沈阳110034 [3]沈阳理工大学,辽宁沈阳110168

出　　处：《工程图学学报》2006年第1期116-118,共3页Journal of Engineering Graphics

摘　　要：针对利用高阶次曲面方程计算点到曲面的距离误差大的问题,提出了利用单纯形法进行优化,获得点到曲面的最近距离。即采用牛顿迭代法确定曲面上离已知点最近的点的参数初始值,利用单纯形法对此初始值进行优化,获得曲面上离已知点最近的点的坐标值,通过该坐标值计算通过该点的法线,已知点被证明在法线上。实践表明,该方法是求点到高阶次曲面距离的有效方法。The algorithm for finding closest distance from known point to known surface based on calculating high degrees equation set leads to big errors and a new method based on the Nelder-Meade algorithm was proposed. To acquire the closest distance between known point and known surface, firstly a Newton method was used to get initial parameters＇ values of a point. Then the parameters were optimized with the Nelder-Meade algorithm and the coordinates of point on the surface were obtained. After that the normal line through the obtained point was calculated. It turned out that the known point is on the normal line. The results of experiment show that the method is efficient for finding the closest distance from known point to known surface of high degrees.

关 键 词：计算机应用 最近距离 单纯形法 高阶次曲面 优化 

分 类 号：TP391.75[自动化与计算机技术—计算机应用技术]