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.
出处
《工程图学学报》
CSCD
北大核心
2006年第1期116-118,共3页
Journal of Engineering Graphics
关键词
计算机应用
最近距离
单纯形法
高阶次曲面
优化
computer application
closest distance
Nelder-Meade algorithm
surface of high degrees
optimization
