求点到空间参数曲线最小距离的几种算法  

Algorithms on calculating minimum distance between point and spatial parametric curves

作　　者：伍丽峰[1] 陈岳坪[1,2] 谌炎辉[1] 王虎奇[1] 

机构地区：[1]广西工学院机械工程系,柳州545006 [2]广东工业大学机电工程学院,广州510006

出　　处：《机械设计与制造》2011年第9期15-17,共3页Machinery Design & Manufacture

基　　金：广西科学基金资助项目(桂科青0832015);广西科学研究与技术开发计划项目(桂科能08126002)

摘　　要：建立了点到空间参数曲线最小距离的数学模型,提出了计算点到空间参数曲线最小距离的三种算法,即基于几何特征的快速迭代法、基于最优化方法的黄金分割法与二次迭代法的组合法以及格点法,分析比较了这三种算法的特点和适用范围,编制了相应的计算机程序,实现了求点到复杂曲线的最小距离,并对三种算法的计算精度和运行时间作了比较。大量算例验证了算法的有效性,其计算精确度高,非常适用于曲面、曲线的匹配计算和三坐标测量机的点相关数据处理,在工程上具有一定的实用价值。A mathematical model of the minimum distance between a point and a spatial parametric curve is established and three algorithms are presented for calculating the distance.These algorithms are： the quick iteration method based on geometric characteristics,the combination of golden section method and quadratic interpolation method and the grid method based on optimization method.Their properties and application scope are also compared and discussed.By programming,the calculating for minimum distance from a point to a complex curve is realized.Moreover the calculation precision and running time are com-pared among them.The effectiveness of the algorithms is verified by a series of tests to be practical,which can be applied to surface and curve matching and some relevant data processing of three coordinate mea-suring machines with its high precision in computation.

关 键 词：参数曲线 最小距离 快速迭代法 黄金分割法 二次插值法 格点法 

分 类 号：TH16[机械工程—机械制造及自动化] Q123.3[生物学—普通生物学]