基于Foley参数法反算三次NURBS曲线的算法研究
隆强,谢延敏,杨川
(西南交通大学 机械工程学院,四川 成都 610031)
摘要:非均匀有理B样条(NURBS)方法已成为定义工业产品几何形状的唯一数学描述方法。工程实践中,常需要通过曲线已知的一批型值点反算曲线。针对三次NURBS曲线反算问题,采用矩阵形式来表示三次NURBS曲线,由已知的型值点及其权因子,利用Foley参数法确定节点矢量,并推导出以抛物条件即贝塞尔条件作为边界条件构造附加方程,反算出三次NURBS曲线的控制点及其权因子。曲线拟合结果表明,该方法生成的插值曲线具有良好的光滑性,很好地适用于工程实践。
关键词:Foley参数化;反算;控制点;权因子;抛物条件
中图分类号O187.1        文献标识码:A         文章编号:10060316 (2012) 07000505
Research of inversing cubic NURBS curve based on Foley parameter method
LONG Qiang,XIE Yan-min,YANG Chuan
(School of Mechanical Engineering,Southwest Jiaotong University,Chengdu 071003,China)
Abstract:NURBS( non-Uniform Rational B-Spline ) has become the only mathematical description of methods for the definition of industrial products geometry. In engineering practice, it is to inverse curve often using a given set of data points in the curve. Inverse problems for cubic NURBS curve. In this paper, the matrix of cubic NURBS curve is given, and according to a given set of data points and weights, a method for inversing control points and weights of NURBS curve is presented, based on Foley parameter method which is used to obtain the knot vector of cubic NURBS and using Bessel conditions determine additional equations. An example is given to prove the method to be correct and practical and can be fit for engineering practice.
Key wordsFoley parameter;inverse;control point;weight;bessel condition

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收稿日期:2012-01-13
基金项目:国家自然科学基金资助项目(51005193)
作者简介:隆强(1984-),男,四川威远人,硕士研究生,主要研究方向为数控技术与加工。

 

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