基于活动仿射标架反求Nurbs曲线/曲面参数

胡事民; 孙家广; 金通光; 汪国昭

引用本文:	胡事民,孙家广,金通光,汪国昭.基于活动仿射标架反求Nurbs曲线/曲面参数.软件学报,2000,11(1):49-53

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基于活动仿射标架反求Nurbs曲线/曲面参数
胡事民^1,2, 孙家广^1,2, 金通光³, 汪国昭³
1.清华大学国家CAD工程中心,北京,100084;2.清华大学计算机科学与技术系,北京,100084;3.浙江大学应用数学系,杭州,310027

摘要:

Nurbs曲线/曲面在反求参数上的数值不稳定性,是Nurbs曲线/曲面的致命缺点.该文介绍了用于参数曲线/曲面求交的活动仿射标架(moving affine frame,简称MAF)方法.基于MAF方法的原理,提出了反求Nurbs曲线/曲面参数的一种新方法.该方法在数值稳定性和效率上均高于各种传统的迭代法,并已应用于商品化三维CAD系统GEMS 5.0.

关键词: 活动仿射标架法,Nurbs曲面,CAD系统.

DOI：

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基金项目:本文研究得到国家自然科学基金（No.69902004）、国家863高科技项目基金（No.863-511-820-017）和国家“九五”科技攻关项目基金（No.96-A01-01-02）资助。

Computing the Parameters of Points on Nurbs Curves and Surfaces via Moving Affine Frame Method

HU Shi-min,SUN Jia-guang,JIN Tong-guang,WANG Guo-zhao

Abstract:

The numerical instability in computing the parameters of the points on Nurbs curves/surfaces is a fatal disadvantage of Nurbs methods. In this paper, the authors introduce the moving affine frame (MAF) method for intersection calculation of parametric curves and surfaces. Based on the principle of a MAF method, a new method for computing the parameters of the points on Nurbs curves and surfaces is presented. The numerical stability and the efficiency of the method are better than all traditional iterative methods. The new method has been applied to the commercial 3D CAD system GEMS5.0.

Key words: Moving affine frame (MAF) method, Nurbs surface, CAD system.