五次B样条的光顺

Five-Order B-Spline Fairing

本文立足于几何的角度 ,侧重于曲率、挠率的变化 ,从奇点、拐点入手 ,提出了光顺的准则 ,引进了一套光顺的方法 ,应用于控制更为灵活、描述更为细腻的非有理五次B样条光顺。采用节点判断 ,分段B样条内部分析 ,宏观与微观相结合 ,研究了按所提准则的光顺具体实现方法 ,并用C语言程序实现了依据本文理论提出的算法 ,获得了较好的效果。

Fairing of curve and surface is one of important tasks in the computer -aided design and computer aided geometric design. It has been put to use in manufacture and design of automobile, ship and plane widely. From a viewpoint of geometry, paying particular attention to change of curvature and torsion, beginning with singular point and limp, we put forward a standard and a way of the fairing .Firstly, we realize the fairing of curve, so far as surface, with the simple triple basic spline. Secondly, we do it by 5 B-spline that is cotrolled more elastically and described more minutely.We adopt the method to judge the curve and surface in knots and analyse the internal piecewise panel of B-spline. Combining macro-analysis with micro-analysis,we research on the concrete means of realizing the fairing by the standard.Tested and verified it by a C program,the result is better.\;