带B样条曲率线的NURBS曲面设计  

Design of NURBS Surface with a B-Spline Line of Curvature

作　　者：张礼林[1] 王国瑾[2,3] Zhang Lilin;Wang Guojin(Shaoxing Vocational ＆ Technical College,Shaoxing 312000;School of Mathematical Sciences,Zhejiang University,Hangzhou 310027;State Key Laboratory of CAD＆CG Zhejiang University,Hangzhou 310058)

机构地区：[1]绍兴职业技术学院,绍兴312000 [2]浙江大学数学科学学院,杭州310027 [3]浙江大学CAD&CG国家重点实验室,杭州310058

出　　处：《计算机辅助设计与图形学学报》2018年第9期1692-1698,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61572430);绍兴职业技术学院科研项目(201656)

摘　　要：为了满足产品设计的需要,提出一种NURBS曲面设计算法用于构造插值曲率线的曲面.首先利用给定已知曲线作为公共曲率线的等参曲面束的表达式、B样条的导矢公式和2个B样条的乘积理论,给出以一条非均匀B样条曲线作为公共曲率线的等参曲面束的显式表达式;然后讨论插值曲面可用NURBS精确表示的必要条件,并给出2种表达式,得出以一条非均匀B样条平面曲线作为公共曲率线的曲面束的NURBS精确表达式,以及控制顶点的计算式.通过实例展示了曲面设计效果,表明算法是可行的.In order to satisfy the requirements of design for the products, an algorithm of design NURBS surfaces is proposed on constructing surfaces interpolating a line of curvature. Firstly, utilizing the mathematical expres- sion of isoparametric surface pencil with a given common line of curvature, as well as the formulae of both the derivatives and the products of B-splines, we provide an explicit expression of isoparametric surface pencil with a non-uniform B-spline common curve of curvature. Furthermore, the necessary condition to express the interpo- lating surface as NURBS form exactly is introduced, and two styles of the expression are given. Then, an exact NURBS expression of surface pencil with a given non-uniform B-spline plane curve of curvature and a formula for calculating the control points of the surface are derived. Finally, the effect of surface design is shown in the experimental results, which demonstrate the effectiveness of the proposed algorithm.

关 键 词：曲面设计 非均匀B样条 NURBS曲面 曲率线 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]