Hodograph computation and bound estimation for rational B-spline curves  

作　　者：Xu Huixia Wang Guojin 

机构地区：[1]Institute of Computer Images and Graphics, Zhejiang University, Hangzhou 310027, China [2]State Key Laboratory of CAD＆CG,ghejiang University, Hangzhou 310027, China

出　　处：《Progress in Natural Science:Materials International》2007年第8期988-992,共5页自然科学进展·国际材料（英文版）

基　　金：Supported by the National Program on Key Basic Research Projects (Grant No.2004CB719400);National Natural Science Foundation of China (Grant Nos.60673031,60333010)

摘　　要：It is necessary to compute the derivative and estimate the bound of rational B-spline curves in design system, which has not been studied to date. To improve the function of computer aided design （CAD） system, and to enhance the efficiency of different algo- rithms of rational B-spline curves, the representation of scaled hodograph and bound of derivative magnitude of uniform planar rational 13- spline curves are derived by applying Dir function, which indicates the direction of Cartesian vector between homogeneous points, discrete B-spline theory and the formula of translating the product into a summation of B-spline functions. As an application of the result above, upper bound of parametric distance between any two points in a uniform planar rational B-spline curve is further presented.计算衍生物并且在设计系统估计合理 B 花键曲线的界限是必要的，它没迄今为止被学习。为了改进计算机的函数，并且提高合理B花键曲线的不同算法的效率，帮助了设计( CAD )系统，放大速度图的表示和一致平面合理B花键曲线的衍生物大小的界限被使用 Dir 导出函数，它显示在同类的点，分离B花键理论和把产品翻译成B花键函数的求和的公式之间的笛卡儿的向量的方向。作为上面的结果的应用，在任何二之间的参量的距离的上面的界限指在一条一致平面合理 B 花键曲线进一步被介绍。

关 键 词：computer aided design （CAD） rational B-spline discrete B-spline hodograph bound of derivative distance between two points. 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]