有理三次圆弧的标准正交基与广义Ball基表示  

Representing rational cubic circular arc by normalized totally positive or generalized Ball methods

作　　者：田奕丰[1,2] 王国瑾[1,2] 

机构地区：[1]浙江大学计算机图像图形研究所,浙江杭州310027 [2]浙江大学CAD&LCG国家重点实验室,浙江杭州310027

出　　处：《浙江大学学报（工学版）》2009年第1期1-7,共7页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(60873111);国家“973”重点基础研究发展规划资助项目(2004CB719400)

摘　　要：为了拓宽由标准正交基与广义Ball(GB)基所构造的新的参数曲线的使用范围,研究了用它们表示圆弧的一整套理论,包括表示圆弧的充要条件、圆心角范围和几何作图法等.以最基本而常用的有理三次形式为研究类型,运用几何代数和基变换这两种方法,研究了以有理三次形式的Delgado-Pe^na(DP)曲线、Wang-Ball曲线与Said-Ball曲线表示圆弧曲线段的方法,找到了用这3种曲线分别表示圆弧的充要条件,推导了算法,并给出了圆心角范围和几何作图法.研究结果既可用于圆弧的各种有理化参数设计,又可用于鉴别一条有理三次DP或GB曲线是否为圆弧.A set of theory including the sufficient and necessary conditions the central angle range of circular arcs and their geometric illustration was for representing circular arcs, investigated to present circular arcs by the new parametric curves in order to extend the application range of the new parametric curves constructed by normalized totally positive basis and generalized Ball （GB） basis. The most basic and com- mon rational cubic form was analyzed. The methods to express circular arcs based on rational cubic Delgado-Pena （DP）, Wang-Ball or Said-Ball curves were investigated by using geometric and algebraic methods and basis conversion. The sufficient and necessary conditions for representing circular arcs respectively by three types of curves were found and the corresponding algorithms were derived. The central angle range of circular arcs and their geometric illustration were given. Results can be applied for designing all kinds of circular arcs＇ rational parameters and identifying whether a rational cubic DP or GB curve is a circular arc.

关 键 词：有理DP曲线 广义BALL曲线 圆弧 设计 鉴别 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]