摘要
本文探讨了用2次周期性NURBS表示闭合圆锥曲线的方法,导出了精确表示椭圆、抛物线和双曲线的条件,并给出了精确表示圆弧的充要条件;提出了用2次NURBS精确表示圆的新方法.和其它基于矩形控制多边形的同类方法相比,其控制点数最少.用2次非周期性NURBS(2次有理Bezier样条)和2次均匀有理B样条描述圆锥曲线的方法均是本文的一个特例.
A new algorithm for representing conies precisely is presented using the periodic NURBS. The algorithm requires only four control vertices to represent a full circle using a circumscribing square. Based on the periodic NURBS, this paper derives the sufficient and necessary conditions of precise representation of conies. The rational Bezier spline and the uniform rational B-spline of degree two are discussed as special examples of NURBS.
出处
《计算机学报》
EI
CSCD
北大核心
1992年第8期572-581,共10页
Chinese Journal of Computers
基金
国家博士后科学基金
关键词
圆锥曲线
B样条
周期性
NURBS
Conic, nonuniform rational B-spline (NURBS), periodicity.
