摘要
实践证明，传统的Ｂ样条曲线升阶算法只能解决端点插值Ｂ样条曲线的升阶问题，当用于其它非均匀Ｂ样条曲线以及均匀Ｂ样条曲线的升阶时均会出现严重错误．本文基于一个新的Ｂ样条恒等式，提出了一个Ｂ样条曲线升阶的新算法．该算法可用于任何均匀和非均匀的Ｂ样条曲线的升阶．当用于一段均匀Ｂ样条曲线的升阶时，不需要在节点矢量中间插入任何节点，升阶后仍为一条均匀Ｂ样条曲线．其计算简便、速度快．本文最后还得到两个新结论：①在一般情况下，用于升阶的节点矢量是不唯一的，只有端点插值Ｂ样条曲线例外．②升阶后的控制多边形不一定更加接近曲线，有时可能离曲线更远．这完全取决于用于升阶的节点矢量．这些结论与传统的升阶理论截然不同．因此，传统的升阶理论不得不进行修正．
In this paper,a new algorithm for degree-raising of various B-splinecurves is presented based on a new identity of B-splines. Unlike other algorithmsfor degree raising, the new algorithm, which is easily and efficiently implemented,can ensure that a segment of uniform B-spline curve of degree k becomes a uniformone of degree (k+1) after degree-raising. The conclusions obtained in the papercompletely contradict the existed theory for degree raising,which implies that theconventional theory for degree raising of B--spline curves has to be revised.
出处
《计算机学报》
EI
CSCD
北大核心
1996年第7期537-542,共6页
Chinese Journal of Computers
基金
国家自然科学基金
关键词
B样条
算法
曲线升阶
CAD
B-spline, curve, degree-raising, algorithm.
