B样条曲线的节点插入问题及两个新算法  

TWO ALGORITHMS FOR INSERTING KNOTS INTO B-SPLINE CURVES

作　　者：秦开怀[1] 关右江[1] 

机构地区：[1]清华大学计算机科学与技术系,清华大学精密仪器系

出　　处：《计算机学报》1997年第6期556-561,共6页Chinese Journal of Computers

基　　金：国家自然科学基金

摘　　要：Ｂｏｅｈｍ算法和Ｏｓｌｏ算法是Ｂ样条曲线的节点插入的经典算法．它们可以有效地将节点插入到端点插值（Ｅｎｄｎｏｉｎｔ－ｉｎｔｅｒｐｏｌａｔｉｎｇ）Ｂ样条曲线．但是，对于其它的Ｂ样条曲线而言，当插入靠近节点矢量两端附近的节点时，所有的经典算法都将出错．本文提出了两个节点插入新算法．它们可以解决节点插入的经典算法中的问题，能够将任意节点插入各种Ｂ样条曲线之中．它们的另一个重要用途是可以用于各种Ｂ样条曲线的升阶．It has been found that errors will occur when the conventional algorithms for knot insertion are used for inserting knots near the endpoints of the knot vector into a uniform B-spline curve. Two algorithms for inserting new knots into B-spline curves are presented in this paper. Unlike the conventional algorithms such as the Boehm's or Olso-algorithm, the new algorithms can efficiently be used for inserting any knots into various B-spline curves including uniform and nonuniform B-spline curves. One of their applications is that the new algorithms can be used for degree raising of both uniform and nonuniform B-spline curves.

关 键 词：B样条 节点插入 升阶 曲线 曲面 算法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]