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J4  2009, Vol. 43 Issue (5): 789-795    DOI: 10.3785/j.issn.1008-973X.2009.05.001
自动化技术、计算机技术     
变次数B-样条曲线
朱平,汪国昭
(浙江大学 计算机图像图形研究所,浙江 杭州 310027)
Multi-degree B-spline curves
 SHU Beng, HONG Guo-Zhao
(Institute of Computer Graphics and Image Processing, Zhejiang University, Hangzhou 310027, China)
 全文: PDF(699 KB)   HTML
摘要:

变次数B-样条(MD-样条)曲线是在不同区间有不同次数的特殊B-样条曲线.为了适应CAD造型系统的发展,研究了最大变化次数小于3的MD-样条曲线.这类MD-样条继承了多项式B-样条的变差缩减性、保凸性等大多数性质,并具有退化性、嵌入节点等独特性质.整个MD-样条曲线至少是Cn-1连续的,这里n为整个曲线段的最小次数.研究了MD-样条与B-样条的关系,可以通过嵌入节点将MD-样条转化为B-样条,同时通过MD-样条能够将B-样条的升阶看成是几何割角的过程.变次数B-样条能够在保持理想精度的条件下,有效地减少控制顶点和节点向量的数目,有利于几何设计和CAD系统的数据传输.

Abstract:

Multi-degree B-spline (MD-spline) curves are special B-spline curves with various degrees on different intervals, thus adapted to the development of CAD modeling system. MD-spline curves whose maximal variational degree was lower than three were investigated. This kind of MD-splines inherit most properties of polynomial B-splines, such as variation diminishing property, convexity preserving property, etc, and enjoy other advantageous properties for modeling, such as degeneration property, knot insertion property. Also the whole MD-spline curve is at least Cn-1, where n is the smallest degree of whole curve segments. In addition, the relation between MD-spline and B-spline was presented. MD-spline can be transformed into B-spline through knot insertion, simultaneously the degree elevation of B-spline can be interpreted as corner cutting process through MD-spline. MD-splines can effectively reduce the numbers  of spline curves control points and knot vectors while keeping the desired accuracy, which are very good for geometric design and data transmission of CAD system.

出版日期: 2009-11-18
:  TP391  
基金资助:

国家自然科学基金资助项目(60773179);国家“973”基础研究发展规划资助项目(2004CB318000).

通讯作者: 汪国昭,男,教授,博导.     E-mail: wanggz@zju.edu.cn
作者简介: 朱平(1982-),男,安徽马鞍山人,博士生,从事计算机辅助几何设计与图形学研究.
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引用本文:

朱平, 汪国昭. 变次数B-样条曲线[J]. J4, 2009, 43(5): 789-795.

SHU Beng, HONG Guo-Zhao. Multi-degree B-spline curves. J4, 2009, 43(5): 789-795.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2009.05.001        http://www.zjujournals.com/eng/CN/Y2009/V43/I5/789

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