[1]姚 兴,杭后俊,李晴晴,等.一类三次均匀B样条曲线曲面[J].计算机技术与发展,2018,28(02):69-73.[doi:10．3969/j．issn．1673－629X．2018．02．016]
　YAO Xing,HANG Houjun,LI Qingqing,et al.A Cubic Uniform B－spline Curve and Surface[J].,2018,28(02):69-73.[doi:10．3969/j．issn．1673－629X．2018．02．016]
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一类三次均匀B样条曲线曲面()
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《计算机技术与发展》[ISSN:1006-6977/CN:61-1281/TN]

卷:
28
期数:
2018年02期
页码:
69-73
栏目:
智能、算法、系统工程
出版日期:
2018-02-10

文章信息/Info

Title:
A Cubic Uniform B－spline Curve and Surface
文章编号:
1673－629X(2018)02－0069－05
作者:
姚 兴; 杭后俊; 李晴晴; 尹天乐
安徽师范大学 数学计算机科学学院，安徽 芜湖 241000
Author(s):
YAO Xing; HANG Hou－jun; LI Qing－qing; YIN Tian－le
School of Mathematics and Computer Science，Anhui Normal University，Wuhu 241000，China
关键词:
B 样条基函数; B 样条曲线; B 样条曲面; 形状参数
Keywords:
B－spline basis function; B－spline curve; B－spline surface; shape parameter
分类号:
TP391
DOI:
10．3969/j．issn．1673－629X．2018．02．016
文献标志码:
A
摘要:
B 样条方法由于其自身的优良性质及强有力的配套技术，已经成为几何造型系统中描述自由曲线曲面的主流方法。但B样条方法也存在自身的缺陷，如只能通过控制点修改曲线曲面形状，调节手段过于单一等。对此，文中深入讨论了均匀B 样条曲线曲面的扩展，寻求在保持控制点位置不变的情况下新的调节方法。首先引入带形状参数的均匀 B 样条基函数，剖析形状参数的几何意义;其次定义带形状参数的三次均匀 B 样条曲线，分析曲线的基本性质，并阐述形状参数对曲线的调节功能;最后将形状参数引入到均匀 B 样条曲面的表示中，重点讨论 B 样条曲面的基本性质以及形状参数对曲面形状的影响，并给出了具体的实例。结果表明，该方法简单易行。
Abstract:
B－splines has been the main method of describing free curves and surfaces in modeling system because of its excellent properties and strong supporting technology．But it also has defects．For example，the method modifies the shape of curves and surfaces only by moving control points and its regulation is simple．For this，we discuss deeply the extension of B－splines and find the new methods without moving the control points．Firstly，the quadratic uniform B－spline basis functions with a shape parameter is introduced and the geometric meaning of the shape parameter is analyzed．Secondly，a cubic uniform B－spline curve with a shape parameter is defined and its basic property is analyzed，and the adjustment functions of the shape parameter to curve are discussed．Finally，we focus on the basic property of B－spline surface and the influence of a shape parameter to surface shape by introduction of shape parameters into the presentation of uniform B－spline surface．The instance shows that the method is simple and feasible．
更新日期/Last Update: 2018-03-27