一类三次均匀B样条曲线曲面  

A Cubic Uniform B-spline Curve and Surface

作　　者：姚兴[1] 杭后俊[1] 李晴晴 尹天乐 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241000

出　　处：《计算机技术与发展》2018年第2期69-73,共5页Computer Technology and Development

基　　金：安徽省高等学校自然科学研究重点项目(KJ2017A326)

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。B-splines has been the main method of describing free curves and surfaces in modeling system because of its excellent propertiesand strong supporting technology. But it also has defects. For example,the method modifies the shape of curves and surfaces only by movingcontrol points and its regulation is simple. For this,we discuss deeply the extension of B-splines and find the new methods without movingthe control points. Firstly,the quadratic uniform B-spline basis functions with a shape parameter is introduced and the geometric meaning ofthe 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 surfaceand 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.

关 键 词：B样条基函数 B样条曲线 B样条曲面 形状参数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]