Bézier曲线的扩展及其应用  

An extension of Bézier curve and its application

作　　者：达买力汗.胡尔曼哈吉 郭清伟[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2014年第6期764-768,共5页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省高等学校省级自然科学研究资助项目(2011AJZR0071)

摘　　要：文章提出带形状参数λ的n+1(n≥2)次多项式调配函数,建立了带形状参数的分段多项式曲线生成法,分析了生成曲线及其调配函数的性质,并给出了扩展曲线G2连续拼接的条件。通过研究发现,在控制多边形不变的情况下,可以通过改变形状参数值调整曲线的形状,随着形状参数值的增加,带形状参数的Bézier曲线将接近于控制多边形,随着曲线阶数的升高,形状参数的取值范围将扩大。实例表明,该方法应用于曲线曲面设计是有效的。A class of blending function of degree n＋1（n≥2） with shape parameter λis presented in this paper .Based on the blending function ,a method of generating piecewise polynomial curves with a shape parameter is given .The properties of the curves and the blending functions are analyzed ,and the condition of G2 continuity of extension curve is discussed .It is found that with the control polygon of the constructed curve unchanged ,the shape of curve can be adjusted by changing the shape parame-ter value .With the increase of the shape parameter value ,the B＆#233;zier curves with shape parameter ap-proximate to the control polygon .With the elevation of the degree of curve ,the feasible range of the shape parameter value will be extended .Examples illustrate that this method of constructing curves and surfaces is useful in CAGD .

关 键 词：形状参数 调配函数 λ-Bezier曲线 曲线拼接 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]