摘要
Bézier曲线在曲线造型设计中有着广泛的应用,文章在四次Bézier曲线中引入形状参数α,将曲线的定义区间由[0,1]扩展为[0,α],构建出带形状参数α的四次α-Bézier曲线。所构建的四次α曲线是传统四次参数曲线的同次扩展,研究了该曲线的性质。它不仅具有传统参数曲线优良的几何特性,如端点性、对称性、几何不变性等,而且通过改变参数α的取值,可对曲线的形状进行灵活的调控,最后用实例说明了该曲线在实际造型设计中的有效性。
Bézier curve is widely used in curve modeling design,parameter α is introduced into the quartic Bézier curve in this paper.The definition interval of curve is extended from[0,1]to[0,α].Then quartic parametric curve with shape parameterαis constructed,which is named quartic α-Bézier curve.The proposed quartic α-curve is extensions of the corresponding traditional quartic parametric curve and the properties of the curve is studied.The curve not only has the excellent geometric characteristics of the traditional paramet-ric curve,such as endpoint,symmetry,geometric invariance,etc,but also the shape of the curve can be flexibly regulated by altering the value of parameter α.Finally,an example is given to illustrate the effectiveness of the curve in practical modeling design.
作者
张丹丹
ZHANG Dandan(Anqing Branch,Anhui Open University,Anqing 246001,China)
出处
《忻州师范学院学报》
2023年第5期5-9,共5页
Journal of Xinzhou Teachers University
基金
安徽省高校自然科学研究重点项目(KJ2021A1257)
安徽省高校自然科学研究重大项目(KJ2021ZD0147)
关键词
四次参数曲线
形状参数
区间扩展
连续
quartic parametric curves
shape parameter
interval extension
continuity
