三次Bézier曲线另一种带三参数的新扩展及其应用  

Another Novel Extension of Cubic Bézier Curves with Three Parameters and Their Applications

作　　者：王成伟[1] 张卷美[2] WANG Chengwei;ZHANG Juanmei(Beijing Institute of Fashion Technology,Beijing 100029,P.R.China;Beijing Electronic Science and Technology Institute,Beijing 100070,P.R.China)

机构地区：[1]北京服装学院,北京市100029 [2]北京电子科技学院,北京市100070

出　　处：《北京电子科技学院学报》2021年第1期47-53,共7页Journal of Beijing Electronic Science And Technology Institute

基　　金：北京市教育委员会科研计划项目资助(项目编号KM201910012002,KM201910012003,KM201810012004);北京服装学院2019年教育教学改革立项项目(项目编号:JG-1924)。

摘　　要：根据曲线自由设计的需求,同时要拥有三角和代数多项式优质性质,本文构造出一组λαβ-TC-Bézier基函数,并讨论了其性质;定义了由该基函数生成λαβ-TC-Bézier曲线,三个形状参数λ、α和β含在曲线中,调节λ、α和β值的大小,可以调节曲线的形状;该曲线可以精确表示椭圆弧、圆弧和抛物线弧等二次曲线,还研究了两段曲线C1连续的拼接条件。According to the requirement of free design that curves should simultaneously have high properties of trigonometry and algebraic polynomials,a set of λαβ-TC-Bézier basis functions are constructed and their properties are discussed.λαβ-TC-Bézier curves generated by the basis functions are defined,which include three shape parameters of λ、α and β to adjust the shape of the curves.The curves are capable of representing conics such as elliptic arc,circular arc and parabolic arc exactly.The joining conditions for C1 continuity of two curves are also analyzed.

关 键 词：BÉZIER曲线 曲线设计 形状参数 扩展 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]