带两个参数的拟Bézier曲线

计算机科学 ›› 2014, Vol. 41 ›› Issue (Z11): 100-102.

带两个参数的拟Bézier曲线

葸海英,张贵仓

西北师范大学数学与统计学院兰州730070;西北师范大学数学与统计学院兰州730070

出版日期:2018-11-14 发布日期:2018-11-14
基金资助:
本文受甘肃省自然科学基金(0803RJZA109)资助

Similar Bézier Curves with Two Shape Parameters

XI Hai-ying and ZHANG Gui-cang

Online:2018-11-14 Published:2018-11-14

摘要/Abstract

摘要： 文章主要将Bernstein基函数中的变量u用函数f(u)代替,将Bernstein基函数进行了推广,生成了新的Bézier曲线,称为拟Bézier曲线。讨论了基函数及其生成的曲线的构造和性质。这种拟Bézier曲线不仅有Bézier曲线的优良性质,而且还产生了一些新的特性,如通过调节因子λ的值可以改变拟Bézier曲线的次数[1],同时拟Bézier曲线也可以通过类似的De Casteljau算法来实现拟De Casteljau算法的几何作图法。但不同的是,对相同参数u,Bézier曲线与拟Bézier曲线所对应的点V_i的位置不同。最后讨论了曲线间的拼接问题,其在应用中有一定的研究价值。

关键词: Berntien基函数,Bézier曲线,拟Bézier曲线,G²光滑拼接,调节参数

Abstract: The paper generalized the Bernstein Bases replacing the variable of u by the function f(u).The structure and quality of the new basis were analyzed.This new curve using this bases not only possesses all of the characters of Bézier curve but also produces some advantages.For example, the curve’s degree can easily be changed by adjusting factor,but u do not changes the shape of the curve,and the position for Bezier curve and the proposed Bézier curve to correspond to the points on the curve is different.Finally,the continuity condition of the curve was also discussed.This bases and curve have some study value.

Key words: Bernstein Base,Bézier curve,Similar Bézier curve ,G2 continuity,Adjust control parameters

葸海英,张贵仓. 带两个参数的拟Bézier曲线[J]. 计算机科学, 2014, 41(Z11): 100-102. https://doi.org/

XI Hai-ying and ZHANG Gui-cang. Similar Bézier Curves with Two Shape Parameters[J]. Computer Science, 2014, 41(Z11): 100-102. https://doi.org/

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