带有参数的Bézier型三角多项式插值曲线  

Bézier-Type Trigonometric Polynomial Interpolation Curves with One Parameter

作　　者：王成伟 WANG Cheng-wei(Department of Fundamental Courses,Beijing Institute of Fashion Technology,Beijing 100029 ,China)

机构地区：[1]北京服装学院基础教学部

出　　处：《北京服装学院学报（自然科学版）》2019年第3期73-77,共5页Journal of Beijing Institute of Fashion Technology：Natural Science Edition

基　　金：北京市教育委员会科研计划项目资助(KM201910012002)

摘　　要：Bezier曲线是计算机辅助几何设计中的一类重要曲线,以带有参数的Bezier型三角多项式曲线为例,对带有参数的Bezier型三角多项式曲线的性质进行了分析,并由此推出带有参数的Bezier型三角多项式曲线比三次Bezier曲线更光滑。然后,构造了带有参数的Bezier型三角多项式插值曲线。该曲线继承了Bezier曲线的一些优良特性,并能充分克服Bezier曲线不能精确表示二次曲线曲面以及某些超越曲线曲面的弱点。最后实例表明了新的插值曲线应用于几何造型的有效性。Bezier curve is an important one curve in CAGD. As an example to Bezier-type trigonometric polynomial curves with one parameter, the characters of Bezier-type trigonometric polynomial curves with one parameter is analyzed, and deduced that Bezier-type trigonometric polynomial curves with one parameter are more smooth than cubic polynomial Bezier curve. Then Bezier-type trigonometric polynomial interpolation curves with one parameter are constructed. The introduced curves inherit some characteristics which the Bezier interpolation curves have. Meanwhile, the new curves can accurately represent some conic and transcendental curve, which are more powerful than the Bezier interpolation curve. At last, the illustrations show that the new interpolation curves are effective in practice on geometric modeling.

关 键 词：三角多项式 BEZIER曲线 插值曲线 

分 类 号：O241.3[理学—计算数学] TP391.72[理学—数学]