可调的类三次Bézier三角插值曲线  

Modifiable Quasi Cubic Bézier Trigonometric Interpolation Curve

作　　者：郭洪恺 杜天琪[1] 江思颖 蓝奕雯 王成伟[2] 

机构地区：[1]北京服装学院材料科学与工程学院,北京100029 [2]北京服装学院基础教学部,北京100029

出　　处：《北京服装学院学报（自然科学版）》2016年第4期70-76,共7页Journal of Beijing Institute of Fashion Technology：Natural Science Edition

基　　金：北京服装学院2016年本科生科研训练项目(NHFZ2016063/005);北京服装学院科学研究一般项目(2016A-14);北京服装学院教育教学改革立项项目(JG-1624);北京服装学院2016校级精品课程提升工程立项项目(JPTS-1609)

摘　　要：Bézier曲线是计算机辅助几何设计中的一类重要曲线,以可调的类三次Bézier三角曲线为例,对可调的类三次Bézier三角曲线的性质进行了分析,并由此推出可调的类三次Bézier三角曲线比三次Bézier曲线更光滑.然后,构造了可调的类三次Bézier三角插值曲线.该曲线继承了Bézier曲线的一些优良特性,并能充分克服Bézier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 one of the important curves in computer-aided geometrical design （CAGD）. Taking the modifiable quasi cubic Bezier trigonometric curve as an example, the charac- ters of this kind curve are analyzed. The above work demonstrated that the modifiable quasi cubic B^zier trigonometric curve was more smooth than the cubic polynomial Bezier curve and the modifia- ble quasi cubic Bezier trigonometric interpolation curves were constructed. These curves inherit not onlysome characteristics of Bezier interpolation curve but can also accurately represent some conic and transcendental curves which Bezier interpolation curves cannot accurately do. Finally, some ca- ses are presented, which demonstrate that the new interpolation curves are more powerful than the Bezier interpolation curve in geometric modeling.

关 键 词：三角曲线 BÉZIER曲线 插值曲线 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术] O241.3[自动化与计算机技术—计算机科学与技术]