与给定多边形相切的C^2连续三角B样条可调曲线及其在造型中的应用  

C^2 Continuous Quasi-cubic Trigonometric Adjustable B-Spline Curves Tangent to Given Polygon and Applications in Modeling

作　　者：王成伟[1] 张卷美[2] WANG Chengwei;ZHANG Juanmei(Beijing Institute of Clothing 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》2020年第1期67-71,共5页Journal of Beijing Electronic Science And Technology Institute

基　　金：2019年国家级大学生创新创业训练计划项目(项目编号:201910018003)。

摘　　要：讨论了与给定控制多边形相切的三角B样条可调曲线的构造方法,所构造的曲线是C^2连续的,而且对可控制多边形是具有保形性。通过切线多边形的顶点简单计算产生了所有的三角B样条可调曲线段的控制点,曲线在一定范围内可以进行局部的修改。实例表明本文的方法是灵活可行的。A method for constructing quasi-cubic trigonometric adjustable B-spline curves tangent to a given control polygon is discussed in this paper.The constructed curves are C^2 continuous and have shape preserving property for controlled polygon.By simply calculating the vertices of the tangent polygon,all control points of quasi-cubic trigonometric adjustable B-spline curve segment are generated,and the curves could be modified locally in a certain range.The examples indicate that the method is flexible and feasible.

关 键 词：CAGD 样条曲线 多边形 形状参数 

分 类 号：O241.3[理学—计算数学] TP391.72[理学—数学]