带2个形状参数的多项式可展曲面造型  

Developable polynomial surface modeling with two shape parameters

作　　者：王海波[1] 杨当福 佘卫勤 刘圣军[1] 刘新儒[1] 陈月安 白燕羽 WANG Haibo;YANG Dangfu;SHE Weiqin;LIU Shengjun;LIU Xinru;CHEN Yuean;BAI Yanyu(Institute of Engineering Modeling and Scientific Computing,Central South University,Changsha 410083,China;AECC South Industry Co.,Ltd.,Zhuzhou 412000,Hunan Province,China)

机构地区：[1]中南大学工程建模与科学计算研究所,湖南长沙410083 [2]中国航发南方工业有限公司,湖南株洲412000

出　　处：《浙江大学学报（理学版）》2021年第2期131-142,共12页Journal of Zhejiang University（Science Edition）

基　　金：湖南省重点研发计划项目(2017NK2383);国家自然科学基金资助项目(61602524)。

摘　　要：构造了一组带2个形状参数的多项式基函数,其为三次伯恩斯坦基函数的扩展。首先,给出了该组基函数的基本性质,分析了基函数的逼近性和形状可调性,讨论了用该组基函数构造插值样条的保正性和保单调性;然后,基于对偶性原理,用该组基函数构造了包络可展曲面和脊线可展曲面,并分析了可展曲面的G^(1),G^(2)及G^(3)连续性;最后,用实例验证了方法的有效性。This paper constructs a set of polynomial basis functions with two shape parameters,which are extensions of the cubic Bernstein basis functions.The basic properties of the basis functions are outlined,then the approximation and the shape tunability are analyzed,and the positive-preserving and monotonicity-preserving of the interpolation splines constructed with the basis functions are discussed.Based on the duality principle,the basis functions are used to construct the envelope developable surface and the spine curve developable surface.Furthermore,the G^(1),G^(2) and G^(3) continuity of the developable surface are analyzed.The numerical experiments show the effectiveness of this method.

关 键 词：形状参数 可展曲面 多项式插值曲线 保形性 连续性分析 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]