Unifying representation of Bézier curve and two kinds of generalized ball curves  

作　　者：ZHU Xiaolin WANG Zhihua 

机构地区：[1]School of Mathematics, Hefei University of Technology, Hefei 230009, China [2]School of Mathematics and Computation Sciences, Anqing Normal University, 246011, China

出　　处：《Computer Aided Drafting,Design and Manufacturing》2012年第2期32-38,共7页计算机辅助绘图设计与制造（英文版）

基　　金：Supported by the Key Project of Chinese Ministry of Education(No.309017);the National Natural Science Foundation of China(No.60473114);the Anhui Provincial Natural Science Foundation(No.07041627)

摘　　要：This paper presents a new basis, the WSB basis, which unifies the Bemstein basis, Wang-Ball basis and Said-Ball basis, and therefore the Bézier curve, Wang-Ball curve and Said-Ball curve are the special cases of the WSB curve based on the WSB basis In addition, the relative degree elevation formula, recursive algorithm and conversion formula between the WSB basis and the Bern- stein basis are given.This paper presents a new basis, the WSB basis, which unifies the Bemstein basis, Wang-Ball basis and Said-Ball basis, and therefore the Bézier curve, Wang-Ball curve and Said-Ball curve are the special cases of the WSB curve based on the WSB basis In addition, the relative degree elevation formula, recursive algorithm and conversion formula between the WSB basis and the Bern- stein basis are given.

关 键 词：BASIS WSB curve Wang-Ball curve Bézier curve degree elevation formula recursive algorithm 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] TQ174[自动化与计算机技术—计算机科学与技术]