[1]任两品,薛均晓,张朝阳,等.基于Möbius变换的复有理圆弧样条[J].郑州大学学报(工学版),2017,38(06):50-53,58.[doi:10.3969/j.issn.1671-6833.2017.03.004]
　Ren Liangpin,Xue Junxiao,Zhang Chaoyang,et al.Circular Arc Representation based on M?bius Transformation[J].Journal of Zhengzhou University (Engineering Science),2017,38(06):50-53,58.[doi:10.3969/j.issn.1671-6833.2017.03.004]
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基于Möbius变换的复有理圆弧样条()
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《郑州大学学报(工学版)》[ISSN:1671-6833/CN:41-1339/T]

卷:
38
期数:
2017年06期
页码:
50-53,58
栏目:
出版日期:
2017-11-20

文章信息/Info

Title:
Circular Arc Representation based on M?bius Transformation
作者:
任两品; 薛均晓; 张朝阳; 王定标
郑州大学软件与应用科技学院,河南郑州,450002
Author(s):
Ren Liangpin; Xue Junxiao;  Zhang Chaoyang;  Wang Dingbiao
College of Software and Applied Science and Technology, Zhengzhou
关键词:
计算机数控; 圆弧样条; Mobius变换
Keywords:
DOI:
10.3969/j.issn.1671-6833.2017.03.004
文献标志码:
A
摘要:
针对工业产品和机械零件设计中的二次圆弧表示问题, 基于Möbius变换的保交比性质和保圆性质, 提出了一种用参数复有理函数精确表示圆弧曲线的方法. 该方法通过构造直线段与圆弧曲线之间的Möbius变换，将圆弧曲线表示为复有理函数的形式，并结合光滑约束条件构造了复有理圆弧样条函数。与Bezier曲线和NURBS曲线等方法相比，该方法能够精确定义二次圆弧曲线，而且不需要反求控制顶点和权因子，实验结果表明所提方法简单易行。
Abstract:
In CNC machinery, the industrial products and machinery parts are often represented by circular arcs. A new method for representing circular arc based on Möbius transformation was presented in the paper. By consturcting the Möbius transformation between a straight line segment and a circular curve segment, the are curve was expressed as a form of complex rational function, and a complex rational are spline function was also constructed based on the smooth constraints and the  Möbius transformation. The reprsentation had no weight factors or control parameters, and it was geometric and affin invariant. Compared with the classical method for representing circular are, such as NURBS or C-curves, the presented method was much simpler.   

相似文献/References:

[1]陈良骥..五轴CNC系统中有效降低非线性误差的两种方法[J].郑州大学学报(工学版),2009,30(02):107.
　CHEN Liangji..Two Methods to Effectively Reduce Nonlinear Errors in Five-axis CNC Systems[J].Journal of Zhengzhou University (Engineering Science),2009,30(06):107.
[2]常家东.涡旋压缩机涡旋盘数控加工研究[J].郑州大学学报(工学版),1998,19(02):76.
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