基于Mbius变换的复有理圆弧样条  

Circular Arc Representation Based on Mbius Transformation

作　　者：任两品 薛均晓 张朝阳 王定标 

机构地区：[1]郑州大学软件与应用科技学院,河南郑州450002

出　　处：《郑州大学学报（工学版）》2017年第6期50-53,58,共5页Journal of Zhengzhou University（Engineering Science）

基　　金：河南省自然科学基金资助项目(162300410262);河南省高校科技创新团队项目(16IRTSTHN027);河南省高等学校重点科研项目(18A4130)

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Mbius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Mbius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.In CNC machinery, the industrial products and machinery parts are often represented by circular arcs.A new method for representing circular arc based on M？bius transformation was presented in the paper. By constructing the M？bius transformation between a straight line segment and a circular curve segment, the arc curve was expressed as a form of complex rational function,and a complex rational arc spline function was also constructed based on the smooth constraints and the M？bius transformation.The representation had no weight factors or control parameters, and it was geometric and affine invariant.Compared with the classical method for representing circular arc,such as NURBS or C-curves,the presented method was much simpler.

关 键 词：计算机数控 圆弧样条 MOEBIUS变换 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]