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Mbius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Mbius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.
出处
《郑州大学学报（工学版）》
CAS
北大核心
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)
