Circular Arc Representation based on M?bius Transformation
[1]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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Journal of Zhengzhou University (Engineering Science)[ISSN
1671-6833/CN
41-1339/T] Volume:
38卷
Number of periods:
2017 06
Page number:
50-53,58
Column:
Public date:
2017-11-20
- Title:
- Circular Arc Representation based on M?bius Transformation
- CLC:
- -
- DOI:
- 10.3969/j.issn.1671-6833.2017.03.004
- 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.
- References:
- -
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