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《Journal of Zhejiang University(Engineering Science)》 2009-01
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Representing rational cubic circular arc by normalized totally positive or generalized Ball methods

TIAN Yi-feng1,2,WANG Guo-jin1,2(1.Institute of Computer Images and Graphics,Zhejiang University,Hangzhou 310027,China;2.State Key Laboratory of CAD&CG,Zhejiang University,Hangzhou 310027,China)  
A set of theory including the sufficient and necessary conditions for representing circular arcs,the central angle range of circular arcs and their geometric illustration was investigated to present circular arcs by the new parametric curves in order to extend the application range of the new parametric curves constructed by normalized totally positive basis and generalized Ball(GB) basis.The most basic and common rational cubic form was analyzed.The methods to express circular arcs based on rational cubic Delgado-Pen~a(DP),Wang-Ball or Said-Ball curves were investigated by using geometric and algebraic methods and basis conversion.The sufficient and necessary conditions for representing circular arcs respectively by three types of curves were found and the corresponding algorithms were derived.The central angle range of circular arcs and their geometric illustration were given.Results can be applied for designing all kinds of circular arcs' rational parameters and identifying whether a rational cubic DP or GB curve is a circular arc.
【Fund】: 国家自然科学基金资助项目(60873111);; 国家“973”重点基础研究发展规划资助项目(2004CB719400)
【CateGory Index】: TP391.72
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