Family of superspirals with completely monotonic curvature given in terms of Gauss hypergeometric function

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• 作者：Rushan Ziatdinov ; ^{rushanziatdinov@yandex.ru} ; ^{rushanziatdinov@gmail.com} ;
• 关键词：Spiral ; Log-aesthetic curve ; Superspiral ; Monotone curvature ; Fair curve ; Surface of revolution ; Superspiraloid
• 刊名：Computer Aided Geometric Design
• 出版年：2012
• 出版时间：October, 2012
• 年：2012
• 卷：29
• 期：7
• 页码：510-518
• 全文大小：632 K

文摘

We present superspirals, a new and very general family of fair curves, whose radius of curvature is given in terms of a completely monotonic Gauss hypergeometric function. The superspirals are generalizations of log-aesthetic curves, as well as other curves whose radius of curvature is a particular case of a completely monotonic Gauss hypergeometric function. High-accuracy computation of a superspiral segment is performed by the Gauss-Kronrod integration method. The proposed curves, despite their complexity, are the candidates for generating , and non-linear superspiral splines.