A Note on Superspirals of Confluent Type

Jun-ichi Inoguchi, Rushan Ziatdinov and Kenjiro T. Miura
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Jun-ichi Inoguchi: Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan
Rushan Ziatdinov: Department of Industrial Engineering, Keimyung University, Daegu 704-701, Korea
Kenjiro T. Miura: Department of Mechanical Engineering, Shizuoka University, Hamamatsu 432-8561, Japan

Mathematics, 2020, vol. 8, issue 5, 1-9

Abstract: Superspirals include a very broad family of monotonic curvature curves, whose radius of curvature is defined by a completely monotonic Gauss hypergeometric function. They are generalizations of log-aesthetic curves, and other curves whose radius of curvature is a particular case of a completely monotonic Gauss hypergeometric function. In this work, we study superspirals of confluent type via similarity geometry. Through a detailed investigation of the similarity curvatures of superspirals of confluent type, we find a new class of planar curves with monotone curvature in terms of Tricomi confluent hypergeometric function. Moreover, the proposed ideas will be our guide to expanding superspirals.

Keywords: superspiral; hypergeometric function; log-aesthetic curve; similarity geometry; aesthetic shape modeling; CAD (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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