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A Note on Superspirals of Confluent Type

Author

Listed:
  • Jun-ichi Inoguchi

    (Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan
    These authors contributed equally to this work.)

  • Rushan Ziatdinov

    (Department of Industrial Engineering, Keimyung University, Daegu 704-701, Korea
    These authors contributed equally to this work.)

  • Kenjiro T. Miura

    (Department of Mechanical Engineering, Shizuoka University, Hamamatsu 432-8561, Japan
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Jun-ichi Inoguchi & Rushan Ziatdinov & Kenjiro T. Miura, 2020. "A Note on Superspirals of Confluent Type," Mathematics, MDPI, vol. 8(5), pages 1-9, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:762-:d:356444
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