A Note on Superspirals of Confluent Type

Author:

Inoguchi Jun-ichiORCID,Ziatdinov RushanORCID,Miura Kenjiro T.ORCID

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.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A physicist's guide to the solution of Kummer's equation and confluent hypergeometric functions;Condensed Matter Physics;2022

2. Lines of Curvature for Log Aesthetic Surfaces Characteristics Investigation;Mathematics;2021-10-24

3. Multi-Criteria Assessment of Shape Quality in CAD Systems of the Future;Proceedings of the 30th International Conference on Computer Graphics and Machine Vision (GraphiCon 2020). Part 2;2020-12-17

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