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The generalized Gielis geometric equation and its application


Shi, P and Ratkowsky, DA and Gielis, J, The generalized Gielis geometric equation and its application, Symmetry, 12, (4) Article 645. ISSN 2073-8994 (2020) [Refereed Article]


Copyright Statement

Copyright 2020 The Authors. Licensed under Creative Commons Attribution 4.0 International (CC BY 4.0)

DOI: doi:10.3390/sym12040645


Many natural shapes exhibit surprising symmetry and can be described by the Gielis equation, which has several classical geometric equations (for example, the circle, ellipse and superellipse) as special cases. However, the original Gielis equation cannot reflect some diverse shapes due to limitations of its power-law hypothesis. In the present study, we propose a generalized version by introducing a link function. Thus, the original Gielis equation can be deemed to be a special case of the generalized Gielis equation (GGE) with a power-law link function. The link function can be based on the morphological features of different objects so that the GGE is more flexible in fitting the data of the shape than its original version. The GGE is shown to be valid in depicting the shapes of some starfish and plant leaves.

Item Details

Item Type:Refereed Article
Keywords:data fitting, hyperbolic functions, leaf shape, polar coordinates, power-law functions, starfish
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Applied mathematics not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Ratkowsky, DA (Dr David Ratkowsky)
ID Code:138684
Year Published:2020
Web of Science® Times Cited:12
Deposited By:TIA - Research Institute
Deposited On:2020-04-21
Last Modified:2021-07-19
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