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The generalized Gielis geometric equation and its application

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Shi, P, Ratkowsky, DA and Gielis, J 2020 , 'The generalized Gielis geometric equation and its application' , Symmetry, vol. 12 , pp. 1-9 , doi: 10.3390/sym12040645.

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Abstract

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 Type: Article
Authors/Creators:Shi, P and Ratkowsky, DA and Gielis, J
Keywords: data fitting, hyperbolic functions, leaf shape, polar coordinates, power-law functions, starfish
Journal or Publication Title: Symmetry
Publisher: MDPI
ISSN: 2073-8994
DOI / ID Number: 10.3390/sym12040645
Copyright Information:

Copyright 2020 The Authors. Licensed under Creative Commons Attribution 4.0 International (CC BY 4.0) https://creativecommons.org/licenses/by/4.0/

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