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The generalized Gielis geometric equation and its application

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posted on 2023-05-20, 13:52 authored by Shi, P, David RatkowskyDavid Ratkowsky, Gielis, J
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.

History

Publication title

Symmetry

Volume

12

Issue

4

Article number

645

Number

645

Pagination

1-9

ISSN

2073-8994

Department/School

Tasmanian Institute of Agriculture (TIA)

Publisher

MDPI

Place of publication

Switzerland

Rights statement

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

Repository Status

  • Open

Socio-economic Objectives

Expanding knowledge in the biological sciences; Expanding knowledge in the mathematical sciences

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