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