Title
Universal natural shapes : from unifying shape description to simple methods for shape analysis and boundary value problems Universal natural shapes : from unifying shape description to simple methods for shape analysis and boundary value problems
Author
Faculty/Department
Faculty of Sciences. Bioscience Engineering
Publication type
article
Publication
Subject
Engineering sciences. Technology
Source (journal)
PLoS ONE
Volume/pages
7(2012) :9 , p. 1-11
ISSN
1932-6203
Article Reference
e29324
Carrier
E-only publicatie
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Gielis curves and surfaces can describe a wide range of natural shapes and they have been used in various studies in biology and physics as descriptive tool. This has stimulated the generalization of widely used computational methods. Here we show that proper normalization of the Levenberg-Marquardt algorithm allows for efficient and robust reconstruction of Gielis curves, including self-intersecting and asymmetric curves, without increasing the overall complexity of the algorithm. Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. In all three methods, descriptive and computational power and efficiency is obtained in a surprisingly simple way.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/47363f/3509.pdf
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