Publication
Title
Universal natural shapes : from unifying shape description to simple methods for shape analysis and boundary value problems
Author
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.
Language
English
Source (journal)
PLoS ONE
Publication
2012
ISSN
1932-6203
Volume/pages
7:9(2012), p. 1-11
Article Reference
e29324
ISI
000309517500001
Medium
E-only publicatie
Full text (Publishers DOI)
Full text (open access)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 06.12.2012
Last edited 14.05.2017
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