title: Universal natural shapes: from unifying shape description to simple methods for shape analysis and boundary value problems.
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.
authors.affiliation: Department Biosciences Engineering, University of Antwerp, Antwerp, Belgium. johan.gielis@ua.ac.be
authors.forename: Johan
authors.initials: J
authors.lastname: Gielis
authors.forename: Diego
authors.initials: D
authors.lastname: Caratelli
authors.forename: Yohan
authors.initials: Y
authors.lastname: Fougerolle
authors.forename: Paolo Emilio
authors.initials: PE
authors.lastname: Ricci
authors.forename: Ilia
authors.initials: I
authors.lastname: Tavkelidze
authors.forename: Tom
authors.initials: T
authors.lastname: Gerats
mesh_terms: D000465:Algorithms; D001695:Biology; D008962:Models, Theoretical; D010825:Physics