Song2022_Article_GenerationOfTubularAndMembrano.pdf (5.29 MB)
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Generation of tubular and membranous shape textures with curvature functionals

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journal contribution
posted on 01.02.2022, 13:37 authored by Anna Song
Tubular and membranous shapes display a wide range of morphologies that are difficult to analyze within a common framework. By generalizing the classical Helfrich energy of biomembranes, we model them as solutions to a curvature optimization problem in which the principal curvatures may play asymmetric roles. We then give a novel phase-field formulation to approximate this geometric problem, and study its Gamma-limsup convergence. This results in an efficient GPU algorithm that we validate on well-known minimizers of the Willmore energy; the software for the implementation of our algorithm is freely available online. Exploring the space of parameters reveals that this comprehensive framework leads to a wide continuum of shape textures. This first step towards a unifying theory will have several implications, in biology for quantifying tubular shapes or designing bio-mimetic scaffolds, but also in computer graphics, materials science, or architecture.

Funding

Crick (Grant ID: 10045, Grant title: Bonnet FC001045)

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