On elastic geodesic grids and their planar to spatial deployment

Abstract
We propose a novel type of planar-to-spatial deployable structures that we call elastic geodesic grids. Our approach aims at the approximation of freeform surfaces with spatial grids of bent lamellas which can be deployed from a planar configuration using a simple kinematic mechanism. Such elastic structures are easy-to-fabricate and easy-to-deploy and approximate shapes which combine physics and aesthetics. We propose a solution based on networks of geodesic curves on target surfaces and we introduce a set of conditions and assumptions which can be closely met in practice. Our formulation allows for a purely geometric approach which avoids the necessity of numerical shape optimization by building on top of theoretical insights from differential geometry. We propose a solution for the design, computation, and physical simulation of elastic geodesic grids, and present several fabricated small-scale examples with varying complexity. Moreover, we provide an empirical proof of our method by comparing the results to laser-scans of the fabricated models. Our method is intended as a form-finding tool for elastic gridshells in architecture and other creative disciplines and should give the designer an easy-to-handle way for the exploration of such structures.

Citation
Pillwein, S., Leimer, K., Birsak, M., & Musialski, P. (2020). On elastic geodesic grids and their planar to spatial deployment. ACM Transactions on Graphics, 39(4). doi:10.1145/3386569.3392490

Acknowledgements
This research was mainly funded by the Vienna Science and Technology Fund (WWTF ICT15-082) and partially also by the Austrian Science Fund (FWF P27972-N31). The authors thank Florian Rist, Christian Müller, and Helmut Pottmann for inspiring discussions, as well as Etienne Vouga and Josh Vekhter for sharing code.

Publisher
Association for Computing Machinery (ACM)

Journal
ACM Transactions on Graphics

DOI
10.1145/3386569.3392490

arXiv
2007.00201

Additional Links
https://dl.acm.org/doi/10.1145/3386569.3392490http://arxiv.org/pdf/2007.00201

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