On elastic geodesic grids and their planar to spatial deployment

Stefan Pillwein, Kurt Leimer, Michael Birsak, Przemyslaw Musialski

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


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.
Original languageEnglish (US)
JournalACM Transactions on Graphics
Issue number4
StatePublished - Aug 12 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-10-23
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.


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