On elastic geodesic grids and their planar to spatial deployment

dc.contributor.authorPillwein, Stefan
dc.contributor.authorLeimer, Kurt
dc.contributor.authorBirsak, Michael
dc.contributor.authorMusialski, Przemyslaw
dc.contributor.departmentVisual Computing Center (VCC)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.institutionTU Wien
dc.contributor.institutionNJIT
dc.date.accessioned2020-10-22T13:06:49Z
dc.date.available2020-10-22T13:06:49Z
dc.date.issued2020-08-12
dc.date.published-online2020-08-12
dc.date.published-print2020-07-08
dc.description.abstractWe 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.
dc.description.sponsorshipThis 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.
dc.eprint.versionPre-print
dc.identifier.arxivid2007.00201
dc.identifier.citationPillwein, 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
dc.identifier.doi10.1145/3386569.3392490
dc.identifier.eid2-s2.0-85092434610
dc.identifier.issn1557-7368
dc.identifier.issn0730-0301
dc.identifier.issue4
dc.identifier.journalACM Transactions on Graphics
dc.identifier.urihttp://hdl.handle.net/10754/665654
dc.identifier.volume39
dc.publisherAssociation for Computing Machinery (ACM)
dc.relation.urlhttps://dl.acm.org/doi/10.1145/3386569.3392490
dc.relation.urlhttp://arxiv.org/pdf/2007.00201
dc.rights© ACM, 2020. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in [JournalTitle], {[Volume], [Issue], (2020-08-12)} http://doi.acm.org/10.1145/3386569.3392490
dc.rightsThis file is an open access version redistributed from: http://arxiv.org/pdf/2007.00201
dc.titleOn elastic geodesic grids and their planar to spatial deployment
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Pillwein, Stefan,equals">Pillwein, Stefan</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Leimer, Kurt,equals">Leimer, Kurt</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Birsak, Michael,equals">Birsak, Michael</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Musialski, Przemyslaw,equals">Musialski, Przemyslaw</a><br><br><h5>KAUST Department</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Visual Computing Center (VCC),equals">Visual Computing Center (VCC)</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division,equals">Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division</a><br><br><h5>Online Publication Date</h5>2020-08-12<br><br><h5>Print Publication Date</h5>2020-07-08<br><br><h5>Date</h5>2020-08-12</span>
display.details.right<span><h5>Abstract</h5>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.<br><br><h5>Citation</h5>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<br><br><h5>Acknowledgements</h5>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.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Association for Computing Machinery (ACM),equals">Association for Computing Machinery (ACM)</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=ACM Transactions on Graphics,equals">ACM Transactions on Graphics</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1145/3386569.3392490">10.1145/3386569.3392490</a><br><br><h5>arXiv</h5><a href="https://arxiv.org/abs/2007.00201">2007.00201</a><br><br><h5>Additional Links</h5>https://dl.acm.org/doi/10.1145/3386569.3392490http://arxiv.org/pdf/2007.00201</span>
kaust.personBirsak, Michael
refterms.dateFOA2020-12-07T13:37:05Z
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