2017
Journal article
Open Access
Position-based tensegrity design
Pietroni N., Tarini M., Vaxman A., Panozzo D., Cignoni P.
Architectural Geometry Tensegrity Form Finding Software Engineering Shape modeling Computer Graphics and Computer-Aided Design
We propose a novel framework for the computational design of tensegrity structures, which are constructions made of struts and cables, held rigid by continuous tension between the elements. Tensegrities are known to be di cult to design-existing design methods are often restricted to us- ing symmetric or templated con gurations, limiting the design space to simple constructions. We introduce an algorithm to automatically create free-form stable tensegrity designs that satisfy both fabrication and geo- metric constraints, and faithfully approximate input geometric shapes. Our approach sidesteps the usual force-based approach in favor of a geometric optimization on the positions of the elements. Equipped with this formu- lation, we provide a design framework to explore the highly constrained space of tensegrity structures. We validate our method with simulations and real-world constructions.
Source: ACM transactions on graphics 36 (2017). doi:10.1145/3130800.3130809
Publisher: Association for Computing Machinery,, New York, N.Y. , Stati Uniti d'America
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John Riefel, Francisco Valero-Cuevas, and Hod Lipson. 2009. Automated discovery and optimization of large irregular tensegrity structures. Computers & Structures 87, 5 (2009), 368-379.
Ben Roth and Walter Whiteley. 1981. Tensegrity frameworks. Trans. of the American Mathematical Society 265, 2 (1981), 419-446.
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Walter Whiteley. 1984. Infinitesimally rigid polyhedra. I. Statics of frameworks. Trans. of the American Mathematical Society 285, 2 (1984), 431-465.
Walter Whiteley. 1989. Rigidity and Polarity. 2. Weaving lines and Tensegrity Frameworks. Geometriae Dedicata 30, 3 (1989), 255-279.
Emily Whiting, John Ochsendorf, and Frédo Durand. 2009. Procedural Modeling of Structurally-sound Masonry Buildings. ACM Trans. Graph. 28, 5, Article 112 (Dec. 2009), 9 pages. DOI:http://dx.doi.org/10.1145/1618452.1618458
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JY Zhang and M Ohsaki. 2006. Adaptive force density method for form-finding problem of tensegrity structures. Int. J. of Solids and Structures 43, 18 (2006), 5658-5673.
JY Zhang and M Ohsaki. 2007. Stability conditions for tensegrity structures. Int. J. of Solids and Structures 44, 11 (2007), 3875-3886.
Jing Yao Zhang and Makoto Ohsaki. 2015. Tensegrity Structures. Vol. 6. Springer Japan.
Paolo Cignoni, Nico Pietroni, Luigi Malomo, and Roberto Scopigno. 2014. Field-aligned Mesh Joinery. ACM Trans. Graph. 33, 1, Article 11 (Feb. 2014), 12 pages. DOI: http://dx.doi.org/10.1145/2537852
Robert Connelly. 2013. Tensegrities and Global Rigidity. Springer New York, New York, NY, 267-278. DOI:http://dx.doi.org/10.1007/978-0-387-92714-5_21
Robert Connelly and Walter Whiteley. 1996. Second-order rigidity and prestress stability for tensegrity frameworks. SIAM J. on Discrete Mathematics 9, 3 (1996), 453-491.
Fernando de Goes, Pierre Alliez, Houman Owhadi, and Mathieu Desbrun. 2013. On the Equilibrium of Simplicial Masonry Structures. ACM Trans. Graph. 32, 4, Article 93 (July 2013), 10 pages. DOI:http://dx.doi.org/10.1145/2461912.2461932
Shintaro Ehara and Yoshihiro Kanno. 2010. Topology design of tensegrity structures via mixed integer programming. Int. J. of Solids and Structures 47, 5 (2010), 571-579.
G Gomez Estrada, H-J Bungartz, and Camilla Mohrdieck. 2006. Numerical form-finding of tensegrity structures. Int. J. of Solids and Structures 43, 22 (2006), 6855-6868.
Gerald Gamrath, Tobias Fischer, and Tristan Gally et al. 2016. The SCIP Optimization Suite 3.2. Technical Report 15-60. Zuse Institute, Berlin.
Buntara Sthenly Gan, Jingyao Zhang, Dinh-Kien Nguyen, and Eiji Nouchi. 2015. Nodebased genetic form-finding of irregular tensegrity structures. Computers & Structures 159 (2015), 61-73.
Damien Gauge, Stelian Coros, Sandro Mani, and Bernhard Thomaszewski. 2014. Interactive Design of Modular Tensegrity Characters. In Proc. of the ACM Symp. on Computer Animation (SCA '14). ACM, Eurographics Association, 8. http: //dl.acm.org/citation.cfm?id=2849517.2849539
Steven J Gortler, Alexander D Healy, and Dylan P Thurston. 2010. Characterizing generic global rigidity. American J. of Mathematics 132, 4 (2010), 897-939.
Ariel Hanaor. 2012. Debunking Tensegrity - A Personal Perspective. Int. J. of Space Structures 27, 2-3 (2012), 179-183. DOI:http://dx.doi.org/10.1260/0266-3511.27.2-3. 179 arXiv:http://dx.doi.org/10.1260/0266-3511.27.2-3.179
Kristian Hildebrand, Bernd Bickel, and Marc Alexa. 2012. Crdbrd: Shape Fabrication by Sliding Planar Slices. Comput. Graph. Forum 31, 2pt3 (May 2012), 583-592. DOI: http://dx.doi.org/10.1111/j.1467-8659.2012.03037.x
Sergi Hernandez Juan and Josep M Mirats Tur. 2008. Tensegrity frameworks: static analysis review. Mechanism and Machine Theory 43, 7 (2008), 859-881.
Martin Kilian, Niloy J. Mitra, and Helmut Pottmann. 2007. Geometric Modeling in Shape Space. ACM Trans. Graph. 26, 3, Article 64 (July 2007). DOI:http://dx.doi.org/ 10.1145/1276377.1276457
Kurilpa Bridge. 2009. (2009). http://www.arup.com/projects/kurilpa_bridge.
Yang Liu, Hao Pan, John Snyder, Wenping Wang, and Baining Guo. 2013. Computing Self-supporting Surfaces by Regular Triangulation. ACM Trans. Graph. 32, 4, Article 92 (July 2013), 10 pages. DOI:http://dx.doi.org/10.1145/2461912.2461927
Yang Liu, Weiwei Xu, Jun Wang, Lifeng Zhu, Baining Guo, Falai Chen, and Guoping Wang. 2011. General Planar Quadrilateral Mesh Design Using Conjugate Direction Field. ACM Trans. Graph. 30, 6 (Dec. 2011), 10. DOI:http://dx.doi.org/10.1145/ 2070781.2024174
Daniel Lobo and Francisco J Vico. 2010. Evolutionary development of tensegrity structures. Biosystems 101, 3 (2010), 167-176.
Eder Miguel, Mathias Lepoutre, and Bernd Bickel. 2016. Computational Design of Stable Planar-rod Structures. ACM Trans. Graph. 35, 4, Article 86 (July 2016), 11 pages. DOI:http://dx.doi.org/10.1145/2897824.2925978
Matthias Müller, Bruno Heidelberger, Marcus Hennix, and John Ratclif. 2007. Position based dynamics. J. of Visual Communication and Image Representation 18, 2 (2007), 109-118.
Needle Tower. 1968. (1968). http://www.kennethsnelson.net/.
Daniele Panozzo, Philippe Block, and Olga Sorkine-Hornung. 2013. Designing Unreinforced Masonry Models. ACM Transactions on Graphics (proc. of ACM SIGGRAPH) 32, 4 (2013), 91:1-91:12.
Chandana Paul, Hod Lipson, and Francisco J Valero Cuevas. 2005. Evolutionary formifnding of tensegrity structures. In Proc. of the 7th annual conf. on Genetic and evolutionary computation. ACM, 3-10.
Nico Pietroni, Davide Tonelli, Enrico Puppo, Maurizio Froli, Roberto Scopigno, and Paolo Cignoni. 2015. Statics Aware Grid Shells. Computer Graphics Forum 34, 2 (2015), 627-641.
András Recski. 2008. Combinatorial Conditions for the Rigidity of Tensegrity Frameworks. Springer Berlin Heidelberg, Berlin, Heidelberg, 163-177. DOI:http://dx.doi.org/10. 1007/978-3-540-77200-2_8
John Riefel, Francisco Valero-Cuevas, and Hod Lipson. 2009. Automated discovery and optimization of large irregular tensegrity structures. Computers & Structures 87, 5 (2009), 368-379.
Ben Roth and Walter Whiteley. 1981. Tensegrity frameworks. Trans. of the American Mathematical Society 265, 2 (1981), 419-446.
Yuliy Schwartzburg and Mark Pauly. 2013. Fabrication-aware Design with Intersecting Planar Pieces. Computer Graphics Forum (proc. of Eurographics 2013) 32, 2 (2013), 317-326.
Mélina Skouras, Stelian Coros, Eitan Grinspun, and Bernhard Thomaszewski. 2015. Interactive Surface Design with Interlocking Elements. ACM Trans. Graph. 34, 6, Article 224 (Oct. 2015), 7 pages. DOI:http://dx.doi.org/10.1145/2816795.2818128
Tomohiro Tachi. 2013. Interactive Freeform Design of Tensegrity. In Advances in Architectural Geometry 2012. Springer, 259-268.
Chengcheng Tang, Xiang Sun, Alexandra Gomes, Johannes Wallner, and Helmut Pottmann. 2014. Form-finding with Polyhedral Meshes Made Simple. ACM Trans. Graph. 33, 4, Article 70 (July 2014), 9 pages. DOI:http://dx.doi.org/10.1145/2601097. 2601213
AG Tibert and Sergio Pellegrino. 2011. Review of form-finding methods for tensegrity structures. Int. J. of Space Structures 26, 3 (2011), 241-255.
Etienne Vouga, Mathias Höbinger, Johannes Wallner, and Helmut Pottmann. 2012. Design of Self-supporting Surfaces. ACM Trans. Graph. 31, 4, Article 87 (July 2012), 11 pages. DOI:http://dx.doi.org/10.1145/2185520.2185583
Walter Whiteley. 1984. Infinitesimally rigid polyhedra. I. Statics of frameworks. Trans. of the American Mathematical Society 285, 2 (1984), 431-465.
Walter Whiteley. 1989. Rigidity and Polarity. 2. Weaving lines and Tensegrity Frameworks. Geometriae Dedicata 30, 3 (1989), 255-279.
Emily Whiting, John Ochsendorf, and Frédo Durand. 2009. Procedural Modeling of Structurally-sound Masonry Buildings. ACM Trans. Graph. 28, 5, Article 112 (Dec. 2009), 9 pages. DOI:http://dx.doi.org/10.1145/1618452.1618458
Emily Whiting, Hijung Shin, Robert Wang, John Ochsendorf, and Frédo Durand. 2012. Structural Optimization of 3D Masonry Buildings. ACM Trans. Graph. 31, 6 (2012), 159:1-159:11.
JY Zhang and M Ohsaki. 2006. Adaptive force density method for form-finding problem of tensegrity structures. Int. J. of Solids and Structures 43, 18 (2006), 5658-5673.
JY Zhang and M Ohsaki. 2007. Stability conditions for tensegrity structures. Int. J. of Solids and Structures 44, 11 (2007), 3875-3886.
Jing Yao Zhang and Makoto Ohsaki. 2015. Tensegrity Structures. Vol. 6. Springer Japan.
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BibTeX entry
@article{oai:it.cnr:prodotti:376318,
title = {Position-based tensegrity design},
author = {Pietroni N. and Tarini M. and Vaxman A. and Panozzo D. and Cignoni P.},
publisher = {Association for Computing Machinery,, New York, N.Y. , Stati Uniti d'America},
doi = {10.1145/3130800.3130809},
journal = {ACM transactions on graphics},
volume = {36},
year = {2017}
}
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