“Position-based tensegrity design” – ACM SIGGRAPH HISTORY ARCHIVES

“Position-based tensegrity design”

  • 2017 SA Technical Papers_Pietroni_Position-Based Tensegrity Design

Conference:


Type(s):


Title:

    Position-based tensegrity design

Session/Category Title:   Form, Furniture and Fashion


Presenter(s)/Author(s):



Abstract:


    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 difficult to design—existing design methods are often restricted to using symmetric or templated configurations, limiting the design space to simple constructions. We introduce an algorithm to automatically create free-form stable tensegrity designs that satisfy both fabrication and geometric 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 formulation, we provide a design framework to explore the highly constrained space of tensegrity structures. We validate our method with simulations and real-world constructions.

References:


    1. Sofien Bouaziz, Mario Deuss, Yuliy Schwartzburg, Thibaut Weise, and Mark Pauly. 2012. Shape-Up: Shaping Discrete Geometry with Projections. Comput. Graph. Forum 31, 5 (Aug. 2012), 1657–1667.
    2. 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.
    3. Robert Connelly. 2013. Tensegrities and Global Rigidity. Springer New York, New York, NY, 267–278.
    4. 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.
    5. 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.
    6. 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. Cross Ref
    7. 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. Cross Ref
    8. Gerald Gamrath, Tobias Fischer, and Tristan Gally et al. 2016. The SCIP Optimization Suite 3.2. Technical Report 15-60. Zuse Institute, Berlin.
    9. Buntara Sthenly Gan, Jingyao Zhang, Dinh-Kien Nguyen, and Eiji Nouchi. 2015. Node-based genetic form-finding of irregular tensegrity structures. Computers & Structures 159 (2015), 61–73.
    10. 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
    11. Steven J Gortler, Alexander D Healy, and Dylan P Thurston. 2010. Characterizing generic global rigidity. American J. of Mathematics 132, 4 (2010), 897–939. Cross Ref
    12. Ariel Hanaor. 2012. Debunking Tensegrity – A Personal Perspective. Int. J. of Space Structures 27, 2–3 (2012), 179–183.
    13. Kristian Hildebrand, Bernd Bickel, and Marc Alexa. 2012. Crdbrd: Shape Fabrication by Sliding Planar Slices. Comput. Graph. Forum 31, 2pt3 (May 2012), 583–592.
    14. Sergi Hernandez Juan and Josep M Mirats Tur. 2008. Tensegrity frameworks: static analysis review. Mechanism and Machine Theory 43, 7 (2008), 859–881. Cross Ref
    15. Martin Kilian, Niloy J. Mitra, and Helmut Pottmann. 2007. Geometric Modeling in Shape Space. ACM Trans. Graph. 26, 3, Article 64 (July 2007).
    16. Kurilpa Bridge. 2009. (2009). http://www.arup.com/projects/kurilpa_bridge.
    17. 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.
    18. 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.
    19. Daniel Lobo and Francisco J Vico. 2010. Evolutionary development of tensegrity structures. Biosystems 101, 3 (2010), 167–176. Cross Ref
    20. 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.
    21. Matthias Müller, Bruno Heidelberger, Marcus Hennix, and John Ratcliff. 2007. Position based dynamics. J. of Visual Communication and Image Representation 18, 2 (2007), 109–118.
    22. Needle Tower. 1968. (1968). http://www.kennethsnelson.net/.
    23. 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.
    24. Chandana Paul, Hod Lipson, and Francisco J Valero Cuevas. 2005. Evolutionary form-finding of tensegrity structures. In Proc. of the 7th annual conf. on Genetic and evolutionary computation. ACM, 3–10.
    25. 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.
    26. András Recski. 2008. Combinatorial Conditions for the Rigidity of Tensegrity Frameworks. Springer Berlin Heidelberg, Berlin, Heidelberg, 163–177.
    27. John Rieffel, Francisco Valero-Cuevas, and Hod Lipson. 2009. Automated discovery and optimization of large irregular tensegrity structures. Computers & Structures 87, 5 (2009), 368–379.
    28. Ben Roth and Walter Whiteley. 1981. Tensegrity frameworks. Trans. of the American Mathematical Society 265, 2 (1981), 419–446. Cross Ref
    29. 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.
    30. 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.
    31. Tomohiro Tachi. 2013. Interactive Freeform Design of Tensegrity. In Advances in Architectural Geometry 2012. Springer, 259–268.
    32. 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.
    33. AG Tibert and Sergio Pellegrino. 2011. Review of form-finding methods for tensegrity structures. Int. J. of Space Structures 26, 3 (2011), 241–255. Cross Ref
    34. 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.
    35. Walter Whiteley. 1984. Infinitesimally rigid polyhedra. I. Statics of frameworks. Trans. of the American Mathematical Society 285, 2 (1984), 431–465. Cross Ref
    36. Walter Whiteley. 1989. Rigidity and Polarity. 2. Weaving lines and Tensegrity Frameworks. Geometriae Dedicata 30, 3 (1989), 255–279. Cross Ref
    37. 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.
    38. 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.
    39. 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. Cross Ref
    40. JY Zhang and M Ohsaki. 2007. Stability conditions for tensegrity structures. Int. J. of Solids and Structures 44, 11 (2007), 3875–3886. Cross Ref
    41. Jing Yao Zhang and Makoto Ohsaki. 2015. Tensegrity Structures. Vol. 6. Springer Japan.


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