“CurveUps: shaping objects from flat plates with tension-actuated curvature” by Guseinov, Miguel and Bickel
Conference:
Type(s):
Title:
- CurveUps: shaping objects from flat plates with tension-actuated curvature
Session/Category Title: Fabricating Curves, Surfaces & Volumes
Presenter(s)/Author(s):
Abstract:
We present a computational approach for designing CurveUps, curvy shells that form from an initially flat state. They consist of small rigid tiles that are tightly held together by two pre-stretched elastic sheets attached to them. Our method allows the realization of smooth, doubly curved surfaces that can be fabricated as a flat piece. Once released, the restoring forces of the pre-stretched sheets support the object to take shape in 3D. CurveUps are structurally stable in their target configuration. The design process starts with a target surface. Our method generates a tile layout in 2D and optimizes the distribution, shape, and attachment areas of the tiles to obtain a configuration that is fabricable and in which the curved up state closely matches the target. Our approach is based on an efficient approximate model and a local optimization strategy for an otherwise intractable nonlinear optimization problem. We demonstrate the effectiveness of our approach for a wide range of shapes, all realized as physical prototypes.
References:
1. Byoungkwon An, Shuhei Miyashita, Michael T Tolley, Daniel M Aukes, Laura Meeker, Erik D Demaine, Martin L Demaine, Robert J Wood, and Daniela Rus. 2014. An end-to-end approach to making self-folded 3D surface shapes by uniform heating. In International Conference on Robotics and Automation (ICRA). 1466–1473. Google ScholarCross Ref
2. Paolo Cignoni, Nico Pietroni, Luigi Malomo, and Roberto Scopigno. 2014. Field-aligned mesh joinery. ACM Trans. Graph. 33, 1 (2014), 11. Google ScholarDigital Library
3. Erik D Demaine and Joseph O’Rourke. 2007. Geometric folding algorithms. Cambridge university press Cambridge.Google Scholar
4. Mario Deuss, Daniele Panozzo, Emily Whiting, Yang Liu, Philippe Block, Olga Sorkine-Hornung, and Mark Pauly. 2014. Assembling self-supporting structures. ACM Trans. Graph. 33, 6 (2014), 1. Google ScholarDigital Library
5. Levi H Dudte, Etienne Vouga, Tomohiro Tachi, and L Mahadevan. 2016. Programming curvature using origami tessellations. Nature materials (Jan. 2016).Google Scholar
6. Michael Eigensatz, Martin Kilian, Alexander Schiftner, Niloy J Mitra, Helmut Pottmann, and Mark Pauly. 2010. Paneling architectural freeform surfaces. ACM Trans. Graph. 29, 4 (2010), 45. Google ScholarDigital Library
7. Samuel M Felton, Michael T Tolley, ByungHyun Shin, Cagdas D Onal, Erik D Demaine, Daniela Rus, and Robert J Wood. 2013. Self-folding with shape memory composites. Soft Matter 9, 32 (July 2013), 7688–7694.Google ScholarCross Ref
8. Akash Garg, Andrew O Sageman-Furnas, Bailin Deng, Yonghao Yue, Eitan Grinspun, Mark Pauly, and Max Wardetzky. 2014. Wire mesh design. ACM Trans. Graph. 33, 4 (2014), 66–1.Google ScholarDigital Library
9. A Sydney Gladman, Elisabetta A Matsumoto, Ralph G Nuzzo, L Mahadevan, and Jennifer A Lewis. 2016. Biomimetic 4D printing. Nature materials 15, 4 (April 2016), 413–418.Google Scholar
10. Elliot Hawkes, B An, NM Benbernou, H Tanaka, S Kim, ED Demaine, D Rus, and RJ Wood. 2010. Programmable matter by folding. Proc. National Academy of Sciences 107, 28 (2010), 12441–12445.Google ScholarCross Ref
11. Kristian Hildebrand, Bernd Bickel, and Marc Alexa. 2012. crdbrd: Shape fabrication by sliding planar slices. In Computer Graphics Forum, Vol. 31. 583–592. Google ScholarDigital Library
12. Yuki Igarashi, Takeo Igarashi, and Jun Mitani. 2012. Beady: interactive beadwork design and construction. ACM Trans. Graph. 31, 4 (2012), 49. Google ScholarDigital Library
13. Martin Kilian, Simon Flöry, Zhonggui Chen, Niloy J Mitra, Alla Sheffer, and Helmut Pottmann. 2008. Curved folding. ACM Trans. Graph. 27, 3 (2008), 75. Google ScholarDigital Library
14. Jungwook Kim, James A Hanna, Myunghwan Byun, Christian D Santangelo, and Ryan C Hayward. 2012. Designing responsive buckled surfaces by halftone gel lithography. Science 335, 6073 (2012), 1201–1205. Google ScholarCross Ref
15. Mina Konaković, Keenan Crane, Bailin Deng, Sofien Bouaziz, Daniel Piker, and Mark Pauly. 2016. Beyond developable: computational design and fabrication with auxetic materials. ACM Trans. Graph. 35, 4 (2016), 89. Google ScholarDigital Library
16. Tsz-Ho Kwok, Charlie C. L. Wang, Dongping Deng, Yunbo Zhang, and Yong Chen. 2015. Four-Dimensional Printing for Freeform Surfaces: Design Optimization of Origami and Kirigami Structures. Journal of Mechanical Design 137 (2015). Google ScholarCross Ref
17. Bruno Lévy, Sylvain Petitjean, Nicolas Ray, and Jérome Maillot. 2002. Least Squares Conformal Maps for Automatic Texture Atlas Generation. ACM Trans. Graph. 21, 3 (July 2002), 362–371. Google ScholarDigital Library
18. F Massarwi, C Gotsman, and G Elber. 2007. Papercraft Models using Generalized Cylinders. 15th Pacific Conference on Computer Graphics and Applications (PG’07) (2007), 148–157. Google ScholarDigital Library
19. Jun Mitani and Takeo Igarashi. 2011. Interactive design of planar curved folding by reflection. Pacific Graphics (short paper) (2011).Google Scholar
20. Jifei Ou, Mélina Skouras, Nikolaos Vlavianos, Felix Heibeck, Chin-Yi Cheng, Jannik Peters, and Hiroshi Ishii. 2016. aeroMorph-Heat-sealing Inflatable Shape-change Materials for Interaction Design. In Proc. 29th Annual Symposium on User Interface Software and Technology. ACM, 121–132. Google ScholarDigital Library
21. A. C. Pipkin. 1986. The relaxed energy density for isotropic elastic membranes. IMA Journal of Applied Mathematics 36 (1986). Google ScholarCross Ref
22. Helmut Pottmann, Alexander Schiftner, Pengbo Bo, Heinz Schmiedhofer, Wenping Wang, Niccolo Baldassini, and Johannes Wallner. 2008. Freeform surfaces from single curved panels. ACM Trans. Graph. 27, 3 (2008), 76. Google ScholarDigital Library
23. Dan Raviv, Wei Zhao, Carrie McKnelly, Athina Papadopoulou, Achuta Kadambi, Boxin Shi, Shai Hirsch, Daniel Dikovsky, Michael Zyracki, Carlos Olguin, and others. 2014. Active printed materials for complex self-evolving deformations. Scientific reports 4 (2014).Google Scholar
24. Jennie Ryu, Matteo D’Amato, Xiaodong Cui, Kevin N Long, H Jerry Qi, and Martin L Dunn. 2012. Photo-origami—Bending and folding polymers with light. Applied Physics Letters 100, 16 (2012), 161908.Google ScholarCross Ref
25. Yuliy Schwartzburg and Mark Pauly. 2013. Fabrication-aware Design with Intersecting Planar Pieces. Computer Graphics Forum 32, 2pt3 (2013), 317–326. Google ScholarCross Ref
26. Robert F Shepherd, Filip Ilievski, Wonjae Choi, Stephen A Morin, Adam A Stokes, Aaron D Mazzeo, Xin Chen, Michael Wang, and George M Whitesides. 2011. Multi-gait soft robot. Proc. National Academy of Sciences 108, 51 (2011), 20400–20403.Google ScholarCross Ref
27. Mélina Skouras, Stelian Coros, Eitan Grinspun, and Bernhard Thomaszewski. 2015. Interactive surface design with interlocking elements. ACM Trans. Graph. 34, 6 (2015), 224.Google ScholarDigital Library
28. Mélina Skouras, Bernhard Thomaszewski, Bernd Bickel, and Markus Gross. 2012. Computational Design of Rubber Balloons. Computer Graphics Forum 31, 2pt4 (May 2012), 835–844. Google ScholarDigital Library
29. Mélina Skouras, Bernhard Thomaszewski, Peter Kaufmann, Akash Garg, Bernd Bickel, Eitan Grinspun, and Markus Gross. 2014. Designing inflatable structures. ACM Trans. Graph. 33, 4 (July 2014), 1–10. Google ScholarDigital Library
30. D. J. Steigmann. 1990. Tension-field theory. Proc. Royal Society of London. Series A: Mathematical and Physical Sciences 429 (1990).Google ScholarCross Ref
31. Chengcheng Tang, Pengbo Bo, Johannes Wallner, and Helmut Pottmann. 2016. Interactive design of developable surfaces. ACM Trans. Graph. 35, 2 (2016), 12. Google ScholarDigital Library
32. Michael T Tolley, Samuel M Felton, Shuhei Miyashita, Daniel Aukes, Daniela Rus, and Robert J Wood. 2014. Self-folding origami: shape memory composites activated by uniform heating. Smart Materials and Structures 23, 9 (2014), 094006.Google ScholarCross Ref
33. Etienne Vouga, Mathias Höbinger, Johannes Wallner, and Helmut Pottmann. 2012. Design of self-supporting surfaces. ACM Trans. Graph. 31, 4 (2012), 87. Google ScholarDigital Library