“Computational design and automated fabrication of kirchhoff-plateau surfaces” by Rodríguez, Otaduy and Thomaszewski
Conference:
Type(s):
Title:
- Computational design and automated fabrication of kirchhoff-plateau surfaces
Session/Category Title: Fabricating Curves, Surfaces & Volumes
Presenter(s)/Author(s):
Abstract:
We propose a computational tool for designing Kirchhoff-Plateau Surfaces—planar rod networks embedded in pre-stretched fabric that deploy into complex, three-dimensional shapes. While Kirchhoff-Plateau Surfaces offer an intriguing and expressive design space, navigating this space is made difficult by the highly nonlinear nature of the underlying mechanical problem. In order to tackle this challenge, we propose a user-guided but computer-assisted approach that combines an efficient forward simulation model with a dedicated optimization algorithm in order to implement a powerful set of design tools. We demonstrate our method by designing a diverse set of complex-shaped Kirchhoff-Plateau Surfaces, each validated through physically-fabricated prototypes.
References:
1. Aric Bartle, Alla Sheffer, Vladimir G. Kim, Danny M. Kaufman, Nicholas Vining, and Floraine Berthouzoz. 2016. Physics-driven Pattern Adjustment for Direct 3D Garment Editing. ACM Trans. Graph. 35, 4, Article 50 (July 2016), 11 pages. Google ScholarDigital Library
2. Miklós Bergou, Basile Audoly, Etienne Vouga, Max Wardetzky, and Eitan Grinspun. 2010. Discrete Viscous Threads. ACM Trans. Graph. (Proc. SIGGRAPH) 29, 4, Article 116 (2010).Google ScholarDigital Library
3. Miklós Bergou, Max Wardetzky, Stephen Robinson, Basile Audoly, and Eitan Grinspun. 2008. Discrete Elastic Rods. ACM Trans. Graph. (Proc. SIGGRAPH) 27, 3, Article 63 (2008).Google ScholarDigital Library
4. Florence Bertails, Basile Audoly, Marie-Paule Cani, Bernard Querleux, Frédéric Leroy, and Jean-Luc Lévêque. 2006. Super-helices for Predicting the Dynamics of Natural Hair. In Proc. of ACM SIGGRAPH ’06. Google ScholarDigital Library
5. Philippe Block and John Ochsendorf. 2007. Thrust Network Analysis: A New Methodology for Three-Dimensional Equilibrium. Journal of the International Association for Shell and Spatial Structures 48, 3, Article 155 (2007).Google Scholar
6. Xiang Chen, Changxi Zheng, Weiwei Xu, and Kun Zhou. 2014. An Asymptotic Numerical Method for Inverse Elastic Shape Design. ACM Trans. Graph. 33, 4, Article 95 (July 2014), 11 pages. Google ScholarDigital Library
7. Xiang ‘Anthony’ Chen, Stelian Coros, Jennifer Mankoff, and Scott E. Hudson. 2015. Encore: 3D Printed Augmentation of Everyday Objects with Printed-over, Affixed and Interlocked Attachments. In ACM SIGGRAPH 2015 Posters (SIGGRAPH ’15). ACM, New York, NY, USA, Article 3, 1 pages. Google ScholarDigital Library
8. Keenan Crane, Ulrich Pinkall, and Peter Schröder. 2011. Spin Transformations of Discrete Surfaces. ACM Trans. Graph. 30, 4, Article 104 (July 2011), 10 pages. Google ScholarDigital Library
9. Fernando de Goes, Pierre Alliez, Houman Owhadi, and Mathieu Desbrun. 2013. On the Equilibrium of Simplicial Masonry Structures. ACM Trans. Graph. 32, 4 (2013). Google ScholarDigital Library
10. Philippe Decaudin, Dan Julius, Jamie Wither, Laurence Boissieux, Alla Sheffer, and Marie-Paule Cani. 2006. Virtual Garments: A Fully Geometric Approach for Clothing Design. Computer Graphics Forum (2006). Google ScholarCross Ref
11. Bailin Deng, Sofien Bouaziz, Mario Deuss, Alexandre Kaspar, Yuliy Schwartzburg, and Mark Pauly. 2015. Interactive Design Exploration for Constrained Meshes. Computer-Aided Design 61 (2015), 13 — 23. Google ScholarDigital Library
12. Alexandre Derouet-Jourdan, Florence Bertails-Descoubes, and Joëlle Thollot. 2010. Stable Inverse Dynamic Curves. ACM Trans. Graph. 29, 6, Article 137 (Dec. 2010), 10 pages. Google ScholarDigital Library
13. Gerhard Dziuk and John E. Hutchinson. 1999. The Discrete Plateau Problem: Algorithm and Numerics. Math. Comput. 68, 225 (Jan. 1999), 1–23. Google ScholarDigital Library
14. Akash Garg, Andrew O. Sageman-Furnas, Bailin Deng, Yonghao Yue, Eitan Grinspun, Mark Pauly, and Max Wardetzky. 2014. Wire Mesh Design. ACM Trans. Graph. (Proc. SIGGRAPH) 33, 4 (2014).Google ScholarDigital Library
15. L. Giomi and L. Mahadevan. 2012. Minimal surfaces bounded by elastic lines. Proceedings: Mathematical, Physical and Engineering Sciences 468, 2143 (2012), 1851–1864. Google ScholarCross Ref
16. Giulio G. Giusteri, Paolo Franceschini, and Eliot Fried. 2016. Instability Paths in the Kirchhoff-Plateau Problem. Journal of Nonlinear Science 26, 4 (2016), 1097–1132. Google ScholarCross Ref
17. Giulio G. Giusteri, Luca Lussardi, and Eliot Fried. 2017. Solution of the Kirchhoff-Plateau Problem. Journal of Nonlinear Science (2017), 1–21. Google ScholarCross Ref
18. Eitan Grinspun, Anil N. Hirani, Mathieu Desbrun, and Peter Schröder. 2003. Discrete Shells. In Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’03). 62–67.Google ScholarDigital Library
19. Christophe Guberan and Carlo Clopath. 2016. Active Shoes. http://www.selfassemblylab.net/ActiveShoes.php. (2016). MIT Self Assembly Lab.Google Scholar
20. Jean Hergel and Sylvain Lefebvre. 2014. Clean Color: Improving Multi-filament 3D Prints. Computer Graphics Forum (2014). Google ScholarDigital Library
21. Martin Kilian, Simon Flöry, Zhonggui Chen, Niloy J. Mitra, Alla Sheffer, and Helmut Pottmann. 2008. Curved Folding. ACM Trans. Graph. 27, 3, Article 75 (Aug. 2008), 9 pages. Google ScholarDigital Library
22. 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, Article 89 (July 2016), 11 pages. Google ScholarDigital Library
23. K. Koohestani. 2014. Nonlinear force density method for the form-finding of minimal surface membrane structures. Communications in Nonlinear Science and Numerical Simulation 19, 6 (2014), 2071 — 2087. Google ScholarCross Ref
24. Yijing Li and Jernej Barbič. 2014. Stable Orthotropic Materials. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’14). 41–46.Google Scholar
25. Julian Lienhard, Holger Alpermann, Christoph Gengnagel, and Jan Knippers. 2013. Active Bending: a Review on Structures where Bending is Used as a Self-Formation Process. International Journal of Space Structures 28, 3–4 (2013), 187–196.Google ScholarCross Ref
26. 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. Google ScholarDigital Library
27. Yang Liu, Helmut Pottmann, Johannes Wallner, Yong-Liang Yang, and Wenping Wang. 2006. Geometric Modeling with Conical Meshes and Developable Surfaces. ACM Trans. Graph. 25, 3 (July 2006), 681–689. Google ScholarDigital Library
28. William H. III Meeks and Joaquín Pérez. 2011. The classical theory of minimal surfaces. Bull. Amer. Math. Soc. 48 (2011), 325–407.Google ScholarCross Ref
29. Eder Miguel, Derek Bradley, Bernhard Thomaszewski, Bernd Bickel, Wojciech Matusik, Miguel A. Otaduy, and Steve Marschner. 2012. Data-Driven Estimation of Cloth Simulation Models. Comput. Graph. Forum 31, 2 (2012), 519–528. Google ScholarDigital Library
30. 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. Google ScholarDigital Library
31. Yuki Mori and Takeo Igarashi. 2007. Plushie: An Interactive Design System for Plush Toys. ACM Trans. Graph. (Proc. SIGGRAPH) (2007).Google ScholarDigital Library
32. Stefanie Mueller, Tobias Mohr, Kerstin Guenther, Johannes Frohnhofen, and Patrick Baudisch. 2014. faBrickation: Fast 3D Printing of Functional Objects by Integrating Construction Kit Building Blocks. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI ’14). ACM, New York, NY, USA, 3827–3834. Google ScholarDigital Library
33. Przemyslaw Musialski, Christian Hafner, Florian Rist, Michael Birsak, Michael Wimmer, and Leif Kobbelt. 2016. Non-linear Shape Optimization Using Local Subspace Projections. ACM Trans. Graph. 35, 4, Article 87 (July 2016), 13 pages. Google ScholarDigital Library
34. J. Nocedal and S. J. Wright. 2006. Numerical Optimization (2nd ed.). Springer, New York.Google Scholar
35. Hao Pan, Yi-King Choi, Yang Liu, Wenchao Hu, Qiang Du, Konrad Polthier, Caiming Zhang, and Wenping Wang. 2012. Robust Modeling of Constant Mean Curvature Surfaces. ACM Trans. Graph. 31, 4, Article 85 (July 2012), 11 pages. Google ScholarDigital Library
36. Daniele Panozzo, Philippe Block, and Olga Sorkine-Hornung. 2013. Designing Unreinforced Masonry Models. ACM Trans. Graph. 32, 4, Article 91 (July 2013), 12 pages. Google ScholarDigital Library
37. Jesús Pérez, Bernhard Thomaszewski, Stelian Coros, Bernd Bickel, José A. Canabal, Robert Sumner, and Miguel A. Otaduy. 2015. Design and Fabrication of Flexible Rod Meshes. ACM Trans. Graph. (Proc. SIGGRAPH) 34, 4, Article 138 (2015).Google ScholarDigital Library
38. Helmut Pottmann, Michael Eigensatz, Amir Vaxman, and Johannes Wallner. 2015. Architectural Geometry. Comput. Graph. 47, C (April 2015), 145–164. Google ScholarDigital Library
39. Christian Schüller, Daniele Panozzo, Anselm Grundhöfer, Henning Zimmer, Evgeni Sorkine, and Olga Sorkine-Hornung. 2016. Computational Thermoforming. ACM Trans. Graph. 35, 4, Article 43 (July 2016), 9 pages. Google ScholarDigital Library
40. 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.Google ScholarDigital Library
41. Mélina Skouras, Bernhard Thomaszewski, Peter Kaufmann, Akash Garg, Bernd Bickel, Eitan Grinspun, and Markus Gross. 2014. Designing Inflatable Structures. ACM Trans. Graph. (Proc. SIGGRAPH) 33, 4 (2014).Google ScholarDigital Library
42. Justin Solomon, Etienne Vouga, Max Wardetzky, and Eitan Grinspun. 2012. Flexible Developable Surfaces. Comput. Graphics Forum 31, 5 (2012).Google Scholar
43. Olga Sorkine. 2005. Laplacian Mesh Processing. In Eurographics 2005 – State of the Art Reports, Yiorgos Chrysanthou and Marcus Magnor (Eds.). The Eurographics Association.Google Scholar
44. J. Spillmann and M. Teschner. 2007. CoRdE: Cosserat Rod Elements for the Dynamic Simulation of One-dimensional Elastic Objects. In Proceedings of the 2007 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’07). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 63–72. http://dl.acm.org/citation.cfm?id=1272690.1272700Google Scholar
45. Chengcheng Tang, Pengbo Bo, Johannes Wallner, and Helmut Pottmann. 2016. Interactive Design of Developable Surfaces. ACM Trans. Graph. 35, 2, Article 12 (Jan. 2016), 12 pages. Google ScholarDigital Library
46. 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. Google ScholarDigital Library
47. Christopher D. Twigg and Zoran Kačić-Alesić. 2011. Optimization for Sag-free Simulations. In Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’11). ACM, New York, NY, USA, 225–236. Google ScholarDigital Library
48. Nobuyuki Umetani, Danny M. Kaufman, Takeo Igarashi, and Eitan Grinspun. 2011. Sensitive Couture for Interactive Garment Modeling and Editing. ACM Trans. Graph. 30, 4, Article 90 (July 2011), 12 pages. Google ScholarDigital Library
49. T. Van Mele, L. De Laet, D. Veenendaal, M. Mollaert, and P. Block. 2013. Shaping tension structures by actively bent linear elements. International Journal of Space Structures 28, 3 (2013), 127–135. Google ScholarCross Ref
50. Amir Vaxman. 2014. A Projective Framework for Polyhedral Mesh Modelling. Comput. Graph. Forum 33, 8 (Dec. 2014), 121–131. Google ScholarDigital Library
51. 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. Google ScholarDigital Library
52. 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. Google ScholarDigital Library
53. Yong-Liang Yang, Yi-Jun Yang, Helmut Pottmann, and Niloy J. Mitra. 2011. Shape Space Exploration of Constrained Meshes. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 30, 6 (2011).Google Scholar
54. Jonas Zehnder, Stelian Coros, and Bernhard Thomaszewski. 2016. Designing Structurally-sound Ornamental Curve Networks. ACM Trans. Graph. 35, 4, Article 99 (2016), 99:1–99:10 pages.Google ScholarDigital Library
55. Haisen Zhao, Fanglin Gu, Qi-Xing Huang, Jorge Garcia, Yong Chen, Changhe Tu, Bedrich Benes, Hao Zhang, Daniel Cohen-Or, and Baoquan Chen. 2016. Connected Fermat Spirals for Layered Fabrication. ACM Trans. Graph. 35, 4, Article 100 (July 2016), 10 pages. Google ScholarDigital Library
56. Henrik Zimmer and Leif Kobbelt. 2014. Zometool rationalization of freeform surfaces. IEEE Trans. on Visualization and Computer Graphics 20, 10 (2014).Google Scholar