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.
Supplemental Material
Available for Download
Supplemental files.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Christophe Guberan and Carlo Clopath. 2016. Active Shoes. http://www.selfassemblylab.net/ActiveShoes.php. (2016). MIT Self Assembly Lab.Google Scholar
- Jean Hergel and Sylvain Lefebvre. 2014. Clean Color: Improving Multi-filament 3D Prints. Computer Graphics Forum (2014). Google ScholarDigital Library
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Yuki Mori and Takeo Igarashi. 2007. Plushie: An Interactive Design System for Plush Toys. ACM Trans. Graph. (Proc. SIGGRAPH) (2007).Google ScholarDigital Library
- 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
- 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
- J. Nocedal and S. J. Wright. 2006. Numerical Optimization (2nd ed.). Springer, New York.Google Scholar
- 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
- 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
- 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
- Helmut Pottmann, Michael Eigensatz, Amir Vaxman, and Johannes Wallner. 2015. Architectural Geometry. Comput. Graph. 47, C (April 2015), 145--164. Google ScholarDigital Library
- 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
- 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
- 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
- Justin Solomon, Etienne Vouga, Max Wardetzky, and Eitan Grinspun. 2012. Flexible Developable Surfaces. Comput. Graphics Forum 31, 5 (2012).Google Scholar
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Amir Vaxman. 2014. A Projective Framework for Polyhedral Mesh Modelling. Comput. Graph. Forum 33, 8 (Dec. 2014), 121--131. Google ScholarDigital Library
- 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
- 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
- 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
- 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
- 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
- Henrik Zimmer and Leif Kobbelt. 2014. Zometool rationalization of freeform surfaces. IEEE Trans. on Visualization and Computer Graphics 20, 10 (2014).Google Scholar
Recommendations
Computational design of weingarten surfaces
In this paper we study Weingarten surfaces and explore their potential for fabrication-aware design in freeform architecture. Weingarten surfaces are characterized by a functional relation between their principal curvatures that implicitly defines ...
Multi-strip smooth developable surfaces from sparse design curves
AbstractCreating developable surfaces from sparse design curves finds important applications in industrial design and modeling. Existing methods aim at finding a quasi-developable surface with as large developability as possible to interpolate ...
Highlights- We propose a method to create seamless multi-strip smooth developable surfaces from an array of design curves.
String Actuated Curved Folded Surfaces
Curved folded surfaces, given their ability to produce elegant freeform shapes by folding flat sheets etched with curved creases, hold a special place in computational Origami. Artists and designers have proposed a wide variety of different fold ...
Comments