“Masonry Shell Structures with Discrete Equivalence Classes” by Chen, Qiu, Song, Deng, Wang, et al. …
Conference:
Type(s):
Title:
- Masonry Shell Structures with Discrete Equivalence Classes
Session/Category Title: Fabrication-Oriented Design
Presenter(s)/Author(s):
Moderator(s):
Abstract:
This paper proposes a method to model masonry shell structures where the shell elements fall into a set of discrete equivalence classes. Such shell structure can reduce the fabrication cost and simplify the physical construction due to reuse of a few template shell elements. Given a freeform surface, our goal is to generate a small set of template shell elements that can be reused to produce a seamless and buildable structure that closely resembles the surface. The major technical challenge in this process is balancing the desire for high reusability of template elements with the need for a seamless and buildable final structure. To address the challenge, we define three error metrics to measure the seamlessness and buildability of shell structures made from discrete equivalence classes and develop a hierarchical cluster-and-optimize approach to generate a small set of template elements that produce a structure closely approximating the surface with low error metrics. We demonstrate the feasibility of our approach on various freeform surfaces and geometric patterns, and validate buildability of our results with four physical prototypes. Code and data of this paper are at https://github.com/Linsanity81/TileableShell.
References:
1. Sigrid Adriaenssens, Philippe Block, Diederik Veenendaal, and Chris Williams (Eds.). 2014. Shell Structures for Architecture: Form Finding and Optimization. Routledge.
2. Ergun Akleman, Vinayak R. Krishnamurthy, Chia-An Fu, Sai Ganesh Subramanian, Matthew Ebert, Matthew Eng, Courtney Starrett, and Haard Panchal. 2020. Generalized Abeille Tiles: Topologically Interlocked Space-filling Shapes Generated Based on Fabric Symmetries. Comp. & Graph. (SMI) 89 (2020), 156–166.
3. K. S. Arun, T. S. Huang, and S. D. Blostein. 1987. Least-Squares Fitting of Two 3-D Point Sets. IEEE Trans. Pat. Ana. & Mach. Int. PAMI-9, 5 (1987), 698–700.
4. Guy Austern, Isaac Guedi Capeluto, and Yasha Jacob Grobman. 2018. Rationalization Methods in Computer Aided Fabrication: A Critical Review. Automation in Construction 90 (2018), 281–293.
5. Sofien Bouaziz, Mario Deuss, Yuliy Schwartzburg, Thibaut Weise, and Mark Pauly. 2012. Shape-Up: Shaping Discrete Geometry with Projections. Comp. Graph. Forum (SGP) 31, 5 (2012), 1657–1667.
6. Sofien Bouaziz, Sebastian Martin, Tiantian Liu, Ladislav Kavan, and Mark Pauly. 2014. Projective Dynamics: Fusing Constraint Projections for Fast Simulation. ACM Trans. on Graph. (SIGGRAPH) 33, 4 (2014), 154:1–154:11.
7. Jan Brütting, Gennaro Senatore, and Corentin Fivet. 2021. Design and Fabrication of A Reusable Kit of Parts for Diverse Structures. Automation in Construction 125 (2021), 103614:1–103614:15.
8. Xuelin Chen, Honghua Li, Chi-Wing Fu, Hao Zhang, Daniel Cohen-Or, and Baoquan Chen. 2018. 3D Fabrication with Universal Building Blocks and Pyramidal Shells. ACM Trans. on Graph. (SIGGRAPH Asia) 37, 6 (2018), 189:1–189:15.
9. Fernando de Goes, Pierre Alliez, Houman Owhadi, and Mathieu Desbrun. 2013. On the Equilibrium of Simplicial Masonry Structures. ACM Trans. on Graph. (SIGGRAPH) 32, 4 (2013), 93:1–93:10.
10. Michael Eigensatz, Martin Kilian, Alexander Schiftner, Niloy J. Mitra, Helmut Pottmann, and Mark Pauly. 2010. Paneling Architectural Freeform Surfaces. ACM Trans. on Graph. (SIGGRAPH) 29, 4 (2010), 45:1–45:10.
11. Chi-Wing Fu, Chi-Fu Lai, Ying He, and Daniel Cohen-Or. 2010. K-set Tilable Surfaces. ACM Trans. on Graph. (SIGGRAPH) 29, 4 (2010), 44:1–44:6.
12. Mathieu Huard, Michael Eigensatz, and Philippe Bompas. 2015. Planar Panelization with Extreme Repetition. In Proc. Advances in Architectural Geometry 2014. 259–279.
13. Alec Jacobson, Daniele Panozzo, et al. 2018. libigl: A simple C++ geometry processing library. https://libigl.github.io/.
14. Gene Ting-Chun Kao, Antonino Iannuzzo, Bernhard Thomaszewski, Stelian Coros, Tom Van Mele, and Philippe Block. 2022. Coupled Rigid-Block Analysis: Stability-Aware Design of Complex Discrete-Element Assemblies. Computer-Aided Design 146 (2022), 103216:1–103216:20.
15. Vinayak R. Krishnamurthy, Ergun Akleman, Sai Ganesh Subramanian, Katherine Boyd, Chia-An Fu, Matthew Ebert, Courtney Starrett, and Neeraj Yadav. 2020. Bi-Axial Woven Tiles: Interlocking Space-Filling Shapes Based on Symmetries of Bi-Axial Weaving Patterns. In Proc. Graphics Interface. 286–298.
16. Ligang Liu, Lei Zhang, Yin Xu, Craig Gotsman, and Steven J. Gortler. 2008. A Local/Global Approach to Mesh Parameterization. Comp. Graph. Forum (SGP) 27, 5 (2008), 1495–1504.
17. Yang Liu, Hao Pan, John Snyder, Wenping Wang, and Baining Guo. 2013. Computing Self-Supporting Surfaces by Regular Triangulation. ACM Trans. on Graph. (SIGGRAPH) 32, 4 (2013), 92:1–92:10.
18. Zhong-Yuan Liu, Zhan Zhang, Di Zhang, Chunyang Ye, Ligang Liu, and Xiao-Ming Fu. 2021. Modeling and Fabrication with Specified Discrete Equivalence Classes. ACM Trans. on Graph. (SIGGRAPH) 40, 4 (2021), 41:1–41:12.
19. Sheng-Jie Luo, Yonghao Yue, Chun-Kai Huang, Yu-Huan Chung, Sei Imai, Tomoyuki Nishita, and Bing-Yu Chen. 2015. Legolization: Optimizing LEGO Designs. ACM Trans. on Graph. (SIGGRAPH Asia) 34, 6 (2015), 222:1–222:12.
20. Long Ma, Ying He, Qian Sun, Yuanfeng Zhou, Caiming Zhang, and Wenping Wang. 2019. Constructing 3D Self-Supporting Surfaces with Isotropic Stress Using 4D Minimal Hypersurfaces of Revolution. ACM Trans. on Graph. 38, 5 (2019), 144:1–144:13.
21. Masaaki Miki, Takeo Igarashi, and Philippe Block. 2015. Parametric Self-supporting Surfaces via Direct Computation of Airy Stress Functions. ACM Trans. on Graph. (SIGGRAPH) 34, 4 (2015), 89:1–89:12.
22. Daniele Panozzo, Philippe Block, and Olga Sorkine-Hornung. 2013. Designing Unreinforced Masonry Models. ACM Trans. on Graph. (SIGGRAPH) 32, 4 (2013), 91:1–91:11.
23. I-Chao Shen, Ming-Shiuan Chen, Chun-Kai Huang, and Bing-Yu Chen. 2020. ZomeFab: Cost-Effective Hybrid Fabrication with Zometools. Comp. Graph. Forum 39, 1 (2020), 322–332.
24. Shen-Guan Shih. 2016. On the Hierarchical Construction of SL Blocks. In Advances in Architectural Geometry. 124–136.
25. Mayank Singh and Scott Schaefer. 2010. Triangle Surfaces with Discrete Equivalence Classes. ACM Trans. on Graph. (SIGGRAPH) 29, 4 (2010), 46:1–46:7.
26. Peng Song. 2022. Interlocking Assemblies: Applications and Methods. Materials Today: Proceedings (International Conference on Additive Manufacturing for a Better World) 70 (2022), 78–82.
27. Peng Song, Chi-Wing Fu, Prashant Goswami, Jianmin Zheng, Niloy J. Mitra, and Daniel Cohen-Or. 2013. Reciprocal Frame Structures Made Easy. ACM Trans. on Graph. (SIGGRAPH) 32, 4 (2013), 94:1–94:13.
28. Sai Ganesh Subramanian, Mathew Eng, Vinayak R. Krishnamurthy, and Ergun Akleman. 2019. Delaunay Lofts: A Biologically Inspired Approach for Modeling Space Filling Modular Structures. Comp. & Graph. (SMI) 82 (2019), 73–83.
29. Chengcheng Tang, Xiang Sun, Alexandra Gomes, Johannes Wallner, and Helmut Pottmann. 2014. Form-finding with Polyhedral Meshes Made Simple. ACM Trans. on Graph. (SIGGRAPH) 33, 4 (2014), 70:1–70:9.
30. Romain Testuz, Yuliy Schwartzburg, and Mark Pauly. 2013. Automatic Generation of Constructable Brick Sculptures. In Proc. Eurographics. short paper.
31. Etienne Vouga, Mathias Höbinger, Johannes Wallner, and Helmut Pottmann. 2012. Design of Self-supporting Surfaces. ACM Trans. on Graph. (SIGGRAPH) 31, 4 (2012), 87:1–87:11.
32. Ziqi Wang, Peng Song, Florin Isvoranu, and Mark Pauly. 2019. Design and Structural Optimization of Topological Interlocking Assemblies. ACM Trans. on Graph. (SIGGRAPH Asia) 38, 6 (2019), 193:1–193:13.
33. Ziqi Wang, Peng Song, and Mark Pauly. 2021a. MOCCA: Modeling and Optimizing Cone-joints for Complex Assemblies. ACM Trans. on Graph. (SIGGRAPH) 40, 4 (2021), 181:1–181:14.
34. Ziqi Wang, Peng Song, and Mark Pauly. 2021b. State of the Art on Computational Design of Assemblies with Rigid Parts. Comp. Graph. Forum (Eurographics) 40, 2 (2021), 633–657.
35. Emily Whiting, John Ochsendorf, and Frédo Durand. 2009. Procedural Modeling of Structurally-Sound Masonry Buildings. ACM Trans. on Graph. (SIGGRAPH Asia) 28, 5 (2009), 112:1–112:9.
36. Emily Whiting, Hijung Shin, Robert Wang, John Ochsendorf, and Frédo Durand. 2012. Structural Optimization of 3D Masonry Buildings. ACM Trans. on Graph. (SIGGRAPH Asia) 31, 6 (2012), 159:1–159:11.
37. Jiaxian Yao, Danny M. Kaufman, Yotam Gingold, and Maneesh Agrawala. 2017. Interactive Design and Stability Analysis of Decorative Joinery for Furniture. ACM Trans. on Graph. 36, 2 (2017). Article No. 20.
38. Yinan Zhang and Devin Balkcom. 2016. Interlocking Structure Assembly with Voxels. In Proc. IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems. 2173–2180.
39. Henrik Zimmer, Marcel Campen, David Bommes, and Leif Kobbelt. 2012. Rationalization of Triangle-Based Point-Folding Structures. Comp. Graph. Forum (Eurographics) 31, 2 (2012), 611–620.
40. Henrik Zimmer and Leif Kobbelt. 2014. Zometool Rationalization of Freeform Surfaces. IEEE Trans. Vis. & Comp. Graphics 20, 10 (2014), 1461–1473.
41. Henrik Zimmer, Florent Lafarge, Pierre Alliez, and Leif Kobbelt. 2014. Zometool Shape Approximation. Graphical Models 76, 5 (2014), 390–401.
