“LineUp: Computing Chain-Based Physical Transformation” by Yu, Ye, Liu, Ying and Wang

  • ©Minjing Yu, Zipeng Ye, Yong-Jin Liu, He Ying, and Charlie C. L. Wang




    LineUp: Computing Chain-Based Physical Transformation

Session/Category Title: Fabrication



    In this article, we introduce a novel method that can generate a sequence of physical transformations between 3D models with different shape and topology. Feasible transformations are realized on a chain structure with connected components that are 3D printed. Collision-free motions are computed to transform between different configurations of the 3D printed chain structure. To realize the transformation between different 3D models, we first voxelize these input models into a similar number of voxels. The challenging part of our approach is to generate a simple path—as a chain configuration to connect most voxels. A layer-based algorithm is developed with theoretical guarantee of the existence and the path length. We find that collision-free motion sequence can always be generated when using a straight line as the intermediate configuration of transformation. The effectiveness of our method is demonstrated by both the simulation and the experimental tests taken on 3D printed chains.


    1. Moritz Bächer, Bernd Bickel, Doug L. James, and Hanspeter Pfister. 2012. Fabricating articulated characters from skinned meshes. ACM Trans. Graph. 31, 4, Article 47 (2012), 47:1–47:9.
    2. Moritz Bächer, Emily Whiting, Bernd Bickel, and Olga Sorkine-Hornung. 2014. Spin-it: Optimizing moment of inertia for spinnable objects. ACM Trans. Graph. 33, 4, Article 96 (2014), 96:1–96:10.
    3. Bernd Bickel, Moritz Bächer, Miguel A. Otaduy, Hyunho Richard Lee, Hanspeter Pfister, Markus Gross, and Wojciech Matusik. 2010. Design and fabrication of materials with desired deformation behavior. ACM Trans. Graph. 29, 4, Article 63 (2010), 63:1–63:10.
    4. Bernd Bickel, Paolo Cignoni, Luigi Malomo, and Nico Pietroni. 2018. State of the art on stylized fabrication. Computer Graphics Forum (2018).
    5. T. Biedl, E. Demaine, M. Demaine, S. Lazard, A. Lubiw, J. O’Rourke, M. Overmars, S. Robbins, I. Streinu, G. Toussaint, and S. Whitesides. 2001. Locked and unlocked polygonal chains in three dimensions. Discrete Comput. Geom. 26, 3 (2001), 269–281.
    6. Jacques Calì, Dan A. Calian, Cristina Amati, Rebecca Kleinberger, Anthony Steed, Jan Kautz, and Tim Weyrich. 2012. 3D-printing of non-assembly, articulated models. ACM Trans. Graph. 31, 6, Article 130 (2012), 130:1–130:8.
    7. Jason H. Cantarella, Erik D. Demaine, Hayley N. Iben, and James F. O’Brien. 2004. An energy-driven approach to linkage unfolding. In Proceedings of the 20th Annual Symposium on Computational Geometry (SCG’04). 134–143.
    8. Siddhartha Chaudhuri, Evangelos Kalogerakis, Leonidas Guibas, and Vladlen Koltun. 2011. Probabilistic reasoning for assembly-based 3D modeling. ACM Trans. Graph. 30, 4, Article 35 (2011), 35:1–35:10.
    9. Siddhartha Chaudhuri and Vladlen Koltun. 2010. Data-driven suggestions for creativity support in 3D modeling. ACM Trans. Graph. 29, 6, Article 183 (2010), 183:1–183:10.
    10. Robert Connelly, Erik D. Demaine, and Günter Rote. 2003. Blowing up polygonal linkages. Discrete Comput. Geom. 30, 2 (2003), 205–239.
    11. Erik D. Demaine, David Eppstein, Jeff Erickson, George W. Hart, and Joseph O’Rourke. 2002. Vertex-unfoldings of simplicial manifolds. In Proceedings of the Eighteenth Annual Symposium on Computational Geometry (SCG’02). 237–243.
    12. Noah Duncan, Lap-Fai Yu, and Sai-Kit Yeung. 2016. Interchangeable components for hands-on assembly based modelling. ACM Trans. Graph. 35, 6, Article 234 (2016), 234:1–234:14.
    13. Herbert Edelsbrunner and Ernst Peter Mücke. 1990. Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Trans. Graph. 9, 1 (1990), 66–104.
    14. Anatolij T. Fomenko and Tosiyasu Kunii. 1997. Topological Modeling for Visualization. Springer.
    15. Thomas Funkhouser, Michael Kazhdan, Philip Shilane, Patrick Min, William Kiefer, Ayellet Tal, Szymon Rusinkiewicz, and David Dobkin. 2004. Modeling by example. ACM Trans. Graph. 23, 3 (2004), 652–663.
    16. Akash Garg, Alec Jacobson, and Eitan Grinspun. 2016. Computational design of reconfigurables. ACM Trans. Graph. 35, 4, Article 90 (2016), 90:1–90:14.
    17. Ruslan Guseinov, Eder Miguel, and Bernd Bickel. 2017. CurveUps: Shaping objects from flat plates with tension-actuated curvature. ACM Trans. Graph. 36, 4, Article 64 (2017), 64:1–64:12.
    18. Justin Harris, Kathy Hirsh-Pasek, and Nora S. Newcombe. 2013. Understanding spatial transformations: Similarities and differences between mental rotation and mental folding. Cognit. Process. 14, 2 (2013), 105–115.
    19. Kailun Hu, Shuo Jin, and Charlie C. L. Wang. 2015. Support slimming for single material based additive manufacturing. Comput.-Aided Des. 65 (2015), 1–10.
    20. Qixing Huang, Vladlen Koltun, and Leonidas Guibas. 2011. Joint shape segmentation with linear programming. ACM Trans. Graph. 30, 6, Article 125 (2011), 125:1–125:12.
    21. Yi-Jheng Huang, Shu-Yuan Chan, Wen-Chieh Lin, and Shan-Yu Chuang. 2016. Making and animating transformable 3D models. Comput. Graphics 54 (2016), 127–134.
    22. Conrado R. Ruiz Jr., Sang N. Le, Jinze Yu, and Kok-Lim Low. 2014. Multi-style paper pop-up designs from 3D models. Comput. Graphics Forum 33, 2 (2014), 487–496.
    23. Evangelos Kalogerakis, Siddhartha Chaudhuri, Daphne Koller, and Vladlen Koltun. 2012. A probabilistic model for component-based shape synthesis. ACM Trans. Graph. 31, 4, Article 55 (2012), 55:1–55:11.
    24. David Ron Karger, Rajeev Motwani, and G. D. S. Ramkumar. 1997. On approximating the longest path in a graph. Algorithmica 18, 1 (1997), 82–98.
    25. Martin Kilian, Simon Flöry, Zhonggui Chen, Niloy J. Mitra, Alla Sheffer, and Helmut Pottmann. 2008. Curved folding. ACM Trans. Graph. 27, 3, Article 75 (2008), 75:1–75:9.
    26. 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 (2016), 89:1–89:11.
    27. Bernhard Korte and Jens Vygen. 2006. Combinatorial Optimization: Theory and Algorithms. 3rd Edition, Springer.
    28. Haruhisa Kurokawa, Akiya Kamimura, Eiichi Yoshida, Kohji Tomita, Shigeru Kokaji, and Satoshi Murata. 2003. M-TRAN II: Metamorphosis from a four-legged walker to a caterpillar. In 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2003. 2454–2459.
    29. Haruhisa Kurokawa, Kohji Tomita, Akiya Kamimura, Shigeru Kokaji, Takashi Hasuo, and Satoshi Murata. 2008. Distributed self-reconfiguration of M-TRAN III modular robotic system. The International Journal of Robotics Research 27, 3–4 (2008), 373–386.
    30. Timothy Langlois, Ariel Shamir, Daniel Dror, Wojciech Matusik, and David I. W. Levin. 2016. Stochastic structural analysis for context-aware design and fabrication. ACM Trans. Graph. 35, 6, Article 226 (2016), 226:1–226:13.
    31. Honghua Li, Ruizhen Hu, Ibraheem Alhashim, and Hao Zhang. 2015. Foldabilizing furniture. ACM Trans. Graph. 34, 4, Article 90 (2015), 90:1–90:12.
    32. Xian-Ying Li, Tao Ju, Yan Gu, and Shi-Min Hu. 2011. A geometric study of v-style pop-ups: Theories and algorithms. ACM Trans. Graph. 30, 4, Article 98 (2011), 98:1–98:10.
    33. 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. Graph. 34, 6, Article 222 (2015), 222:1–222:12.
    34. Silvano Martello and Paolo Toth. 1990. Knapsack Problems: Algorithms and Computer Implementations. John Wiley 8 Sons, Inc., New York, NY.
    35. Meher McArthur and Robert J. Lang. 2012. Folding Paper: The Infinite Possibilities of Origami. Turtle Publishing.
    36. Rico Moeckel, Cyril Jaquier, Kevin Drapel, Elmar Dittrich, Andres Upegui, and Auke Jan Ijspeert. 2006. Exploring adaptive locomotion with YaMoR, a novel autonomous modular robot with bluetooth interface. Industrial Robot: An International Journal 33, 4 (2006), 285–290.
    37. Przemyslaw Musialski, Thomas Auzinger, Michael Birsak, Michael Wimmer, and Leif Kobbelt. 2015. Reduced-order shape optimization using offset surfaces. ACM Trans. Graph. 34, 4, Article 102 (2015), 102:1–102:9.
    38. Joseph O’Rourke. 2011. How To Fold It: The Mathematics of Linkages, Origami, and Polyhedra. Cambridge University Press.
    39. Julian Panetta, Qingnan Zhou, Luigi Malomo, Nico Pietroni, Paolo Cignoni, and Denis Zorin. 2015. Elastic textures for additive fabrication. ACM Trans. Graph. 34, 4 (2015), 135:1–135:12.
    40. Jesús Pérez, Miguel A. Otaduy, and Bernhard Thomaszewski. 2017. Computational design and automated fabrication of Kirchhoff-plateau surfaces. ACM Trans. Graph. 36, 4, Article 62 (2017), 62:1–62:12.
    41. Michael Rubenstein, Alejandro Cornejo, and Radhika Nagpal. 2014. Programmable self-assembly in a thousand-robot swarm. Science 345, 6198 (2014), 795–799.
    42. Graham G. Ryland and Harry H. Cheng. 2010. Design of iMobot, an intelligent reconfigurable mobile robot with novel locomotion. In IEEE International Conference on Robotics and Automation (ICRA’10). 60–65.
    43. Behnam Salemi, Mark Moll, and Weimin Shen. 2006. SUPERBOT: A deployable, multi-functional, and modular self-reconfigurable robotic system. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS’06). 3636–3641.
    44. Galen Hajime Sasaki. 1987. Optimization by Simulated Annealing: A Time-Complexity Analysis. Ph.D. Dissertation, University of Illinois at Urbana-Champaign.
    45. Christian Schumacher, Bernd Bickel, Jan Rys, Steve Marschner, Chiara Daraio, and Markus Gross. 2015. Microstructures to control elasticity in 3D printing. ACM Trans. Graph. 34, 4, Article 136 (2015), 136:1–136:13.
    46. Oana Sidi, Oliver van Kaick, Yanir Kleiman, Hao Zhang, and Daniel Cohen-Or. 2011. Unsupervised co-segmentation of a set of shapes via descriptor-space spectral clustering. ACM Trans. Graph. 30, 6, Article 126 (2011), 126:1–126:10.
    47. Mélina Skouras, Bernhard Thomaszewski, Stelian Coros, Bernd Bickel, and Markus Gross. 2013. Computational design of actuated deformable characters. ACM Trans. Graph. 32, 4, Article 82 (2013), 82:1–82:10.
    48. Peng Song, Chi-Wing Fu, Yueming Jin, Hongfei Xu, Ligang Liu, Pheng-Ann Heng, and Daniel Cohen-Or. 2017a. Reconfigurable interlocking furniture. ACM Trans. Graph. 36, 6, Article 174 (2017), 174:1–174:14.
    49. Peng Song, Xiaofei Wang, Xiao Tang, Chi-Wing Fu, Hongfei Xu, Ligang Liu, and Niloy J. Mitra. 2017b. Computational design of wind-up toys. ACM Trans. Graph. 36, 6, Article 238 (2017), 238:1–238:13.
    50. Ondrej Stava, Juraj Vanek, Bedrich Benes, Nathan Carr, and Radomír Měch. 2012. Stress relief: Improving structural strength of 3D printable objects. ACM Trans. Graph. 31, 4, Article 48 (2012), 48:1–48:11.
    51. Joan Stiles and Catherine Stern. 2001. Developmental change in spatial cognitive processing: Complexity effects and block construction performance in preschool children. J. Cognit. Dev. 2, 2 (2001), 157–187.
    52. Kasper Stoy, David Brandt, and David J. Christensen. 2010. Self-Reconfigurable Robots: An Introduction. The MIT Press.
    53. Ileana Streinu. 2000. A combinatorial approach to planar non-colliding robot arm motion planning. In Proceedings of the 41st Annual Symposium on Foundations of Computer Science (FOCS’00). 443–453.
    54. Timothy Sun and Changxi Zheng. 2015. Computational design of twisty joints and puzzles. ACM Trans. Graph. 34, 4, Article 101 (2015), 101:1–101:11.
    55. Disney Storybook Art Team. 2010. Toy Story 3 Mix 8 Match. Disney Pr, ISBN13 9781423121411.
    56. Nobuyuki Umetani, Yuki Koyama, Ryan Schmidt, and Takeo Igarashi. 2014. Pteromys: Interactive design and optimization of free-formed free-flight model airplanes. ACM Trans. Graph. 33, 4, Article 65 (2014), 65:1–65:10.
    57. Jonathan Wai, David Lubinski, and Camilla P. Benbow. 2009. Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology 101, 4 (2009), 817–835.
    58. Shiqing Xin, Chi-Fu Lai, Chi-Wing Fu, Tien-Tsin Wong, Ying He, and Daniel Cohen-Or. 2011. Making burr puzzles from 3D models. ACM Trans. Graph. 30, 4, Article 97 (2011), 97:1–97:8.
    59. Gary Yngve and Greg Turk. 2002. Robust creation of implicit surfaces from polygonal meshes. IEEE Trans. Visual. Comput. Graphics 8, 4 (2002), 346–359.
    60. Zhong You. 2014. Folding structures out of flat materials. Science 345, 6197 (2014), 623–624.
    61. Minjing Yu, Yong-Jin Liu, and Charlie C. L. Wang. 2017. EasySRRobot: An easy-to-build self-reconfigurable robot with optimized design. In IEEE International Conference on Robotics and Biomimetics (IEEE-ROBIO’17). 1094–1099.
    62. Minjing Yu, Yong-Jin Liu, Guozhen Zhao, Chun Yu, and Yuanchun Shi. 2018. Spatial ability improvement by tangible interaction: A case study with EasySRRobot. In Proceedings of the 2018 CHI Conference Extended Abstracts on Human Factors in Computing Systems (CHI EA’18). ACM, LBW013:1–LBW013:6.
    63. Ye Yuan, Changxi Zheng, and Stelian Coros. 2018. Computational design of transformables. Comput.theor Graphics Forum 37 (2018), 103–113.
    64. Wen-Qi Zhang and Yong-Jin Liu. 2011. Approximating the longest paths in grid graphs. Theor. Comput. Sci. 412, 39 (2011), 5340–5350.
    65. Xiaoting Zhang, Xinyi Le, Zihao Wu, Emily Whiting, and Charlie C. L. Wang. 2016. Data-driven bending elasticity design by shell thickness. Comput. Graph. Forum 35, 5 (2016), 157–166.
    66. Qingnan Zhou, Julian Panetta, and Denis Zorin. 2013. Worst-case structural analysis. ACM Trans. Graph. 32, 4, Article 137 (2013), 137:1–137:12.
    67. Yahan Zhou, Shinjiro Sueda, Wojciech Matusik, and Ariel Shamir. 2014. Boxelization: Folding 3D objects into boxes. ACM Trans. Graph. 33, 4, Article 71 (2014), 71:1–71:8.

ACM Digital Library Publication:

Overview Page: