“Popup: automatic paper architectures from 3D models” by Li, Shen, Huang, Ju and Hu

  • ©Xian-Ying Li, Chao-Hui Shen, Shi-Sheng Huang, Tao Ju, and Shi-Min Hu




    Popup: automatic paper architectures from 3D models



    Paper architectures are 3D paper buildings created by folding and cutting. The creation process of paper architecture is often labor-intensive and highly skill-demanding, even with the aid of existing computer-aided design tools. We propose an automatic algorithm for generating paper architectures given a user-specified 3D model. The algorithm is grounded on geometric formulation of planar layout for paper architectures that can be popped-up in a rigid and stable manner, and sufficient conditions for a 3D surface to be popped-up from such a planar layout. Based on these conditions, our algorithm computes a class of paper architectures containing two sets of parallel patches that approximate the input geometry while guaranteed to be physically realizable. The method is demonstrated on a number of architectural examples, and physically engineered results are presented.


    1. Belcastro, S., and Hull, T. 2002. Modelling the folding of paper into three dimensions using affine transformations. Linear Algebra and its Applications 348, 273–282.Google Scholar
    2. Bianchini, M., Siliakus, I., and Aysta, J. 2009. The paper architect. Crown, New York.Google Scholar
    3. Birmingham, D. 1997. Pop Up! A Manual of Paper Mechanisms. Tarquin Publications, UK.Google Scholar
    4. Carter, D. 1999. The Elements of Pop-up. Little Simon, New York.Google Scholar
    5. Chatani, M., Nakamura, S., and Ando, N. 1987. Practice of origamic architecture and origami with personal computer. Kodansha, Tokyo.Google Scholar
    6. Cheong, C. M., Zainodin, H., and Suzuki, H. 2009. Origamic
    4: Origamic Architecture in the Cartesian Coordinates System. A. K. Peters, Natick.Google Scholar
    7. Cohen, J., Olano, M., and Manocha, D. 1998. Appearance-preserving simplification. In SIGGRAPH ’98: Proc. 25th annual conference on Computer graphics and interactive techniques, ACM, New York, NY. USA, 115–122. Google ScholarDigital Library
    8. Demaine, E., and O’Rourke, J. 2007. Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press, Cambridge. Google ScholarDigital Library
    9. Garland, M., and Heckbert, P. S. 1997. Surface simplification using quadric error metrics. In SIGGRAPH ’97: Proc. 24th annual conference on Computer graphics and interactive techniques, ACM, New York, NY. USA, 209–216. Google ScholarDigital Library
    10. Glassner, A. 2002. Interactive pop-up card design, part 2. IEEE Comput. Graph. Appl. 22, 2, 74–85. Google ScholarDigital Library
    11. Hara, T., and Sugihara, K. 2009. Computer aided design of pop-up books with two-dimentional v-fold structures. In Proc. 7th Japan Conference on Computational Geometry and Graphs.Google Scholar
    12. Hendrix, S. L., and Eisenberg, M. A. 2006. Computer-assisted pop-up design for children: computationally enriched paper engineering. Adv. Technol. Learn. 3, 2, 119–127. Google ScholarDigital Library
    13. Hull, T. 1994. On the mathematics of flat origamis. Congr. Numer. 100, 215–224.Google Scholar
    14. Julius, D., Kraevoy, V., and Sheffer, A. 2005. D-charts: Quasi-developable mesh segmentation. Computer Graphics Forum 24, 3, 581–590.Google ScholarCross Ref
    15. Kilian, M., Flöry, S., Chen, Z., Mitra, N. J., Sheffer, A., and Pottmann, H. 2008. Curved folding. ACM Trans. Graphics 27, 3, 75:1–9. Google ScholarDigital Library
    16. Lai, Y.-K., Zhou, Q.-Y., Hu, S.-M., and Martin, R. R. 2006. Feature sensitive mesh segmentation. In Proc. 2006 ACM symposium on Solid and physical modeling, ACM, 25. Google ScholarDigital Library
    17. Lai, Y.-K., Hu, S.-M., Martin, R. R., and Rosin, P. L. 2009. Rapid and effective segmentation of 3d models using random walks. Computer Aided Geometric Design 26, 6, 665–679. Google ScholarDigital Library
    18. Lee, Y. T., Tor, S. B., and Soo, E. L. 1996. Mathematical modelling and simulation of pop-up books. Computers & Graphics 20, 1, 21–31.Google Scholar
    19. Li, Y., Yu, J., Ma, K.-L., and Shi, J. 2007. 3d paper-cut modeling and animation. Comput. Animat. Virtual Worlds 18, 4–5, 395–403. Google ScholarDigital Library
    20. Massarwi, F., Gotsman, C., and Elber, G. 2007. Papercraft models using generalized cylinders. In PG ’07: Proc. 15th Pacific Conference on Computer Graphics and Applications, IEEE Computer Society, Washington, DC. USA, 148–157. Google ScholarDigital Library
    21. Mehra, R., Zhou, Q., Long, J., Sheffer, A., Gooch, A., and Mitra, N. J. 2009. Abstraction of man-made shapes. ACM Trans. Graphics 28, 5, 137:1–10. Google ScholarDigital Library
    22. Mitani, J., and Suzuki, H. 2004. Computer aided design for origamic architecture models with polygonal representation. In CGI ’04: Proceedings of the Computer Graphics International, IEEE Computer Society, Washington, DC. USA, 93–99. Google ScholarDigital Library
    23. Mitani, J., and Suzuki, H. 2004. Making papercraft toys from meshes using strip-based approximate unfolding. ACM Trans. Graphics 23, 3, 259–263. Google ScholarDigital Library
    24. Mitani, J., Suzuki, H., and Uno, H. 2003. Computer aided design for origamic architecture models with voxel data structure. Transactions of Information Processing Society of Japan 44, 5, 1372–1379.Google Scholar
    25. Shamir, A. 2008. A survey on mesh segmentation techniques. Computer Graphics Forum 27, 6, 1539–1556.Google ScholarCross Ref
    26. Shatz, I., Tal, A., and Leifman, G. 2006. Paper craft models from meshes. The Visual Computer 22, 9, 825–834. Google ScholarDigital Library
    27. Siliakus, I. Art in the gallery of Ingrid Siliakus, http://ingrid-siliakus.exto.org.Google Scholar
    28. Stormer, G. Virtual gallery of origamic architectures, http://webpages.charter.net/gstormer.Google Scholar
    29. Tachi, T. 2009. Origamizing polyhedral surfaces. IEEE Transactions on Visualization and Computer Graphics 16, 2, 298–311. Google ScholarDigital Library
    30. Uehara, R., and Teramoto, S. 2006. The complexity of a pop-up book. In Proc. 18th Canadian Conference on Computational Geometry, 3–6.Google Scholar
    31. Wang, C. 2008. Computing length-preserved free boundary for quasi-developable mesh segmentation. IEEE Transactions on Visualization and Computer Graphics 14, 1, 25–36. Google ScholarDigital Library
    32. Wei, J., and Lou, Y. 2010. Feature preserving mesh simplification using feature sensitive metric. Journal of Computer Science & Technology 25, 3, to appear. Google ScholarDigital Library
    33. Whiting, E., Ochsendorf, J., and Durand, F. 2009. Procedural modeling of structurally-sound masonry buildings. ACM Trans. Graphics 28, 5, 1–9. Google ScholarDigital Library
    34. Xu, J., Kaplan, C. S., and Mi, X. 2007. Computer-generated papercutting. In PG ’07: Proc. 15th Pacific Conference on Computer Graphics and Applications, IEEE Computer Society, Washington, DC. USA, 343–350. Google ScholarDigital Library
    35. Yamauchi, H., Gumhold, S., Zayer, R., and Seidel, H. 2005. Mesh segmentation driven by gaussian curvature. The Visual Computer 21, 8, 659–668.Google ScholarCross Ref

ACM Digital Library Publication:

Overview Page: