The Visual Computer

, Volume 32, Issue 5, pp 569–578 | Cite as

Inner engraving for the creation of a balanced LEGO sculpture

  • Jhen-Yao Hong
  • Der-Lor WayEmail author
  • Zen-Chung Shih
  • Wen-Kai Tai
  • Chin-Chen Chang
Original Article


LEGO is a globally popular toy composed of colorful interlocking plastic bricks that can be assembled in many ways; however, this special feature makes designing a LEGO sculpture particularly challenging. Building a stable sculpture is not easy for a beginner; even an experienced user requires a good deal of time to build one. This paper provides a novel approach to creating a balanced LEGO sculpture for a 3D model in any pose, using centroid adjustment and inner engraving. First, the input 3D model is transformed into a voxel data structure. Next, the model’s centroid is adjusted to an appropriate position using inner engraving to ensure that the model stands stably. A model can stand stably without any struts when the center of mass is moved to the ideal position. Third, voxels are merged into layer-by-layer brick layout assembly instructions. Finally, users will be able to build a LEGO sculpture by following these instructions. The proposed method is demonstrated with a number of LEGO sculptures and the results of the physical experiments are presented.


LEGO Brick layout Voxel Center of mass Legolization 


  1. 1.
    Akenine-Möller, T.: Fast 3D triangle-box overlap testing. In: Proceedings of the SIGGRAPH, Courses, vol. 8 (2005)Google Scholar
  2. 2.
    Andrew, A.M.: Another efficient algorithm for convex hulls in two dimensions. Inf. Process. Lett. 9(5), 216–219 (1979)CrossRefzbMATHGoogle Scholar
  3. 3.
    Gower, R., Heydtmann, A., Petersen, H.: LEGO: automated model construction. In: 32nd European Study Group with Industry, Final Report, pp. 81–94. Technical University of Denmark (1998)Google Scholar
  4. 4.
    Holroyd, M., Baran, I., Lawrence, J., Matusik, W. : Computing and fabricating multilayer models. ACM Trans. Graph. 30(6) (2011) (Article 187)Google Scholar
  5. 5.
    lizuka, S., Endo, Y., Mitani, J., Kanamori, Y., Fukui, Y.: An interactive design system for pop-up cards with a physical simulation. Visual Comput. 27(6–8) 605–612 (2011)Google Scholar
  6. 6.
    Kilian, M., Flöry, S., Chen, Z., Mitra, N.-J., Sheffer, A., Pottmann, H.: Curved folding. ACM Trans. Graph. 27(3), 1–9 (2008)CrossRefGoogle Scholar
  7. 7.
    Kim, J.W., Kang, K.K., Lee, J.H.: Survey on Automated LEGO Assembly Construction. In: Poster Proceedings of 22nd International Conferences in Central Europe on Computer Graphics, Visualization and Computer Vision, pp. 89–96 (2014)Google Scholar
  8. 8.
    Lambrecht, B.: Voxelization of boundary representations using oriented LEGOR plates. University of California, Berkeley. (2008)
  9. 9.
    Li, X.-Y., Shen, C.-H., Huang, S.-S., Ju, T., Hu, S.-M.: Popup: automatic paper architectures from 3D models. ACM Trans. Graph. 29(4) (2010) (Article. 111)Google Scholar
  10. 10.
    Li, X.-Y., Ju, T., Gu, Y., Hu, S.-M.: A Geometric Study of V-style Pop-ups: Theories and Algorithms. ACM Trans. Graph. 30(4) (2011) (Article. 98)Google Scholar
  11. 11.
    Lo, K.-Y., Fu, C.-W., Li, H.: 3D Polyomino puzzle. ACM Trans. Graph. 28(5) (2009) (Article 157)Google Scholar
  12. 12.
    Luo, L., Baran, I., Rusinkiewicz, S., Matusik, W.: Chopper: partitioning models into 3D-printable parts. ACM Trans. Graph. 31(6) (2012) (Article 129)Google Scholar
  13. 13.
    Medeiros e Sá, A., Rodriguez Echavarria, K., Arnold, D.: Dual joints for 3D-structures. Visual Comput. 30(2) 1321–1331 (2013)Google Scholar
  14. 14.
    Ono, S., André, A., Chang, Y., Nakajima, M.: LEGO builder: automatic generation of LEGO assembly manual from 3D polygon model. ITE Trans. Media Technol. Appl. 1(4), 354–360 (2013)CrossRefGoogle Scholar
  15. 15.
    Petrovic, P.: Solving LEGO brick layout problem using evolutionary algorithms. Norwegian University of Science and Technology, Technical Report (2001)Google Scholar
  16. 16.
    Peysakhov, M., Regli, W.: Using assembly representations to enable evolutionary design of Lego structures. Artif. Intell. Eng. Design Anal. Manuf. 17, 155–168 (2003)Google Scholar
  17. 17.
    Prévost, R., Whiting, E., Lefebvre, S., Sorkine-Hornung, O.: Make it stand: balancing shapes for 3D fabrication. ACM Trans. Graph. 32(4) (2013) (Article 81)Google Scholar
  18. 18.
    Rivers, A., Adams, A., Durand, F. : Sculpting by numbers. ACM Trans. Graph. 31(6) (2012) (Article 157)Google Scholar
  19. 19.
    Rivers, A., Moyer, I. E., Durand, F.: Positioncorrecting tools for 2D digital fabrication. ACM Trans. Graph. 31(4) (2012) (Article 88)Google Scholar
  20. 20.
    Shatz, I., Tal, A., Leifman, G.: Paper craft models from meshes. Visual Comput. 22(9–11), 825–834 (2006)CrossRefGoogle Scholar
  21. 21.
    Smal, E.: Automated brick sculpture construction. MS. Thesis, The University of Stellenbosch (2008)Google Scholar
  22. 22.
    Song, P., Fu, C.W., Cohen-Or, D.: Recursive interlocking puzzles. ACM Trans. Graph. 31(6) (2012) (Article 128)Google Scholar
  23. 23.
    Stava, O., Vanek, J., Benes, B., Carr, N., Měch, R.: Stress relief: improving structural strength of 3D printable objects. ACM Trans. Graph. 31(4) (2012) (Article 48)Google Scholar
  24. 24.
    Tachi, T.: Origamizing polyhedral surfaces. IEEE Trans. Vis. Comput. Graph. 16(2), 298–311 (2009)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Testuz, R., Schwartzburg, Y., Pauly, M.: Automatic generation of constructable brick sculptures. In: Proceedings of Eurographics, short papers, pp. 81–84 (2013)Google Scholar
  26. 26.
    Van Zijl, L., Smal, E.: Cellular automata with cell clustering. In: Proceedings of Automata: Theory and Applications of Cellular Automata, pp. 425–440. Bristol (2008)Google Scholar
  27. 27.
    Way, D.-L., Tsai, Y.-S., Shih, Z.-C.: Origami pop-up card generation from 3D models using a directed acyclic graph. J. Inf. Sci. Eng. 29(6), 1195–1210 (2013)Google Scholar
  28. 28.
    Weyrich, T., Deng, J., Barnes, C., Rusinkiewicz, S., Finkelstein, A.: Digital bas-relief from 3D scenes. ACM Trans. Graph. 26(3) (2007) (Article 32)Google Scholar
  29. 29.
  30. 30.
    Xin, S.-Q., Lai, C.-F., Fu, C.-W., Wong, T.-T., He, Y., Cohenor, D.: Making burr puzzles from 3D models. ACM Trans. Graph. 30(4) (2011) (Article 97)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Jhen-Yao Hong
    • 2
  • Der-Lor Way
    • 1
    Email author
  • Zen-Chung Shih
    • 2
  • Wen-Kai Tai
    • 3
  • Chin-Chen Chang
    • 4
  1. 1.Department of New Media ArtTaipei National University of ArtsTaipeiTaiwan
  2. 2.Institute of Multimedia EngineeringNational Chiao-Tung UniversityHsinchuTaiwan
  3. 3.Department of Computer Science and Information EngineeringNational Dong-Hwa UniversityHualienTaiwan
  4. 4.Department of Computer Science and Information EngineeringNational United UniversityMiaoliTaiwan

Personalised recommendations