Skip to main content
SpringerLink
Log in

Inner engraving for the creation of a balanced LEGO sculpture

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Akenine-Möller, T.: Fast 3D triangle-box overlap testing. In: Proceedings of the SIGGRAPH, Courses, vol. 8 (2005)

  2. Andrew, A.M.: Another efficient algorithm for convex hulls in two dimensions. Inf. Process. Lett. 9(5), 216–219 (1979)

    Article  MATH  Google Scholar 

  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)

  4. Holroyd, M., Baran, I., Lawrence, J., Matusik, W. : Computing and fabricating multilayer models. ACM Trans. Graph. 30(6) (2011) (Article 187)

  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)

  6. Kilian, M., Flöry, S., Chen, Z., Mitra, N.-J., Sheffer, A., Pottmann, H.: Curved folding. ACM Trans. Graph. 27(3), 1–9 (2008)

    Article  Google Scholar 

  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)

  8. Lambrecht, B.: Voxelization of boundary representations using oriented LEGOR plates. University of California, Berkeley. http://lego.bldesign.org/LSculpt/lambrecht_legovoxels.pdf (2008)

  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)

  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)

  11. Lo, K.-Y., Fu, C.-W., Li, H.: 3D Polyomino puzzle. ACM Trans. Graph. 28(5) (2009) (Article 157)

  12. Luo, L., Baran, I., Rusinkiewicz, S., Matusik, W.: Chopper: partitioning models into 3D-printable parts. ACM Trans. Graph. 31(6) (2012) (Article 129)

  13. Medeiros e Sá, A., Rodriguez Echavarria, K., Arnold, D.: Dual joints for 3D-structures. Visual Comput. 30(2) 1321–1331 (2013)

  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)

    Article  Google Scholar 

  15. Petrovic, P.: Solving LEGO brick layout problem using evolutionary algorithms. Norwegian University of Science and Technology, Technical Report (2001)

  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. 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)

  18. Rivers, A., Adams, A., Durand, F. : Sculpting by numbers. ACM Trans. Graph. 31(6) (2012) (Article 157)

  19. Rivers, A., Moyer, I. E., Durand, F.: Positioncorrecting tools for 2D digital fabrication. ACM Trans. Graph. 31(4) (2012) (Article 88)

  20. Shatz, I., Tal, A., Leifman, G.: Paper craft models from meshes. Visual Comput. 22(9–11), 825–834 (2006)

    Article  Google Scholar 

  21. Smal, E.: Automated brick sculpture construction. MS. Thesis, The University of Stellenbosch (2008)

  22. Song, P., Fu, C.W., Cohen-Or, D.: Recursive interlocking puzzles. ACM Trans. Graph. 31(6) (2012) (Article 128)

  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)

  24. Tachi, T.: Origamizing polyhedral surfaces. IEEE Trans. Vis. Comput. Graph. 16(2), 298–311 (2009)

    Article  MathSciNet  Google Scholar 

  25. Testuz, R., Schwartzburg, Y., Pauly, M.: Automatic generation of constructable brick sculptures. In: Proceedings of Eurographics, short papers, pp. 81–84 (2013)

  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)

  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. Weyrich, T., Deng, J., Barnes, C., Rusinkiewicz, S., Finkelstein, A.: Digital bas-relief from 3D scenes. ACM Trans. Graph. 26(3) (2007) (Article 32)

  29. Winkler, D.: Automated brick layout. BrickFest. http://www.brickshelf.com/gallery/happyfrosh/BrickFest2005/automatedbricklayout.pdf (2005)

  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)

Download references

Author information

Authors and Affiliations

  1. Department of New Media Art, Taipei National University of Arts, No.1 Hsueh-Yuan Road, Peitou, Taipei, 112, Taiwan

    Der-Lor Way

  2. Institute of Multimedia Engineering, National Chiao-Tung University, 1001 University Road, Hsinchu, 300, Taiwan

    Jhen-Yao Hong & Zen-Chung Shih

  3. Department of Computer Science and Information Engineering, National Dong-Hwa University, Hualien, Taiwan

    Wen-Kai Tai

  4. Department of Computer Science and Information Engineering, National United University, Miaoli, Taiwan

    Chin-Chen Chang

Authors
  1. Jhen-Yao Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Der-Lor Way
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zen-Chung Shih
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wen-Kai Tai
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Chin-Chen Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Der-Lor Way.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hong, JY., Way, DL., Shih, ZC. et al. Inner engraving for the creation of a balanced LEGO sculpture. Vis Comput 32, 569–578 (2016). https://doi.org/10.1007/s00371-015-1072-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-015-1072-4

Keywords

Search

Navigation