“Synthesis of filigrees for digital fabrication”

  • ©Weikai Chen, Xiaolong Zhang, Shiqing Xin, Yang Xia, Sylvain Lefebvre, and Wenping Wang




    Synthesis of filigrees for digital fabrication





    Filigrees are thin patterns found in jewelry, ornaments and lace fabrics. They are often formed of repeated base elements manually composed into larger, delicate patterns. Digital fabrication simplifies the process of turning a virtual model of a filigree into a physical object. However, designing a virtual model of a filigree remains a time consuming and challenging task. The difficulty lies in tightly packing together the base elements while covering a target surface. In addition, the filigree has to be well connected and sufficiently robust to be fabricated. We propose a novel approach automating this task. Our technique covers a target surface with a set of input base elements, forming a filigree strong enough to be fabricated. We exploit two properties of filigrees to make this possible. First, as filigrees form delicate traceries they are well captured by their skeleton. This affords for a simpler definition of operators such as matching and deformation. Second, instead of seeking for a perfect packing of the base elements we relax the problem by allowing appearance preserving partial overlaps. We optimize a filigree by a stochastic search, further improved by a novel boosting algorithm that records and reuses good configurations discovered during the process.We illustrate our technique on a number of challenging examples reproducing filigrees on large objects, which we manufacture by 3D printing. Our technique affords for several user controls, such as the scale and orientation of the elements.


    1. Bathe, K.-J. 2006. Finite element procedures. Klaus-Jurgen Bathe.Google Scholar
    2. Cheng, D., and Wong, K., 2009. 3doodler seashell pattern lace plastic dress. http://www.s-h-i-g-o.com/#!project/c147c.Google Scholar
    3. Diamanti, O., Vaxman, A., Panozzo, D., and Sorkine-Hornung, O. 2014. Designing n-PolyVector fields with complex polynomials. Computer Graphics Forum 33, 5, 1–11. Google ScholarDigital Library
    4. Dubuisson, M. P., and Jain, A. K. 1994. A modified Hausdorff distance for object matching. In Pattern Recognition, vol. 1, 566–568.Google ScholarCross Ref
    5. Dumas, J., Lu, A., Lefebvre, S., Wu, J., and Dick, C. 2015. By-Example Synthesis of Structurally Sound Patterns. ACM Transactions on Graphics (TOG) 34, 4. Google ScholarDigital Library
    6. Harker, J., 2011. Crania Anatomica Filigre: Me to You. https://www.kickstarter.com/projects/joshharker/crania-anatomica-filigre-me-to-you.Google Scholar
    7. Hu, W., Chen, Z., Pan, H., Yu, Y., Grinspun, E., and Wang, W. 2016. Surface mosaic synthesis with irregular tiles. IEEE Trans. Vis. Comput. Graph. 22, 3, 1302–1313. Google ScholarDigital Library
    8. Hurtut, T., Landes, P.-E., Thollot, J., Gousseau, Y., Drouillhet, R., and Coeurjolly, J.-F. 2009. Appearance-guided synthesis of element arrangements by example. In Proceedings of the 7th International Symposium on Non-photorealistic Animation and Rendering, ACM, 51–60. Google ScholarDigital Library
    9. Jacobson, A., Panozzo, D., et al., 2016. libigl: A simple C++ geometry processing library. http://libigl.github.io/libigl/.Google Scholar
    10. Kazhdan, M., and Hoppe, H. 2013. Screened Poisson surface reconstruction. ACM Transactions on Graphics (TOG) 32, 3, 29. Google ScholarDigital Library
    11. Lefebvre, S., and Hoppe, H. 2005. Parallel controllable texture synthesis. ACM Transactions on Graphics (TOG) 24, 3, 777–786. Google ScholarDigital Library
    12. Lefebvre, S., and Hoppe, H. 2006. Appearance-space texture synthesis. ACM Transactions on Graphics (TOG) 25, 3, 541–548. Google ScholarDigital Library
    13. Li, Y., Bao, F., Zhang, E., Kobayashi, Y., and Wonka, P. 2011. Geometry synthesis on surfaces using field-guided shape grammars. Visualization and Computer Graphics, IEEE Transactions on 17, 2, 231–243. Google ScholarDigital Library
    14. Ma, C., Wei, L.-Y., and Tong, X. 2011. Discrete element textures. ACM Transactions on Graphics (TOG) 30, 4, 62:1–62:10. Google ScholarDigital Library
    15. Martínez, J., Dumas, J., Lefebvre, S., and Wei, L.-Y. 2015. Structure and appearance optimization for controllable shape design. ACM Transactions on Graphics (TOG) 34, 6, 229:1–229:11. Google ScholarDigital Library
    16. Praun, E., Finkelstein, A., and Hoppe, H. 2000. Lapped textures. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, SIGGRAPH ’00, 465–470. Google ScholarDigital Library
    17. Riccioti, R., 2013. Mucem museum concrete filigree. http://www.lemayonline.com/en/wow/mucem-photographed-by-edmund-sumner.Google Scholar
    18. Sederberg, T. W., and Parry, S. R. 1986. Free-form deformation of solid geometric models. In ACM SIGGRAPH computer graphics, vol. 20, 151–160. Google ScholarDigital Library
    19. Stava, O., Vanek, J., Benes, B., Carr, N., and Měch, R. 2012. Stress relief: Improving structural strength of 3D printable objects. ACM Transactions on Graphics (TOG) 31, 4, 48:1–48:11. Google ScholarDigital Library
    20. Turk, G. 2001. Texture synthesis on surfaces. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’01, 347–354. Google ScholarDigital Library
    21. Umetani, N., and Schmidt, R. 2013. Cross-sectional structural analysis for 3D printing optimization. In SIGGRAPH Asia 2013 Technical Briefs, 5:1–5:4. Google ScholarDigital Library
    22. Wei, L.-Y., and Levoy, M. 2001. Texture synthesis over arbitrary manifold surfaces. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’01, 355–360. Google ScholarDigital Library
    23. Wei, L.-Y., Lefebvre, S., Kwatra, V., and Turk, G. 2009. State of the art in example-based texture synthesis. In Eurographics ’09 State of the Art Report, 93–117.Google Scholar
    24. Wei, L.-Y. 2010. Multi-class blue noise sampling. ACM Transactions on Graphics (TOG) 29, 4, 79. Google ScholarDigital Library
    25. Zehnder, J., Coros, S., and Thomaszewski, B. 2016. Designing structurally-sound ornamental curve networks. SIGGRAPH 2016, to appear. Google ScholarDigital Library
    26. Zhang, J., Zhou, K., Velho, L., Guo, B., and Shum, H.-Y. 2003. Synthesis of progressively-variant textures on arbitrary surfaces. ACM Transactions on Graphics (TOG) 22, 3, 295–302. Google ScholarDigital Library
    27. Zhou, K., Huang, X., Wang, X., Tong, Y., Desbrun, M., Guo, B., and Shum, H.-Y. 2006. Mesh quilting for geometric texture synthesis. ACM Transactions on Graphics (TOG) 25, 3, 690–697. Google ScholarDigital Library
    28. Zhou, Q., Panetta, J., and Zorin, D. 2013. Worst-case structural analysis. ACM Transactions on Graphics (TOG) 32, 4, 137:1–137:12. Google ScholarDigital Library
    29. Zhou, S., Jiang, C., and Lefebvre, S. 2014. Topology-constrained synthesis of vector patterns. ACM Transactions on Graphics (TOG) 33, 6, 1–11. Google ScholarDigital Library
    30. Zienkiewicz, O. C., and Taylor, R. L. 2005. The finite element method for solid and structural mechanics. Butterworth-Heinemann.Google Scholar

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