Computational Visual Media

, Volume 4, Issue 1, pp 33–42 | Cite as

Robust edge-preserving surface mesh polycube deformation

  • Hui Zhao
  • Na Lei
  • Xuan Li
  • Peng Zeng
  • Ke Xu
  • Xianfeng Gu
Open Access
Research Article


Polycube construction and deformation are essential problems in computer graphics. In this paper, we present a robust, simple, efficient, and automatic algorithm to deform the meshes of arbitrary shapes into polycube form. We derive a clear relationship between a mesh and its corresponding polycube shape. Our algorithm is edge-preserving, and works on surface meshes with or without boundaries. Our algorithm outperforms previous ones with respect to speed, robustness, and efficiency. Our method is simple to implement. To demonstrate the robustness and effectivity of our method, we have applied it to hundreds of models of varying complexity and topology. We demonstrate that our method compares favorably to other state-of-the-art polycube deformation methods.


deformation polycube topology polycube geometry stretching energy 



We wish to thank the anonymous reviewers for encouragement and thoughtful suggestions. We are grateful for Prof. Steven J. Gortler for motivation and insightful guidance which made this paper possible. We also thank Yue Li for help in our experiments. The mesh models are courtesy of the Aim@Shape Repository, the Stanford 3D Scanning Repository and Ref. [21]. We used Mitsuba [31] for rendering images. Our algorithms were implemented using the MeshDGP [32] framework. We also thank the Libigl team [33] for reference. The project was partially supported by NSFC 61772105, 61720106005, and 11271156, NSF DMS-1418255, and AFOSR FA9550-14-1-0193.


  1. [1]
    Tarini, M.; Hormann, K.; Cignoni, P.; Montani, C. PolyCube-maps. ACM Transactions on Graphics Vol. 23, No. 3, 853–860, 2004.CrossRefGoogle Scholar
  2. [2]
    Gu, X.; Gortler, S. J.; Hoppe, H. Geometry images. ACM Transactions on Graphics Vol. 21, No. 3, 355–361, 2002.CrossRefGoogle Scholar
  3. [3]
    Chang, C.-C.; Lin, C.-Y. Texture tiling on 3D models using automatic polycube-maps and Wang tiles. Journal of Information Science and Engineering Vol. 26, No. 1, 291–305, 2010.Google Scholar
  4. [4]
    Garcia, I.; Xia, J.; He, Y.; Xin, S.-Q.; Patow, G. Interactive applications for sketch-based editable polycube map. IEEE Transactions on Visualization and Computer Graphics Vol. 19, No. 7, 1158–1171, 2013.CrossRefGoogle Scholar
  5. [5]
    Yao, C.-Y.; Lee, T.-Y. Adaptive geometry image. IEEE Transactions on Visualization and Computer Graphics Vol. 14, No. 4, 948–960, 2008.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Wang, H.; Jin, M.; He, Y.; Gu, X.; Qin, H. User-controllable polycube map for manifold spline construction. In: Proceedings of the 2008 ACM Symposium on Vol.d and Physical Modeling, 397–404, 2008.Google Scholar
  7. [7]
    Gregson, J.; Sheffer, A.; Zhang, E. All-hex mesh generation via volumetric polycube deformation. Computer Graphics Forum Vol. 30, No. 5, 1407–1416, 2011.CrossRefGoogle Scholar
  8. [8]
    Han, S.; Xia, J.; He, Y. Hexahedral shell mesh construction via volumetric polycube map. In: Proceedings of the 14th ACM Symposium on Vol.d and Physical Modeling, 127–136, 2010.Google Scholar
  9. [9]
    Livesu, M.; Vining, N.; Sheffer, A.; Gregson, J.; Scateni, R. PolyCut: Monotone graph-cuts for PolyCube base-complex construction. ACM Transactions on Graphics Vol. 32, No. 6, Article No. 171, 2013.Google Scholar
  10. [10]
    Xia, J.; He, Y.; Yin, X.; Han, S.; Gu, X. Directproduct volumetric parameterization of handlebodies via harmonic fields. In: Proceedings of the Shape Modeling International Conference, 3–12, 2010.Google Scholar
  11. [11]
    Fan, Z.; Jin, X.; Feng, J.; Sun, H. Mesh morphing using polycube-based cross-parameterization. Computer Animation and Virtual Worlds Vol. 16, Nos. 3–4, 499–508, 2005.CrossRefGoogle Scholar
  12. [12]
    Wang, H.; He, Y.; Li, X.; Gu, X.; Qin, H. Polycube splines. Computer-Aided Design Vol. 40, No. 6, 721–733, 2008.CrossRefzbMATHGoogle Scholar
  13. [13]
    He, Y.; Yin, X.; Luo, F.; Gu, X. Harmonic volumetric parameterization using green’s functions on star shapes. In: Proceedings of the Symposium on Geometry Processing, 2008.Google Scholar
  14. [14]
    Li, X.; Guo, X.; Wang, H.; He, Y.; Gu, X.; Qin, H. Harmonic volumetric mapping for solid modeling applications. In: Proceedings of the 2007 ACM symposium on Vol.d and Physical Modeling, 109–120, 2007.CrossRefGoogle Scholar
  15. [15]
    Liu, L.; Zhang, Y.; Liu, Y.; Wang, W. Featurepreserving T-mesh construction using skeleton-based polycubes. Computer-Aided Design Vol. 58, 162–172, 2015.Google Scholar
  16. [16]
    He, Y.; Wang, H.; Fu, C.-W.; Qin, H. A divideand-conquer approach for automatic polycube map construction. Computers & Graphics Vol. 33, No. 3, 369–380, 2009.CrossRefGoogle Scholar
  17. [17]
    Huang, J.; Jiang, T.; Shi, Z.; Tong, Y.; Bao, H.; Desbrun, M. l1-based construction of polycube maps from complex shapes. ACM Transactions on Graphics Vol. 33, No. 3, Article No. 25, 2014.Google Scholar
  18. [18]
    Lin, J.; Jin, X.; Fan, Z.; Wang, C. C. L. Automatic polycube-maps. In: Advances in Geometric Modeling and Processing. GMP 2008. Lecture Notes in Computer Science, Vol. 4975. Chen, F.; Jüttler, B. Eds. Springer, Berlin, Heidelberg, 3–16, 2008.Google Scholar
  19. [19]
    Alexa, M.; Cohen-Or, D.; Levin, D. As-rigid-aspossible shape interpolation. In: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, 157–164, 2000.Google Scholar
  20. [20]
    Wan, S.; Yin, Z.; Zhang, K.; Zhang, H.; Li, X. A topology-preserving optimization algorithm for polycube mapping. Computers & Graphics Vol. 35, No. 3, 639–649, 2011.CrossRefGoogle Scholar
  21. [21]
    Fu, X.-M.; Bai, C.-Y.; Liu, Y. Efficient volumetric polycube-map construction. Computer Graphics Forum Vol. 35, No. 7, 97–106, 2016.CrossRefGoogle Scholar
  22. [22]
    Cherchi, G.; Livesu, M.; Scateni, R. Polycube simplification for coarse layouts of surfaces and volumes. Computer Graphics Forum Vol. 35, No. 5, 11–20, 2016.CrossRefGoogle Scholar
  23. [23]
    Yu, Y.; Zhou, K.; Xu, D.; Shi, X.; Bao, H.; Guo, B.; Shum, H.-Y. Mesh editing with poisson-based gradient field manipulation. ACM Transactions on Graphics Vol. 23, No. 3, 644–651, 2004.CrossRefGoogle Scholar
  24. [24]
    Xu, D.; Zhang, H.; Wang, Q.; Bao, H. Poisson shape interpolation. Graphical Models Vol. 68, No. 3, 268–281, 2006.CrossRefzbMATHGoogle Scholar
  25. [25]
    Zayer, R.; Rössl, C.; Karni, Z.; Seidel, H.-P. Harmonic guidance for surface deformation. Computer Graphics Forum Vol. 24, No. 3, 601–609, 2005.CrossRefGoogle Scholar
  26. [26]
    Eppstein, D.; Mumford, E. Steinitz theorems for orthogonal polyhedra. In: Proceedings of the 26th Annual Symposium on Computational Geometry, 429–438, 2010.Google Scholar
  27. [27]
    Chao, I.; Pinkall, U.; Sanan, P.; Schröder, P. A simple geometric model for elastic deformations. ACM Transactions on Graphics Vol. 29, No. 4, Article No. 38, 2010.Google Scholar
  28. [28]
    Botsch, M.; Sorkine, O. On linear variational surface deformation methods. IEEE Transactions on Visualization and Computer Graphics Vol. 14, No. 1, 213–230, 2008.CrossRefGoogle Scholar
  29. [29]
    Sorkine, O.; Alexa, M. As-rigid-as-possible surface modeling. In: Proceedings of Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, 109–116, 2007.Google Scholar
  30. [30]
    Zhao, H.; Gortler, S. J. A report on shape deformation with a stretching and bending energy. arXiv preprint arXiv:1603.06821, 2016.Google Scholar
  31. [31]
    Jakob, W. Mitsuba renderer. 2010. Available at Scholar
  32. [32]
    Zhao, H. MeshDGP: A C Sharp mesh processing framework. 2016. Available at Scholar
  33. [33]
    Jacobson, A.; Panozzo, D.; Schüller, C. libigl: A simple C++ geometry processing library. 2016. Available at Scholar

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Authors and Affiliations

  • Hui Zhao
    • 1
  • Na Lei
    • 2
    • 5
  • Xuan Li
    • 3
  • Peng Zeng
    • 1
  • Ke Xu
    • 4
  • Xianfeng Gu
    • 3
  1. 1.Tsinghua UniversityBeijingChina
  2. 2.Dalian University of TechnologyDalianChina
  3. 3.State University of New York at Stony BrookStony BrookUSA
  4. 4.Beijing University of TechnologyBeijingChina
  5. 5.Key Laboratory for Ubiquitous Network and Service Software of Liaoning ProvinceLiaoningChina

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