Robust edge-preserving surface mesh polycube deformation
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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.
Keywordsdeformation 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. . We used Mitsuba  for rendering images. Our algorithms were implemented using the MeshDGP  framework. We also thank the Libigl team  for reference. The project was partially supported by NSFC 61772105, 61720106005, and 11271156, NSF DMS-1418255, and AFOSR FA9550-14-1-0193.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Eppstein, D.; Mumford, E. Steinitz theorems for orthogonal polyhedra. In: Proceedings of the 26th Annual Symposium on Computational Geometry, 429–438, 2010.Google Scholar
- 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
- 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
- Zhao, H.; Gortler, S. J. A report on shape deformation with a stretching and bending energy. arXiv preprint arXiv:1603.06821, 2016.Google Scholar
- Jakob, W. Mitsuba renderer. 2010. Available at http://www.mitsuba-renderer.org.Google Scholar
- Zhao, H. MeshDGP: A C Sharp mesh processing framework. 2016. Available at http://meshdgp.github.io/.Google Scholar
- Jacobson, A.; Panozzo, D.; Schüller, C. libigl: A simple C++ geometry processing library. 2016. Available at http://libigl.github.io/libigl/.Google Scholar
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