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ℓ_1-Based Construction of Polycube Maps from Complex Shapes

Huang, Jin and Jiang, Tengfei and Shi, Zeyun and Tong, Yiying and Bao, Hujun and Desbrun, Mathieu (2014) ℓ_1-Based Construction of Polycube Maps from Complex Shapes. ACM Transactions on Graphics, 33 (3). Art. No. 25. ISSN 0730-0301. doi:10.1145/2602141.

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Polycube maps of triangle meshes have proved useful in a wide range of applications, including texture mapping and hexahedral mesh generation. However, constructing either fully automatically or with limited user control a low-distortion polycube from a detailed surface remains challenging in practice. We propose a variational method for deforming an input triangle mesh into a polycube shape through minimization of the ℓ_1-norm of the mesh normals, regularized via an as-rigid-as-possible volumetric distortion energy. Unlike previous work, our approach makes no assumption on the orientation, or on the presence of features in the input model. User-guided control over the resulting polycube map is also offered to increase design flexibility. We demonstrate the robustness, efficiency, and controllability of our method on a variety of examples, and explore applications in hexahedral remeshing and quadrangulation.

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URLURL TypeDescription
Desbrun, Mathieu0000-0003-3424-6079
Alternate Title:ℓ1-Based Construction of Polycube Maps from Complex Shapes
Additional Information:© 2014 ACM. Received September 2013; accepted December 2013. This work was partially supported by NSFC (no. 61210007, no. 61170139), China 863 Program (no. 2012AA011503) and the Fundamental Research Funds for the Central Universities (no. 2013FZA5015). Y. Tong was supported by NSF (CMMI-1250261 and IIS-0953096). M. Desbrun was supported by NSF grant CCF-1011944. We would like to thank the anonymous reviewers for their valuable comments and suggestions. Special thanks to Ying He and James Gregson for providing help on making comparison. Fertility and bust are courtesy of Utrecht University. Dancing children is courtesy of IMATI-GE. Bulldog and gargoyle are courtesy of VCG-ISTI. Kitten is courtesy of Frank ter Haar. Venus, rockerArm, casting, and livingstone elephant are courtesy of INRIA. Fandisk, elk, bumpy torus, and bunny are courtesy of Max Planck Institute for Computer Science. Rod, kiss, angel, anc101, nastycheese, and cognit are provided by INRIA Gamma dataset. All the other models are provided by the AIM@SHAPE Shape Repository.
Funding AgencyGrant Number
National Science Foundation of China61210007
National Science Foundation of China61170139
China 863 Program2012AA011503
Fundamental Research Funds for the Central Universities2013FZA5015
Subject Keywords:Algorithms; Theory; Polycube map generation; l(1) optimization; sparse normal field
Issue or Number:3
Record Number:CaltechAUTHORS:20140707-131442627
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:46887
Deposited By: Tony Diaz
Deposited On:07 Jul 2014 20:39
Last Modified:10 Nov 2021 17:31

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