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Published May 2014 | Accepted Version
Journal Article Open

ℓ_1-Based Construction of Polycube Maps from Complex Shapes

Abstract

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.

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.

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Created:
August 22, 2023
Modified:
October 26, 2023