Abstract
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.
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Acknowledgements
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.
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Hui Zhao received his M.Phil. degree from the Computer Science and Engineering Department at Hong Kong University of Science and Technology in 2007. He was a visiting scholar in Harvard University from 2015 to 2016. He has developed mesh processing software (MeshDGP) and published five books on computer graphics.
Na Lei is currently a professor at the DUT-RU International School of Information Sciences and Engineering at Dalian University of Technology. She was a visiting professor at the University of Texas at Austin from 2007 to 2008, at the State University of New York at Stony Brook from 2014 to 2015 and at Tsinghua University from 2015 to 2016. Her research interests include computational geometry, computer graphics, and computer vision.
Xuan Li received his B.Sc. degree from the Department of Mathematical Sciences at Tsinghua University. He is pursuing his Ph.D. degree in the Department of Computer Science at Stony Brook University. His research interests are in computational conformal geometry and computer graphics.
Peng Zeng received his bachelor degree from the Mathematics Department at Jilin University in 2016. He is currently a Ph.D. student in the Yau Mathematical Sciences Center at Tsinghua University. His current research focuses on computational conformal geometry, Teichmuller theory, 3-manifolds, and computer graphics.
Ke Xu is an undergraduate student at Beijing University of Technology and is interested in computer graphics and rendering.
Xianfeng Gu received his Ph.D. degree in computer science from Harvard University in 2003. He is an associate professor of computer science and the director of the 3D Scanning Laboratory at Stony Brook University. His current research interests include computer vision, graphics, geometric modeling, and medical imaging. His major works include global conformal surface parameterization in graphics, tracking and analysis of facial expression in vision, manifold splines in modeling, brain mapping and virtual colonoscopy in medical imaging, and computational conformal geometry. He won a U.S. National Science Foundation CAREER Award in 2004.
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Zhao, H., Lei, N., Li, X. et al. Robust edge-preserving surface mesh polycube deformation. Comp. Visual Media 4, 33–42 (2018). https://doi.org/10.1007/s41095-017-0100-x
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DOI: https://doi.org/10.1007/s41095-017-0100-x