Abstract
We propose a novel method to compute globally injective parameterizations with arbitrary positional constraints on disk topology meshes. Central to this method is the use of a scaffold mesh that reduces the globally injective constraint to a locally flipfree condition. Hence, given an initial parameterized mesh containing flipped triangles and satisfying the positional constraints, we only need to remove the flips of a overall mesh consisting of the parameterized mesh and the scaffold mesh while always meeting positional constraints. To successfully apply this idea, we develop two key techniques. Firstly, an initialization method is used to generate a valid scaffold mesh and mitigate difficulties in eliminating flips. Secondly, edge-based remeshing is used to optimize the regularity of the scaffold mesh containing flips, thereby improving practical robustness. Compared to state-of-the-art methods, our method is much more robust. We demonstrate the capability and feasibility of our method on a large number of complex meshes.
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Acknowledgements
We would like to thank the anonymous reviewers for their constructive suggestions and comments. This work was supported by the National Natural Science Foundation of China (61802359, 62025207) and USTC Research Funds of the Double First-Class Initiative (YD0010002003).
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Qi Wang received her B.Sc. degree in 2018 from the University of Science and Technology of China. She is currently a Ph.D. candidate in the School of Mathematical Sciences, University of Science and Technology of China. Her research interests include geometric processing and computer graphics.
Wen-Xiang Zhang received his B.Sc. degree in 2018 from Shandong University. He is currently a Ph.D. candidate in the School of Mathematical Sciences, University of Science and Technology of China. His research interests include geometric processing and computer graphics.
Yuan-Yuan Cheng received her B.Sc. degree in 2019 from Nanjing University of Science and Technology. She is currently a Ph.D. candidate in the School of Mathematical Sciences, University of Science and Technology of China. Her research interests include geometric processing and computer graphics.
Ligang Liu is a professor in the School of Mathematical Sciences, University of Science and Technology of China. He received his B.Sc. (1996) and his Ph.D. (2001) degrees from Zhejiang University, China. Between 2001 and 2004, he worked at Microsoft Research Asia. He worked at Zhejiang University during 2004–2012. He paid an academic visit to Harvard University during 2009 and 2011. His research interests include digital geometric processing, computer graphics, and image processing. He serves as associate editors for IEEE Transactions on Visualization and Computer Graphics, IEEE Computer Graphics and Applications, Computer Graphics Forum, Computer Aided Geometric Design, and The Visual Computer. His research work can be found at his research website: http://staff.ustc.edu.cn/∼lgliu.
Xiao-Ming Fu received his B.Sc. degree in 2011 and his Ph.D. degree in 2016 from the University of Science and Technology of China. He is currently an associate professor in the School of Mathematical Sciences, University of Science and Technology of China. His research interests include geometric processing and computer-aided geometric design. His research work can be found at his research website: http://staff.ustc.edu.cn/∼fuxm.
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Wang, Q., Zhang, WX., Cheng, YY. et al. Practical construction of globally injective parameterizations with positional constraints. Comp. Visual Media 9, 265–277 (2023). https://doi.org/10.1007/s41095-022-0269-5
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DOI: https://doi.org/10.1007/s41095-022-0269-5