Abstract
We propose simple and efficient optimization-based untangling strategies for 2D polygonal and 3D polyhedral meshes. The first approach uses a size-based mesh metric, which eliminates inverted elements by averaging element size over the entire mesh. The second method uses a hybrid quality metric, which untangles inverted elements by simultaneously averaging element size and improving element shape. The last method using a variant of the hybrid quality metric gives a high penalty for inverted elements and employs an adaptive sigmoid function for handling various mesh sizes. Numerical experiments are presented to show the effectiveness of the proposed untangling strategies for various 2D polygonal and 3D polyhedral meshes.
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Acknowledgments
This research was begun when the first author was a Postdoctoral Fellow at the Los Alamos National Laboratory. The first author would like to thank to Rao Garimella at the Los Alamos National Laboratory for providing test meshes and helpful discussions. The first author was supported by the Incheon National University Research Grant in 2013. The authors also wish to thank the three anonymous referees for their careful reading of the paper and for their helpful suggestions.
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Kim, J., Chung, J. Untangling polygonal and polyhedral meshes via mesh optimization. Engineering with Computers 31, 617–629 (2015). https://doi.org/10.1007/s00366-014-0379-5
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DOI: https://doi.org/10.1007/s00366-014-0379-5