Quadrilateral mesh generation I: Metric based method

Wei Chen Dalian University of Technology Xiaopeng Zheng Dalian University of Technology Jingyao Ke University of Science and Technology of China Na Lei Dalian University of Technology Zhongxuan Luo Dalian University of Technology Xianfeng Gu Stony Brook University

Computational Geometry TBD mathscidoc:1911.43001

Computer Methods in Applied Mechanics and Engineering, 356, 652-668, 2019
This work proposes a novel metric based algorithm for quadrilateral mesh generating. Each quad-mesh induces a Riemannian metric satisfying special conditions: the metric is a flat metric with cone singularities conformal to the original metric, the total curvature satisfies the Gauss–Bonnet condition, the holonomy group is a subgroup of the rotation group $\{e^{ik\pi/2}\}$, there is cross field obtained by parallel translation which is aligned with the boundaries, and its streamlines are finite geodesics. Inversely, such kind of metric induces a quad-mesh. Based on discrete Ricci flow and conformal structure deformation, one can obtain a metric satisfying all the conditions and obtain the desired quad-mesh. This method is rigorous, simple and automatic. Our experimental results demonstrate the efficiency and efficacy of the algorithm.
Quadrilateral mesh; Flat Riemannian metric; Geodesic; Discrete Ricci flow; Conformal structure deformation
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@inproceedings{wei2019quadrilateral,
  title={Quadrilateral mesh generation I: Metric based method},
  author={Wei Chen, Xiaopeng Zheng, Jingyao Ke, Na Lei, Zhongxuan Luo, and Xianfeng Gu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191106100355610766505},
  booktitle={Computer Methods in Applied Mechanics and Engineering},
  volume={356},
  pages={652-668},
  year={2019},
}
Wei Chen, Xiaopeng Zheng, Jingyao Ke, Na Lei, Zhongxuan Luo, and Xianfeng Gu. Quadrilateral mesh generation I: Metric based method. 2019. Vol. 356. In Computer Methods in Applied Mechanics and Engineering. pp.652-668. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191106100355610766505.
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