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Tetrahedral Mesh Construction for Unit Tangent Bundle over Genus-Zero Surfaces

Xiaotian Yin Wei Han Xianfeng Gu Shing-Tung Yau

Differential Geometry mathscidoc:1912.43704

21th International Meshing Roundtable, 2012
Unit tangent bundle of a surface carries various information of tangent vector fields on that surface. For 2-spheres (ie genus-zero closed surfaces), the unit tangent bundle is a closed 3-manifold that has non-trivial topology and cannot be embedded in R3. Therefore it cannot be constructed by existing mesh generation algorithms directly. This work aims at the first discrete construction of unit tangent bundles over 2-spheres using tetrahedral meshes. We propose a two-stage algorithm for the construction, which starts from constructing two local bundles and then combines them into a global bundle.
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@inproceedings{xiaotian2012tetrahedral,
  title={Tetrahedral Mesh Construction for Unit Tangent Bundle over Genus-Zero Surfaces},
  author={Xiaotian Yin, Wei Han, Xianfeng Gu, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205112572433268},
  booktitle={21th International Meshing Roundtable},
  year={2012},
}
Xiaotian Yin, Wei Han, Xianfeng Gu, and Shing-Tung Yau. Tetrahedral Mesh Construction for Unit Tangent Bundle over Genus-Zero Surfaces. 2012. In 21th International Meshing Roundtable. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205112572433268.
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