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

Yin, Xiaotian, Wei Han, Xianfeng Gu, and Shing-Tung Yau

Research Notes, 21st International Meshing Roundtable, Springer-Verlag, pp.Research Note, October 7-10 2012

IMR
PROCEEDINGS

21st International Meshing Roundtable
San Jose, CA
October 7-10, 2012

Mathematics Department, Harvard University, MA, U.S.A.
Computer Science Department, Stony Brook University, NY, U.S.A.
Email: {xyin,weihan,yau}@math.harvard.edu, gu@cs.sunysb.edu

Summary
Unit tangent bundle of a surface carries various information of tangent vector fields on that surface. For 2-spheres (i.e. 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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