Solving The Cutting Flow Problem for Prismatic Mesh Subdivision

Xiaotian Yin Wei Han Xianfeng Gu Shing-Tung Yau

Computational Geometry mathscidoc:1912.43716

2012.11
This paper is motivated by the problem of subdividing a prismatic mesh to a tetrahedral mesh (without inserting Steiner points) so as to not only match arbitrarily prescribed boundary conditions but also allow arbitrary topologies in the base mesh. We explore all possible combinations of these two factors, and propose a complete solution to this 3D problem by converting it to an equivalent 2D graph problem, called cutting flow problem. For each case, we not only prove the sufficient and necessary condition for the existence of solutions, but also provide linear and provable algorithms to compute a solution whenever there is one.
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@inproceedings{xiaotian2012solving,
  title={Solving The Cutting Flow Problem for Prismatic Mesh Subdivision},
  author={Xiaotian Yin, Wei Han, Xianfeng Gu, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205201499150280},
  year={2012},
}
Xiaotian Yin, Wei Han, Xianfeng Gu, and Shing-Tung Yau. Solving The Cutting Flow Problem for Prismatic Mesh Subdivision. 2012. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205201499150280.
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