A Construction of Anisotropic Meshes Based on Quasi-Conformal Mapping

  • Yuxue Ren
  • Na LeiEmail author
  • Hang Si
  • Xianfeng David Gu
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 127)


In this paper we discuss an algorithm to generate anisotropic mesh based on metric tensors. We transform this problem to finding a quasi conformal mapping f defined on an isotropic mesh, such that the image of f is an anisotropic triangulation. According to the metric tensors, the Beltrami coefficients of f can be calculated, then we use discrete Yamabe flow to construct f. The topology of the original triangulation will be updated if necessary, while the number of vertices won’t be changed during the process. We also use our method to compute the intersection of functions, and experiments show that the interpolation functions on anisotropic meshes have less errors than the interpolation functions on isotropic mesh.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Yuxue Ren
    • 1
    • 2
  • Na Lei
    • 2
    • 3
    Email author
  • Hang Si
    • 4
  • Xianfeng David Gu
    • 5
  1. 1.School of MathematicsJilin UniversityChangchunChina
  2. 2.Beijing Advanced Innovation Center for Imaging TechnologyCapital Normal UniversityBeijingChina
  3. 3.DUT-RU ISEDalian University of TechnologyDalianChina
  4. 4.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  5. 5.Department of Computer ScienceStony Brook UniversityStony BrookUSA

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