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A Curvature-Adapted Anisotropic Surface Re-meshing Method

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New Challenges in Grid Generation and Adaptivity for Scientific Computing

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 5))

Abstract

We present a method for re-meshing surfaces in order to follow the intrinsic anisotropy of the surfaces. In particular, we use the information related to the normals to the surfaces, and embed the surfaces into a higher dimensional space (here we embed the surfaces in a six-dimensional space). This allows us to settle an isotropic mesh optimization problem in this embedded space: starting from an initial mesh of a surface, we optimize the mesh by improving the mesh quality measured in the embedded space. The mesh is optimized by properly combining common local mesh operations, i.e., edge flipping, edge contraction, vertex smoothing, and vertex insertion. All operations are applied directly on the three-dimensional surface mesh and the resulting mesh is curvature adapted. This new method improves the approach proposed by Lévy and Bonneel (Variational anisotropic surface meshing with Voronoi parallel linear enumeration. In: Proceedings of the 21st International Meshing Roundtable, pp. 349–366. Springer, New York, 2013), by allowing to preserve sharp features. The reliability and robustness of the proposed re-meshing technique is shown via a number of examples.

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Authors and Affiliations

  1. Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy

    Franco Dassi

  2. Weierstrass Institute, Mohrenstr. 39, 10117, Berlin, Germany

    Hang Si

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  1. Franco Dassi
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  2. Hang Si
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Correspondence to Franco Dassi .

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  1. MOX Dipartimento di Matematica, Politecnico di Milano, Milano, Milano, Italy

    Simona Perotto

  2. MOX Dipartimento di Matematica, Politecnico di Milano, Milano, Milano, Italy

    Luca Formaggia

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Dassi, F., Si, H. (2015). A Curvature-Adapted Anisotropic Surface Re-meshing Method. In: Perotto, S., Formaggia, L. (eds) New Challenges in Grid Generation and Adaptivity for Scientific Computing. SEMA SIMAI Springer Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-06053-8_2

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