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    Surface meshing with curvature convergence

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    Type
    Article
    Authors
    Li, Huibin
    Zeng, Wei
    Morvan, Jean-Marie
    Chen, Liming
    Gu, Xianfengdavid
    KAUST Department
    Visual Computing Center (VCC)
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2014-06
    Permanent link to this record
    http://hdl.handle.net/10754/563570
    
    Metadata
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    Abstract
    Surface meshing plays a fundamental role in graphics and visualization. Many geometric processing tasks involve solving geometric PDEs on meshes. The numerical stability, convergence rates and approximation errors are largely determined by the mesh qualities. In practice, Delaunay refinement algorithms offer satisfactory solutions to high quality mesh generations. The theoretical proofs for volume based and surface based Delaunay refinement algorithms have been established, but those for conformal parameterization based ones remain wide open. This work focuses on the curvature measure convergence for the conformal parameterization based Delaunay refinement algorithms. Given a metric surface, the proposed approach triangulates its conformal uniformization domain by the planar Delaunay refinement algorithms, and produces a high quality mesh. We give explicit estimates for the Hausdorff distance, the normal deviation, and the differences in curvature measures between the surface and the mesh. In contrast to the conventional results based on volumetric Delaunay refinement, our stronger estimates are independent of the mesh structure and directly guarantee the convergence of curvature measures. Meanwhile, our result on Gaussian curvature measure is intrinsic to the Riemannian metric and independent of the embedding. In practice, our meshing algorithm is much easier to implement and much more efficient. The experimental results verified our theoretical results and demonstrated the efficiency of the meshing algorithm. © 2014 IEEE.
    Citation
    Li, H., Zeng, W., Morvan, J. M., Chen, L., & Gu, X. D. (2014). Surface Meshing with Curvature Convergence. IEEE Transactions on Visualization and Computer Graphics, 20(6), 919–934. doi:10.1109/tvcg.2013.253
    Sponsors
    This work was supported under the Grants ANR 2010 INTB 0301 01, NSF DMS-1221339, NSF Nets-1016829, NSF CCF-1081424 and NSF CCF-0830550.
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Journal
    IEEE Transactions on Visualization and Computer Graphics
    DOI
    10.1109/TVCG.2013.253
    ae974a485f413a2113503eed53cd6c53
    10.1109/TVCG.2013.253
    Scopus Count
    Collections
    Articles; Visual Computing Center (VCC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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