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Convergence Analysis of Discrete Differential Geometry Operators over Surfaces

  • Zhiqiang Xu
  • Guoliang Xu
  • Jia-Guang Sun
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3604)

Abstract

In this paper, we study the convergence property of several discrete schemes of the surface normal. We show that the arithmetic mean, area-weighted averaging, and angle-weighted averaging schemes have quadratic convergence rate for a special triangulation scenario of the surfaces. By constructing a counterexample, we also show that it is impossible to find a discrete scheme of normals that has quadratic convergence rate over any triangulated surface and hence give a negative answer for the open question raised by D.S.Meek and D.J. Walton. Moreover, we point out that one cannot build a discrete scheme for Gaussian curvature, mean curvature and Laplace-Beltrami operator that converges over any triangulated surface.

Keywords

Convergence Analysis Gaussian Curvature Discretization Scheme Mesh Surface Negative Answer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Zhiqiang Xu
    • 1
  • Guoliang Xu
    • 2
  • Jia-Guang Sun
    • 3
  1. 1.Department of Computer ScienceTsinghua UniversityBeijingChina
  2. 2.ICMSEC, LSEC, Academy of Mathematics and System SciencesChinese Academy of SciencesBeijingChina
  3. 3.School of SoftwareTsinghua UniversityBeijingChina

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