Discrete & Computational Geometry

, Volume 43, Issue 4, pp 798–823 | Cite as

Uniform Convergence of Discrete Curvatures from Nets of Curvature Lines

  • Ulrich BauerEmail author
  • Konrad Polthier
  • Max Wardetzky
Open Access


We study discrete curvatures computed from nets of curvature lines on a given smooth surface and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.


Discrete curvatures Polyhedral surfaces Cotangent formula Curvature lines 


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Institute for Numerical and Applied MathematicsUniversity of GöttingenGöttingenGermany
  2. 2.Department of Mathematics and Computer ScienceFreie Universität BerlinBerlinGermany

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