• search hit 33 of 48
Back to Result List

Generalized Shape Operators on Polyhedral Surfaces

Please always quote using this URN:urn:nbn:de:0296-matheon-8679
  • This work concerns the approximation of the shape operator of smooth surfaces in $\mathbb{R}^{3}$ from polyhedral surfaces. We introduce two generalized shape operators that are vector-valued linear functionals on a Sobolev space of vector fields and can be rigorously defined on smooth and on polyhedral surfaces. We consider polyhedral surfaces that approximate smooth surfaces and prove two types of approximation estimates: one concerning the approximation of the generalized shape operators in the operator norm and one concerning the pointwise approximation of the (classic) shape operator, including mean and Gaussian curvature, principal curvatures, and principal curvature directions. The estimates are confirmed by numerical experiments.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Klaus Hildebrandt, Konrad Polthier
URN:urn:nbn:de:0296-matheon-8679
Referee:John M. Sullivan
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/12/11
Release Date:2011/12/11
Tag:
Institute:Freie Universität Berlin
MSC-Classification:53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)
65-XX NUMERICAL ANALYSIS
Preprint Number:829
Verstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.