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Generalized Shape Operators on Polyhedral Surfaces

Please always quote using this URN:urn:nbn:de:0296-matheon-7832
  • This work concerns the approximation of the shape operator of smooth surfaces in 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. We show experimental results that confirm our estimates.

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Metadaten
Author:Klaus Hildebrandt, Konrad Polthier
URN:urn:nbn:de:0296-matheon-7832
Referee:John M. Sullivan
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/12/11
Release Date:2011/12/11
Institute:Freie Universität Berlin
MSC-Classification:68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section {04 in that areag 68-00 General reference works (handbooks, dictionaries, bibliographies, etc.) / 68Uxx Computing methodologies and applications / 68U05 Computer graphics; computational geometry [See also 65D18]
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section {04 in that areag 68-00 General reference works (handbooks, dictionaries, bibliographies, etc.) / 68Uxx Computing methodologies and applications / 68U07 Computer-aided design [See also 65D17]
Preprint Number:827
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