Generalized shape operators on polyhedral surfaces

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Generalized shape operators on polyhedral surfaces
This work concerns the approximation of the shape operator of smooth surfaces in R3 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.
Klaus Hildebrandt, Konrad Polthier
Added 24 Aug 2011
Updated 24 Aug 2011
Type Journal
Year 2011
Where CAGD
Authors Klaus Hildebrandt, Konrad Polthier
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