Exact and interpolatory quadratures for curvature tensor estimation

The computation of the curvature of smooth surfaces has a long history in differential geometry and is essential for many geometric modeling applications such as feature detection. We present a novel approach to calculate the mean curvature from arbitrary normal curvatures. Then, we demonstrate how...

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Bibliographic Details
Published in:Computer aided geometric design 2007-11, Vol.24 (8), p.443-463
Main Authors: Langer, Torsten, Belyaev, Alexander, Seidel, Hans-Peter
Format: Article
Language:English
Subjects:
Convergence analysis
Curvature tensor
Discretization
Exact quadrature
Mean curvature
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Summary:The computation of the curvature of smooth surfaces has a long history in differential geometry and is essential for many geometric modeling applications such as feature detection. We present a novel approach to calculate the mean curvature from arbitrary normal curvatures. Then, we demonstrate how the same method can be used to obtain new formulae to compute the Gaussian curvature and the curvature tensor. The idea is to compute the curvature integrals by a weighted sum by making use of the periodic structure of the normal curvatures to make the quadratures exact. Finally, we derive an approximation formula for the curvature of discrete data like meshes and show its convergence if quadratically converging normals are available.
ISSN:0167-8396
1879-2332
DOI:10.1016/j.cagd.2006.09.006