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A discrete Laplace-Beltrami operator for simplicial surfaces

Please always quote using this URN:urn:nbn:de:0296-matheon-3032
  • We define a discrete Laplace-Beltrami operator for simplicial surfaces. It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the one defined by Pinkall and Polthier (the so called “cotan formula”) except that it is based on the intrinsic Delaunay triangulation of the simplicial surface. This leads to new definitions of discrete harmonic and holomorphic functions, discrete mean curvature, and discrete minimal surfaces.

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Metadaten
Author:Alexander I. Bobenko, Boris A. Springborn
URN:urn:nbn:de:0296-matheon-3032
Referee:Günter M. Ziegler
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2006/03/15
Release Date:2006/03/14
Tag:
Institute:Technische Universität Berlin
Zuse Institute Berlin (ZIB)
MSC-Classification:52-XX CONVEX AND DISCRETE GEOMETRY / 52Bxx Polytopes and polyhedra / 52B70 Polyhedral manifolds
53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx) / 53Axx Classical differential geometry / 53A05 Surfaces in Euclidean space
53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx) / 53Axx Classical differential geometry / 53A10 Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Preprint Number:315
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