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On approximation of the Laplace–Beltrami operator and the Willmore energy of surfaces
Author(s) -
Hildebrandt Klaus,
Polthier Konrad
Publication year - 2011
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2011.02025.x
Subject(s) - laplace operator , laplace transform , laplace–beltrami operator , mathematics , operator (biology) , willmore energy , mathematical analysis , pure mathematics , geometry , p laplacian , principal curvature , mean curvature , biochemistry , chemistry , repressor , transcription factor , gene , boundary value problem , curvature
Discrete Laplace–Beltrami operators on polyhedral surfaces play an important role for various applications in geometry processing and related areas like physical simulation or computer graphics. While discretizations of the weak Laplace–Beltrami operator are well‐studied, less is known about the strong form. We present a principle for constructing strongly consistent discrete Laplace–Beltrami operators based on the cotan weights. The consistency order we obtain, improves previous results reported for the mesh Laplacian. Furthermore, we prove consistency of the discrete Willmore energies corresponding to the discrete Laplace–Beltrami operators.