Localized discrete Laplace-Beltrami operator over triangular mesh
Li, Xinge1; Xu, Guoliang1; Zhang, Yongjie Jessica2
AbstractThe Laplace-Beltrami operator is the foundation of describing geometric partial differential equations, and it also plays an important role in the fields of computational geometry, computer graphics and image processing, such as surface parameterization, shape analysis, matching and interpolation. However, constructing the discretized Laplace-Beltrami operator with convergent property has been an open problem. In this paper we propose a new discretization scheme of the Laplace-Beltrami operator over triangulated surfaces. We prove that our discretization of the Laplace-Beltrami operator converges to the Laplace-Beltrami operator at every point of an arbitrary smooth surface as the size of the triangular mesh over the surface tends to zero. Numerical experiments are conducted, which support the theoretical analysis. (C) 2015 Elsevier B.V. All rights reserved.
KeywordLaplace-Beltrami operator Surface triangulation Discretization Convergence
Funding ProjectNSFC[11101401] ; NSFC[81173663] ; NSFC Fund for Creative Research Groups of China[11321061] ; PECASE Award[N000141410234] ; NSF CAREER Award[OCI-1149591]
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Software Engineering ; Mathematics, Applied
WOS IDWOS:000364887700004
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Document Type期刊论文
Corresponding AuthorXu, Guoliang
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing, Peoples R China
2.Carnegie Mellon Univ, Dept Mech Engn, Computat Biomodeling Lab, Pittsburgh, PA 15213 USA
Recommended Citation
GB/T 7714
Li, Xinge,Xu, Guoliang,Zhang, Yongjie Jessica. Localized discrete Laplace-Beltrami operator over triangular mesh[J]. COMPUTER AIDED GEOMETRIC DESIGN,2015,39:67-82.
APA Li, Xinge,Xu, Guoliang,&Zhang, Yongjie Jessica.(2015).Localized discrete Laplace-Beltrami operator over triangular mesh.COMPUTER AIDED GEOMETRIC DESIGN,39,67-82.
MLA Li, Xinge,et al."Localized discrete Laplace-Beltrami operator over triangular mesh".COMPUTER AIDED GEOMETRIC DESIGN 39(2015):67-82.
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