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Localized discrete Laplace-Beltrami operator over triangular mesh

文献类型：期刊论文

作者Li, Xinge1; Xu, Guoliang1; Zhang, Yongjie Jessica2
刊名COMPUTER AIDED GEOMETRIC DESIGN
出版日期2015-11-01
卷号39页码:67-82
关键词Laplace-Beltrami operator Surface triangulation Discretization Convergence
ISSN号0167-8396
DOI10.1016/j.cagd.2015.09.001
英文摘要The 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.
资助项目NSFC[11101401] ; NSFC[81173663] ; NSFC Fund for Creative Research Groups of China[11321061] ; PECASE Award[N000141410234] ; NSF CAREER Award[OCI-1149591]
WOS研究方向Computer Science ; Mathematics
语种英语
WOS记录号WOS:000364887700004
出版者ELSEVIER SCIENCE BV
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/21287]  
专题中国科学院数学与系统科学研究院
通讯作者Xu, Guoliang
作者单位1.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
推荐引用方式
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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