Localized discrete Laplace-Beltrami operator over triangular mesh

doi:10.1016/j.cagd.2015.09.001

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	Localized discrete Laplace-Beltrami operator over triangular mesh
	Li, Xinge 1; Xu, Guoliang 1; Zhang, Yongjie Jessica 2
	2015-11-01
发表期刊	COMPUTER AIDED GEOMETRIC DESIGN
ISSN	0167-8396
卷号	39 页码:67-82
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.
关键词	Laplace-Beltrami operator Surface triangulation Discretization Convergence
DOI	10.1016/j.cagd.2015.09.001
语种	英语
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
WOS类目	Computer Science, Software Engineering ; Mathematics, Applied
WOS记录号	WOS:000364887700004
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21288
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.