A general framework for surface modeling using geometric partial differential equations

doi:10.1016/j.cagd.2007.06.002

CSpace

	A general framework for surface modeling using geometric partial differential equations
	Xu, Guoliang 1,2; Zhang, Qin 2
	2008-03-01
发表期刊	COMPUTER AIDED GEOMETRIC DESIGN
ISSN	0167-8396
卷号	25 期号:3 页码:181-202
摘要	In this paper, a general framework for surface modeling using geometric partial differential equations (PDEs) is presented. Starting with a general integral functional, we derive an Euler-Lagrange equation and then a geometric evolution equation (also known as geometric flow). This evolution equation is universal, containing several well-known geometric partial differential equations as its special cases, and is discretized under a uniform framework over surface meshes. The discretization of the equation involves approximations of curvatures and several geometric differential operators which are consistently discretized based on a quadratic fitting scheme. The proposed algorithm can be used to construct surfaces for geometric design as well as simulate the behaviors of various geometric PDEs. Comparative experiments show that the proposed approach can handle a large number of geometric PDEs and the numerical algorithm is efficient. (C) 2007 Elsevier B.V. All rights reserved.
关键词	surface modeling geometric PDEs triangular surface mesh
DOI	10.1016/j.cagd.2007.06.002
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Mathematics, Applied
WOS记录号	WOS:000254156900006
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/6808
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, Inst Computat Math, LSEC, Beijing 100080, Peoples R China 2.Beijing Informat Sci & Technol Univ, Dept Math, Beijing 100085, Peoples R China
推荐引用方式 GB/T 7714	Xu, Guoliang,Zhang, Qin. A general framework for surface modeling using geometric partial differential equations[J]. COMPUTER AIDED GEOMETRIC DESIGN,2008,25(3):181-202.
APA	Xu, Guoliang,&Zhang, Qin.(2008).A general framework for surface modeling using geometric partial differential equations.COMPUTER AIDED GEOMETRIC DESIGN,25(3),181-202.
MLA	Xu, Guoliang,et al."A general framework for surface modeling using geometric partial differential equations".COMPUTER AIDED GEOMETRIC DESIGN 25.3(2008):181-202.