Angle deficit approximation of Gaussian curvature and its convergence over quadrilateral meshes

doi:10.1016/j.cad.2007.01.007

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	Angle deficit approximation of Gaussian curvature and its convergence over quadrilateral meshes
	Liu, Dan; Xu, Guoliang
	2007-06-01
发表期刊	COMPUTER-AIDED DESIGN
ISSN	0010-4485
卷号	39 期号:6 页码:506-517
摘要	We propose a discrete approximation of Gaussian curvature over quadrilateral meshes using a linear combination of two angle deficits. Let g(ij) and b(ij) be the coefficients of the first and second fundamental forms of a smooth parametric surface F. Suppose F is sampled so that a surface mesh is obtained. Theoretically we show that for vertices of valence four, the considered two angle deficits are asymptotically equivalent to rational functions in g(ij) and b(ij) under some special conditions called the parallelogram criterion. Specifically, the numerators of the rational functions are homogenous polynomials of degree two in b(ij) with closed form coefficients, and the denominators are g(11g22) - g(12)(2). Our discrete approximation of the Gaussian curvature derived from the combination of the angle deficits has quadratic convergence rate under the parallelogram criterion. Numerical results which justify the theoretical analysis are also presented. (C) 2007 Elsevier Ltd. All rights reserved.
关键词	angle deficit Gaussian curvature quadrilateral mesh convergence
DOI	10.1016/j.cad.2007.01.007
语种	英语
WOS研究方向	Computer Science
WOS类目	Computer Science, Software Engineering
WOS记录号	WOS:000247850000007
出版者	ELSEVIER SCI LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4941
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	Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Liu, Dan,Xu, Guoliang. Angle deficit approximation of Gaussian curvature and its convergence over quadrilateral meshes[J]. COMPUTER-AIDED DESIGN,2007,39(6):506-517.
APA	Liu, Dan,&Xu, Guoliang.(2007).Angle deficit approximation of Gaussian curvature and its convergence over quadrilateral meshes.COMPUTER-AIDED DESIGN,39(6),506-517.
MLA	Liu, Dan,et al."Angle deficit approximation of Gaussian curvature and its convergence over quadrilateral meshes".COMPUTER-AIDED DESIGN 39.6(2007):506-517.