Linear interpolation of shape operators for umbilical points through local parametrization

doi:10.1016/j.cagd.2023.102223

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	Linear interpolation of shape operators for umbilical points through local parametrization
	Che, WuJun
刊名	COMPUTER AIDED GEOMETRIC DESIGN
	2023-09-01
卷号	105 页码:15
关键词	Umbilical point Linear interpolation Local parametrization Shape operator Weingarten map
ISSN号	0167-8396
DOI	10.1016/j.cagd.2023.102223
通讯作者	Che, WuJun(wujun.che@ia.ac.cn)
英文摘要	Curvature analysis is frequently employed in shape interrogation. Umbilical points are of particular interest in curvature analysis because of their identical normal curvatures in all tangential directions. Locating the umbilical points is the basis of geometric analysis. On the one hand, as singularities, umbilical points severely hinder the analysis (e.g., in nets of curvature lines). On the other hand, they provide qualitative information about the intrinsic shape of a surface and are therefore desirable quantities in some applications. In this study, we develop a straightforward and effective method to detect generic umbilical points on triangular meshes. This method is applicable to any type of admissible parametrization. We propose two local parametrization schemes-orthogonal projection and conformal transformation-to be used with the proposed method. Furthermore, we systematically analyze our method and prove its convergence behavior. The algorithm used in our approach is flexible and straightforward to implement for triangular meshes of arbitrary topology. & COPY; 2023 Elsevier B.V. All rights reserved.
资助项目	National Key Ramp;D Program of China[2018YFB1403902] ; Beijing Natural Science Foundation[L192005] ; National Natural Science Foundation of China[61471359]
WOS关键词	CURVATURE
WOS研究方向	Computer Science ; Mathematics
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:001030159400001
资助机构	National Key Ramp;D Program of China ; Beijing Natural Science Foundation ; National Natural Science Foundation of China
内容类型	期刊论文
源URL	[http://ir.ia.ac.cn/handle/173211/53714]
专题	数字内容技术与服务研究中心_新媒体服务与管理技术
通讯作者	Che, WuJun
作者单位	Chinese Acad Sci, Inst Automat, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Che, WuJun. Linear interpolation of shape operators for umbilical points through local parametrization[J]. COMPUTER AIDED GEOMETRIC DESIGN,2023,105:15.
APA	Che, WuJun.(2023).Linear interpolation of shape operators for umbilical points through local parametrization.COMPUTER AIDED GEOMETRIC DESIGN,105,15.
MLA	Che, WuJun."Linear interpolation of shape operators for umbilical points through local parametrization".COMPUTER AIDED GEOMETRIC DESIGN 105(2023):15.