Linear interpolation of shape operators for umbilical points through local parametrization

doi:10.1016/j.cagd.2023.102223

CASIA OpenIR > 数字内容技术与服务研究中心 > 版权智能与文化计算

	Linear interpolation of shape operators for umbilical points through local parametrization
	Che, WuJun
发表期刊	COMPUTER AIDED GEOMETRIC DESIGN
ISSN	0167-8396
	2023-09-01
卷号	105 页码:15
通讯作者	Che, WuJun(wujun.che@ia.ac.cn)
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.
关键词	Umbilical point Linear interpolation Local parametrization Shape operator Weingarten map
DOI	10.1016/j.cagd.2023.102223
关键词[WOS]	CURVATURE
收录类别	SCI
语种	英语
资助项目	National Key Ramp;D Program of China[2018YFB1403902] ; Beijing Natural Science Foundation[L192005] ; National Natural Science Foundation of China[61471359]
项目资助者	National Key Ramp;D Program of China ; Beijing Natural Science Foundation ; National Natural Science Foundation of China
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Mathematics, Applied
WOS记录号	WOS:001030159400001
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.ia.ac.cn/handle/173211/53715
专题	数字内容技术与服务研究中心_版权智能与文化计算
通讯作者	Che, WuJun
作者单位	Chinese Acad Sci, Inst Automat, Beijing 100190, Peoples R China
第一作者单位	中国科学院自动化研究所
通讯作者单位	中国科学院自动化研究所
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.