Linear interpolation of shape operators for umbilical points through local parametrization
文献类型：期刊论文
| 作者 | Che, WuJun
|
| 刊名 | COMPUTER AIDED GEOMETRIC DESIGN
 |
| 出版日期 | 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. |
| WOS关键词 | CURVATURE |
| 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研究方向 | Computer Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:001030159400001 |
| 出版者 | ELSEVIER |
| 资助机构 | National Key Ramp;D Program of China ; Beijing Natural Science Foundation ; National Natural Science Foundation of China |
| 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. |
入库方式： OAI收割
来源：自动化研究所
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。