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Volume 17, Issue 4
Manifold Triangular Mesh Editing Based on Finite Differences and Fourier Series

Qunzhi Jin & Yuanfeng Jin

DOI: 10.4208/nmtma.OA-2024-0022

Numer. Math. Theor. Meth. Appl., 17 (2024), pp. 933-955.

Published online: 2024-12

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  • Abstract

In this paper, the proposed method utilizes finite difference and Fourier series methods to calculate the mean curvature vectors and normalized curvature weights at the vertices of manifold triangular meshes. Specifically, this stable method achieves the $L^2$ convergence of the mean curvature vector. Furthermore, by comparing the method proposed in this paper with previously proposed classical methods, the results show that this method effectively balances precision and stability, and significantly reduces the larger errors observed on triangular meshes with small angles (approximately $0^◦$).

  • Keywords

Finite difference method, Fourier series, discrete curvature, small angles.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-17-933, author = {Jin , Qunzhi and Jin , Yuanfeng}, title = {Manifold Triangular Mesh Editing Based on Finite Differences and Fourier Series}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2024}, volume = {17}, number = {4}, pages = {933--955}, abstract = {

In this paper, the proposed method utilizes finite difference and Fourier series methods to calculate the mean curvature vectors and normalized curvature weights at the vertices of manifold triangular meshes. Specifically, this stable method achieves the $L^2$ convergence of the mean curvature vector. Furthermore, by comparing the method proposed in this paper with previously proposed classical methods, the results show that this method effectively balances precision and stability, and significantly reduces the larger errors observed on triangular meshes with small angles (approximately $0^◦$).

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2024-0022 }, url = {http://global-sci.org/intro/article_detail/nmtma/23647.html} }
TY - JOUR T1 - Manifold Triangular Mesh Editing Based on Finite Differences and Fourier Series AU - Jin , Qunzhi AU - Jin , Yuanfeng JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 933 EP - 955 PY - 2024 DA - 2024/12 SN - 17 DO - http://doi.org/10.4208/nmtma.OA-2024-0022 UR - https://global-sci.org/intro/article_detail/nmtma/23647.html KW - Finite difference method, Fourier series, discrete curvature, small angles. AB -

In this paper, the proposed method utilizes finite difference and Fourier series methods to calculate the mean curvature vectors and normalized curvature weights at the vertices of manifold triangular meshes. Specifically, this stable method achieves the $L^2$ convergence of the mean curvature vector. Furthermore, by comparing the method proposed in this paper with previously proposed classical methods, the results show that this method effectively balances precision and stability, and significantly reduces the larger errors observed on triangular meshes with small angles (approximately $0^◦$).

Jin , Qunzhi and Jin , Yuanfeng. (2024). Manifold Triangular Mesh Editing Based on Finite Differences and Fourier Series. Numerical Mathematics: Theory, Methods and Applications. 17 (4). 933-955. doi:10.4208/nmtma.OA-2024-0022
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