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 - <p style="text-align: justify;">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 $0^◦$).</p>