Recent progress in the Laplace-Beltrami operator and its applications to digital geometry processing（数字几何处理中Laplace-Beltrami算子的离散化理论与应用研究综述）
Published in Journal of Computer-Aided Design & Computer Graphics, 2015
Abstract: Digital geometry processing focus on 2-dimensional surfaces in 3-dimentional space.Laplace-Beltrami operator is a differential operator defined on Riemannian manifolds.Discrete Laplace-Beltrami operator is a useful tool in applications such as 3-dimentional model analysis.Diverse methods of discretization lead to distinct mathematical properties related to the applications they aim at respectively.This paper provides a survey on theory and application of discrete Laplace-Beltrami operator.We hope this paper can provide some help for researchers to learn how Laplace-Beltrami operator works in digital geometry processing with in-depth understanding and identify possible directions for further research and new applications.
Recommended citation: Dian Fan, Yong-Jin Liu, Ying He (2015) Recent progress in the Laplace-Beltrami operator and its applications to digital geometry processing（数字几何处理中Laplace-Beltrami算子的离散化理论与应用研究综述）. Journal of Computer-Aided Design & Computer Graphics, Vol. 27, No. 4, pp.559-569, in Chinese, 2015.