CAJ | 학술논문

数字几何处理的主要研究对象是三维空间中的二维曲面， Laplace-Beltrami算子是定义在黎曼流形上的微分算子，其在网格曲面上的离散形式在三维模型分析等应用中具有重要作用，是一类基本的几何工具。不同的离散方法具有不同的数学性质，所适用的应用场景也不相同。文中对 Laplace-Beltrami 算子的离散化理论与应用进行综述，希望能够使读者对该算子的功能有基本了解，对数字几何处理的最新研究进展有进一步的认识，并对未来的研究方向及应用前景有所启发。
수자궤하처리적주요연구대상시삼유공간중적이유곡면， Laplace-Beltrami산자시정의재려만류형상적미분산자，기재망격곡면상적리산형식재삼유모형분석등응용중구유중요작용，시일류기본적궤하공구。불동적리산방법구유불동적수학성질，소괄용적응용장경야불상동。문중대 Laplace-Beltrami 산자적리산화이론여응용진행종술，희망능구사독자대해산자적공능유기본료해，대수자궤하처리적최신연구진전유진일보적인식，병대미래적연구방향급응용전경유소계발。
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 use-ful 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 re-searchers to learn how Laplace-Beltrami operator works in digital geometry processing with in-depth under-standing and identify possible directions for further research and new applications.