摘要
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.
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.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2015年第4期559-569,共11页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金(61432003
61322206
61272228)
清华大学自主科研计划(20131089252)
可视媒体智能处理与内容安全北京高校工程研究中心项目
