In this paper, we propose a meshless method of computing eigenvalues and eigenfunctions of a given surface embedded in $\mathbb R^3$. We use point cloud data as input and generate the lattice approximation for some neighborhood of the surface. We compute the eigenvalues and eigenvectors of the cubic lattice graph as an approximation of the eigenvalues and eigenfunctions of the Laplace-Beltrami operator on the surface. We perform extensive numerical experiments on surfaces with various topology and compare our computed eigenvalues from point cloud surface with exact solutions and standard finite element methods using triangle mesh.

翻译：在本文中, 我们提出一种无孔不入的方法, 计算嵌入 $\mathbb R $3$ 的某一表面的精华值和元功能。 我们使用点云数据作为输入, 并生成地表某些邻近地区的拉蒂斯 立方图的精华值和元值近似值。 我们用三角网格来计算 Laplace- Beltrami 操作员在地表上的精华值和元值。 我们用各种表层进行广泛的数字实验, 用精确的解决方案和标准限值元素方法比较我们从点云表面计算的精度值。