  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.
