@article{CGF28-5:1475-1484:2009,
journal = {Computer Graphics Forum},
title = {{Estimating the Laplace-Beltrami Operator by Restricting 3D Functions}},
author = {Ming Chuang and Linjie Luo and Benedict J. Brown and Szymon Rusinkiewicz and Michael Kazhdan },
year = {2009},
pages = {1475-1484},
volume= {28},
number= {5},
URL = {http://diglib.eg.org/EG/CGF/volume28/issue5/v28i5pp1475-1484.pdf},
abstract = {We present a novel approach for computing and solving the Poisson equation over the surface of a mesh. As in previous approaches, we define the Laplace-Beltrami operator by considering the derivatives of functions defined on the mesh. However, in this work, we explore a choice of functions that is decoupled from the tessellation. Specifically, we use basis functions (second-order tensor-product B-splines) defined over 3D space, and then restrict them to the surface. We show that in addition to being invariant to mesh topology, this definition of the Laplace-Beltrami operator allows a natural multiresolution structure on the function space that is independent of the mesh structure, enabling the use of a simple multigrid implementation for solving the Poisson equation.}
}