Chuang, MingLuo, LinjieBrown, Benedict J.Rusinkiewicz, SzymonKazhdan, Michael2015-02-232015-02-2320091467-8659https://doi.org/10.1111/j.1467-8659.2009.01524.xWe 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.10.1111/j.1467-8659.2009.01524.x1475-1484