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Estimating the Laplace-Beltrami Operator by Restricting 3D Functions Ming Chuang, Linjie Luo, Benedict J. Brown,
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. Citation (BibTeX) Ming Chuang, Linjie Luo, Benedict J. Brown, Szymon Rusinkiewicz, and Michael Kazhdan. Paper |