Estimating the Laplace-Beltrami Operator by Restricting 3D Functions
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Date
2009
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd
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.
Description
@article{10.1111:j.1467-8659.2009.01524.x,
journal = {Computer Graphics Forum},
title = {{Estimating the Laplace-Beltrami Operator by Restricting 3D Functions}},
author = {Chuang, Ming and Luo, Linjie and Brown, Benedict J. and Rusinkiewicz, Szymon and Kazhdan, Michael},
year = {2009},
publisher = {The Eurographics Association and Blackwell Publishing Ltd},
ISSN = {1467-8659},
DOI = {10.1111/j.1467-8659.2009.01524.x}
}