Estimating the Laplace-Beltrami operator by restricting 3D functions

  • Authors:

  • Ming Chuang;Linjie Luo;Benedict J. Brown;Szymon Rusinkiewicz;Michael Kazhdan

  • Affiliations:

  • Johns Hopkins University, Baltimore, MD;Princeton University, Princeton, NJ;Katholieke Universiteit Leuven, Leuven, Belgium;Princeton University, Princeton, NJ;Johns Hopkins University, Baltimore, MD

  • Venue:
  • SGP '09 Proceedings of the Symposium on Geometry Processing
  • Year:
  • 2009

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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.