### 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.

Original language | English (US) |
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Pages (from-to) | 1475-1484 |

Number of pages | 10 |

Journal | Eurographics Symposium on Geometry Processing |

Volume | 28 |

Issue number | 5 |

State | Published - Dec 1 2009 |

### All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Geometry and Topology

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## Cite this

*Eurographics Symposium on Geometry Processing*,

*28*(5), 1475-1484.