Title: Estimating the Laplace-Beltrami Operator by Restricting 3D Functions
Authors: Chuang, Ming ×
Luo, Linjie
Brown, Benedict
Rusinkiewicz, Szymon
Kazhdan, Michael #
Issue Date: Jul-2009
Publisher: North Holland
Series Title: Computer Graphics Forum vol:28 issue:5 pages:1475-1484
Conference: Eurographics symposium on geometry processing edition:7 location:Berlin, Germany date:15-17 July 2009
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: Chuang M., Luo L., Brown B., Rusinkiewicz S., Kazhdan M., ''Estimating the Laplace-Beltrami operator by restricting 3D functions'', Computer graphics forum, vol. 28, no. 5, pp. 1475-1484, July 2009 (7th Eurographics symposium on geometry processing, July 15-17, 2009, Berlin, Germany).
ISSN: 0167-7055
Publication status: published
KU Leuven publication type: IT
Appears in Collections:ESAT - PSI, Processing Speech and Images
× corresponding author
# (joint) last author

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