Estimating the Laplace-Beltrami Operator by Restricting 3D Functions
Chuang, Ming × Luo, Linjie Brown, Benedict Rusinkiewicz, Szymon Kazhdan, Michael #
Computer Graphics Forum vol:28 issue:5 pages:1475-1484
Eurographics symposium on geometry processing edition:7 location:Berlin, Germany date:15-17 July 2009
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.
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).