Estimating the Laplace-Beltrami Operator by Restricting 3D Functions

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dc.contributor.authorChuang, Mingen_US
dc.contributor.authorLuo, Linjieen_US
dc.contributor.authorBrown, Benedict J.en_US
dc.contributor.authorRusinkiewicz, Szymonen_US
dc.contributor.authorKazhdan, Michaelen_US
dc.date.accessioned2015-02-23T15:43:33Z
dc.date.available2015-02-23T15:43:33Z
dc.date.issued2009en_US
dc.description.abstractWe 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.en_US
dc.description.number5en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume28en_US
dc.identifier.doi10.1111/j.1467-8659.2009.01524.xen_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages1475-1484en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2009.01524.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltden_US
dc.titleEstimating the Laplace-Beltrami Operator by Restricting 3D Functionsen_US
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SGP09: Eurographics Symposium on Geometry Processing