Estimating the laplace-beltrami operator by restricting 3D functions

Ming Chuang, Linjie Luo, Benedict J. Brown, Szymon M. Rusinkiewicz, Michael Kazhdan

Research output: Contribution to journalArticle

30 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)1475-1484
Number of pages10
JournalComputer Graphics Forum
Volume28
Issue number5
DOIs
StatePublished - Jan 1 2009

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Mathematical operators
Poisson equation
Splines
Tensors
Topology
Derivatives

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design

Cite this

Chuang, Ming ; Luo, Linjie ; Brown, Benedict J. ; Rusinkiewicz, Szymon M. ; Kazhdan, Michael. / Estimating the laplace-beltrami operator by restricting 3D functions. In: Computer Graphics Forum. 2009 ; Vol. 28, No. 5. pp. 1475-1484.
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Estimating the laplace-beltrami operator by restricting 3D functions. / Chuang, Ming; Luo, Linjie; Brown, Benedict J.; Rusinkiewicz, Szymon M.; Kazhdan, Michael.

In: Computer Graphics Forum, Vol. 28, No. 5, 01.01.2009, p. 1475-1484.

Research output: Contribution to journalArticle

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