Skip to Main content Skip to Navigation
Conference papers

Laplace-Beltrami Eigenfunctions Towards an algorithm that " understands " geometry

Bruno Lévy 1
1 ALICE - Geometry and Lighting
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : One of the challenges in geometry processing is to automatically reconstruct a higher-level representation from raw geometric data. For instance, computing a parameter-ization of an object helps attaching information to it and converting between various representations. More generally , this family of problems may be thought of in terms of constructing structured function bases attached to surfaces. In this paper, we study a specific type of hierarchical function bases, defined by the eigenfunctions of the Laplace-Beltrami operator. When applied to a sphere, this function basis corresponds to the classical spherical harmonics. On more general objects, this defines a function basis well adapted to the geometry and the topology of the object. Based on physical analogies (vibration modes), we first give an intuitive view before explaining the underlying theory. We then explain in practice how to compute an approximation of the eigenfunctions of a differential operator, and show possible applications in geometry processing.
Complete list of metadata

Cited literature [31 references]  Display  Hide  Download

https://hal.inria.fr/inria-00105566
Contributor : Nicolas Ray <>
Submitted on : Thursday, September 22, 2016 - 2:27:11 PM
Last modification on : Friday, February 26, 2021 - 3:28:08 PM

File

SMI_Laplacian.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Bruno Lévy. Laplace-Beltrami Eigenfunctions Towards an algorithm that " understands " geometry. IEEE International Conference on Shape Modeling and Applications - SMI 2006, Jun 2006, Matsushima, Japan. pp.13, ⟨10.1109/SMI.2006.21⟩. ⟨inria-00105566⟩

Share

Metrics

Record views

951

Files downloads

1010