Date

2022-8-29

Author

Yazgan, Misranur

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When the complexity of a mesh starts introducing high computational costs, mesh simplification methods come into the picture, to reduce the number of elements utilized to represent the mesh. Majority of the simplification methods focus on preserving the appearance of the mesh, ignoring the spectral properties of the differential operators derived from the mesh. The spectrum of the Laplace-Beltrami operator is essential for a large subset of applications in geometry processing. Coarsening a mesh without considering its spectral properties might result with incorrect calculations on the simplified mesh. Given a 3D triangular mesh, this thesis aims to decrease its resolution by applying mesh simplification, while focusing on preserving the spectral properties of the associated cotangent Laplace-Beltrami operator. Unlike the existing spectrum-preserving coarsening methods, this work utilizes solely the eigenvalues of the operator, in order to preserve the spectrum. The presented method is partition based, in a way that the input mesh is divided into smaller patches and each patch is simplified individually. The method is evaluated on a variety of meshes, by using functional maps and quantitative norms. These metrics are used to measure how well the eigenvalues and eigenvectors of the Laplace-Beltrami operator computed on the input mesh are maintained by the output mesh. At the end of this thesis, it is demonstrated that the achieved spectrum preservation is at least as effective as the existing spectral coarsening methods.

Subject Keywords

Laplace-Beltrami operator, Mesh simplification, Spectral mesh simplification, Spectral coarsening, Geometry processing

URI

https://hdl.handle.net/11511/99624

Collections

Graduate School of Natural and Applied Sciences, Thesis