Polygon Laplacian Made Robust

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dc.contributor.authorBunge, Astriden_US
dc.contributor.authorBukenberger, Dennis R.en_US
dc.contributor.authorWagner, Sven Dominiken_US
dc.contributor.authorAlexa, Marcen_US
dc.contributor.authorBotsch, Marioen_US
dc.contributor.editorBermano, Amit H.en_US
dc.contributor.editorKalogerakis, Evangelosen_US
dc.date.accessioned2024-04-30T09:08:05Z
dc.date.available2024-04-30T09:08:05Z
dc.date.issued2024
dc.description.abstractDiscrete Laplacians are the basis for various tasks in geometry processing. While the most desirable properties of the discretization invariably lead to the so-called cotangent Laplacian for triangle meshes, applying the same principles to polygon Laplacians leaves degrees of freedom in their construction. From linear finite elements it is well-known how the shape of triangles affects both the error and the operator's condition. We notice that shape quality can be encapsulated as the trace of the Laplacian and suggest that trace minimization is a helpful tool to improve numerical behavior. We apply this observation to the polygon Laplacian constructed from a virtual triangulation [BHKB20] to derive optimal parameters per polygon. Moreover, we devise a smoothing approach for the vertices of a polygon mesh to minimize the trace. We analyze the properties of the optimized discrete operators and show their superiority over generic parameter selection in theory and through various experiments.en_US
dc.description.number2
dc.description.sectionheadersMeshes
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume43
dc.identifier.doi10.1111/cgf.15025
dc.identifier.issn1467-8659
dc.identifier.pages15 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.15025
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf15025
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution-NonCommercial 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by-nc/4.0/
dc.subjectCCS Concepts: Computing methodologies -> Mesh geometry models; Mathematics of computing -> Mesh generation; Discretization
dc.subjectComputing methodologies
dc.subjectMesh geometry models
dc.subjectMathematics of computing
dc.subjectMesh generation
dc.subjectDiscretization
dc.titlePolygon Laplacian Made Robusten_US
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