Optimized Dual-Volumes for Tetrahedral Meshes

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dc.contributor.authorJacobson, Alecen_US
dc.contributor.editorHu, Ruizhenen_US
dc.contributor.editorLefebvre, Sylvainen_US
dc.date.accessioned2024-06-20T07:54:55Z
dc.date.available2024-06-20T07:54:55Z
dc.date.issued2024
dc.description.abstractConstructing well-behaved Laplacian and mass matrices is essential for tetrahedral mesh processing. Unfortunately, the de facto standard linear finite elements exhibit bias on tetrahedralized regular grids, motivating the development of finite-volume methods. In this paper, we place existing methods into a common construction, showing how their differences amount to the choice of simplex centers. These choices lead to satisfaction or breakdown of important properties: continuity with respect to vertex positions, positive semi-definiteness of the implied Dirichlet energy, positivity of the mass matrix, and unbiased-ness on regular grids. Based on this analysis, we propose a new method for constructing dual-volumes which explicitly satisfy all of these properties via convex optimization.en_US
dc.description.number5
dc.description.sectionheadersMeshing
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume43
dc.identifier.doi10.1111/cgf.15133
dc.identifier.issn1467-8659
dc.identifier.pages9 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.15133
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf15133
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.titleOptimized Dual-Volumes for Tetrahedral Meshesen_US
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