A Survey on Discrete Laplacians for General Polygonal Meshes

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dc.contributor.authorBunge, Astriden_US
dc.contributor.authorBotsch, Marioen_US
dc.contributor.editorBousseau, Adrienen_US
dc.contributor.editorTheobalt, Christianen_US
dc.date.accessioned2023-05-03T06:13:38Z
dc.date.available2023-05-03T06:13:38Z
dc.date.issued2023
dc.description.abstractThe Laplace Beltrami operator is one of the essential tools in geometric processing. It allows us to solve numerous partial differential equations on discrete surface meshes, which is a fundamental building block in many computer graphics applications. Discrete Laplacians are typically limited to standard elements like triangles or quadrilaterals, which severely constrains the tessellation of the mesh. But in recent years, several approaches were able to generalize the Laplace Beltrami and its closely related gradient and divergence operators to more general meshes. This allows artists and engineers to work with a wider range of elements which are sometimes required and beneficial in their field. This paper discusses the different constructions of these three ubiquitous differential operators on arbitrary polygons and analyzes their individual advantages and properties in common computer graphics applications.en_US
dc.description.documenttypestar
dc.description.number2
dc.description.sectionheadersState of the Art Reports
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume42
dc.identifier.doi10.1111/cgf.14777
dc.identifier.issn1467-8659
dc.identifier.pages521-544
dc.identifier.pages24 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.14777
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14777
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by-nc/4.0/
dc.titleA Survey on Discrete Laplacians for General Polygonal Meshesen_US
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