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The Diamond Laplace for polygonal and polyhedral meshes

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dc.contributor.authorBunge, Astrid
dc.contributor.authorBotsch, Mario
dc.contributor.authorAlexa, Marc
dc.date.accessioned2022-03-08T11:17:44Z
dc.date.available2022-03-08T11:17:44Z
dc.date.issued2021-08-23
dc.description.abstractWe introduce a construction for discrete gradient operators that can be directly applied to arbitrary polygonal surface as well as polyhedral volume meshes. The main idea is to associate the gradient of functions defined at vertices of the mesh with diamonds: the region spanned by a dual edge together with its corresponding primal element — an edge for surface meshes and a face for volumetric meshes. We call the operator resulting from taking the divergence of the gradient Diamond Laplacian. Additional vertices used for the construction are represented as affine combinations of the original vertices, so that the Laplacian operator maps from values at vertices to values at vertices, as is common in geometry processing applications. The construction is local, exactly the same for all types of meshes, and results in a symmetric negative definite operator with linear precision. We show that the accuracy of the Diamond Laplacian is similar or better compared to other discretizations. The greater versatility and generally good behavior come at the expense of an increase in the number of non-zero coefficients that depends on the degree of the mesh elements.en
dc.identifier.urihttp://hdl.handle.net/2003/40774
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-22631
dc.language.isoende
dc.relation.ispartofseriesComputer graphics forum;40(5)
dc.rights.urihttps://creativecommons.org/licenses/by-nc/4.0/
dc.subjectDiscrete Laplace Operatoren
dc.subjectDiscrete Differential Geometryen
dc.subjectDDFVen
dc.subject.ddc004
dc.subject.rswkIterierter Laplace-Operatorde
dc.subject.rswkDifferentialgeometriede
dc.titleThe Diamond Laplace for polygonal and polyhedral meshesen
dc.typeTextde
dc.type.publicationtypearticlede
dcterms.accessRightsopen access
eldorado.secondarypublicationtruede
eldorado.secondarypublication.primarycitationBunge, A., Botsch, M. and Alexa, M. (2021), The Diamond Laplace for Polygonal and Polyhedral Meshes. Computer Graphics Forum, 40: 217-230. https://doi.org/10.1111/cgf.14369de
eldorado.secondarypublication.primaryidentifierhttps://doi.org/10.1111/cgf.14369de

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