Polygon Laplacian Made Simple

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dc.contributor.authorBunge, Astriden_US
dc.contributor.authorHerholz, Philippen_US
dc.contributor.authorKazhdan, Mishaen_US
dc.contributor.authorBotsch, Marioen_US
dc.contributor.editorPanozzo, Daniele and Assarsson, Ulfen_US
dc.date.accessioned2020-05-24T12:52:14Z
dc.date.available2020-05-24T12:52:14Z
dc.date.issued2020
dc.description.abstractThe discrete Laplace-Beltrami operator for surface meshes is a fundamental building block for many (if not most) geometry processing algorithms. While Laplacians on triangle meshes have been researched intensively, yielding the cotangent discretization as the de-facto standard, the case of general polygon meshes has received much less attention. We present a discretization of the Laplace operator which is consistent with its expression as the composition of divergence and gradient operators, and is applicable to general polygon meshes, including meshes with non-convex, and even non-planar, faces. By virtually inserting a carefully placed point we implicitly refine each polygon into a triangle fan, but then hide the refinement within the matrix assembly. The resulting operator generalizes the cotangent Laplacian, inherits its advantages, and is empirically shown to be on par or even better than the recent polygon Laplacian of Alexa and Wardetzky [AW11] - while being simpler to compute.en_US
dc.description.number2
dc.description.sectionheadersMeshes and Subdivision
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume39
dc.identifier.doi10.1111/cgf.13931
dc.identifier.issn1467-8659
dc.identifier.pages303-313
dc.identifier.urihttps://doi.org/10.1111/cgf.13931
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13931
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectComputing methodologies
dc.subjectMesh geometry models
dc.subjectTheory of computation
dc.subjectComputational geometry
dc.titlePolygon Laplacian Made Simpleen_US
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