A Laplacian for Nonmanifold Triangle Meshes

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dc.contributor.authorSharp, Nicholasen_US
dc.contributor.authorCrane, Keenanen_US
dc.contributor.editorJacobson, Alec and Huang, Qixingen_US
dc.date.accessioned2020-07-05T13:25:59Z
dc.date.available2020-07-05T13:25:59Z
dc.date.issued2020
dc.description.abstractWe describe a discrete Laplacian suitable for any triangle mesh, including those that are nonmanifold or nonorientable (with or without boundary). Our Laplacian is a robust drop-in replacement for the usual cotan matrix, and is guaranteed to have nonnegative edge weights on both interior and boundary edges, even for extremely poor-quality meshes. The key idea is to build what we call a ''tufted cover'' over the input domain, which has nonmanifold vertices but manifold edges. Since all edges are manifold, we can flip to an intrinsic Delaunay triangulation; our Laplacian is then the cotan Laplacian of this new triangulation. This construction also provides a high-quality point cloud Laplacian, via a nonmanifold triangulation of the point set. We validate our Laplacian on a variety of challenging examples (including all models from Thingi10k), and a variety of standard tasks including geodesic distance computation, surface deformation, parameterization, and computing minimal surfaces.en_US
dc.description.number5
dc.description.sectionheadersDiscrete Differential Geometry
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume39
dc.identifier.doi10.1111/cgf.14069
dc.identifier.issn1467-8659
dc.identifier.pages69-80
dc.identifier.urihttps://doi.org/10.1111/cgf.14069
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14069
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.subjectMathematics of computing
dc.subjectDiscretization
dc.subjectPartial differential equations
dc.titleA Laplacian for Nonmanifold Triangle Meshesen_US
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