Discrete Distortion in Triangulated 3-Manifolds

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dc.contributor.authorMesmoudi, Mohammed Mostefaen_US
dc.contributor.authorDe Floriani, Leilaen_US
dc.contributor.authorPort, Umbertoen_US
dc.date.accessioned2015-02-21T17:32:26Z
dc.date.available2015-02-21T17:32:26Z
dc.date.issued2008en_US
dc.description.abstractWe introduce a novel notion, that we call discrete distortion, for a triangulated 3-manifold. Discrete distortion naturally generalizes the notion of concentrated curvature defined for triangulated surfaces and provides a powerful tool to understand the local geometry and topology of 3-manifolds. Discrete distortion can be viewed as a discrete approach to Ricci curvature for singular flat manifolds. We distinguish between two kinds of distortion, namely, vertex distortion, which is associated with the vertices of the tetrahedral mesh decomposing the 3-manifold, and bond distortion, which is associated with the edges of the tetrahedral mesh. We investigate properties of vertex and bond distortions. As an example, we visualize vertex distortion on manifold hypersurfaces in R4 defined by a scalar field on a 3D mesh. distance fields.en_US
dc.description.number5en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume27en_US
dc.identifier.doi10.1111/j.1467-8659.2008.01272.xen_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages1333-1340en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2008.01272.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltden_US
dc.titleDiscrete Distortion in Triangulated 3-Manifoldsen_US
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27-Issue 5
SGP08: Eurographics Symposium on Geometry Processing