Can Mean-Curvature Flow be Modified to be Non-singular?

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dc.contributor.authorKazhdan, Michaelen_US
dc.contributor.authorSolomon, Jakeen_US
dc.contributor.authorBen-Chen, Mirelaen_US
dc.contributor.editorEitan Grinspun and Niloy Mitraen_US
dc.date.accessioned2015-02-28T07:44:15Z
dc.date.available2015-02-28T07:44:15Z
dc.date.issued2012en_US
dc.description.abstractThis work considers the question of whether mean-curvature flow can be modified to avoid the formation of singularities. We analyze the finite-elements discretization and demonstrate why the original flow can result in numerical instability due to division by zero. We propose a variation on the flow that removes the numerical instability in the discretization and show that this modification results in a simpler expression for both the discretized and continuous formulations. We discuss the properties of the modified flow and present empirical evidence that not only does it define a stable surface evolution for genus-zero surfaces, but that the evolution converges to a conformal parameterization of the surface onto the sphere.en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume31
dc.identifier.doi10.1111/j.1467-8659.2012.03179.x
dc.identifier.issn1467-8659en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2012.03179.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltd.en_US
dc.subjectI.3.5 [Computer Graphics]en_US
dc.subjectGeometric algorithmsen_US
dc.subjectlanguagesen_US
dc.subjectand systemsen_US
dc.subjectSurface Flowen_US
dc.titleCan Mean-Curvature Flow be Modified to be Non-singular?en_US
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SGP12: Eurographics Symposium on Geometry Processing