Can mean-curvature flow be modified to be non-singular?

Michael Kazhdan, Jake Solomon, Mirela Ben-Chen

Research output: Contribution to journalArticlepeer-review

65 Scopus citations

Abstract

This 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.

Original languageAmerican English
Pages (from-to)1745-1754
Number of pages10
JournalComputer Graphics Forum
Volume31
Issue number5
DOIs
StatePublished - 2012
Externally publishedYes

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