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

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    Date
    2012
    Author
    Kazhdan, Michael
    Solomon, Jake
    Ben-Chen, Mirela
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    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.
    BibTeX
    @article {10.1111:j.1467-8659.2012.03179.x,
    journal = {Computer Graphics Forum},
    title = {{Can Mean-Curvature Flow be Modified to be Non-singular?}},
    author = {Kazhdan, Michael and Solomon, Jake and Ben-Chen, Mirela},
    year = {2012},
    publisher = {The Eurographics Association and Blackwell Publishing Ltd.},
    ISSN = {1467-8659},
    DOI = {10.1111/j.1467-8659.2012.03179.x}
    }
    URI
    http://dx.doi.org/10.1111/j.1467-8659.2012.03179.x
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    • 31-Issue 5
    • SGP12: Eurographics Symposium on Geometry Processing

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