Can Mean-Curvature Flow be Modified to be Non-singular?
Loading...
Date
2012
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd.
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.
Description
@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}
}