Kazhdan, MichaelSolomon, JakeBen-Chen, MirelaEitan Grinspun and Niloy Mitra2015-02-282015-02-2820121467-8659https://doi.org/10.1111/j.1467-8659.2012.03179.xThis 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.I.3.5 [Computer Graphics]Geometric algorithmslanguagesand systemsSurface Flow10.1111/j.1467-8659.2012.03179.x