  We present careful numerical convergence studies, using parameterized curves
to reach very high resolutions in two dimensions, of a level set method for
multiphase curvature motion known as the Voronoi implicit interface method. Our
tests demonstrate that in the unequal, additive surface tension case, the
Voronoi implicit interface method does not converge to the desired limit. We
then present a variant that maintains the spirit of the original algorithm, and
appears to fix the non-convergence. As a bonus, the new variant extends the
Voronoi implicit interface method to unequal mobilities.
