In this talk, we revisit the problem of formation of neck-pinch
singularities in mean curvature flow of non-convex surafcesin 3D.
Examining the problem from the lens of geometry processing, we identify a
numerical issue in the flow and propose a conformalization approach that
bypasses the singularity. Empirically, we show that when applied to
genus-zero surfaces, the conformalized flow evolves to conformal
parameterization of the surface over a sphere.
Time permitting, we will further look at the problem of registering
spherical parameterizations over the Möbius group. We propose a novel
centering technique for canonically posing the parameterization with
respect to inversions (falling back to standard FFT techniques for
registering the rotational component) and show that the approach may
generalize to a larger class of deformations.