Numerical computation of the cut locus via a variational approximation of the distance function

We propose a new method for the numerical computation of the cut locus of a compact submanifold of R3 without boundary. This method is based on a convex variational problem with conic constraints, with proven convergence. We illustrate the versatility of our approach by the approximation of Voronoi cells on embedded surfaces of R3.

Remarks on Manifolds with Two-Sided Curvature Bounds

We discuss folklore statements about distance functions in manifolds with two-sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.