“…This quantity is of interest in topological data analysis, where it determines the density of sample points needed to compute the persistent homology of X. We refer to [3,5,10] for recent progress on sampling at the interface of topological data analysis with metric algebraic geometry. The distance from a point y on X to the medial axis could be considered the local reach of X. Equivalently, this is the distance from y to the boundary of its Voronoi cell Vor X (y).…”