  Voronoi cells of varieties encode many features of their metric geometry. We
prove that each Voronoi or Delaunay cell of a plane curve appears as the limit
of a sequence of cells obtained from point samples of the curve. We use this
result to study metric features of plane curves, including the medial axis,
curvature, evolute, bottlenecks, and reach. In each case, we provide algebraic
equations defining the object and, where possible, give formulas for the
degrees of these algebraic varieties. We show how to identify the desired
metric feature from Voronoi or Delaunay cells, and therefore how to approximate
it by a finite point sample from the variety.

Metric Geometry;Computational Geometry;Algebraic Geometry