Fortune's Voronoi sweepline method for convex sites

This note sketches very brierly a description of Fortune's sweepline algorithm for Voronoi diagrams, in terms of a so-called `moving beachline.' This description was mentioned to the author by Richard Cole. The note argues that the approach applies to general convex sites in the plane. The details were later worked out by Andrew Farrell in his M.Sc. dissertation (1994), `Fortune's Voronoi diagram algorithm extended to convex sites.'