A straightforward iterative algorithm for the planar Voronoi diagram

Abstract

Several published algorithms construct the planar N-point Voronoi diagram by adding the points in turn to a diagram already constructed for a subset of those points. The algorithm described here works in this way, but stipulates that every added point be outside the convex hull of the already constructed partial diagram. This stipulation, which is implemented by presorting the points by increasing x-coordinate, ensures that the core of the algorithm runs in almost linear time. The algorithm is inherently iterative, not recursive, and provides a rapid, efficient way to construct the Voronoi diagram for large data sets.