Voronoi diagrams and arrangements

Herbert Edelsbrunner, Raimund Seidel
1986 Discrete & Computational Geometry  
We propose a uniform and general framework for defining and dealing with Voronoi diagrams. In this framework a Voronoi diagram is a partition of a domain D induced by a finite number of real valued functions on D. Valuable insight can be gained when one considers how these real valued functions partition D ×R. With this view it turns out that the standard Euclidean Voronoi diagram of point sets in R d along with its order-k generalizations are intimately related to certain arrangements of
more » ... lanes. This fact can be used to obtain new Voronoi diagram algorithms. We also discuss how the formalism of arrangements can be used to solve certain intersection and union problems.
doi:10.1007/bf02187681 fatcat:qaoojhms2va7ve7u7ejuzmkqwe