The State of the Art of Voronoi Diagram Research

Abstract

AbstractThe notion of Voronoi diagrams refer to a conceptually simple geometric construct that is based on a finite set of points in a Euclidean space. Intuitively speaking, it is such a simple notion that it can be described to a non-specialist. Indeed even some social and cultural settings can be described that would convey the essence of the concept. Consider for instance a number of strangers who are standing still in a room at random locations. In what region of space can an individual freely move his/her arms without appearing to be impolite to the others? Without having a precise definition of this personal space, each individual would most likely have an intuitive notion of it. If each individual is reduced to a single point occupying a specific location in the room, the personal space of a particular point is its Voronoi cell, the set of all points that are closer to that point than to any of the other points. Each Voronoi cell is a polyhedral region. The Voronoi diagram of the set of points is the partitioning of the space into the collection of Voronoi cells, together with their boundaries.KeywordsVoronoi DiagramComputational GeometryDelaunay TriangulationVoronoi CellPersonal SpaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.