Fully Dynamic and Kinematic Voronoi Diagrams in GIS

This paper gives a survey of static, dynamic, and kinematic Voronoi diagrams as a basic tool for Geographic Information Systems (GIS). We show how the Voronoi diagram with its dual, the Delaunay multigraph, can be used to maintain the topology of the map objects of a GIS. The presented method allows the insertion, deletion, and translation of points and line segments in a Voronoi diagram of n gcncrators. All clcmcntary operations are available in O(log n) expected time using expected linear storage. The Voronoi approach also greatly simplifies some of the basic traditional GIS queries and allows even new types of higher level queries. The concept of a persistent, locally-modifiable spatial data structure that is always complete provides an important new approach to spatial data handling that is not available with existing systems.