Three Approaches to Automated Topology, and How Computational Geometry Helps

Traditional polygon-arc-node topology is standard in vector GIS, but it has its limitations. This is particularly evident at the digitizing stage, which often appears excessively complex and tedious, Other methods, however, are capable of maintaining some forms of topology “automatically”, and this paper is an overview of three approaches based on the Voronoi diagram (or the equivalent Delaunay triangulation). The first uses standard point Voronoi diagrams to speed up the polygon digitizing process; the second uses the constrained Delaunay triangulation to represent terrain as a triangulated irregular network with included linear features; and the third uses the Voronoi diagram of line segments and points to generate dynamically a more complete version of the traditional topology. These and other aspects of spatial relationships are studied in the field of computational geometry, which is increasingly applicable to GIS problems.