The Balance Between Geometry and Topology

Abstract

The architecture of Geographic Information Systems (GISs) is changing: more and more systems are based on the integrated architecture, i.e. storing geometric data in the Data Base Management System (DBMS) together with administrative data. The first step in building a Geo-DBMS is by having data types and operators for simple features (i.e. geometric primitives): point, line and polygon. This has reached a level of standardisation and is now implemented in several commercial DBMSs. The next step is to have support for the topologically structured features in the DBMS, i.e. complex features. The DBMS can then check and guarantee consistency. In addition, complex operations can be executed within the DBMS. Despite the fact that topologically structured models are well known and that it is not difficult to store the topological references, it still remains an unresolved issue as to how to effectively implement these models within a relational DBMS. In this paper, we describe the design and implementation of a topologically structured management at the DBMS level. Our focus is to translate topological structures into geometric primitives. It is then possible to define a DBMS view on a topological primitive, which makes this appear as a geometric primitive. This process supports the best of both worlds: on the one hand there are advantages of the topological structure (no redundancy) and on the other hand the ease of explicit geometric primitives in querying, analysis and presentation is available.