A Topological Data Model for Spatial Databases

There is a growing demand for engineering applications which need a sophisticated treatment of geometric properties. Implementations of Euclidian geometry, commonly used in current commercial Geographic Information Systems and CAD/CAM, are impeded by the finiteness of computers and their numbering systems. To overcome these deficiencies a spatial data model is proposed which is based upon the mathematical theory of simplices and simplicial complexes from combinatorial topology and introduces and as an extension to the closed world assumption. It guarantees the preservation of topology under affine transformations. This model leads to straightforward algorithms which are described. The implementation as a general spatial framework on top of an object-oriented database management system is discussed.