Topological Access Methods for Spatial and Spatiotemporal Data

Abstract

In order to perform topological queries on geographic data, it is necessary to first develop a topological access method (TOAM). Using the fact that any (incidence or other binary) relation produces a topology which includes the common usage of topology for spatial or spatiotemporal data, here, such a TOAM is developed on the basis of the previously applied concept of Property Graph used in order to manage topological information in data of any dimension, whether time dependent or not. As a matter of fact, it is necessary to have a TOAM in order to query such a graph, and also to have data which are topologically consistent in a certain sense. While the rendering of topological consistency was the concern of previous work, here, the aim is to develop a methodology which builds on this concept. In the end, an experimental test of this approach on a small city model is performed. It turned out that the Euler characteristic, a well-known topological invariant, can be helpful for the initial data validation. Practically, this present theoretical work is seen to be necessary in view of future innovative applications, e.g., in the context of city model simulations, including distributed geo-processing.

Keywords

• geometrically induced topology
• simplicial complexes
• topological algorithms
• watertight volumetric model
• topological access method