EFFICIENT SPATIO-TEMPORAL MODELLING TO ENABLE TOPOLOGICAL ANALYSIS

Abstract. Time-dependent analysis scenarios such as heat, wind or flood analysis in cities and in landscapes need a correct and consistent modelling of geometry and topology over time. However, hitherto efficient time-dependent geometry models and topological analysis based on a mathematically sound theory were neglected when modelling objects in the built and natural environment. This is surprising as incorrect topological relationships over time such as not fitting neighbourhoods of surfaces or solids inevitably lead to wrong analysis results. In this paper we propose the combination of a spatio-temporal geometry model together with a topological schema to provide accessible and consistent objects over time. Where an efficient spatio-temporal geometry model reduces redundant geometric data and enables spatio-temporal queries, an efficient topological model minimizes the number of relations as far as possible and enables robust topological queries. The geometry model uses the concepts of point tubes, delta storage as well as net components and pre- and post-objects to enable the change of geometry and topology over time for natural structures, e.g., digital terrain models (DTM). Geometry here are the boundary and interior coordinates of the objects whereas topology here is interpreted in a wider sense than only focusing on geometrically induced topology to maintain topological consistency by the management of incidence relations. In addition, the topological schema introduces three basic bidirectional relation types to manage aggregations, abstractions and incidences in order to provide a general abstract topological schema for the management of complex intra- and inter-related spatio-temporal objects to enable the modelling of consistent complex topology over time. Finally, a conclusion is given highlighting the applicability of the approach and future research.