Description, definition and proof of a qualitative state change of moving objects along a road network

Research has been done in generating, indexing, modelling and querying network-based moving objects. However, little work has been done in building a calculus of relations between these objects. In Van de Weghe et al. (2004b) an empirical approach based on an illustrative example is worked out in order to be able to represent and reason about the relative trajectories of pairs of objects moving along a road network. The approach has been called the Qualitative Trajectory Calculus along a road Network (QTC-N). This paper gives a more theorectical and analytical view on this calculus.