QTC3D: Extending the qualitative trajectory calculus to three dimensions

Spatial interactions between agents (humans, animals, or machines) carry information of high value to human or electronic observers. However, not all the information contained in a pair of continuous trajectories is important and thus the need for qualitative descriptions of interaction trajectories arises. The Qualitative Trajectory Calculus (QTC) (Van de Weghe, 2004) is a promising development towards this goal. Numerous variants of QTC have been proposed in the past and QTC has been applied towards analyzing various interaction domains. However, an inherent limitation of those QTC variations that deal with lateral movements is that they are limited to two-dimensional motion; therefore, complex three-dimensional interactions, such as those occurring between flying planes or birds, cannot be captured. Towards that purpose, in this paper QTC3D is presented: a novel qualitative trajectory calculus that can deal with full three-dimensional interactions. QTC3D is based on transformations of the Frenet-Serret frames accompanying the trajectories of the moving objects. Apart from the theoretical exposition, including definition and properties, as well as computational aspects, we also present an application of QTC3D towards modeling bird flight. Thus, the power of QTC is now extended to the full dimensionality of physical space, enabling succinct yet rich representations of spatial interactions between agents.