  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 QTC3Dis 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.
