Representing spatial relations between arbitrarily oriented objects

A representation is developed for modeling the spatial relations between any two objects along with a set of transitivity relations for inferring indirect spatial knowledge. This logic provides the ability to make bounded inferences based on uncertain knowledge. Other advantages are that: (a) much spatial knowledge is relative, and it is often not possible to describe this knowledge in terms of absolute references; (b) local references are less prone to error accumulation; and (c) the relevant spatial information is abstracted in a qualitative form. The development proceeds in two stages: first, the relations are modeled in an orthogonal world where all edges are aligned to a set of axes. Next, several possible models for representing angular relations are considered, and a compact algebra is derived to describe arbitrary angular relations