Efficient Spatial Reasoning with Rectangular Cardinal Relations and Metric Constraints

In many real-world applications of knowledge representation and reasoning formalisms, one needs to cope with a number of spatial aspects in an integrated and efficient way. In this paper, we focus our attention on the so-called Rectangular Cardinal Direction calculus for qualitative spatial reasoning on cardinal relations between rectangles whose sides are parallel to the axes of a fixed reference system. We show how to extend its convex tractable fragment with metric constraints preserving tractability. The resulting formalism makes it possible to efficiently reason about spatial knowledge specified by one qualitative constraint network and two metric networks (one for each spatial dimension). In particular, it allows one to represent definite or imprecise knowledge on directional relations between rectangles and to derive additional information about them, as well as to deal with metric constraints on the height/width of a rectangle or on the vertical/horizontal distance between the sides of two rectangles. We believe that the formalism features a good combination of simplicity, efficiency, and expressive power, making it adequate for spatial applications like, for instance, web-document query processing and automatic layout generation.