A Tractable Formalism for Combining Rectangular Cardinal Relations with Metric Constraints

Knowledge representation and reasoning in real-world applications often require to integrate multiple aspects of space. 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 aligned to the axes of the plane. We first show how to extend a tractable fragment of such a calculus with metric constraints preserving tractability. Then, we illustrate how the resulting formalism makes it possible to represent available 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 rectangles.