Reasoning about ordering

Abstract

Ordering information is a special type of spatial information that derives from the linear, planar or spatial ordering of points. A definition of ordering information in terms of the orientation of simplexes is used in this paper to introduce a system of line segment relations which generalizes Allen's system of interval relations to two dimensions. It shows that this generalization differs in interesting properties from the generalizations based on topological relations which have been proposed so far. The conceptual neighborhood structure of the line segment relations provides the foundation of ordering information reasoning. This is illustrated with an example from motion planning. Finally, the problem of representing ordering information is addressed. In that context the cell complex representation of Frank and Kuhn is compared with the approach presented here.