Oriented matroids as a foundation for space in GIS

We provide an expository account, from the viewpoint of geographic information science, of oriented matroids. The importance of these structures is that they provide an approach to space which is discrete and hence can be used for robust computation. A finite set of points in the plane can be given the structure of an oriented matroid and this finite structure captures enough of the geometrical structure of the idealized continuous plane to be able to perform useful computations such as finding the convex hull of a subset of the points. The advantage of oriented matroids over some approaches to discrete space, such as Schneider’s realms, is that they are purely finite combinatorial structures that make no mention of RnRn or QnQn, even though the intended models are finite subsets of these spaces.