RIM: a ray intersection model for the analysis of the between relationship of spatial objects in a 2D plane

Abstract

ABSTRACT The term between is frequently used to describe spatial arrangements of objects where one described core object is positioned in the space bounded by two or more peripheral objects. As such, the relation between involves spatial configurations of at least three spatial objects. However, most of the existing qualitative spatial reasoning models focus only on binary spatial relations, and there is currently no single model that enables adequate reasoning about this ternary spatial relation. This paper proposes a novel model for expressing nuanced spatial relationships between three spatial objects, called the Ray Intersection Model (RIM). RIM evaluates rays cast between two peripheral spatial objects, and their topological relations with the core object to determine its position relative to the peripheral objects. RIM leaves the binary classification of the core object as between/not between to the user and application context. Although RIM supports all types of 2D spatial objects (i.e. points, lines, and polygons), its expressiveness is demonstrated in this paper by analyzing the total of 28 distinct configurations of triplets of polygon objects in a 2D plane. RIM has been computationally implemented and we demonstrate how RIM can be applied to analyze the arrangements of buildings at a university campus.