A tesseral approach to N-dimensional spatial reasoning

Abstract

A qualitative multi-dimensional spatial reasoning system is described founded on a tesseral representation of space. Spatial problems are presented to this system in the form of a script describing the nature of the N-dimensional space (the object space), the spatial objects of interest and the relations that are desired to exist between those objects. Objects are defined in terms of classes and instances of classes with locations and shapes defined as sets of tesseral addresses. Relations are expressed in terms of topological set relations which may be quantified through the application of tesseral offsets. Solutions to spatial problems are generated using a heuristically guided constraint satisfaction mechanism. The heuristics are directed at limiting the growth of the search tree through a constraint selection strategy applied at each stage of the satisfaction process. The general advantages of the system are that it is conceptually simple, computationally effective and universally applicable to N-dimensional problem solving.