A Reasoning Method for Qualitative Distance Change Based on OPRA\-4 Direction Relations

Spatial information includes many relations such as direction, topology, shape, distance, etc. Qualitative spatial representation and reasoning has become an important subfield of artificial intelligence, and has gained increasing popularity in recent years with applications in spatial information systems, robot navigation, natural language understanding, intelligent transportation system and so on. Previous studies are mostly oriented to static spatial objects, and focus on a single kind of spatial relation. The research on constraints between different kinds of spatial relations is insufficient, and it is difficult to make use of one kind of spatial relation to reason about the evolution of another spatial relation effectively. In this study, we focus on the qualitative direction relations and distance changes of moving spatial objects. Firstly, the relative moving direction between two spatial objects is described by a combination of the position relations between the corresponding ray and the circle. Secondly, the restrictions of the combinations on the qualitative distance changes, and the corresponding relationship between the combinations and oriented point algebra with granularity of 4 (OPRA\-4) are studied respectively. And then the connection between the OPRA\-4 direction relations and the qualitative distance changes is established. Finally, an approach to reasoning about the qualitative distance changes with basic OPRA\-4 direction relations is presented. The correctness and effectiveness of the approach are illustrated by an example of continuous k nearest neighbor queries of moving objects in traffic field.