Approximate spatial reasoning using vague object boundaries

Abstract

This paper presents a method of accomplishing approximate spatial reasoning directly with solid models. By representing solids as vague objects, simple spatial reasoning is performed in an approximate and direct fashion. A vague object is a simplified solid object where sharp edges are replaced with smooth transitions from solid to its surroundings. A vague object can be compared to a cloud with smoothly varying density that resembles a real solid object. Vague objects can be used to represent spatial concepts as well. A spatial concept is defined as a relation between objects, either solid or vague. Many simple spatial concepts can be visualized as vague objects, and for simple spatial reasoning, they can be implemented as such. The use of vague objects to represent both solid objects and the relations between them is the foundation of an approximate spatial reasoning system. The purpose of this approach is to implement a form of spatial reasoning that mimics human spatial reasoning for judging and reasoning about simple relationships. The method presented has a significant advantage in that reasoning can be performed directly from solid model data. >