中文摘要：

3维空间中位置关系的定性描述和推理是当前城市和矿山GIS界的重要理论课题之一,主要涉及如何用定性距离和方向关系来综合描述目标对象及相对于其参照物的空间位置关系的方法。本文基于投影系统划分空间方向区域,利用解析几何工具表达距离关系和方向关系,建立组合距离和方向关系来描述位置关系的概念框架,导出位置关系组合推理的一般表达式,并通过例子说明一些典型的位置关系定性推理过程和结果。

英文摘要：

Qualitative representation and reasoning of positional relationships are recognized as one of the promising theoretical themes in three-dimensional （3D） GISs which are related to urban information management, planning and services as well as mining engineering fields. The focus of the studies deals with the methodologies on the descriptions of spatial objects and the determinations of their geo-referenced relationships. In this paper, a geometrical projection-based system was applied to divide a 3D space into sub-divisions. Analytical geometry was used as mathematical tool to qualitatively represent both distance and direction relationships, which were then integrated to develop a conceptual framework to depict positional relationships. A generalized equation for qualitative reasoning of positional relations was derived as the result from the integrated reasoning. Empirical examples were provided to show the qualitative reasoning process and results of positional relationships for some classical cases.