An approach is given that develops spatial operators about the basic geometric elements common to spatial data structures. In this fashion, a single set of spatial operators may be accessed by any system that reduces its operands to such basic generic representations. Algorithms based on this premise have been formulated to perform operations such as separation, overlap, and intersection. Moreover, this generic approach is well suited for algorithms that exploit concurrent properties of spatial operators. The results may provide a framework for a geometry engine to support fundamental manipulations within a geographic information system.