A General and Efficient Implementation of Geometric Operators and Predicates

Shape and location of objects in a spatial database are commonly represented by geometric data such as points, lines and regions. Numerous geometric operators and predicates have been proposed for spatial database systems. Existing work on their implementation concentrate on individual operators and predicates. This approach makes the realization of geometric operators and predicates in a spatial database system diicult since they are diverse and their implementation in general are complex. In this paper, we present a simple plane-sweep algorithm that can be easily modiied to realize eeciently a set of frequently used line-region and region-region geometric operators and predicates. The design of this uniied algorithm is based on the observation that the covering of elementary regions along the sweep line are updated locally and the implementation of these operators and predicates diier only with the output actions at an intersection point. Any geometric operator or predicate, the output of which can be determined by examining incident edges and covering information at intersection points, can be implemented easily with the algorithm. To demonstrate its generality, extendibility, simplicity and eeciency, we concentrate on several popular geometric operators and predicates. All these operators and predicates can be realized in O((N + I) logN) time in the worst case, where N is the number of edges in the operands and I is the number of intersecting pairs. The proposed algorithm is fully implemented in C++ and is tested on a Sun workstation. Although the paper focuses on operators and predicates involving at most two regions, this algorithm can be generalized nicely to r regions, where r>2. We describe what changes are needed to make to the basic algorithm to accommodate this generalization.