Spatial data base queries: Relational algebra versus computational geometry

Abstract

Conventional queries against relational databases can be expressed in relational algebra. But, when dealing with geometric and spatial queries, one also needs to use computational geometry algorithms.

Starting from examples taken in urban planning and in CADCAM, using different types of geometric modelling, we show what kinds of queries can be solved by relational algebra and computational geometry respectively. Among spatial queries, we essentially focus on:

• -point-in-polygon queries,

• -region queries,

• -vacant places within a window.

Among spatial models, we present the conventional segment-oriented (wireframe) model requiring computational geometry algorithms for query evaluation, the Peano relation model allowing the using of algebra and a mixed model requiring both geometry and algebra. So, we show that the representation based on linear quadtrees together with Peano relations allows the solving of a spatial query subclass simply by using an extension of relational algebra called Peano Tuple Algebra.

We conclude this paper by pointing out the necessity to design spatial DBMS's in conjunction with the geometric representation and to extend query languages to deal with spatial queries.