6. Conclusion 5. Route Planning

and the destination points are in different maps. For instance, bus-stop T3 can be reached from C1 by highway line H2 (or H1) to C3 and then by bus trip R1: S 22 (C1H2) ∧ S 34 (C3H2) ∧ T 22 (C3R1) ∧ T 23 (T3R1). Additional types of connections can be defined to express situations involving routes from a station to another. In procedural terms the previous definitions reduce to a search for intersections. Direction information can be used in choosing a line which is in the direction of the destination, when several choices are available. This paper describes how symbolic spatial indexes can be used in several computational tasks involving direction and topological relations in 2D space. In particular we have dealt with spatial information retrieval, composition of spatial relations, route planning and update operations. Several extensions can be developed to increase the applicability of the concepts presented in the paper. For instance, PQBE can be extended with the inclusion of topological expressions for queries of the form " Show the route from station C5 to T1 that involves the smallest number of intermediate connection ". The composition operator can also be extended to handle composition of both direction and topological relations. Although these problems have been studied independently (e.g., a study about composition of topological relations can be found in Egenhofer, 1991), to our knowledge there does not exist previous work that combines both approaches. There are also additional application domains where symbolic spatial indexes can be used. Lee et al. (1992) developed algorithms for image similarity retrieval based on variations of 2D strings. Similar algorithms can be developed for spatial indexes. Information processing using spatial indexes, and relation-based representations in general, involves symbolic and not numerical computation and avoids the usual problems of geometric representations, like finite resolution and geometric consistency. Although relation-based systems cannot be used in all applications involving spatial knowledge (e.g., applications involving quantitative reasoning and visualisation), we believe that there is a wide scope of potential applications ranging from Qualitative Spatial Reasoning and Spatial Databases to Robot Navigation and Computational Vision. A system which can only represent direction relations in 2D space is inadequate for several practical applications that also involve neighbourhood, inclusion, overlap or other topological queries. In this section we will show how we can use symbolic spatial indexes that incorporate direction and topological information in route planning. Previous systems …