Abstract
The importance of topological relationships between spatial objects is recognized in many disciplines. In the field of spatial databases, topological relationships have played an important role, providing mechanisms for spatial constraint specification and spatial indexing techniques. The use of spatial data in a map form has become popular, resulting in spatial data models such as topologies or, more generally, map geometries, which model collections of spatial objects that satisfy certain topological constraints. However, the topological relationships between map geometries remain unexplored. In this paper, we identify the set of valid topological relationships between map geometries, and then provide a mechanism by which they can be directly implemented on top of existing systems by using topological relationships between regions.
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References
Clementini, E., Di Felice, P., Califano, G.: Composite Regions in Topological Queries. Information Systems 20, 579–594 (1995)
Dugundi, J.: Topology. Allyn and Bacon (1966)
Egenhofer, M.J., Herring, J.: Categorizing Binary Topological Relations Between Regions, Lines, and Points in Geographic Databases. Technical report, National Center for Geographic Information and Analysis, University of California, Santa Barbara (1990)
Egenhofer, M.J., Clementini, E., Di Felice, P.: Topological Relations between Regions with Holes. Int. Journal of Geographical Information Systems 8, 128–142 (1994)
Erwig, M., Schneider, M.: Partition and Conquer. In: Frank, A.U. (ed.) COSIT 1997. LNCS, vol. 1329, pp. 389–408. Springer, Heidelberg (1997)
Güting, R.H.: Geo-relational algebra: A model and query language for geometric database systems. In: Schek, H.J., Saltor, F., Ramos, I., Alonso, G. (eds.) EDBT 1998. LNCS, vol. 1377, pp. 506–527. Springer, Heidelberg (1998)
Güting, R.H., Schneider, M.: Realm-Based Spatial Data Types: The ROSE Algebra. VLDB Journal 4, 100–143 (1995)
Herring, J.: TIGRIS: Topologically Integrated Geographic Information Systems. In: 8th International Symposium on Computer Assisted Cartography, pp. 282–291 (1987)
Hoel, E.G., Menon, S., Morehouse, S.: Building a Robust Relational Implementation of Topology. In: Hadzilacos, T., Manolopoulos, Y., Roddick, J.F., Theodoridis, Y. (eds.) SSTD 2003. LNCS, vol. 2750, pp. 508–524. Springer, Heidelberg (2003)
Huang, Z., Svensson, P., Hauska, H.: Solving spatial analysis problems with geosal, a spatial query language. In: Proceedings of the 6th Int. Working Conf. on Scientific and Statistical Database Management, pp. 1–17. Institut f. Wissenschaftliches Rechnen Eidgenoessische Technische Hochschule Zürich (1992)
Ledoux, H., Gold, C.: A Voronoi-Based Map Algebra. In: Int. Symp. on Spatial Data Handling (July 2006)
Randell, D.A., Cui, Z., Cohn, A.: A Spatial Logic Based on Regions and Connection. In: International Conference on Principles of Knowledge Representation and Reasoning, pp. 165–176 (1992)
Schneider, M., Behr, T.: Topological Relationships between Complex Spatial Objects. ACM Trans. on Database Systems (TODS) 31(1), 39–81 (2006)
Tilove, R.B.: Set Membership Classification: A Unified Approach to Geometric Intersection Problems. IEEE Trans. on Computers C-29, 874–883 (1980)
Tomlin, C.D.: Geographic Information Systems and Cartographic Modelling. Prentice-Hall, Englewood Cliffs (1990)
Voisard, A., David, B.: Mapping conceptual geographic models onto DBMS data models. Technical Report TR-97-005, Berkeley, CA (1997)
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McKenney, M., Schneider, M. (2008). Topological Relationships between Map Geometries. In: Haritsa, J.R., Kotagiri, R., Pudi, V. (eds) Database Systems for Advanced Applications. DASFAA 2008. Lecture Notes in Computer Science, vol 4947. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78568-2_11
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DOI: https://doi.org/10.1007/978-3-540-78568-2_11
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