Computational geometry: an introduction
Computational geometry: an introduction
Numerical stability of geometric algorithms
SCG '87 Proceedings of the third annual symposium on Computational geometry
Applied computational geometry: towards robust solutions of basic problems
Journal of Computer and System Sciences
Rounding arrangements dynamically
Proceedings of the eleventh annual symposium on Computational geometry
Realm-based spatial data types: the ROSE algebra
The VLDB Journal — The International Journal on Very Large Data Bases
Spatial SQL: A Query and Presentation Language
IEEE Transactions on Knowledge and Data Engineering
Geo-Relational Algebra: A Model and Query Language for Geometric Database Systems
EDBT '88 Proceedings of the International Conference on Extending Database Technology: Advances in Database Technology
Geo-SAL: A Query Language for Spatial Data Analysis
SSD '91 Proceedings of the Second International Symposium on Advances in Spatial Databases
Realms: A Foundation for Spatial Data Types in Database Systems
SSD '93 Proceedings of the Third International Symposium on Advances in Spatial Databases
Implementation of the ROSE Algebra: Efficient Algorithms for Realm-Based Spatial Data Types
SSD '95 Proceedings of the 4th International Symposium on Advances in Spatial Databases
A Qualitative Account of Discrete Space
GIScience '02 Proceedings of the Second International Conference on Geographic Information Science
Spatiotemporal Aggregate Computation: A Survey
IEEE Transactions on Knowledge and Data Engineering
Proceedings of the 13th annual ACM international workshop on Geographic information systems
Semantic-augmented support in spatial-temporal multimedia blog management
TMRA'06 Proceedings of the 2nd international conference on Topic maps research and applications
DualgridFF: a robust, consistent and efficient physical data model for spatial databases
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
Connectivity in the regular polytope representation
Geoinformatica
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Systems of spatial data types and operations, or spatial algebras, are fundamental for the implementation of spatial database systems. Several designs of such algebras have been proposed in the last decade, and recently commercial DBMS offer such algebras in the form of extension packages (e.g., “data blades”). However, actual implementations are generally severely restricted when compared to designs in the literature. A main reason is that at the implementation level one cannot further ignore the problems of robustness and topological correctness arising from the discrete number representations used in computers. Therefore, implemented packages either avoid “problematic” operations, or accept inconsistencies and topological errors in the answers of queries due to rounding effects. The ROSE algebra [12], proposed and implemented earlier, goes a long way towards avoiding such problems, since it was defined from scratch with robustness problems in mind. It is founded on a discrete geometric basis called a realm. The ROSE algebra guarantees a correct behavior of operations and has an entirely robust implementation. Unfortunately, the realm concept and its interaction with DBMS are difficult to implement, and certain kinds of topological problems still remain. In this paper we introduce the concept of dual grid, which provides a new approach for the representation of spatial information that avoids any robustness and topological correctness problem and allows a less restrictive implementation of spatial algebras. As an example, we show how can it be used for implementing the ROSE algebra without realms, and show that such an implementation does not suffer from the side effects and disadvantages of the original realm-based one.