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In this paper the authors have offered geometric realms as a concept to solve several problems related to spatial data types for database systems. In particular, realms solve the geometric consistency problem as well as problems of numeric robustness and topological correctness. Realm-based structures can be used for the definition of quite general spatial data types and guarantee all the desired closure properties in theory as well as in computational practice. Starting from integer arithmetics, they have developed bottom-up a precise formal framework that makes it easy to define spatial algebras and to implement them correctly.
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