Formalization of Advanced Map Operations
Martin Erwig, Markus Schneider · 2000
Maps are a fundamental metaphor in GIS. We introduce several new operations on maps that go far beyond well-known operations like overlay or reclassification. In particular, we identify and generalize operations that are of practical interest for spatial analysis and that can be useful in many GIS applications. We give a precise definition of these operations based on a formal model of spatial partitions. This provides a theoretical foundation for maps which also serves as a specification for implementations. 1 INTRODUCTION Numerous applications in spatially-oriented disciplines like geography, cartography, and related areas, as well as in computer-assisted systems like geographical information systems and spatial database systems witness the importance of maps or spatial partitions. A map is a fundamental and well-known metaphor and a widely recognized geometric and topological structure that is capable of carrying a large amount of information. In a former paper (Erwig et al., 199...