Topological Relationships of Complex Points and Complex Regions

Topological relationships between spatial objects have been a focus of research on spatial data handling and reasoning for a long time. Especially as predicates they support the design of suitable query languages for spatial data retrieval and analysis in databases. Unfortunately, they are so far only applicable to simplified abstractions of spatial objects like single points, continuous lines, and simple regions, as they occur in systems like current geographical information systems and spatial database systems. Since these abstractions are usually not sufficient to cope with the complexity of geographic reality, their generalization is needed which especially has influence on the nature, definition, and number of their topological relationships. This paper partially closes this gap and first introduces very general spatial data types for complex points and complex regions. It then defines the corresponding complete sets of mutually exclusive, topological relationships. Keywords. Topological predicate, spatial data type, 9-intersection model

The Honeycomb Model of Spatio-Temporal Partitions

. We define a formal model of spatio-temporal partitions which can be used to model temporally changing maps. We investigate new applications and generalizations of operations that are well-known for static spatial maps. We then define a small set of operations on spatio-temporal partitions that are powerful enough to express all these tasks and more. Spatio-temporal partitions combine the general notion of temporal objects and the powerful spatial partition abstraction into a new, highly expressive spatio-temporal data modeling tool. 1 Introduction The subject of this paper is the temporal evolution of maps. The metaphor of a map has turned out to be a fundamental and ubiquitous spatial concept in many spatially-oriented disciplines like geography and cartography as well as in computer-assisted systems like geographical informations systems (GIS), spatial database systems, and image database systems, but also simply for human's spatial orientation in everyday life. A map is a widely ..