Information Sciences: an International Journal
Topological Relations Between Regions in R² and Z²
SSD '93 Proceedings of the Third International Symposium on Advances in Spatial Databases
ER '99 Proceedings of the Workshops on Evolution and Change in Data Management, Reverse Engineering in Information Systems, and the World Wide Web and Conceptual Modeling
On 3D Topological Relationships
DEXA '00 Proceedings of the 11th International Workshop on Database and Expert Systems Applications
Topological relationships between complex spatial objects
ACM Transactions on Database Systems (TODS)
Metric details of topological line-line relations
International Journal of Geographical Information Science
An interval-based representation of temporal knowledge
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 1
A spatial odyssey of the interval algebra: 1. directed intervals
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
COSIT'07 Proceedings of the 8th international conference on Spatial information theory
The head-body-tail intersection for spatial relations between directed line segments
GIScience'06 Proceedings of the 4th international conference on Geographic Information Science
Spherical topological relations
Journal on Data Semantics III
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
Cognitive invariants of geographic event conceptualization: what matters and what refines?
GIScience'10 Proceedings of the 6th international conference on Geographic information science
Automatic extraction of destinations, origins and route parts from human generated route directions
GIScience'10 Proceedings of the 6th international conference on Geographic information science
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The 9+-intersection is an extension of the 9-intersection, which distinguishes the topological relations between various spatial objects by the pattern of a nested matrix. This paper develops a small set of constraints on this matrix, which is applicable to arbitrary pairs of spatial objects in various spaces. Based on this set of universal constraints, the sets of matrix patterns, each representing a candidate for topological relations, are derived for every possible pair of basic objects (points, directed/non-directed line segments, regions, and bodies) embedded in R1, R2, R3, S1, and S2. The derived sets of candidates are consistent with the sets of topological relations ever identified, as well as yield the identification of some missing sets of topological relations. Finally, the topological relations between a region and a region with a hole in R2and S2are identified to demonstrate the applicability of our approach to deriving topological relations between more complicated objects.