Temporal reasoning based on semi-intervals
Artificial Intelligence
Composite regions in topological queries
Information Systems
Topological relations in the world of minimum bounding rectangles: a study with R-trees
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Topological queries in spatial databases
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Maintaining knowledge about temporal intervals
Communications of the ACM
Qualitative Representation of Spatial Knowledge
Qualitative Representation of Spatial Knowledge
A Small Set of Formal Topological Relationships Suitable for End-User Interaction
SSD '93 Proceedings of the Third International Symposium on Advances in Spatial Databases
Qualitative and Topological Relationships in Spatial Databases
SSD '93 Proceedings of the Third International Symposium on Advances in Spatial Databases
Topological Relations between Regions in Raster
SSD '95 Proceedings of the 4th 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
Reasoning about Gradual Changes of Topological Relationships
Proceedings of the International Conference GIS - From Space to Territory: Theories and Methods of Spatio-Temporal Reasoning on Theories and Methods of Spatio-Temporal Reasoning in Geographic Space
A Model for Expressing topological Integrity Constraints in Geographic Databases
Proceedings of the International Conference GIS - From Space to Territory: Theories and Methods of Spatio-Temporal Reasoning on Theories and Methods of Spatio-Temporal Reasoning in Geographic Space
A Strategy for Drawing a Conceptual Neighborhood Diagram Schematically
Diagrams '08 Proceedings of the 5th international conference on Diagrammatic Representation and Inference
Refining Topological Relations between Regions Considering Their Shapes
GIScience '08 Proceedings of the 5th international conference on Geographic Information Science
The 9 + -Intersection: A Universal Framework for Modeling Topological Relations
GIScience '08 Proceedings of the 5th international conference on Geographic Information Science
Projective Relations on the Sphere
ER '08 Proceedings of the ER 2008 Workshops (CMLSA, ECDM, FP-UML, M2AS, RIGiM, SeCoGIS, WISM) on Advances in Conceptual Modeling: Challenges and Opportunities
COSIT'07 Proceedings of the 8th international conference on Spatial information theory
Semi-automated derivation of conceptual neighborhood graphs of topological relations
COSIT'09 Proceedings of the 9th international conference on Spatial information theory
Composing cardinal direction relations basing on interval algebra
KSEM'10 Proceedings of the 4th international conference on Knowledge science, engineering and management
The family of conceptual neighborhood graphs for region-region relations
GIScience'10 Proceedings of the 6th international conference on Geographic information science
The head-body-tail intersection for spatial relations between directed line segments
GIScience'06 Proceedings of the 4th international conference on Geographic Information Science
Topological relations of arrow symbols in complex diagrams
Diagrams'06 Proceedings of the 4th international conference on Diagrammatic Representation and Inference
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Analysis of global geographic phenomena requires non-planar models. In the past, models for topological relations have focused either on a two-dimensional or a three-dimensional space. When applied to the surface of a sphere, however, neither of the two models suffices. For the two-dimensional planar case, the eight binary topological relations between spatial regions are well known from the 9-intersection model. This paper systematically develops the binary topological relations that can be realized on the surface of a sphere. Between two regions on the sphere there are three binary relations that cannot be realized in the plane. These relations complete the conceptual neighborhood graph of the eight planar topological relations in a regular fashion, providing evidence for a regularity of the underlying mathematical model. The analysis of the algebraic compositions of spherical topological relations indicates that spherical topological reasoning often provides fewer ambiguities than planar topological reasoning. Finally, a comparison with the relations that can be realized for one-dimensional, ordered cycles draws parallels to the spherical topological relations.