Temporal reasoning based on semi-intervals
Artificial Intelligence
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
Maintaining knowledge about temporal intervals
Communications of the ACM
Topological Invariants for Lines
IEEE Transactions on Knowledge and Data Engineering
Efficient Processing of Spatial Queries in Line Segment Databases
SSD '91 Proceedings of the Second International Symposium on Advances in Spatial Databases
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
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
Using Orientation Information for Qualitative Spatial Reasoning
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
Developments in Spatio-Temporal Query Languages
DEXA '99 Proceedings of the 10th International Workshop on Database & Expert Systems Applications
Consistent Queries over Cardinal Directions Across Different Levels of Detail
DEXA '00 Proceedings of the 11th International Workshop on Database and Expert Systems Applications
Metric details of topological line-line relations
International Journal of Geographical Information Science
A spatial odyssey of the interval algebra: 1. directed intervals
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Structure and semantics of arrow diagrams
COSIT'05 Proceedings of the 2005 international conference on Spatial Information Theory
Spherical topological relations
Journal on Data Semantics III
Topological relations of arrow symbols in complex diagrams
Diagrams'06 Proceedings of the 4th international conference on Diagrammatic Representation and Inference
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
A Reference System for Topological Relations between Compound Spatial Objects
ER '09 Proceedings of the ER 2009 Workshops (CoMoL, ETheCoM, FP-UML, MOST-ONISW, QoIS, RIGiM, SeCoGIS) on Advances in Conceptual Modeling - Challenging Perspectives
Semi-automated derivation of conceptual neighborhood graphs of topological relations
COSIT'09 Proceedings of the 9th international conference on Spatial information theory
The family of conceptual neighborhood graphs for region-region relations
GIScience'10 Proceedings of the 6th international conference on Geographic information science
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Directed line segments are fundamental geometric elements used to model through their spatial relations such concepts as divergence, confluence, and interference. A new model is developed that captures spatial relations between pairs of directed line segments through the intersections of the segments' heads, bodies, and tails. This head-body-tail intersection identifies 68 classes of topological relations between two directed line segments highlighting two equal-sized subsets of corresponding relations that differ only by their empty and non-empty body-body intersections. The relations' con-ceptual neighborhood graph takes the shape of a torus inside a torus, one for each subset. Another 12 classes of topological relation classes are distinguished if the segments' exteriors are considered as well, lining up such that their conceptual neighborhood graph forms another torus that contains the other two tori. These conceptual neighborhoods as well as the relations' composition table enable spatial inferences and similarity assessments in a consistent and reasoned manner.