Topological graph theory
On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
A logical framework for depiction and image interpretation
Artificial Intelligence
Research issues in spatial databases
ACM SIGMOD Record - Directions for future database research & development
A comparison of methods for representing topological relationships
Information Sciences—Applications: An International Journal
Composite regions in topological queries
Information Systems
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Qualitative Representation of Spatial Knowledge
Qualitative Representation of Spatial Knowledge
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
An introduction to spatial database systems
The VLDB Journal — The International Journal on Very Large Data Bases - Spatial Database Systems
Spatial SQL: A Query and Presentation Language
IEEE Transactions on Knowledge and Data Engineering
Topological Relations Between Regions in R² and Z²
SSD '93 Proceedings of the Third International Symposium on Advances in Spatial Databases
Neighborhood Query and Analysis with GeoSAL, a Spatial Database Language
SSD '93 Proceedings of the Third 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
Qualitative and Topological Relationships in Spatial Databases
SSD '93 Proceedings of the Third International Symposium on Advances in Spatial Databases
Lossless Representation of Topological Spatial Data
SSD '95 Proceedings of the 4th International Symposium on Advances in Spatial Databases
Inferences from Combined Knowledge about Topology and Directions
SSD '95 Proceedings of the 4th International Symposium on Advances in Spatial Databases
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
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
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
A Global Framework for Qualitative Shape Description
Geoinformatica
A general strategy for decomposing topological invariants of spatial databases and an application
Data & Knowledge Engineering
Spatial Databases-Accomplishments and Research Needs
IEEE Transactions on Knowledge and Data Engineering
COSIT '99 Proceedings of the International Conference on Spatial Information Theory: Cognitive and Computational Foundations of Geographic Information Science
Shape-Based Similarity Query for Trajectory of Mobile Objects
MDM '03 Proceedings of the 4th International Conference on Mobile Data Management
Topological relationships between complex spatial objects
ACM Transactions on Database Systems (TODS)
Detection of spatial conflicts between rivers and contours in digital map updating
International Journal of Geographical Information Science
Metric details of topological line-line relations
International Journal of Geographical Information Science
Integral vs. Separable Attributes in Spatial Similarity Assessments
Proceedings of the international conference on Spatial Cognition VI: Learning, Reasoning, and Talking about Space
Refining Topological Relations between Regions Considering Their Shapes
GIScience '08 Proceedings of the 5th international conference on Geographic Information Science
Topological feature vectors for exploring topological relationships
International Journal of Geographical Information Science
Topological relations from metric refinements
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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
A refined line-line spatial relationship model for spatial conflict detection
ER'05 Proceedings of the 24th international conference on Perspectives in Conceptual Modeling
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A set of topological invariants for relations between lines embedded in the 2-dimensional Euclidean space is given. The set of invariants is proven to be necessary and sufficient to characterize topological equivalence classes of binary relations between simple lines. The topology of arbitrarily complex geometric scenes is described with a variation of the same set of invariants. Polynomial time algorithms are given to assess topological equivalence of two scenes. The relevance of identifying such a set of invariants and efficient algorithms is due to application areas of spatial database systems, where a model for describing topological relations between planar features is sought.