On-line construction of the convex hull of a simple polyline
Information Processing Letters
Various views on spatial prepositions
AI Magazine
Qualitative representation of positional information
Artificial Intelligence
Computational geometry in C (2nd ed.)
Computational geometry in C (2nd ed.)
A new approach to cyclic ordering of 2D orientations using ternary relation algebras
Artificial Intelligence
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
ACM SIGMOD Record
Qualitative Representation of Spatial Knowledge
Qualitative Representation of Spatial Knowledge
Place learning in humans: The role of distance and direction information
Spatial Cognition and Computation
Computing Common Tangents Without a Separating Line
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
The House Is North of the River: Relative Localization of Extended Objects
COSIT 2001 Proceedings of the International Conference on Spatial Information Theory: Foundations of Geographic Information Science
Double-Crossing: Decidability and Computational Complexity of a Qualitative Calculus for Navigation
COSIT 2001 Proceedings of the International Conference on Spatial Information Theory: Foundations of Geographic Information Science
Modeling the Basic Meanings of Path Relations
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
A Graded Approach to Directions between Extended Objects
GIScience '02 Proceedings of the Second International Conference on Geographic Information Science
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
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
Cognitively adequate modelling of spatial reference in human-robot interaction
ICTAI '00 Proceedings of the 12th IEEE International Conference on Tools with Artificial Intelligence
Projective relations for 3D space: computational model, application, and psychological evaluation
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Semantics of collinearity among regions
OTM'05 Proceedings of the 2005 OTM Confederated international conference on On the Move to Meaningful Internet Systems
Qualitative spatial reasoning about relative point position
Journal of Visual Languages and Computing
A Qualitative Model for Visibility Relations
KI '07 Proceedings of the 30th annual German conference on Advances in Artificial Intelligence
Refining Topological Relations between Regions Considering Their Shapes
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
A qualitative approach to localization and navigation based on visibility information
COSIT'09 Proceedings of the 9th international conference on Spatial information theory
Reasoning about cardinal directions between extended objects
Artificial Intelligence
Ensuring semantic spatial constraints in virtual environments using UML/OCL
Proceedings of the 17th ACM Symposium on Virtual Reality Software and Technology
Distributed spatial reasoning for wireless sensor networks
CONTEXT'11 Proceedings of the 7th international and interdisciplinary conference on Modeling and using context
Referring expressions in location based services: the case of the 'opposite' relation
ER'11 Proceedings of the 30th international conference on Advances in conceptual modeling: recent developments and new directions
Projective relations in a 3d environment
GIScience'06 Proceedings of the 4th international conference on Geographic Information Science
Cardinal directions between complex regions
ACM Transactions on Database Systems (TODS)
Integrating semantic directional relationships into virtual environments: a meta-modelling approach
EGVE - JVRC'11 Proceedings of the 17th Eurographics conference on Virtual Environments & Third Joint Virtual Reality
Directional relations and frames of reference
Geoinformatica
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Current spatial database systems offer limited querying capabilities beyond binary topological relations. This paper introduces a model for projective relations between regions to support other qualitative spatial queries. The relations are ternary because they are based on the collinearity invariant of three points under projective geometry. The model is built on a partition of the plane into separate zones that are obtained from projective properties of two reference objects: Then, by considering the empty/nonempty intersections of a primary object with these zones, the model is able to distinguish between 34 different projective relations. Then, the paper proposes original algorithms for computing the relations under the assumption that regions of the plane are stored as vector polygons in a spatial database. These algorithms run in optimal O(n \log n) time.