Computational geometry: an introduction
Computational geometry: an introduction
Predicate migration: optimizing queries with expensive predicates
SIGMOD '93 Proceedings of the 1993 ACM SIGMOD international conference on Management of data
SIGMOD '94 Proceedings of the 1994 ACM SIGMOD international conference on Management of data
Composite regions in topological queries
Information Systems
Information Sciences: an International Journal
Multidimensional access methods
ACM Computing Surveys (CSUR)
Maintaining knowledge about temporal intervals
Communications of the ACM
Realm-based spatial data types: the ROSE algebra
The VLDB Journal — The International Journal on Very Large Data Bases
Spatial SQL: A Query and Presentation Language
IEEE Transactions on Knowledge and Data Engineering
Topological Invariants for Lines
IEEE Transactions on Knowledge and Data Engineering
Optimization and Evaluation of Disjunctive Queries
IEEE Transactions on Knowledge and Data Engineering
PROBE Spatial Data Modeling and Query Processing in an Image Database Application
IEEE Transactions on Software Engineering
An Efficient Pictorial Database System for PSQL
IEEE Transactions on Software Engineering
Geo-Relational Algebra: A Model and Query Language for Geometric Database Systems
EDBT '88 Proceedings of the International Conference on Extending Database Technology: Advances in Database Technology
Realms: A Foundation for Spatial Data Types in Database Systems
SSD '93 Proceedings of the Third International Symposium on Advances in Spatial Databases
A Canonical Model for a Class of Areal Spatial Objects
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
Implementation of the ROSE Algebra: Efficient Algorithms for Realm-Based Spatial Data Types
SSD '95 Proceedings of the 4th International Symposium on Advances in Spatial Databases
Topological Relationships of Complex Points and Complex Regions
ER '01 Proceedings of the 20th International Conference on Conceptual Modeling: Conceptual Modeling
Topological relationships between complex spatial objects
ACM Transactions on Database Systems (TODS)
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
International Journal of Geographical Information Science
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Topological relationships between spatial objects such as overlap, disjoint, and inside have for a long time been a focus of research in a number of disciplines like cognitive science, robotics, linguistics, artificial intelligence, and spatial reasoning. In particular as predicates, they support the design of suitable query languages for spatial data retrieval and analysis in spatial database systems and Geographic Information Systems. While conceptual aspects of topological predicates (like their definition and reasoning with them) as well as strategies for avoiding unnecessary or repetitive predicate evaluations (like predicate migration and spatial index structures) have been emphasized, the development of correct and efficient implementation techniques for them has been rather neglected. Recently, the design of topological predicates for different combinations of complex spatial data types has led to a large increase of their numbers and accentuated the need for their efficient implementation. The goal of this article is to develop efficient implementation techniques of topological predicates for all combinations of the complex spatial data types point2D, line2D, and region2D, as they have been specified by different authors and in different commercial and public domain software packages. Our solution is a two-phase approach. In the exploration phase, for a given scene of two spatial objects, all topological events like intersection and meeting situations are recorded in two precisely defined topological feature vectors (one for each argument object of a topological predicate) whose specifications are characteristic and unique for each combination of spatial data types. These vectors serve as input for the evaluation phase which analyzes the topological events and determines the Boolean result of a topological predicate or the kind of topological predicate. This paper puts an emphasis on the exploration phase and the definition of the topological feature vectors. In addition, it presents a straightforward evaluation method.