A characterization of an affine invariant triangulation
Geometric modelling
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Spatio-temporal data handling with constraints
Proceedings of the 6th ACM international symposium on Advances in geographic information systems
Requirements, definitions, and notations for spatiotemporal application environments
Proceedings of the 6th ACM international symposium on Advances in geographic information systems
Complete geometric query languages
Journal of Computer and System Sciences
Chorochronos: a research network for spatiotemporal database systems
ACM SIGMOD Record
A foundation for representing and querying moving objects
ACM Transactions on Database Systems (TODS)
Introduction to constraint databases
Introduction to constraint databases
Reliable and Efficient Pattern Matching Using an Affine Invariant Metric
International Journal of Computer Vision
Comparing Images Using the Hausdorff Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
COSIT '97 Proceedings of the International Conference on Spatial Information Theory: A Theoretical Basis for GIS
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
A Theory of Spatio-Temporal Database Queries
DBPL '01 Revised Papers from the 8th International Workshop on Database Programming Languages
A Geometric Framework for Specifying Spatiotemporal Objects
TIME '99 Proceedings of the Sixth International Workshop on Temporal Representation and Reasoning
Towards a Theory of Movie Database Queries
TIME '00 Proceedings of the Seventh International Workshop on Temporal Representation and Reasoning (TIME'00)
Classes of Spatio-Temporal Objects and their Closure Properties
Annals of Mathematics and Artificial Intelligence
SQLST: a spatio-temporal data model and query language
ER'00 Proceedings of the 19th international conference on Conceptual modeling
Spatial aggregation: Data model and implementation
Information Systems
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In the geometric data model [6], spatio-temporal data are modelled as a finite collection of triangles that are transformed by time-dependent affinities. To facilitate querying and animation of spatio-temporal data, we present a normal form for data in the geometric data model. We propose an algorithm for constructing this normal form via a spatio-temporal triangulation of geometric data objects. This algorithm generates new geometric objects that form a partition both in space and in time. A particular property of the proposed partition is that it is invariant under time-dependent affine transformations, and hence independent of the coordinate system chosen when modelling the spatio-temporal data. We can show that our algorithm works correctly and has a polynomial time complexity (in the number of input triangles and the maximal degree of the transformation functions). We also discuss several possible applications of this spatio-temporal triangulation.