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Moving Objects Information Management: The Database Challenge
NGITS '02 Proceedings of the 5th International Workshop on Next Generation Information Technologies and Systems
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
Indexing multi-dimensional time-series with support for multiple distance measures
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
GIS '06 Proceedings of the 14th annual ACM international symposium on Advances in geographic information systems
Dynamics-aware similarity of moving objects trajectories
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
The definition and computation of trajectory and subtrajectory similarity
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
Mobility, Data Mining and Privacy: Geographic Knowledge Discovery
Mobility, Data Mining and Privacy: Geographic Knowledge Discovery
A qualitative trajectory calculus and the composition of its relations
GeoS'05 Proceedings of the First international conference on GeoSpatial Semantics
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One of the formalisms to qualitatively describe polylines in the plane are double-cross matrices. In a double-cross matrix the relative position of any two line segments in a polyline is described with respect to a double cross based on their start points. Two polylines are called DC-similar if their double-cross matrices are identical. Although double-cross matrices have been widely applied, a geometric interpretation of the similarity they express is still lacking. In this paper, we provide a first step in the geometric interpretation of this qualitative definition of similarity. In particular, we give an effective characterization of what DC-similarity means for polylines that are drawn on a grid. We also provide algorithms that, given a DC-matrix, check whether it is realizable by a polyline on a grid and that construct, if possible, in quadratic time example polylines that satisfy this matrix. We also describe algorithms to reconstruct polylines, satisfying a given double-cross matrix, in the two-dimensional plane, that is, not necessarily on a grid.