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The query Q consists of all these rectangles. Then we retrieve the set S of trajectories that intersect this set of rectangles. The refinement step is as follows. M of route segments that the object travels between starttime and endtime. If the object is not alive on all these route segments, then T is eliminated from S. M is a subset of M. (2Bt): ALONG SHORTEST PATH / SOMETIME BETWEEN, assuming that the cost 5 is given in terms of travel time: The filter step is the same as in 2At. The refinement step is as follows.

Here, spatial objects are associated with two temporal aspects, and a set of operators for querying is provided. However, this model does not provide an expressive type system, but basically proposes only a single type, termed ST-complex, with a limited set of operations. In addition, two papers exist that consider spatiotemporal data as a sequence of spatial snapshots and in this context address implementation issues related to the representation of discrete changes of spatial regions over time [12].

J. Egenhofer 1995) to model direction relations. These methods are crude approximations that often lead to incorrect directions when concave region objects are involved. The directionrelation (Goyal and Egenhofer, in press) overcomes these deficiencies as it avoids generalizations to points or approximations by rectangles. The method also extends to other geometric types such as lines and points (Goyal and Egenhofer 2000). This paper develops a computational method for assessing similarity of cardinal directions that are modeled with the detailed direction-relation matrix (Goyal and Egenhofer, in press).

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