Time-dependent affine triangulation of spatio-temporal data

Abstract

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 spatiotemporal 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.

Spatial aggregation: Data model and implementation

“…Haesevoets et al [15,16] define affine-invariant triangulations of the plane based on the fact that any set of (both ways unbounded) lines, partitions the plane in a set of convex polygons and show that this partition is invariant under affine transformations of the plane. Definition 6 extends these notions to all geometric components in a thematic layer.…”

“…Metadata are stored in XML documents containing three kinds of elements: Subpolygonization, Layer, and Measure. 15 The Subpolygonization element (identified with a tag of the same name) includes the location of the instances of each sub-geometry (sub-node, sub-polygon or sub-line) in the data repository (in our implementation, the PostGIS database where the map is stored). It also includes the name of the table containing the instance of each sub-geometry, the names of the key fields, and the identifiers allowing to associate elements of the original geometries with the elements of the corresponding subgeometries.…”

“…See http://msdn2.microsoft.com/en-us/library/ ms145506.aspx. 15 In what follows we denote sub-geometries the geometries that are originated by the subpolygonization process (e.g., a polyline originates sub-lines, or a polygon originates sub-polygons). Also, we denote indistinctly geometric elements or geometric objects the instances of a geometry.…”

Spatio-temporal data management based on ORDB

“…A well STDM should have a well representation of spatio-temporal process and contributes to effective management of spatio-temporal data [8]. Savary [9] classified various spatio-temporal models into two species in terms of modeling objective, including process oriented data model and time snap oriented model.…”

Affine-Invariant Triangulation of Spatio-Temporal Data with an Application to Image Retrieval

“…Acknowledgments: An extended abstract, containing few technical details and examples, appeared as [42]. An earlier version of the application part appeared as part of [27].…”