| R. Laurini, D. Thomson, Fundamentals of Spatial Information Systems, Academic Press, London, 1992. |
.... A common modeling of geographic objects such as, for instance, a road network, or a set of land use parcels distinguishes two parts: 1) an alphanumerical description and (2) a spatial component which corresponds to the shape and location of the object in the embedding 2 dimensional space [31, 49, 38]. The description of a road includes for instance its name and its number of lanes, whereas its spatial component consists of the set of points describing the road s geometry. This description can be viewed as an identifier for the set of points of its geometry. A practical rationale behind this ....
R. Laurini and D. Thompson. Fundamentals of Spatial Information Systems. Number 37 in The A.P.I.C. Series. Academic Press, New York, 1992.
....from a collection of (distinct or similar) parts which should be assembled in some order. The design can be represented by partially ordered collections with repetitions for parts that occur in various positions. Partially ordered duplicates are also common in geographical information systems [LT92] where geometric components have multiple occurrences, and these occurrences are generally partially ordered. Different themes (such as ground occupancy, roads, etc. are represented on different maps that share a lot of the geometry, resulting therefore in a duplication of the geometric cells ....
....in U denote atomic components. It is rather natural to use a pomset to model compound objects, since their realization is based on sequential and parallel processes, for which the pomsets have been precisely introduced. Let us now consider a more complex example from spatial information systems [LT92] with data for resource managment and transportation planing. Roads for instance can be represented by a type f( roadname,segment] g, where roadname and segment are strings. This pomset is partially ordered. Each road (identified by its name) is defined as a sequence of segments. There are no ....
R. Laurini and Thompson. Fundamentals of Spatial Information Systems. The A.P.I.C. Series, No. 37. Academic Press, 1992.
....implicit to the geometric description of a polygon. Geometric constraints are related to the implementation, and are covered here in a higher level view, considering only the shape of geographic objects. Consistency rules associated to the representation of spatial objects are discussed in [9]. This paper is organized as follows. Section 2 presents a classification of the spatial integrity constraints. Section 3 describes the OMT G data model and its associated spatial integrity constraints. Section 4 discusses an example of use of OMT G. Finally, Section 5 presents our conclusions. ....
Laurini, R., Thompson, D. Fundamentals of spatial information systems. Academic Press, 1992.
.... repopulation, epidemiologic analysis, and earthquake studies and for commercial applications such as market analysis, utility facilities distribution, and mineral exploration [17] In support of these applications, GIS systems store, manipulate, and search through enormous amounts of spatial data [13, 18, 25, 27]. NASA s EOS project GIS system [13] for example, is expected to manipulate petabytes (thousands of terabytes, or millions of gigabytes) of data Typical subproblems that need to be solved in GIS systems include point location, triangulating maps, generating contours from triangulated elevation ....
R. Laurini and A. D. Thompson. Fundamentals of Spatial Information Systems. A.P.I.C. Series, Academic Press, New York, NY, 1992.
....Author is currently visiting Duke University, e maih der cs. duke. edu This research was supported in part by National Science Foundation grant CCR 9007851 and by Army Research Office grant DAAL03 91 G 0035. Large scale problems involving geometric data are ubiquitous in spatial databases [24,32,33] , geographic information systems (GIS) 10,24,33] constraint logic programming [19,20] object oriented databases [38] statistics, virtual reality systems, and computer graphics [33] As an example, NASAls soon to be petabyte sized databases are designed to facili tate a variety of complex ....
....e maih der cs. duke. edu This research was supported in part by National Science Foundation grant CCR 9007851 and by Army Research Office grant DAAL03 91 G 0035. Large scale problems involving geometric data are ubiquitous in spatial databases [24,32,33] geographic information systems (GIS) [10,24,33], constraint logic programming [19,20] object oriented databases [38] statistics, virtual reality systems, and computer graphics [33] As an example, NASAls soon to be petabyte sized databases are designed to facili tate a variety of complex geometric queries [10] Im portant operations on ....
R. Laurini & D. Thompson, Fundamentals of Spatial Information Systems, A.P.I.C. Series, Academic Press, New York, NY, 1992.
.... epidemiologic analysis, and earthquake studies and for commercial applications such as market analysis, utility facilities distribution, and mineral ex ploration [17] In support of these applications, GIS systems store, manipulate, and search through enormous amounts of spatial data [13, 18, 25, 27]. NASA s EOS project GIS system [13] for example, is expected to manipulate petabytes (thousands of terabytes, or millions of gigabytes) of data Typical subproblems that need to be solved in GIS systems include point location, triangulating maps, generating contours from triangulated elevation ....
R. Laurini and A.D. Thompson. Fundamentals of Spatial Information Systems. A.P.I.C. Series, Academic Press, New York, NY, 1992.
....Ys VTime 02 6 6 6 2 10 4 0 02 6 6 6 2 10 4 9 02 4 4 4 0 8 2 10 02 4 4 4 0 8 2 19 02 4 4 4 0 8 2 20 02 4 4 4 0 8 2 29 Table 1. Conceptual model of the spario temporal data shown in Figure i In our spatial model we use triangles to represent polygons; a similar ap proach was proposed in [11, 18]. A polygon having n vertexes can be decomposed into n 2 triangles in O(nlogn) TIME. Decomposing a polygon into a set of triangles makes determine spatial relationships between two polygons easy to do. We extended the triangulation method to use sets of directed triangles to represent polygons ....
....directed triangles to represent polygons at the conceptual level. The three edges of a triangle are directed lines and form a counterclockwise circle. The directed triangulation method not only makes testing whether a point is inside a triangle need fewer calculations than the method proposed in [18] but also can handle holes in polygons. We use user defined aggregates [24] to support spatial operators such as area, inside, etc. temporal operators such as duration, overlap, etc. and spariotemporal operators such as moving distance, etc. 3 Temporal Operators As has been discussed in [7, ....
R. Laurini and D. Thompson. Fundamentals of Spatial Information Systems. Academic Press, 1992
....with tradition occurred. One of the consequences of this is that GIS only rarely handle three dimensional data adequately, another that time is also an afterthought, typically with di#erent map layers for di#erent points in time. Formal presentations of geometries for spatial data may be found in [18] and [25] Two major families of GIS may still be found, despite the fact that they are both specific realisations of more general models for handling spatial data. One family fits the surveying paradigm better, by focussing on the precise position of points, and objects derived from them, such ....
Robert Laurini and Derek Thompson. Fundamentals of spatial information systems. Academic Press, London, 1992.
....of a cell or subquadrant from its coordinates and vice versa. Nulty[23] working with geometric range searching problems, noted that the Hilbert curve has excellent clustering properties , but found it less convenient than the N Curve or the Sierpinski curve (pp. 26 27) Laurini and Thompson [18] found the Hilbert and Peano curves to be more robust, that is better performers over a range of requirements , in spatial information systems. But, in the case of the Hilbert curve, it is quite complex to get keys. In fact, they provideacodingalgorithm expressly to demonstrate the awkwardness ....
.... recursive procedures [2] 10] 15] 16] 29] On the other hand, algorithms for point coding, the sorts of procedures needed when actually applying the Hilbert curve, tend to be more complex and ad hoc, generally unrelated to each other or to the drawing routines [6] 7] 8] 9] 11] 17] [18], 26] 27] This state of affairs means that a promising tool may be underutilized. It also suggests that an important criterion for choosing a spacefilling curve for a practical application is usability. This is not surprising, but it means that certain spacefilling curves maynotbegiven ....
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Robert Laurini and Derek Thompson. Fundamentals of Spatial Information Systems. Academic Press, Ltd., San Diego, CA, 1992.
....present experimental results based on real and synthetic data. The results show that careful query scheduling can improve substantially the overall performance of multiple range query processing. 1 Introduction Two basic research directions exist aiming at improving efficiency in a Spatial DBMS [4, 8, 13]. The first direction involves the design of robust spatial data structures and algorithms [2] the second one focuses on the design of clever query optimizers. Most of the work in the latter area deals with the optimization of a single (possibly complex) spatial query [1] Here, we concentrate on ....
....curves. A Peano curve can be constructed by interleaving the bits of coordinates and . The generation of the Hilbert curve is more complex, i.e. it is constructed by means of a process that uses rotation and mirroring. Algorithms for the generation of the 2 d Hilbert curve can be found in [6, 8]. The goodness of a space filling curve is measured with respect to its ability to preserve proximity. Although there are no analytical results to demonstrate the superiority of the Hilbert curve, experiments [6] show that it is the best distance preserving curve. Therefore, in the rest of the ....
R. Laurini and D. Thompson: "Fundamentals of spatial information systems", Academic Press, London, 1992.
....curve tracing acontinuous circuit over an octahedral surface. The curveshown is one of a number of possible curves that could have been drawn. Figure 4.3 shows a spacefilling curve tracing a continuous circuit over a tetrahedral surface. For flattened views of all the Platonic solids, see [25]. This is in the spirit of the earlier work on hierarchical global data models. It is more general in the sense that we do not specify a particular initial partition of the sphere (or equivalently, a base polyhedron) just that it be a triangular tessellation, with no vertices appearing in the ....
Robert Laurini and Derek Thompson. Fundamentals of Spatial Information Systems. Academic Press, Ltd., San Diego, CA, 1992.
....Keywords: distributed databases, multidimensional data, similarity queries, query processing 1. Introduction Multidimensional data appear in many modern applications in diverse fields. Geographical Information Systems (G.I. S) require the storage and manipulation of objects in 2 d and 3 d spaces [14, 19]; Image Video Retrieval by Similarity and Pattern Recognition require the extraction of features from the images and the mapping of these features in a high dimensional space, in order to speed up query processing [11, 17] in Time Series databases, the objects are first transformed (e.g. by means ....
R. Laurini and D. Thompson, Fundamentals of Spatial Information Systems, Academic Press: London, 1992.
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R. Laurini, D. Thomson, Fundamentals of Spatial Information Systems, Academic Press, London, 1992.
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R. Laurini and D. Thompson: "Fundamentals of spatial information systems", Academic Press, London, 1992.
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Laurini, R., and Thompson, D., 1992, Fundamentals of Spatial Information Systems. Academic Press, London
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R. Laurini and D. Thompson. Fundamentals of Spatial Information Systems. The APIC series. Academic Press, 1994.
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R. Laurini, D. Thompson: `Fundamentals of Spatial Information Systems', Academic Press Ltd, 1992.
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Laurini, R., and Thompson, D. Fundamentals of Spatial Information Systems. Academic Press, London, 1992.
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R. Laurini and D. Thompson. Fundamentals of Spatial Information Systems. Academic Press, 1992
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Laurini, R., Thompson, D. Fundamentals of Spatial Information Systems,6th prnt. The A.P.I.C. Series, Vol. 37. Academic Press,London,1998.
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R. Laurini, D. Thomson, Fundamentals of Spatial Information Systems, Academic Press, London, 1992.
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R. Laurini and D. Thompson. Fundamentals of Spatial Information Systems. Academic Press, London, 1992.
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R. Laurini and D. Thompson. Fundamentals of spatial information systems. Academic Press, 1992.
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R. Laurini and D. Thompson, Fundamentals of Spatial Information Systems. London: Academic Press, 1992.
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Robert Laurini and Derek Thompson. Fundamentals of Spatial Information Systems. Academic Press, Ltd., San Diego, CA, 1992.
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