how to change font to barcode in excel Spatial Queries in Software

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2334 Spatial Queries
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There are a number of types of queries that involve spatial locations Nearness queries request objects that lie near a speci ed location A query to nd all restaurants that lie within a given distance of a given point is an example of a nearness query The nearest-neighbor query requests the object that is nearest to a speci ed point For example, we may want to nd the nearest gasoline station Note that this query does not have to specify a limit on the distance, and hence we can ask it even if we have no idea how far the nearest gasoline station lies Region queries deal with spatial regions Such a query can ask for objects that lie partially or fully inside a speci ed region A query to nd all retail shops within the geographic boundaries of a given town is an example
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Queries may also request intersections and unions of regions For example, given region information, such as annual rainfall and population density, a query may request all regions with a low annual rainfall as well as a high population density Queries that compute intersections of regions can be thought of as computing the spatial join of two spatial relations for example, one representing rainfall and the other representing population density with the location playing the role of join attribute In general, given two relations, each containing spatial objects, the spatial join of the two relations generates either pairs of objects that intersect, or the intersection regions of such pairs Several join algorithms ef ciently compute spatial joins on vector data Although nested-loop join and indexed nested-loop join (with spatial indices) can be used, hash joins and sort merge joins cannot be used on spatial data Researchers have proposed join techniques based on coordinated traversal of spatial index structures on the two relations See the bibliographical notes for more information In general, queries on spatial data may have a combination of spatial and nonspatial requirements For instance, we may want to nd the nearest restaurant that has vegetarian selections, and that charges less than $10 for a meal Since spatial data are inherently graphical, we usually query them by using a graphical query language Results of such queries are also displayed graphically, rather than in tables The user can invoke various operations on the interface, such as choosing an area to be viewed (for example, by pointing and clicking on suburbs west of Manhattan), zooming in and out, choosing what to display on the basis of selection conditions (for example, houses with more than three bedrooms), overlay of multiple maps (for example, houses with more than three bedrooms overlayed on a map showing areas with low crime rates), and so on The graphical interface constitutes the front end Extensions of SQL have been proposed to permit relational databases to store and retrieve spatial information ef ciently, and also allowing queries to mix spatial and nonspatial conditions Extensions include allowing abstract data types, such as lines, polygons, and bit maps, and allowing spatial conditions, such as contains or overlaps
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2335 Indexing of Spatial Data
Indices are required for ef cient access to spatial data Traditional index structures, such as hash indices and B-trees, are not suitable, since they deal only with onedimensional data, whereas spatial data are typically of two or more dimensions
23351 k-d Trees
To understand how to index spatial data consisting of two or more dimensions, we consider rst the indexing of points in one-dimensional data Tree structures, such as binary trees and B-trees, operate by successively dividing space into smaller parts For instance, each internal node of a binary tree partitions a one-dimensional interval
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