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Simplex Range Searching

Windowing Revisited
  • Mark de Berg
  • Marc van Kreveld
  • Mark Overmars
  • Otfried Cheong Schwarzkopf

Abstract

In Chapter 2 we saw that geographic information systems often store a map in a number of separate layers. Each layer represents a theme from the map, that is, a specific type of feature such as roads or cities. Distinguishing layers makes it easy for the user to concentrate her attention on a specific feature. Sometimes one is not interested in all the features of a given type, but only in the ones lying inside a certain region. Chapter 10 contains an example of this: from a road map of the whole of the U.S.A. we wanted to select the part lying inside a much smaller region. There the query region, or window, was rectangular, but it is easy to imagine situations where the region has a different shape. Suppose that we have a map layer whose theme is population density. The density is shown on the map by plotting a point for every 5,000 people, say. An example of such a map is given in Figure 16.1. If we want to estimate the impact of building, say, a new airport at a given location, it is useful to know how many people live in the affected area. In geometric terms we have a set of points in the plane and we want to count the points lying inside a query region (for instance, the region within which the noise of planes exceeds a certain level).

Figure 16.1

Population density of the Netherlands

Keywords

Range Query Query Point Query Time Cutting Tree Partition Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Mark de Berg
    • 1
  • Marc van Kreveld
    • 2
  • Mark Overmars
    • 2
  • Otfried Cheong Schwarzkopf
    • 2
  1. 1.Department of Computer ScienceTU EindhovenEindhoventhe Netherlands
  2. 2.Department of Computer ScienceUtrecht UniversityUtrechtThe Netherlands

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