Simplex Range Searching
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).
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