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The places discussed in Section 2.1.1, Place, vary enormously in size and shape. Weather observations are obtained from stations that may occupy only a few square meters of the Earth’s surface (from instruments that occupy only a small fraction of the station’s area), whereas statistics published for Russia are based on a land area of more than 17 million sq km. In spatial analysis it is customary to refer to places as objects. In studies of roads or rivers the objects of interest are long and thin, and will often be represented as lines of zero width. In studies of climate the objects of interest may be weather stations of minimal extent, and will often be represented as points. On the other hand many studies of social or economic patterns may need to consider the two-dimensional extent of places, which will therefore be represented as areas, and in some studies where elevations or depths are important it may be appropriate to represent places as volumes. To a spatial statistician, these points, lines, areas, or volumes are known as the attributes’ spatial support.

Each of these four classes of objects has its own techniques of representation in digital systems. The software for capturing and storing spatial data, analyzing and visualizing them, and reporting the results of analysis must recognize and handle each of these classes. But digital systems must ultimately represent everything in a language of just two characters, 0 and 1 or “off” and “on”, and special techniques are required to represent complex objects in this way. In practice, points, lines, and areas are most often represented in the following standard forms:

Points as pairs of coordinates, in latitude/longitude or some other standard system

Lines as ordered sequences of points connected by straight lines

Areas as ordered rings of points, also connected by straight lines to form polygons. In some cases areas may contain holes, and may include separate islands, such as in representing the State of Michigan with its separate Upper Peninsula, or the State of Georgia with its offshore islands. This use of polygons to represent areas is so pervasive that many spatial analysts refer to all areas as polygons, whether or not their edges are actually straight

Lines represented in this way are often termed polylines, by analogy to polygons (see Table 1‑1 for a more formal definition). Three-dimensional volumes are represented in several different ways, and as yet no one method has become widely adopted as a standard. The related term edge is used in several ways within GIS. These include: to denote the border of polygonal regions; to identify the individual links connecting nodes or vertices in a network; and as a general term relating to the distinct or indistinct boundary of areas or zones. In many parts of spatial analysis the related term, edge effect is applied. This refers to possible bias in the analysis which arises specifically due to proximity of features to one or more edges. For example, in point pattern analysis computation of distances to the nearest neighboring point, or calculation of the density of points per unit area, may both be subject to edge effects.

Figure 2‑3, below, shows a simple example of points, lines, and areas, as represented in a typical map display. The hospital, boat ramp, and swimming area will be stored in the database as points with associated attributes, and symbolized for display. The roads will be stored as polylines, and the road type symbols (U.S. Highway, Interstate Highway) generated from the attributes when each object is displayed. The lake will be stored as two polygons with appropriate attributes. Note how the lake consists of two geometrically disconnected pieces, linked in the database to a single set of attributes — objects in a GIS may consist of multiple parts, as long as each part is of the same type.

Figure 2‑3 An example map showing points, lines, and areas appropriately symbolized


see text for explanation

It can be expensive and time-consuming to create the polygon representations of complex area objects, and so analysts often resort to simpler approaches, such as choosing a single representative point. But while this may be satisfactory for some purposes, there are obvious problems with representing the entirety of a large country such as Russia as a single point. For example, the distance from Canada to the U.S. computed between representative points in this way would be very misleading, given that they share a very long common boundary.