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Actual and Derived Isarithmic Mapping

All isarithmic maps can be distinguished on the basis of whether the control points used to determine the location of the isolines occur at actual points, isometric, or are derived from the surrounding area, isoplethic. For example, elevation occurs and can be measured at points, and it is possible to verify whether a contour line matches the real surface (isometric map). In contrast, an isarithmic map of population density, where control point values are derived from the densities of enumeration areas such as census tracts or counties, does not correspond to a physical surface (isoplethic map). In addition, the value for an enumeration area refers to the whole unit area and must be arbitrarily assigned to a location within the enumeration unit, usually the centroid. Derived values may be ratios (as with population densities) or means, standard deviations, or other statistical observations. It is impossible to determine whether the isolines resulting from derived values correspond to an actual surface, because the values are not observable at points.

Contour Lines by Stereoplotter

Most contour maps have been derived using a stereoplotter, a photomechanical device that allows a trained operator to trace contour lines based on elevation information extracted from stereopairs of aerial photographs with approximately 60% overlap to create parallax, so that the images appear to be in true three dimensions when viewed with stereo glasses. Accurate elevation measurements were derived by viewing the surface stereographically and by adjusting a device called a platen, visually placing a point on the apparent surface. Geometric calculations related to distance differences between a set of points observed in both photos allow accurate point elevations or contours to be derived. Using this method, an entire topographic map could be created in a week or two, depending upon the complexity of the surface features. Although the method was perfected in Germany in the 1920s, the most widely used of these devices was the Kelsh optical projection stereoplotter, introduced by Harry T. Kelsh in 1945. Optical projection stereoplotters were replaced by computer-assisted analytical stereoplotters by the 1970s.

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