Part 1: Distortion-Spectrum Fundamentals A New Tool for Analyzing and Visualizing Map Distortions

The basic techniques for calculating map distortions are reviewed, and several new concepts in analytic cartography are introduced together with the pertinent terminology: standardization of distortions against the reference projection, standard unit of distortion (SUD), and the distortion spectrum. The latter offers a succinct summary of the distortion content in a projection, which is quantitative and visual at the same time. Its main use is to compare different kinds of distortion (for example, in areas, shapes, or distances) within a projection, and among different projections. It also allows one to express quantitatively that, for example, a particular projection is much closer to the equal-area property than to that of conformality, and by exactly how much. The practical utility of the new concepts is demonstrated through examples of comparative distortion analysis of common projections.