A CLASSIFICATION OF MAP PROJECTIONS1

Abstract

THE desire for a classification of map projections stems from the fact that an infinite number of distinct projections are possible. Hence, the fundamental problem in classifying map projections is the partitioning of this infinite set into a comprehensible and useful finite number of all-inclusive and preferably non-overlapping classes. Several classifications of map projections are to be found in the cartographic literature. The advantages and disadvantages of each, of course, depend on the purpose, just as the properties by which classes are to be distinguished depend on the purpose. The classification based on geometric models (perspectivities) separating projections into conic, cylindric, planar, polyconic, polycylindric, etc., is convenient and is often used. The major shortcoming of this system is that it is not allinclusive. Another most important method of classification, based on the preservation of certain geometric properties of the surface of the referent object, separates the conformal projections from the equal-area projections, leaving a third class which is neither. Preservation of additional properties yields further classes; e.g., geodesic maps (for the sphere there is the gnomonic projection and all linear transforms thereof), azimuthal projections, equidistant projections (including polar isometries such as the azimuthal equidistant), and many more. In fact, Felix Klein, the German mathematician, defined a geometry as the study of properties preserved by a particular group of transformations. From this point of view, a classification according to properties preserved is the very essence of geometry. Thus one has projective transformations and projective geometry, affine transformations and affine geometry, Euclidean