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Map projection aspects

ABSTRACT A projection aspect is usually defined in references as the relation to the so-called auxiliary surface. However, such surfaces do not usually exist in map projection theory, which raises the issue of defining projection aspects without reference to auxiliary surfaces. This paper explains how projection aspects can be defined in two ways which are not mutually exclusive. According to the first definition, the aspect is the position of a projection axis in relation to the axis of geographic parameterization of a sphere. The projection axis is the axis of the pseudogeographic parameterization of a sphere, based on which the basic equations of map projection are defined. The basic equations of map projection are selected according to agreement and/or custom. According to this definition, aspects can be normal, transverse or oblique. According to the second definition, an aspect is the representation of the area in the central part of a map, and can be polar, equatorial or oblique. Therefore, it is possible for a map projection to have a normal and polar aspect, but it can also have a normal and equatorial aspect. The second definition is not recommended for use, due to its ambiguity.