A Comparison of Pseudocylindrical Map Projections

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Abstract
There are at least 80 published pseudocylindrical map projections, with straight parallels and curved meridians. Of these, about 40 are equal area (a few of which are not significantly different from others), and about 20 have equidistant parallels. Many are mentioned only qualitatively if at all in references other than the original sources. Some 40 inventors are involved. Seven significantly different projections using sinusoids offer alternatives, such as flat or pointed poles, equal area, or equidistant parallels. A dozen elliptical pseudocylindricals offer these variations, perhaps more attractively, with added possibilities from full versus partial ellipses. Five parabolics are rounder and probably preferable aesthetically to their sinusoidal counterparts. Nine projections with hyperbolas or converging straight lines for meridians are almost useless. Over two dozen projections use less well-known curves in attempts to give maps less real or apparent distortion. They include seven pseudocylindricals that are at least as prevalent in published atlases as the utilized handful of classically-curved projections. The projections are described here with definitive formulas and comparisons of appearance, theory, and standard parallels to facilitate choices and calculations.

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