Cylindrical Projection

A cylindrical projection of points on a unit sphere centered at consists of extending the line for each point until it intersects a cylinder tangent to the sphere at its equator at a corresponding point . If the sphere is tangent to the cylinder at longitude , then a point on the sphere with latitude and longitude is mapped to a point on the cylinder with height .

Unwrapping and flattening out the cylinder then gives the Cartesian coordinates

			(1)
			(2)

The cylindrical projection of the Earth is illustrated above.

This form of the projection, however, is seldom used in practice, and the term "cylindrical projection" is used instead to refer to any projection in which lines of longitude are mapped to equally spaced parallel lines and lines of latitude (parallels) are mapped to parallel lines with arbitrary mathematically spaced separations (Snyder 1987, p. 5). For example, the common Mercator projection uses the complicated transformation

(3)

instead of in order to achieve certain desirable properties in the projection.

Craig (1882) used the term "cylindric" instead of "cylindrical" (Lee 1944), but this convention did not catch on.