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Cylindrical Projection


CylindricalProjDiagram

A cylindrical projection of points on a unit sphere centered at O consists of extending the line OS for each point S until it intersects a cylinder tangent to the sphere at its equator at a corresponding point C. If the sphere is tangent to the cylinder at longitude lambda_0, then a point on the sphere with latitude phi and longitude lambda is mapped to a point on the cylinder with height tanphi.

CylindricalProjection3D

Unwrapping and flattening out the cylinder then gives the Cartesian coordinates

x=lambda-lambda_0
(1)
y=tanphi.
(2)
CylindricalProjection

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

 y=ln[tan(1/4pi+1/2phi)]
(3)

instead of tanphi 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.


See also

Behrmann Cylindrical Equal-Area Projection, Cylindrical Equal-Area Projection, Cylindrical Equidistant Projection, Gall Orthographic Projection, Mercator Projection, Miller Cylindrical Projection, Peters Projection, Pseudocylindrical Projection

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References

Craig, T. A Treatise on Projections. Washington, DC: U. S. Government Printing Office, 1882.Lee, L. P. "The Nomenclature and Classification of Map Projections." Empire Survey Rev. 7, 190-200, 1944.Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, 1987.

Referenced on Wolfram|Alpha

Cylindrical Projection

Cite this as:

Weisstein, Eric W. "Cylindrical Projection." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CylindricalProjection.html

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