Space-oblique Mercator projection

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Space-oblique Mercator projection. Usgs map space oblique mercator.PNG
Space-oblique Mercator projection.

Space-oblique Mercator projection is a map projection devised in the 1970s for preparing maps from Earth-survey satellite data. It is a generalization of the oblique Mercator projection that incorporates the time evolution of a given satellite ground track to optimize its representation on the map. The oblique Mercator projection, on the other hand, optimizes for a given geodesic.



The space-oblique Mercator projection (SOM) was developed by John P. Snyder, Alden Partridge Colvocoresses and John L. Junkins in 1976. Snyder had an interest in maps, originating back to his childhood and he regularly attended cartography conferences while on vacation. In 1972, the United States Geological Survey (USGS) needed to develop a system for reducing the amount of distortion caused when satellite pictures of the ellipsoidal Earth were printed on a flat page. Colvocoresses, the head of the USGS's national mapping program, asked attendees of a geodetic sciences conferences for help solving the projection problem in 1976. [1] Snyder attended the conference and became motivated to work on the problem armed with his newly purchased pocket calculator and devised the mathematical formulas needed to solve the problem. After submitting his calculations to Waldo Tobler for review, Snyder submitted these to the USGS at no charge. Impressed with his work, USGS officials offered Snyder a job with the organization, which he accepted. [1] His formulas were used to produce maps from Landsat 4 images launched in the summer of 1978.

Projection description

The space-oblique Mercator projection provides continual, nearly conformal mapping of the swath sensed by a satellite. Scale is true along the ground track, varying 0.01 percent within the normal sensing range of the satellite. Conformality is correct within a few parts per million for the sensing range. Distortion is essentially constant along lines of constant distance parallel to the ground track. The space-oblique Mercator is the only projection presented that takes the rotation of Earth into account.


The forward equations for the Space-oblique Mercator projection for the sphere are as follows:

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Hammer projection map projection

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Cassini projection map projection

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Cylindrical equal-area projection

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Eckert IV projection

The Eckert IV projection is an equal-area pseudocylindrical map projection. The length of the polar lines is half that of the equator, and lines of longitude are semiellipses, or portions of ellipses. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections. In each pair, the meridians have the same shape, and the odd-numbered projection has equally spaced parallels, whereas the even-numbered projection has parallels spaced to preserve area. The pair to Eckert IV is the Eckert III projection.

Armadillo projection

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Rectangular polyconic projection

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The Eckert-Greifendorff projection is an equal-area map projection described by Max Eckert-Greifendorff in 1935. Unlike his previous six projections, It is not pseudocylindrical.


  1. 1 2 Stockton, Nick (June 20, 2014). "Get to Know a Projection: The Space-Oblique Mercator". Wired.