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| [[Image:Usgs map space oblique mercator.PNG|thumb|300px|Space-oblique Mercator projection.]]
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| '''Space-oblique Mercator projection''' is a [[map projection]].
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| ==History==
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| 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. When the [[United States Geological Survey]] (USGS) needed to develop a system for reducing the amount of distortion caused when [[satellite]] pictures of the [[Ellipse|ellipsoidal]] Earth were printed on a flat page, they appealed for help at one such conference. Snyder worked on the problem armed with his newly purchased pocket calculator and devised the mathematical formulas needed to solve the problem. He submitted these to the USGS at no charge, starting off a new career at USGS. His formulas were used to produce maps from [[Landsat 4]] images launched in the summer of 1978.
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| ==Projection description==
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| The space-oblique Mercator projection provides continual [[Conformal map|conformal mapping]] of the [[swath]]{{dn|date=January 2012}} sensed by a satellite. [[Scale (map)|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. SOM is the only projection presented that takes the rotation of Earth into account.
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| ==Equations==
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| The forward equations for the Space Oblique Mercator projection for the sphere are as follows:
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| :<math>
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| \begin{align}
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| \frac{x}{R} &= \int_{0}^{\lambda'} \frac{H-S^2}{\left(1+S^2\right)^{1/2}}d\lambda' - \frac{S}{\left(1+S^2\right)^{1/2}}\ln\tan\left(\frac{\pi}{4}+\frac{\phi'}{2}\right) \\
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| \frac{y}{R} &= \left(H+1\right) \int_{0}^{\lambda'} \frac{S}{\left(1+S^2\right)^{1/2}}d\lambda' + \frac{1}{\left(1+S^2\right)^{1/2}}\ln\tan\left(\frac{\pi}{4}+\frac{\phi'}{2}\right) \\
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| S &= \left(P_{2}/P_{1}\right) \sin i \cos \lambda' \\
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| H &= 1 - \left(P_{2}/P_{1}\right) \cos i \\
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| \tan\lambda' &= \cos i \tan \lambda_{t} + \sin i \tan \phi / \cos \lambda_{t} \\
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| \sin\phi' &= \cos i \sin \phi - \sin i \cos \phi \sin \lambda_{t} \\
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| \lambda_{t} &= \lambda + \left(P_{2}/P_{1}\right) \lambda'. \\
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| \phi &= \text{geodetic (or geographic) latitude.} \\
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| \lambda &= \text{geodetic (or geographic) longitude.} \\
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| P_{2} &= \text{time required for revolution of satellite.} \\
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| P_{1} &= \text{length of Earth rotation.} \\
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| i &= \text{angle of inclination.} \\
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| R &= \text{radius of Earth.} \\
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| x,y &= \text{rectangular map coordinates.}
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| \end{align}
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| </math> | |
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| ==References==
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| *John Hessler, Projecting Time: John Parr Snyder and the Development of the Space Oblique Mercator Projection, Library of Congress, 2003
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| *[http://pubs.usgs.gov/bul/1518/report.pdf Snyder's 1981 Paper Detailing the Projection's Derivation]
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| {{Map Projections}}
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| [[Category:Cartographic projections]]
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| {{Cartography-stub}}
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