- Aitoff projection
The Aitoff projection is a modified azimuthal
map projection . Proposed byDavid A. Aitoff in1889 , it is the equatorial form of theazimuthal equidistant projection , but stretched into a 2:1 ellipse while halving the longitude from the central meridian::x = mathrm{azeq}_xleft(fraclambda 2, phi ight),
:y = frac 1 2 mathrm{azeq}_y left(fraclambda 2, phi ight)
where mathrm{azeq}_x and mathrm{azeq}_y are the x and y components of the equatorial azimuthal equidistant projection. Written out explicitly, the projection is:
:x = frac{2 cos(phi) sinleft(fraclambda 2 ight)}{mathrm{sinc}(alpha)},
:y = frac{sin(phi)}{mathrm{sinc}(alpha)},
where
:alpha = arccosleft(cos(phi)cosleft(fraclambda 2 ight) ight),
and mathrm{sinc}(alpha) is the unnormalized sinc function with the discontinuity removed. In all of these formulas, lambda is the longitude from the central meridian and phi is the latitude.
Three years later,
Ernst Hermann Heinrich Hammer suggested the use of theLambert azimuthal equal-area projection in the same manner as Aitoff, producing theHammer projection . While Hammer was careful to cite Aitoff, there has been some confusion since, wherein Aitoff has been attributed to Hammer's projection. ["Flattening the Earth: Two Thousand Years of Map Projections", John P. Snyder, 1993, pp.130-133, ISBN 0-226-76747-7.]References
ee also
*
Mollweide projection
*Hammer projection
* [http://map.gsfc.nasa.gov/m_mm.html]External links
* [http://www.radicalcartography.net/?projectionref Table of common projections]
* [http://www.uff.br/mapprojections/Aitoff_en.html An interactive Java Applet to study the metric deformations of the Aitoff Projection] .
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