Lambert conformal conic projection
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A Lambert conformal conic projection (LCC) is a conic map projection, which is often used for aeronautical charts. In essence, the projection superimposes a cone over the sphere of the Earth, with two reference parallels secant to the globe and intersecting it. This minimizes distortion from projecting a three dimensional surface to a two-dimensional surface. There is no distortion along the standard parallels, but distortion increases further from the chosen parallels. As the name indicates, maps using this projection are conformal.
Pilots favor these charts because a straight line drawn on a Lambert conformal conic projection approximates a great-circle route between endpoints.
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[edit] Transformation
Spherical coordinates can be transformed into Lambert conformal conic projection coordinates with the following formulas[1], where λ is the longitude, λ0 the reference longitude, φ the latitude, φ0 the reference latitude, and φ1 and φ2 the standard parallels:
- x = ρsin[n(λ − λ0)]
- y = ρ0 − ρcos[n(λ − λ0)]
where
![n = \frac{\ln(\cos \phi_1 \sec \phi_2)}{\ln [\tan (\frac14 \pi + \frac12 \phi_2) \cot (\frac14 \pi + \frac12\phi_1)]}](http://upload.wikimedia.org/math/2/7/9/279721ee5afba31bcf501e61e2d96b2c.png)
[edit] See also
- Lambert cylindrical equal-area projection
- Lambert azimuthal equal-area projection
- Johann Heinrich Lambert
[edit] References
- ^ Weisstein, Eric. "Lambert Conformal Conic Projection". Wolfram MathWorld. Wolfram Research. http://mathworld.wolfram.com/LambertConformalConicProjection.html. Retrieved on 2009-02-07.
[edit] External links
- Table of examples and properties of all common projections, from radicalcartography.net
- An interactive Java Applet to study the metric deformations of the Lambert Conformal Conic Projection
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