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Lambert Conformal Conic Projection

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LambertConformalConicProjection

Let lambda be the longitude, lambda_0 the reference longitude, phi the latitude, phi_0 the reference latitude, and phi_1 and phi_2 the standard parallels. Then the transformation of spherical coordinates to the plane via the Lambert conformal conic projection is given by

x=rhosin[n(lambda-lambda_0)]
(1)
y=rho_0-rhocos[n(lambda-lambda_0)],
(2)

where

F=(cosphi_1tan^n(1/4pi+1/2phi_1))/n
(3)
n=(ln(cosphi_1secphi_2))/(ln[tan(1/4pi+1/2phi_2)cot(1/4pi+1/2phi_1)])
(4)
rho=Fcot^n(1/4pi+1/2phi)
(5)
rho_0=Fcot^n(1/4pi+1/2phi_0).
(6)

The inverse formulas are

phi=2tan^(-1)[(F/rho)^(1/n)]-1/2pi
(7)
lambda=lambda_0+theta/n,
(8)

where

rho=sgn(n)sqrt(x^2+(rho_0-y)^2)
(9)
theta=tan^(-1)(x/(rho_0-y)),
(10)

with F, rho_0, and n as defined above.

See also

Conformal Projection, Conic Projection, Lambert Azimuthal Equal-Area Projection, Lambert Cylindrical Equal-Area Projection

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References

Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, pp. 104-110, 1987.

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Lambert Conformal Conic Projection

Cite this as:

Weisstein, Eric W. "Lambert Conformal Conic Projection." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LambertConformalConicProjection.html

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