Lambert Conformal Conic Projection
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 = [画像:(cosphi_1tan^n(1/4pi+1/2phi_1))/n]
(3)
![画像:(ln(cosphi_1secphi_2))/(ln[tan(1/4pi+1/2phi_2)cot(1/4pi+1/2phi_1)])](/index.cgi/larger-text/https://mathworld.wolfram.com/images/equations/LambertConformalConicProjection/Inline18.svg){kind=link}
rho = Fcot^n(1/4pi+1/2phi)
(5)
rho_0 = Fcot^n(1/4pi+1/2phi_0).
(6)
The inverse formulas are
phi = [画像:2tan^(-1)[(F/rho)^(1/n)]-1/2pi]
![画像:2tan^(-1)[(F/rho)^(1/n)]-1/2pi](/index.cgi/larger-text/https://mathworld.wolfram.com/images/equations/LambertConformalConicProjection/Inline27.svg){kind=link}
(7)
lambda = [画像:lambda_0+theta/n,]
(8)
where
rho = sgn(n)sqrt(x^2+(rho_0-y)^2)
(9)
theta = [画像: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 ProjectionExplore with Wolfram|Alpha
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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.Referenced on Wolfram|Alpha
Lambert Conformal Conic ProjectionCite this as:
Weisstein, Eric W. "Lambert Conformal Conic Projection." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LambertConformalConicProjection.html