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Azimuthal Equidistant Projection

azeq

An azimuthal projection which is neither equal-area nor conformal. Let phi_1 and lambda_0 be the latitude and longitude of the center of the projection, then the transformation equations are given by

x=k^'cosphisin(lambda-lambda_0)
(1)
y=k^'[cosphi_1sinphi-sinphi_1cosphicos(lambda-lambda_0)].
(2)

Here,

k^'=c/(sinc)
(3)

and

cosc=sinphi_1sinphi+cosphi_1cosphicos(lambda-lambda_0),
(4)

where c is the angular distance from the center. The inverse formulas are

phi=sin^(-1)(coscsinphi_1+(ysinccosphi_1)/c)
(5)

and

lambda={lambda_0+tan^(-1)((xsinc)/(ccosphi_1cosc-ysinphi_1sinc)) for phi_1!=+/-90 degrees; lambda_0+tan^(-1)(-x/y) for phi_1=90 degrees; lambda_0+tan^(-1)(x/y) for phi_1=-90 degrees,
(6)

with the angular distance from the center given by

c=sqrt(x^2+y^2).
(7)

See also

Azimuthal Projection, Equidistant 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. 191-202, 1987.

Referenced on Wolfram|Alpha

Azimuthal Equidistant Projection

Cite this as:

Weisstein, Eric W. "Azimuthal Equidistant Projection." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AzimuthalEquidistantProjection.html

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