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Orthographic Projection


OrthographicProjection

The orthographic projection is a projection from infinity that preserves neither area nor angle. It is given by

x=cosphisin(lambda-lambda_0)
(1)
y=cosphi_1sinphi-sinphi_1cosphicos(lambda-lambda_0),
(2)

where phi is the latitude, lambda is the longitude, and lambda_0 and phi_1 are reference longitudes and latitudes, respectively.

The inverse transformations are

phi=sin^(-1)(coscsinphi_1+(ysinccosphi_1)/rho)
(3)
lambda=lambda_0+tan^(-1)((xsinc)/(rhocosphi_1cosc-ysinphi_1sinc)),
(4)

where

rho=sqrt(x^2+y^2)
(5)
c=sin^(-1)rho
(6)

and the two-argument form of the inverse tangent function is best used for this computation.


See also

Stereographic Projection, Vertical Perspective 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. 145-153, 1987.

Referenced on Wolfram|Alpha

Orthographic Projection

Cite this as:

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

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