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Vertical Perspective Projection

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VerticalPerspectiveProjection

The vertical perspective projection is a map projection that corresponds to the appearance of a globe when directly viewed from some distance away with the z-axis of the viewer aligned parallel to the positive z-axis of the globe. It is given by the transformation equations

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

where P is the distance of the point of perspective in units of sphere radii and

cosc=sinphi_1sinphi+cosphi_1cosphicos(lambda-lambda_0)
(3)
k^'=(P-1)/(P-cosc).
(4)

Note that points corresponding to cosc<1/P are on the back side of the globe and so should be suppressed when making the projection.

See also

Orthographic Projection, Perspective, Stereographic 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. 173-178, 1987.

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Vertical Perspective Projection

Cite this as:

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

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