Vertical Perspective Projection
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^' = [画像:(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 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. 173-178, 1987.Referenced on Wolfram|Alpha
Vertical Perspective ProjectionCite this as:
Weisstein, Eric W. "Vertical Perspective Projection." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/VerticalPerspectiveProjection.html