[Proj] Ellipsoidal Orthographic

[Charles Karney]

Noel,

You use an iterative method to solve for the reverse projection.  But
the reverse projection can be written in closed form.  Recovering the 3d
position [x,y,z] from the easting and northing entails solving a
quadratic equation, so that you get 2 or 0 (or exceptionally 1) root, as
expected.

I can provide you with the outline of the solution if you want.

   --Charles


On 06/28/11 07:43, Noel Zinn (cc) wrote:
> The only equations for the ellipsoidal orthographic that I've ever found
> published (in a book or journal) are those of Bugayevskiy and Snyder (1995),
> which are complicated and (the authors acknowledge) truncated.  Following
> EPSG Guidance Note 7, Part 2, I've prepared a presentation on the
> ellipsoidal orthographic that offers simple, exact equations.  The
> derivation also suggests that the ellipsoidal orthographic is unique among
> projections, being transitional between distorted cartography in 2D and
> undistorted visualization in 3D on a computer in ECEF or ENU (topocentric)
> coordinates.  A link to the presentation follows:
>
> http://www.hydrometronics.com/downloads/Ellipsoidal%20Orthographic%20Projection.pdf
>
> Does anyone in this group have other sources of information on the
> ellipsoidal orthographic?