Closed-form inverse for Eisenlohr

[jasondavies]

Is there a closed-form inverse for Eisenlohr?

I'm having trouble finding much literature aside from the original paper in German, and I can't see an explicit inverse mentioned there.

Thanks!

[daan]

Coincidentally, I have investigated this very question extensively for two reasons unrelated to each other. I’m convinced there is no closed-form solution.

Regards,
— daan

[jasondavies]

Hi daan,

Thanks, that's very helpful!

[jasondavies]

In case anyone is interested, I've finally managed to implement the inverse Eisenlohr using Newton–Raphson (via partial derivatives). I think I can safely say it’s the most complex I’ve implemented by far, as the expressions for the partial derivatives are quite lengthy. For the initial estimate, I was lazy and used an inverse August projection.

I’m hoping daan will suggest a better initial estimate, but this seems to work well (although with a slight adjustment for |φ| > 89°).

[daan]

No, I have nothing better: The reverse August is what I use as initial estimate for my own Eisenlohr reverse formulation.


— daan