Mapthematics Forums

Thank you, that's very helpful once again. When you said "secant method", did you mean "bisection method"? Since the secant method is a finite difference approximation to Newton—Raphson, it doesn't guarantee convergence, whereas the bisection method is more robust and suitable fo...

It's me again! I'm wondering if you have any hints regarding an inverse for the Chamberlin Trimetric. According to Christensen (1992): The inverse transformation is solved rather easily by a rough estimate of the position on the sphere, followed by an iteration of the forward solution. It's encourag...

Fascinating, thanks. I’ll consider it a fun exercise to figure out how to recreate it.

Fantastically helpful, thank you!

What's the unsual-looking map projection in one of those slides?

I understand what a datum is: the Earth is not a sphere, so it can be better approximated using an oblate spheroid, so a datum is the specification of such a spheroid (usually relative to particular anchor points etc.) What I find confusing is how to take this into account when projecting a map. Of ...

OK, I've implemented the latitude via Newton–Raphson, and it converges very rapidly so I'm happy. I'm still interested in knowing whether a closed-form exists (or if not, whether it's easy to show why).

Me again! Yes, I'm relentless! I'm curious about Van der Grinten IV: finding the longitude was trivial, but the latitude eludes me. Do you know of a closed-form inverse for the latitude? I have a feeling there is no such thing, as the formula for latitude is fairly complicated. P.S. I'm pretty sure ...

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 ...

Hi daan,

Thanks, that's very helpful!