What projection could be used for a very large mountain?

[Thurlor]

@ ManOfSteel

Imagine unwrapping the surface of the mountain then laying it flat. If the mountain were a simple cone it would be easy.

I realise none of this is really needed, but the idea I have is of a civilization living on the slopes of a giant mountain/volcano (probably as large as Olympus Mons on Mars). Anyway, they flatten all of there maps so as there is no distortion from height.

[vorropohaiah]

Anyway, they flatten all of there maps so as there is no distortion from height.

I'm sure there's people more knowledgeable than me in this field, though your statement there is somewhat counter productive, as, given your other example of a cone, flattening such an object has to leave distortion - if not height, then with width. I'd say try and come up with something we dont have in the real world, which also serves to give their culture something distinct, making them seem more real. dont ask what though i have enough on my plate coming up with thing for my world! :p

and i like the idea you're aiming for, makes sense to me.

[Hai-Etlik]

@ ManOfSteel

Imagine unwrapping the surface of the mountain then laying it flat. If the mountain were a simple cone it would be easy.

I realise none of this is really needed, but the idea I have is of a civilization living on the slopes of a giant mountain/volcano (probably as large as Olympus Mons on Mars). Anyway, they flatten all of there maps so as there is no distortion from height.

Put simply, there's no such projection for pretty much the same reason there are none for a globe, both have complex curvature. I'd draw such a map the same way I would any other similarly large scale map. Any projection tangent or secant to the globe near the mountain would work. The easiest to understand would be an orthographic projection centred on the mountain (Roughly, the view of the mountain from directly above it in space.) If there are any really steep areas with significant details, try covering them with side view insets.

You could also make a conical/pyramidal simplification of the mountain which does have simple curvature. Then project the surface of the mountain onto that, then unwrap. You will still end up with a discontinuity this way where you "cut" the cone but you will only need the one. This is roughly what is done on the globe in using a ellipsoid to approximate the more correct geoid (An equipotential surface of the Earth's gravitational field.). Defining the mountain to cone projection would be a bit of a pain though as would picking a particular cone (We have a lot of different ellipsoids for approximating the geoid)