I am trying to find a way to connect two random points on a sphere so that they form an arc with a given altitude. I believe this is very much like a greater circle problem with the exception that I want the arc between the points (the midpoint) to be above the surface of the sphere. As a plus I would also like the arcs to draw themselves on.

Any hints on a good place to start?

Hi,

don't know if this is the result you were thinking of. Much dirtier than a nice solution to the greater circle, but maybe close to what you were thinking. Changing the seed value on the scatter moves the points around, probably not ideal for you, but was a quick way of getting them on there

that is perfect, so much more simple than I had imagined.
I'll need to do it for lots of points but I think I can build on this to do that.
I appreciate your taking the time to show this

no problem, it's a very simple and rough example. There are lots of more sophisticated ways around the problem, but a starting point is always good