I want to project a catalog of stars on a sphere to the computer screen. As a non-mathematician I was looking for a ready made solution and I found some interesting geographical projections, like Mercator.
Here's the riddle I'm struggling with:
Is the outcome of a projection from a sphere's surface to a plane (2-dimensional geographical map) identical to the projection of the inner side of a sphere's surface to a plane (2-dimensional starchart)?
I'm pretty sure that this is true for points, but I'm not sure if it also works for lines and areas.
Any hint would be appreciated.
