I am interested in a problem where a camera is mounted on the Earth that has a mechanism for altitude and azimuth adjustments. The longitude, latitude and altitude of the camera are known, and the camera is assumed to be level. The input is a longitude, latitude and altitude, and the output needs to be the alt-az coordinates of the camera to point at the specified location on Earth.
My question is that this seems like something that many people would have looked at already, but I think I am missing the proper keywords for a search. Instead, I'm thinking of it as a change of coordinates problem, or a function $\mathbb{R}^3\rightarrow\mathbb{R}^2$.
Could someone point me in the right direction on this problem in terms of keywords or terminology? Ultimately, I am interested in a sort of self-calibration where I don't know much about the levelness of the camera, but that is for later.