I am writing a simulation of an automated telescope observation program. One part of this is to run a spiral scan pattern on and around objects of interest. I would like to tile this scan pattern so that each image is immediately adjacent to each other (perhaps with a specified level of overlap). The telescopes I'm simulating are Az-El.
My primary objects of interest are GEO satellites, and that combined with the specific simulation framework used makes Az-El a little more natural to work with than celestial coordinates.
Given the Az-El of the object of interest, I'm trying to determine the Az-El pointing directions for all of the images. As I understand it, I can define an image location in pixel coordinates relative to the central image centered on the object of interest and then project this into Az-El (or other spherical) coordinates. I'm not entirely sure how to do this. I see online and in codes lots of spherical projections (gnomonic, arc, orthographic, for example) but I don't know which one is the right one to use for what I'm trying to do. Is my understanding of the procedure correct, and which projection should I use?