What about "creating" triangles with two points on your box thingy (two corners at a time) and the third on your camera world pos, then using simple trig to find the angle at the camera point. Then compare that angle to your FoV? Won't tell you exactly how many pixels are on screen, but might let you estimate on a level that is good enough?
Thanks for the idea. It's actually one of the most fitting suggestions so far
I was already doing something similar, but not using triangles with two box corners. Instead I just calculated the camera view angle to one single box corner. It's kind of working but as you say only a very rough approximation approach. I came here under the impression that there might exist a better way to do this...
Btw, what would be the benefit of using triangles. And no, the box is not axis aligned.