This is just a thought - perhaps it would make animations simpler at a possible cost of slightly increased rendering times. A simple cylinder type of primitive/bounding box which you set up to encompass a scene. A full 360 irradiance map is calculated in a radial fashion within these boundaries.
Not ruin your suggestion, but wouldn’t a half sphere be better as it won’t have a hole in the top of it like a cylinder would? Just wondering why you suggest a cylinder?
Why would the cylinder have a hole in the top - you mean a tube? All you would be looking to do with a cylinder is define a scene’s/irmaps boundaries. I guess a dome could work too or even a square for that matter. Just seemed like a cylinder seemed like a more efficient shape.
Sorry my bad! Far too late at night to be posting! 
Good idea!
Re: IrradianceMap Cylinder
I don’t think this would work. Remeber an irradience map is somewhat view-dependent in its calculations. It requires tracing rays from the camera throughout the scene. What you’re describing would need a theoretically infinite number of cameras to render, to compensate for things that you can see from one viewpoint, but not another.
If you are rendering a single object that you want to view from multiple locations with a precomputed irrmap, its fairly trivial to setup an animated camera that moves in a dome (or cylindrical, but dome would be better because the change in angle as you go up would let you see more “inside” or “on top” of things) that moves a set increment in direction per frame. Then just do the irrmap for the sequence for this moving camera. You can do the same thing for rendering out an image sequence to use for a QTVR object.
I don’t see why it would. There could be a spinner just as there is a sides spinner on a cylinder primitive and you could dial it up and dial it down. Each side/face would essentially act as a camera - in animations how many nth frames of IRMaps are computed and added together? It’s not every single frame.
You also don’t usually compute fly throughs/IRMaps from above or below typical Line of Sight straight-on. So why would this be any different? Dome or cylinder would be a matter of perference.