I was trying to figure out the math for covering a spherical panorama with a minimal amount of shots providing sufficient overlap, and realized that I had a tool nearly perfectly made for this: Povray.
The sphericalpano.zip contains three files for povray, but you only need to edit the panostructure.inc that defines the lens focal length, camera sensor dimensions and how you are planning to shoot the panorama. The panosim.ini contains povray settings for input, output and quality, and panosim.pov contains the scene construction. To run, just execute povray panosim.ini and look at the results. If you can see any black or if the overlaps are very small, increase number of shots. The center column has colored frames to help you analyze the results.
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