Use fov and center pan and tilt values to calculate boundary's pan and tilt?

Question

I have the current fov and the center pan and tilt values. How would I calculate what the pan and tilt values are of the edges(i.e. min pan value and max tilt) with this information?

Answer 1

The minimum (that is, the bottom of the viewport) tilt is simply the current center tilt minus half the FOV, possibly bounded at 90 degrees. The maximum can be located similarly. Beware that the tilt values can exceed 90 degrees if the viewport encompasses one of the poles of the projection sphere, and you must decide if you are interested in how far onto the opposite hemisphere the viewport extends or if you are only interested in the maximum rendered tilt (+/-90 degrees for any viewport that spans a pole).

Minimum and maximum pan are poorly defined, as the edges of a rectilinear viewport will not be parallel to the lines of longitude on the projection sphere, so the pan extents at the north end of the viewport will be greater than at the south end (in the case of positive tilt).