Perhaps the easiest (to understand) solution, at least for the
landscape vs portrait mode problem, is to take max(HFOV, VFOV), in
other words, the FOV of the greatest dimension. This is pretty easy to
guess from a user perspective in case of missing EXIF information.
I've thought about a DFOV as well, but I don't really think this is
the best way to circumvent issues like these.

Focal length is nice of course, but what it does exactly is dependent
on the sensor or film size (hence the existence of the all but
beautiful "focal length 35mm equivalent"), which in practice can make
it less obvious, and also it's less easy to guess, especially when one
does not have a photographer's background.

In the end I think there are good and bad things with any chosen unit.
Working internally with a focal length in pixels (or a pixels per
angle ratio) and presenting a FOV to the outside world might be a nice
mean.

--
Bart
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