> The fast method would be to compute the eight corners, transform them, and
create
> a new BB that contains the eight transformed points.

I guess, if you don't care about accuracy, then a more optimized approach
would be to transform the center of the bounding box and its "radius" and
then compute a new BB from the transformed data. (The OP did ask about the
most efficient method, IIRC.)
   -Paul

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