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It seems to me that 3drotate does what you are
looking for, via the -rotparent and -gridparent
options.
It may be a little irritating, but if you want to do
this and only have a matrix for the rotation, you
could consider running 3drotate with your matrix,
running 3dresample to get the desired grid, and
then using the result as rotparent and gridparent
(just to do it all again, but in one step).