Scaling rectangles making my head hurt-

Question

I’ve got four rectangles: the main stage, a sprite (an
LDM), the stage within the LDM, and a boundingRect of objects
within the LDM (so the coordinates are relative to the LDM stage,
not the main stage). I need a transform (scale, rotate, and
translate) that when applied to the LDM sprite produces a best fit
between the boundingRect within the LDM and the main stage. The
rotation will either be 0 or 90. The following code gets the scale
and rotation but I’m having trouble figuring out the
translation once a scale has been applied. It looks like the map()
method should help but so far I haven’t been able to make use
of it.

Answer 1

I’m sure I’ll get this if I just work through it
methodically but maybe someone will beat me to it. The following
two links show the pre-scale and post-scale arrangement of
rectangles drawn at 25% scale. Some notes:
The small colored boxes represent sprites within the LDM.
The bounding box around these sprites is calculated on the
fly (the sprites are positioned by the user)
The main stage size is fixed.
The LDM sprite starting size is fixed but its position on the
main stage is not (it can be scrolled by the user).
The LDM sprite must be scaled, rotated, and translated such
that the bounding box (which scales within the LDM) achieves a best
fit on the main stage.
http://www.appliedcd.com/FTP-Guest/pre_scale.jpg
http://www.appliedcd.com/FTP-Guest/post_scale.jpg
PS: <soapbox>It would be nice if Adobe enabled inline
picts or attachements. There have been a couple of times when I
thought an illustration would help.</soapbox>