To review, my basic aim is to produce very precise perspective
transformations in order to merge panoramas which involve very large
images.   Unfortunately, there seems to be no way to specify target
points except by dragging, but even given that, there is an additional
problem.    Typically, I have a facade in which the top and bottom may
not be exactly parallel.   In order to get them that way, I need to move
corners on top and bottom of the building to desired positions.   I can
move the top corner more or less to where I want it.  But when I try to
move the bottom corner where I want it, I end up moving the top corner.
(The only exception is when the original top was actually at the upper
handle on that side.  In that case, it stays at the new position when
the bottom is moved.)   If Igo back to correct the top, the bottom
moves.  You can iterate this process until you get it about right, which
works well for moderate sized images, but for large images and precise
positioning, it takes quite a while and is very frustrating.

I've investigated the mathematics behind this, which involves projective
geometry and cross ratios.   Using that, I can determine where I have to
move the upper and lower handles to get points in between to go where I
want them to go.   That would work, but the formulas are pretty involved
and cumbersome to apply.  I experimented with using selections, but that
doesn't work because what is outside the selection is not moved and so
lines can be bent.

I don't see any other way to accomplish what I want except successive
approximations or using the formulas.  Can anyone suggest an alternate
Leonard Evens <[EMAIL PROTECTED]>
Mathematics Department, Northwestern University

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