OK, I have uploaded a new OBJs-Shadows-Picking-v2.zip to the files
section. I fixed the shadow map size problem by constraining the size
to the lesser of the window's height and width. The self-shadowing is
also fixed.

As for the remaining 'problem' (antialiasing), I tried the hidden
window suggestion: all the shadow rendering took place in the hidden
window and then I just copied the resulting image to the main window.
I was able to get a nice looking result by making the hidden window a
decent size like 1024x1024, but the frame rate just wasn't acceptable
(about 13 fps). Perhaps my implementation was lacking, but I wonder if
it would be a better idea to use a frame buffer object instead.
Unfortunately, I don't know how to do that. My one attempt based on
some code from the internet resulted in a complete lockup of my Mac.
Since I am reasonably pleased with the results of my non-fbo code,
I've decided to move on.
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