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Saving window contents in off-screen bitmaps

I need to transfer the contents of a window to an offscreen bitmap
when the window is deactivated and to restore the window's contents
from the offscreen bitmap when it is activated.  I'm taking this
approach because it is too expensive to regenerate the window's
contents from scratch (these windows are graphs which may contain
thousands of points and I don't want to save all of those points just
so I can redraw the window).  Can anyone tell me how to do this?  I
thought that it would be straightforward using the window's portBits
and portRect fields, the MAKE-BITMAP function, and the COPY-BITS
function, but I must be doing something wrong since I can't seem to
get this to work.

Any help would be greatly appreciated.

Randall D. Beer
Dept. of Computer Engineering and Science
Dept. of Biology
Case Western Reserve University