Hei Doug,
not sure if this hint helps since Martin wrote that your coverage seems
to have overlaps.
However, I just recently added to OpenJUMP source code a function to
simplify polygonal tesseleations: see Tools/Generalization/Simplify
Polygon Coverage
It does more or less what Martin describes: extracting the common edges,
simplify those, and polygonize them again.
Unfortunately we have a problem with the nightly built of OpenJUMP .. so
you need to pull the last code via SVN.
I hope this helps a bit
stefan
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