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> > The problem is that you’ll accumulate error when you have both rotations
> > and translations.
> >
> 
> There's no dynamics modeling going on here, we're talking about interactive
> movements of parts.  So there's no error buildup and using rationals seems
> to address a non-problem.  If its disturbing to have 60 become 59.9999
> after two rotations put angles in bins fine enough to represent what you
> need.  If it's a problem if edges of a large part might alias under
> different rotations, use angular bins small enough to discriminate between
> adjacent cells at the far corner of your board.  1 1m board with um grid
> needs maybe 10M angular bins to make a slam dunk, not so many really

I would try to avoid accumulate rotations and instead say it should be rotated 60 degrees.

A fine scaled grid seems reasonable and a similar approach often need to be used to compare float data values.