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Date: Sun, 13 Sep 2015 17:48:59 -0400
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From: DJ Delorie <dj AT delorie DOT com>
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	John Doty on Sun, 13 Sep 2015 15:00:26 -0600)
Subject: Re: [geda-user] Apollon
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> Yes. But that's more of a problem with floating point.

"60" isn't floating point, though.  Angles are convenient numbers to
use, it's the result of using those angles that gets messy.  Using a
vector for angles means that pretty much *every* angle becomes a
floating point problem, because the actual angle will always be some
epsilon away from what the user intended.

> What you really want in the Cartesian representation is sines and
> cosines, but sin( 60 degrees ) is irrational, not representable in
> floating point.

That's what I said.  Most rational angles cannot be represented as a
rational vector.

Also, most rational vectors do not have a rational magnitude.

> Perfect undo is easy. Angles are represented by pairs of integers,
> with no roundoff error within that closed system. You only
> accumulate error with respect to your external expectations going
> forward. But how many layers of rotation do you typically have in a
> practical design? Maybe three, four? Within the system, all
> calculations are exact.

I bring it up only because it's been an issue before, before the
nanometers switch.  Rotating by X then -X did not result in the
original.

I'm also now thinking "select all elements rotated by 60 degrees" is
going to be an imprecise operation (not that we had it *at all*
before now).

We also have to be careful that "rotate left 60" is the same as
"rotate right -60".  Hmmm... the vector needs to be normalized (a unit
vector), so an angle like "123/456" would have to include a scale,
which would either be itself irrational (square roots) or introduce
yet another epsilon.  Which means undoing a rotation might not be
exact.

Perhaps the only way to avoid problems with sin/cos is to avoid using
them at all - you always store the relationships between parts and
subparts as a translation and a rotation, so the rotation (in degrees
or whatever) can be retained as-is, rather than the result of using
that rotation.