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Subject:	Re: [geda-user] Re: some more geometry module tweaks (sorry, wall of text)
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From:	John Doty <jpd AT noqsi DOT com>
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Date:	Wed, 6 Jan 2016 07:00:54 -0500
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On Jan 5, 2016, at 11:53 PM, gedau AT igor2 DOT repo DOT hu wrote:

>=20
>=20
> On Tue, 5 Jan 2016, Britton Kerin (britton DOT kerin AT gmail DOT com) [via =
geda-user AT delorie DOT com] wrote:
>=20
>>=20
>> Igor and I have been discussing pcb geometry kernel design, I'm ccing =
the
>> list in case anyone has strong opinions.
>>=20
>> [snip]
>>=20
>>     Question is: should a big geometry refactoring fix old bugs or
>>     questionalbe numeric conversions or just do the same thing with
>>     different code org?
>>=20
>>     For all the time, I assumed the first.
>>=20
>>=20
>> I agree, but we may have different ideas of what the fix would be.  =
If you
>> want to stop using floating point entirely, it's a huge effort, and =
ints
>> won't do what you want either, you need rationals.  If by fix you =
mean
>=20
> Although later part of the mail had a list like this, that doesn't =
include rationals so I'll repeat it for those who didn't have the chance =
to follow our conversation. The options I currently see:
>=20
> 1. go for maximal precision, be theoretically/mathematically correct =
in all situations, no rounding ever: rationals.

There=92s a catch, though. You can have rational translations or =
rational rotations, but not both. If you base your allowed rotations on =
the angles in triangles whose sides are Pythagorean triples you can =
represent them with rational rotation matrices. However, neat rational =
fractions of a right angle don=92t have associated Pythagorean triples =
(Euclid famously showed this for 45 degrees).

I might try the Pythagorean route if I was doing this, but maybe more =
because it looks interesting rather than for practicality.

John Doty              Noqsi Aerospace, Ltd.
http://www.noqsi.com/
jpd AT noqsi DOT com



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