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Date:	Sun, 13 Sep 2015 20:05:42 -0800
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Subject:	Re: [geda-user] Apollon
From:	"Britton Kerin (britton DOT kerin AT gmail DOT com) [via geda-user AT delorie DOT com]" <geda-user AT delorie DOT com>
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On Sun, Sep 13, 2015 at 6:03 PM, John Doty <jpd AT noqsi DOT com> wrote:

>
> On Sep 13, 2015, at 7:38 PM, DJ Delorie <dj AT delorie DOT com> wrote:
>
> >
> > So... internally *every* value is a fraction?
>
> Yep.
>
> >  I imagine integer
> > overflow might be a non-trivial problem to solve.
>
> Not one you need to worry about in a language that supports rationals. I
> use rationals in Mathematica all the time: floating point is poison to
> complicated algebra. The techniques are well know and efficient, although
> not as efficient as floating point hardware.
>
> >
> > But if the whole point is to defer imprecise operations, what is the
> > advantage of this over just storing the angles as degrees and doing
> > the math on the fly?
>
> The problem is that you=E2=80=99ll accumulate error when you have both ro=
tations
> 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

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<div dir=3D"ltr"><br><div class=3D"gmail_extra"><br><div class=3D"gmail_quo=
te">On Sun, Sep 13, 2015 at 6:03 PM, John Doty <span dir=3D"ltr">&lt;<a hre=
f=3D"mailto:jpd AT noqsi DOT com" target=3D"_blank">jpd AT noqsi DOT com</a>&gt;</span> w=
rote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;borde=
r-left:1px #ccc solid;padding-left:1ex"><span class=3D""><br>
On Sep 13, 2015, at 7:38 PM, DJ Delorie &lt;<a href=3D"mailto:dj AT delorie DOT co=
m">dj AT delorie DOT com</a>&gt; wrote:<br>
<br>
&gt;<br>
&gt; So... internally *every* value is a fraction?<br>
<br>
</span>Yep.<br>
<span class=3D""><br>
&gt;=C2=A0 I imagine integer<br>
&gt; overflow might be a non-trivial problem to solve.<br>
<br>
</span>Not one you need to worry about in a language that supports rational=
s. I use rationals in Mathematica all the time: floating point is poison to=
 complicated algebra. The techniques are well know and efficient, although =
not as efficient as floating point hardware.<br>
<span class=3D""><br>
&gt;<br>
&gt; But if the whole point is to defer imprecise operations, what is the<b=
r>
&gt; advantage of this over just storing the angles as degrees and doing<br=
>
&gt; the math on the fly?<br>
<br>
</span>The problem is that you=E2=80=99ll accumulate error when you have bo=
th rotations and translations.<br></blockquote><div><br></div><div style=3D=
"">There&#39;s no dynamics modeling going on here, we&#39;re talking about =
interactive movements of parts.=C2=A0 So there&#39;s no error buildup and u=
sing rationals seems to address a non-problem.=C2=A0 If its disturbing to h=
ave 60 become 59.9999 after two rotations put angles in bins fine enough to=
 represent what you need.=C2=A0 If it&#39;s a problem if edges of a large p=
art might alias under different rotations, use angular bins small enough to=
 discriminate between adjacent cells at the far corner of your board. =C2=
=A01 1m board with um grid needs maybe 10M angular bins to make a slam dunk=
, not so many really =C2=A0</div><div>=C2=A0</div></div></div></div>

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