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Subject:	Re: [geda-user] some more geometry module tweaks (sorry, wall of text)
From:	"Edward Hennessy (ehennes AT sbcglobal DOT net) [via geda-user AT delorie DOT com]" <geda-user AT delorie DOT com>
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Date:	Wed, 6 Jan 2016 20:17:05 -0800
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> On Jan 6, 2016, at 5:04 PM, Britton Kerin (britton DOT kerin AT gmail DOT com) [via geda-user AT delorie DOT com] <geda-user AT delorie DOT com> wrote:
> 
> 
> 
> On Wed, Jan 6, 2016 at 3:47 PM, John Doty <jpd AT noqsi DOT com> wrote:
> 
> On Jan 6, 2016, at 7:29 PM, Britton Kerin (britton DOT kerin AT gmail DOT com) [via geda-user AT delorie DOT com] <geda-user AT delorie DOT com> wrote:
> 
>> Yeah DJ hinted at this as well.  My knee-jerk reaction is to use an even winder type for the internal floating point representation.  Short of arbitrary precision there's no way to support arbitrary intermediate results, but if you can count bye ones all the way to a squared value that would seem to cover all the simple geometrical calculations we're interested in.  Things like hypot() help, but I admit I don't fully understand exactly how much.  They certainly keep the numbers smaller and thereby prevent overflow, but I don't fully understand the consequences for intermediate results outside the range where the float can represent all integers.
> 
> This particular calculation is numerically stable, even if written as sqrt(x*x+y*y). It can’t generally be perfect, but it’s not the kind of thing that sends numerical analysts into cold sweats.
> 
> Going through and auditing geometry.h for big things they're mostly in hypot() but there are a few others. 
> 
> Do you know about the sensitivity of these:
> 
>   http://mathworld.wolfram.com/Circle-LineIntersection.html
>   http://mathworld.wolfram.com/Circle-CircleIntersection.html
> 
> Britton

To make it easy, the circle could be converted to a polygon. The polygons work well with line sweep algorithms:

https://www.youtube.com/watch?v=dePDHVovJlE

Another great presentation for rectangle intersection:

https://www.youtube.com/watch?v=p9cChQlgx08

Here is the line intersection line sweep code inside libgeda:

http://git.geda-project.org/geda-gaf/tree/libgeda/src/m_hatch.c

If you need a bit more accuracy for geometric calculations, the problem can be translated to center around the origin, convert to double, then run the calculations, and then translate back to the original location, then back to integer.

Ed

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