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Re: How does 'arc' work?

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On Sunday, December 1, 2013 5:48:50 AM UTC-6, luser- -droog wrote:
> On Saturday, November 23, 2013 5:06:27 PM UTC-6, jdaw1 wrote:
> 
> > For a quarter circle of unit radius, PostScript has the internal control points at (0,0.552) and (0.552,0). The number is likely to be an approximation to (√957 - 21)÷18 ≈ 0.55196759, which minimises ∫(r²–1)² wrt angle for a 90° cubic Bézier.
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> > 
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> > 
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> > 
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> > 0.552 has the radius too large by a factor of 1 +0.000212 at 17.39° and 90–this, and too small by a factor of 1 –0.000151 at 45°. So the radius is correct to one part in at least ≈4714. At 1200 d.p.i., that’s correct to within a pixel for a diameters ≤ 7.857″ ≈ 19.96 cm.
> 
> 
> 
> Ok. Thank you. That's very useful. I suppose for the remaining 
> 
> segments I can find the points by an application of deCasteljau, 
> 
> splitting until the desired angle and then discarding half of the 
> 
> list. Might not be terribly efficient. But this is pass 1: 
> 
> make it work.

I have found quite a few pdfs online that go into excruciating 
detail. But I haven't read them enough times to really 
understand it all yet. :)

-
sleepy

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How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2013-11-20 23:23 -0800
  Re: How does 'arc' work? bugbear <bugbear@trim_papermule.co.uk_trim> - 2013-11-21 14:05 +0000
    Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2013-12-01 04:03 -0800
  Re: How does 'arc' work? jdaw1 <jdawiseman@gmail.com> - 2013-11-23 15:06 -0800
    Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2013-12-01 03:48 -0800
      Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2013-12-01 03:58 -0800
        Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2013-12-10 23:02 -0800
          Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2013-12-11 00:17 -0800
            Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2013-12-11 00:20 -0800
              Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2013-12-11 01:37 -0800
              Re: How does 'arc' work? tlvp <mPiOsUcB.EtLlLvEp@att.net> - 2014-02-28 03:47 -0500
                Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2014-03-01 00:30 -0800
          Re: How does 'arc' work? jdaw1 <jdawiseman@gmail.com> - 2014-04-29 13:10 -0700
  Re: How does 'arc' work? jdaw1 <jdawiseman@gmail.com> - 2014-05-02 06:29 -0700
    Re: How does 'arc' work? jdaw1 <jdawiseman@gmail.com> - 2014-05-08 02:21 -0700

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