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Re: How does 'arc' work?

Newsgroups comp.lang.postscript
Date 2013-12-01 03:48 -0800
References <356283f9-d422-4515-8bd6-5ad0cf625f07@googlegroups.com> <a8c2ee20-a057-4055-8e35-cda59526aec7@googlegroups.com>
Message-ID <2bebfa0f-c416-44c3-aca4-2b0afbead55e@googlegroups.com> (permalink)
Subject Re: How does 'arc' work?
From luser- -droog <mijoryx@yahoo.com>

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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.
> 
> 
> 
> 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.

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Thread

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> - 2019-02-02 16:19 -0800
  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
      Re: How does 'arc' work? jdaw1 <jdawiseman@gmail.com> - 2016-04-01 15:28 -0700
        Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2016-04-02 21:35 -0700
          Re: How does 'arc' work? jdaw1 <jdawiseman@gmail.com> - 2016-04-03 13:54 -0700
            Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2016-04-18 21:40 -0700
              Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2016-04-19 15:04 -0700
                Re: How does 'arc' work? jdaw1 <jdawiseman@gmail.com> - 2016-04-20 02:06 -0700
                Re: How does 'arc' work? jdaw1 <jdawiseman@gmail.com> - 2016-04-20 05:18 -0700
                Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2016-04-22 00:40 -0700
                Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2016-04-22 11:32 -0700
                Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2016-04-23 20:49 -0700
                Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2016-04-23 22:46 -0700
                Re: How does 'arc' work? jdaw1 <jdawiseman@gmail.com> - 2016-04-24 04:01 -0700
                Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2016-04-30 21:47 -0700
                Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2016-05-01 02:59 -0700
        Re: How does 'arc' work? Scott Hemphill <hemphill@hemphills.net> - 2016-04-03 10:40 -0400
          Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2016-04-05 21:48 -0700
            Re: How does 'arc' work? Scott Hemphill <hemphill@hemphills.net> - 2016-04-06 10:37 -0400
            Re: How does 'arc' work? luser- -droog <mijoryx@yahoo.com> - 2016-04-07 23:59 -0700
            Re: How does 'arc' work? jdaw1 <jdawiseman@gmail.com> - 2016-04-19 02:54 -0700

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