How does 'arc' work?

Newsgroups	comp.lang.postscript
Date	2013-11-20 23:23 -0800
Message-ID	<356283f9-d422-4515-8bd6-5ad0cf625f07@googlegroups.com> (permalink)
Subject	How does 'arc' work?
From	luser- -droog <mijoryx@yahoo.com>

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This may seem like a silly question to some. But how does 'arc'
construct curves to approximate the arc section?

I know you can make a full circle with 4 Bezier curves
whose control points are arranged on a square. (ASCII ART:

   * o *
 *       *
 o       o
 *       *
   * o *                                       )

So for smaller intervals, do you just trim-up this template?
Constructing as many full quadrants as necessary and smaller
pieces for the ends?

Say you want to do: (0,0) [45..180] r=1.
You want the -x,+y quadrant in full,

   * o
 *
 o 

But then, for the partial piece in +x,+y,
hm, I suppose you actually have to compute
the Bezier approximation, huh?

x = r cos t
y = r sin t
45 <= t <= 90

So the end points, of course, are

x = 1 cos 45 = sqrt 2
y = 1 sin 45 = sqrt 2

x = 1 cos 90 = 0
y = 1 sin 90 = 1

and the control points are
...

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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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