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Groups > comp.lang.postscript > #2537

Re: How does 'arc' work?

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I tried coming at it from a different angle. I re-read chapter 7
http://www.math.ubc.ca/~cass/graphics/manual/pdf/ch7.pdf
and tried to write the arc->Bezier as a general tool for
parametric curves. But when it finally mostly worked, the
tangent vectors are again the wrong lengths. So I visually
tweaked the constant so the first few iterations seem to match up.

$ cat bez.ps
%!

% a r g s [/a /r /g /s] n  .  -
/argsbegin {
    dict begin
    dup length 1 sub -1 0 {
        2 copy get
        4 3 roll def
        pop
    } for
    pop
} def

/2= {
    2 copy exch =only (,)print =
    gsave
        2 copy newpath
        currentlinewidth 3 mul 0 360 arc fill
    grestore
} def

% t0 t1 f g f' g' N  .  -  (creates path)
/piecewisebezier {
    {t0 t1 f g f' g' N} 16 argsbegin
    /h t1 t0 sub N div def
    (h=)print h =
    /h3 h 1.8 div def  % h 3 div  makes the vectors too short
    (h3=)print h3 =
    /t t0 def
    /updatexy {
        (t=)print t =
        /x  t f  def
        /y  t g  def
        /x' t f' h3 mul def
        /y' t g' h3 mul def
        %(x,y=)print x =only (,)print y =
    } def
    updatexy

    x y
    2=
    moveto  % (f(t0), g(t0))

    N {
        x x' add
        y y' add  % (f(t)+f'(t)*dt/3, g(t)+g'(t)*dt/3)
        2=

        /t t h add def
        updatexy
        x x' sub
        y y' sub  % (f(t+dt)-f'(t+dt)*dt/3, g(t+dt)-g'(t+dt)*dt/3)
        2=

        x y             % (f(t+dt), g(t+dt))
        2=

        curveto
        %lineto pop pop pop pop
    } repeat
    end
} def

300 400 translate
currentlinewidth
300 dup dup scale
div setlinewidth

0 1 {90 mul cos}{90 mul sin}{90 mul sin neg}{90 mul cos} 1 piecewisebezier stroke
2 1 3 {
    0 1 {90 mul cos}{90 mul sin}{90 mul sin neg}{90 mul cos} 7 6 roll piecewisebezier stroke
} for
showpage



coordinates:
h=1.0
h3=0.555556
t=0
1.0,0.0
1.0,0.555556
t=1.0
0.555556,1.0
0.0,1.0
h=0.5
h3=0.277778
t=0
1.0,0.0
1.0,0.277778
t=0.5
0.903525,0.510688
0.707107,0.707107
0.510688,0.903525
t=1.0
0.277778,1.0
0.0,1.0
h=0.333333
h3=0.185185
t=0
1.0,0.0
1.0,0.185185
t=0.333333
0.958618,0.339625
0.866025,0.5
0.773433,0.660375
t=0.666667
0.660375,0.773433
0.5,0.866025
0.339625,0.958618
t=1.0
0.185185,1.0
0.0,1.0

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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> - 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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