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Re: a smooth curve through given points ?

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On 2016-08-13, Peter Billam <peter@www.pjb.com.au> wrote:
> OK, I'll give it a go (don't hold your breaths, though).  I'm not
> really motivated by plotting smooth graphs, but by drawing curves
> for arty stuff, like http://www.pjb.com.au/art/posters/index.html
> It should also make it easy to copy a smooth curve from a .jpg or
> .png, because you just note the pixel-positions at a few places
> along the curve and let the algorithm do the rest. If it's not
> right yet, you insert an extra pixel-position into your list...

I have a prototype: it can either be called by
  [x1 y1 x2 y2 ... xN yN] points2curve stroke
in which case is makes up its own starting and ending angles,
or by
  [x1 y1 ... xN yN] initialangle finalangle points2curve stroke
if you need to fix the launch- and landing- angles, which you do
eg: for drawing smooth closed curves that join up smoothly.
The plan is to roll it into
  http://www.pjb.com.au/comp/line_drawing.html
which needs a bit of revision anyway...

/xmax currentpagedevice (PageSize) get 0 get def
/ymax currentpagedevice (PageSize) get 1 get def

/points2curve {  % [x1 y1 ... xN yN] initial_angle final_angle points2curve
  % http://stackoverflow.com/questions/7715788/find-bezier-control-points-for-curve-passing-through-n-points
  % http://www.math.ucla.edu/~baker/149.1.02w/handouts/dd_splines.pdf
  % https://corner.squareup.com/2012/07/smoother-signatures.html
  25 dict begin
  /a_top exch def
  a_top type (arraytype) eq { /points a_top def
  } { /final_angle a_top def  /initial_angle exch def /points exch def
  } ifelse
  /p_0_x points 0 get def
  /p_0_y points 1 get def
  p_0_x p_0_y moveto
  /initial_angle where { pop /subangle_m1 initial_angle def } if
  /p_im1_x p_0_x def  /p_im1_y p_0_y def
  2 2 points length 4 sub { /i exch def
    points i       get /p_i_x   exch def
    points i 1 add get /p_i_y   exch def
    points i 2 add get /p_ip1_x exch def
    points i 3 add get /p_ip1_y exch def
    /angle_before  p_i_y p_im1_y sub p_i_x p_im1_x sub atan def
    /angle_after   p_ip1_y p_i_y sub p_ip1_x p_i_x sub atan def
	angle_before 180 gt { /angle_before angle_before 360 sub def } if
	angle_after  180 gt { /angle_after  angle_after  360 sub def } if
    /angle_tangent angle_before angle_after add .5 mul def
    /dist_before
      p_i_y p_im1_y sub dup mul  p_i_x p_im1_x sub dup mul add sqrt def
    /dist_after
      p_i_y p_ip1_y sub dup mul  p_i_x p_ip1_x sub dup mul add sqrt def
    /subangle_m1 where { pop } { /subangle_m1 angle_before def } ifelse
    p_im1_x  subangle_m1 cos dist_before mul 0.40 mul add
    p_im1_y  subangle_m1 sin dist_before mul 0.40 mul add
    p_i_x  angle_tangent cos dist_before mul 0.40 mul sub
    p_i_y  angle_tangent sin dist_before mul 0.40 mul sub
    p_i_x p_i_y curveto
    /p_im1_x p_i_x def  /p_im1_y p_i_y def
    /subangle_m1 angle_tangent def
  } for
  /final_angle where { pop } { /final_angle subangle_m1 def } ifelse
  p_i_x   subangle_m1 cos dist_before mul 0.40 mul add
  p_i_y   subangle_m1 sin dist_before mul 0.40 mul add
  p_ip1_x final_angle cos dist_before mul 0.40 mul sub
  p_ip1_y final_angle sin dist_before mul 0.40 mul sub
  p_ip1_x p_ip1_y curveto   % last point
  end
} def
xmax .002 mul setlinewidth
[ 220 50 100 100 100 200 200 250 300 210 320 100 220 50 ] 170 170
points2curve stroke
[ 400 50 380 100 430 200 360 300 450 400 380 500 410 600 400 700 ] 120 90
points2curve stroke
showpage

Regards,  Peter

-- 

Peter Billam    www.pjb.com.au    www.pjb.com.au/comp/contact.html

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a smooth curve through given points ? Peter Billam <peter@www.pjb.com.au> - 2016-08-12 08:10 +0000
  Re: a smooth curve through given points ? Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-08-12 01:12 -0700
  Re: a smooth curve through given points ? tlvp <mPiOsUcB.EtLlLvEp@att.net> - 2016-08-12 21:59 -0400
    Re: a smooth curve through given points ? tlvp <mPiOsUcB.EtLlLvEp@att.net> - 2016-08-13 22:42 -0400
  Re: a smooth curve through given points ? luser droog <luser.droog@gmail.com> - 2016-08-12 21:49 -0700
    Re: a smooth curve through given points ? Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-08-12 21:59 -0700
      Re: a smooth curve through given points ? luser droog <luser.droog@gmail.com> - 2016-08-12 22:21 -0700
      Re: a smooth curve through given points ? luser droog <luser.droog@gmail.com> - 2016-08-18 15:01 -0700
        Re: a smooth curve through given points ? luser droog <luser.droog@gmail.com> - 2016-08-19 13:10 -0700
          Re: a smooth curve through given points ? luser droog <luser.droog@gmail.com> - 2016-08-19 13:13 -0700
    Re: a smooth curve through given points ? luser droog <luser.droog@gmail.com> - 2016-08-12 22:00 -0700
    Re: a smooth curve through given points ? Peter Billam <peter@www.pjb.com.au> - 2016-08-13 09:44 +0000
      Re: a smooth curve through given points ? Peter Billam <peter@www.pjb.com.au> - 2016-08-15 01:00 +0000
        Re: a smooth curve through given points ? John Forkosh <forkosh@panix.com> - 2016-08-15 03:08 +0000
          Re: a smooth curve through given points ? Peter Billam <peter@www.pjb.com.au> - 2016-08-15 09:36 +0000
            Re: a smooth curve through given points ? JohnF <john@please.see.sig.for.email.com> - 2016-08-16 01:28 +0000
              Re: a smooth curve through given points ? Peter Billam <peter@www.pjb.com.au> - 2016-08-16 23:32 +0000
                Re: a smooth curve through given points ? tlvp <mPiOsUcB.EtLlLvEp@att.net> - 2016-08-17 01:07 -0400
    Re: a smooth curve through given points ? JohnF <john@please.see.sig.for.email.com> - 2016-08-14 06:17 +0000
  Re: a smooth curve through given points ? jdaw1 <jdawiseman@gmail.com> - 2016-08-16 03:14 -0700
  Re: a smooth curve through given points ? Alan <alan.isaac@gmail.com> - 2016-08-18 14:42 -0700
    Re: a smooth curve through given points ? luser droog <luser.droog@gmail.com> - 2016-08-18 15:19 -0700
      Re: a smooth curve through given points ? Alan <alan.isaac@gmail.com> - 2016-08-18 18:52 -0700
        Re: a smooth curve through given points ? luser droog <luser.droog@gmail.com> - 2016-08-18 21:47 -0700
          Re: a smooth curve through given points ? Alan <alan.isaac@gmail.com> - 2016-08-19 06:01 -0700
            Re: a smooth curve through given points ? luser droog <luser.droog@gmail.com> - 2016-08-19 14:06 -0700
  Re: a smooth curve through given points ? luser droog <luser.droog@gmail.com> - 2016-11-03 22:03 -0700
    Re: a smooth curve through given points ? JohnF <john@please.see.sig.for.email.com> - 2016-11-05 05:19 +0000
    Re: a smooth curve through given points ? don lancaster <don@tinaja.com> - 2016-11-05 10:12 -0700

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