Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > comp.lang.postscript > #2774

Re: a smooth curve through given points ?

Show key headers only | View raw

Peter Billam <peter@www.pjb.com.au> wrote:
> 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...

Peter's code reproduced without leading "> "s
reproduced below

%% ---- cut here ----
/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
%% ---- cut here ----

> 
> Regards,  Peter

Very nice. I tested it with various other x,y1...x,yn's,
and it seems to behave pretty nicely for the stuff I tested.
Like you, I put together some ps for "arty stuff" (your words
above), and you might find some of that useful. See
  http://www.forkosh.com/images/decorative/decorative13.jpg
for an example. Same_directory/decorative13.ps has all the ps.
And note %comments crediting Gernot Hoffmann -- I don't
know ps well enough to have done it myself (but I did write
the C program that generates the data).
-- 
John Forkosh  ( mailto:  j@f.com  where j=john and f=forkosh )

Back to comp.lang.postscript | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread

Thread

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

csiph-web