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Groups > comp.lang.postscript > #3428

Re: Snipping the ears

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On Saturday, July 20, 2019 at 6:51:02 PM UTC-5, luser droog wrote:
> On Saturday, July 20, 2019 at 3:18:58 PM UTC-5, luser droog wrote:
> > After 27 posts in the other thread, I thought it'd be nice to
> > have a fresher start on the remaining issues with my code.
> > 
> > The task is to take the glyph of the number 9 using 'charpath',
> > then traverse the curves like a turtlw with a paintbrush hanging
> > out one arm's-length away. 
> > 
> > The tricky part would be dealing with the actual Bezier curves,
> > so I call 'flattenpath' first so I can work with just line 
> > segments. The 'setflat' operator can be used to control how
> > finely the curves are cut into line segments.
> > 
> > (Or maybe, the curves true secret path to the desired result??)
> > 
> > Anyway, to traverse the line segments I use a control structure
> > I cooked up, called 'fortuplem'. It works kind of like 'forall',
> > but it takes 2 parameters n and m. n is the step-value between
> > iterations, and m is the width of a slice of the array produce
> > using 'getinterval'. Calling with n=2 m=2 iterates over the
> > points in the line. Calling with n=2 m=4 iterates over 2 point
> > slices. So I can run through these 2 points slices, get a vector
> > between them, normalize, take the perpendicular vector, scale
> > by my "arm's length" and produce a new transformed point.
> > This just needs one special case for the wrap around the end
> > from the last point to the first.
> > 
> > 
> > So, this all *works* with the untidy caveat that it produces
> > "ears" when the input path has a tight bend in the curve.
> > 
> > Detecting and pruning these ears would make the output nicer
> > and more usable. A further nicety would be implementing miter
> > or bevel joins for the other side of the tight bends.
> > 
> > 
> > Any, here's the current state of the code, including the laborious
> > fixes for the 2 "hacks" described at the end of the last thread.
> > 
> 
> I've said this before, but I think I can detect the ears now.
> I take the vector out of each point, take the angle, take the
> diff between adjacent angles, then take the signs of that angular
> change.
> 
> If I've reasoned correctly, this gives me a chart of left turns vs.
> right turns for each point. Running it on the left hand offset curve
> (-n offsetpath) gives me this:
> 
[snip]> 
> And I see a lonely "1* -1 1*" in the first curve, and a "-1* 1 -1*" in the second,
> which makes sense considering that the two curves are deliberately described
> in differing orientations to take advantage of the even/odd rule. 
> 
> Running it one the right hand curve (+n offsetpath) gives me this:
> 
[snip]> 
> Which shows no ears on the inner curve, but several spots of weirdness in
> the outer curve. There's an interesting "-1* 1 1 1 -1*" which looks like the
> bunched up points on the foot the '9'. 
> 
> And two little wiggles "1* -1 1 -1 1 -1*" and "1* -1 1 -1*" which I don't
> know what those are. 
> 
> So, now to try actually snipping. I'll tackly the simple ones first I think.
> "-1* 1 -1*" and "1* -1 1*" patterns. I think I need the incoming and outgoing vectors and then take their intersection as they approach their
> points.
> 
> I'm not sure what to do with the fat ear and the ripples.

Sigh. It's turning into the same rats' nest as before. So, let's start over.
This fresh program does not do any offsetting yet. It also preserves curves.
Just dumping the numbers for now to get a sense of what's going on in there.
A few 'linetos' here and there but lots of 'curvetos' (the 6 element subarrays).

So, the question changes. Can we detect sharp turns in the curveto operands?
And then do something sensible to produce an offset for that portion?
Wikipedia has some info: https://en.wikipedia.org/wiki/Parallel_curve

$ cat stroke3.ps
%!


/args-begin { dup length dict begin { exch def } forall } def
/map { [ 3 1 roll forall ] } def
/spill { aload pop } def
/head { 0 exch getinterval } def
/tail { 1 index length 1 index sub getinterval } def
/last { 1 index length 1 index sub exch getinterval } def
/droplast { 1 index length exch sub 0 exch getinterval } def
/fortuplem {
  {p m n a} args-begin
    0 n /a load length m sub
    [ /a load /exch cvx m /getinterval cvx /p load /exec cvx ] cvx
  end for
} def

/p-p { exch 3 1 roll sub 3 1 roll sub exch } def
/p+v { exch 3 1 roll add 3 1 roll add exch } def
/v*n { 3 2 roll 1 index mul 3 1 roll mul } def
/perp { neg exch } def
/mag { dup mul exch dup mul exch add sqrt } def
/norm { 2 copy mag 1 exch div v*n } def
/ang { exch atan } def
/aa { array astore } def

/closedsubpaths { [ {[ 3 1 roll 2 aa} {2 aa} {6 aa} {]} pathforall ] {{]}stopped{exit}if}loop } def

/drawpath {
  {
    dup length 1 eq { spill spill moveto }{
      dup 1 head spill spill moveto
      1 tail  { dup length 2 eq { spill lineto }{ spill curveto } ifelse } forall
      closepath
    } ifelse
  } forall
} def

/offsetbyvectors {
  /n exch def
  {
    dup length 2 ne {
      offsetsubpath
    } if
  } map
} def


/offsetpath {
  closedsubpaths exch
  pop dup ==%offsetbyvectors
  newpath
  drawpath
} def

/Calibri-Bold 600 selectfont
100 100 moveto (9) true charpath
gsave stroke grestore
gsave
  20 setlinewidth strokepath
  1 setlinewidth
  %stroke
grestore

1 0 0 setrgbcolor
gsave
  10 offsetpath
  stroke
grestore
-10 offsetpath
stroke

showpage quit


Output:
$ gsnd -q stroke3.ps
[[[380.375 306.421875] [380.25 290.875 379.59375 275.078125 378.03125 258.609375] [376.457031 241.9375 373.492188 226.007813 369.109375 210.21875] [364.695313 194.351563 358.691406 179.414063 350.984375 165.1875] [342.957031 150.90625 333.347656 138.546875 321.171875 127.921875] [308.9375 116.988281 294.179688 108.863281 276.734375 102.625] [259.039063 96.1875 238.675781 93.28125 214.90625 93.28125] [206.21875 93.1875 198.1875 93.8671875 189.90625 95.03125] [181.320313 96.1875 174.066406 97.6640625 167.234375 99.421875] [160.332031 101.03125 154.613281 103.019531 149.84375 104.96875] [144.789063 106.59375 141.613281 108.910156 139.46875 110.953125] [137.164063 112.6875 135.765625 115.976563 134.796875 119.875] [133.5625 123.488281 133.34375 129.238281 133.34375 136.25] [133.226563 142.601563 133.484375 147.851563 133.765625 151.75] [133.800781 155.394531 134.640625 158.660156 135.515625 160.796875] [136.226563 162.675781 137.472656 164.359375 138.734375 165.046875] [139.757813 165.71875 141.515625 166.078125 143.265625 166.078125] [145.519531 166.050781 148.921875 165.394531 153.203125 164.03125] [157.425781 162.65625 162.707031 161.101563 168.84375 159.34375] [174.707031 157.476563 181.957031 156.035156 189.75 154.671875] [197.289063 153.082031 206.21875 152.625 215.78125 152.625] [231.882813 152.414063 245.976563 155.546875 257.28125 161.390625] [268.5 167.113281 277.753906 175.140625 284.765625 185.078125] [291.53125 195.0 296.953125 206.523438 300.265625 219.578125] [303.5 232.4375 305.441406 246.375 305.828125 260.8125] [296.582031 254.882813 286.035156 250.226563 273.359375 246.03125] [260.570313 241.832031 246.175781 239.75 229.8125 239.75] [209.46875 239.5 192.679688 242.378906 178.640625 247.640625] [164.394531 252.6875 153.207031 260.5 144.4375 270.4375] [135.519531 280.238281 129.28125 292.472656 125.28125 306.703125] [121.195313 320.695313 119.296875 337.007813 119.296875 354.9375] [119.195313 373.53125 122.117188 391.238281 127.765625 407.125] [133.164063 422.96875 141.804688 436.75 152.921875 448.34375] [163.726563 459.820313 177.875 468.953125 194.4375 475.390625] [210.851563 481.695313 230.195313 485.046875 252.03125 485.046875] [269.5625 485.03125 284.921875 482.992188 298.078125 478.890625] [311.207031 474.5 322.535156 468.945313 331.984375 461.34375] [341.113281 453.632813 349.335938 444.546875 355.671875 433.734375] [361.78125 422.675781 366.972656 410.882813 370.578125 397.625] [373.988281 384.164063 376.710938 370.046875 378.171875 354.640625] [379.582031 339.03125 380.375 323.171875 380.375 306.421875]] [[304.078125 316.9375] [304.050781 337.476563 302.90625 355.234375 300.5625 369.265625] [298.039063 383.207031 294.722656 394.5 290.046875 402.875] [285.351563 410.96875 279.519531 417.207031 272.5 420.71875] [265.3125 423.988281 257.289063 425.984375 247.9375 425.984375] [238.457031 425.65625 230.875 424.375 224.25 421.15625] [217.539063 417.894531 212.117188 413.414063 207.734375 407.5625] [203.113281 401.53125 200.09375 394.796875 197.9375 386.796875] [195.476563 378.539063 194.71875 370.035156 194.71875 360.484375] [194.476563 350.0 195.644531 341.050781 197.5 333.15625] [199.1875 325.21875 202.273438 318.742188 206.265625 313.578125] [210.175781 308.21875 215.476563 304.5625 221.90625 302.03125] [228.039063 299.488281 236.144531 298.234375 245.3125 298.234375] [256.5 298.15625 267.269531 299.9375 277.3125 303.34375] [287.25 306.632813 296.273438 311.28125 304.078125 316.9375]] [[404.101563 100.0]]]
[[[380.375 306.421875] [380.25 290.875 379.59375 275.078125 378.03125 258.609375] [376.457031 241.9375 373.492188 226.007813 369.109375 210.21875] [364.695313 194.351563 358.691406 179.414063 350.984375 165.1875] [342.957031 150.90625 333.347656 138.546875 321.171875 127.921875] [308.9375 116.988281 294.179688 108.863281 276.734375 102.625] [259.039063 96.1875 238.675781 93.28125 214.90625 93.28125] [206.21875 93.1875 198.1875 93.8671875 189.90625 95.03125] [181.320313 96.1875 174.066406 97.6640625 167.234375 99.421875] [160.332031 101.03125 154.613281 103.019531 149.84375 104.96875] [144.789063 106.59375 141.613281 108.910156 139.46875 110.953125] [137.164063 112.6875 135.765625 115.976563 134.796875 119.875] [133.5625 123.488281 133.34375 129.238281 133.34375 136.25] [133.226563 142.601563 133.484375 147.851563 133.765625 151.75] [133.800781 155.394531 134.640625 158.660156 135.515625 160.796875] [136.226563 162.675781 137.472656 164.359375 138.734375 165.046875] [139.757813 165.71875 141.515625 166.078125 143.265625 166.078125] [145.519531 166.050781 148.921875 165.394531 153.203125 164.03125] [157.425781 162.65625 162.707031 161.101563 168.84375 159.34375] [174.707031 157.476563 181.957031 156.035156 189.75 154.671875] [197.289063 153.082031 206.21875 152.625 215.78125 152.625] [231.882813 152.414063 245.976563 155.546875 257.28125 161.390625] [268.5 167.113281 277.753906 175.140625 284.765625 185.078125] [291.53125 195.0 296.953125 206.523438 300.265625 219.578125] [303.5 232.4375 305.441406 246.375 305.828125 260.8125] [296.582031 254.882813 286.035156 250.226563 273.359375 246.03125] [260.570313 241.832031 246.175781 239.75 229.8125 239.75] [209.46875 239.5 192.679688 242.378906 178.640625 247.640625] [164.394531 252.6875 153.207031 260.5 144.4375 270.4375] [135.519531 280.238281 129.28125 292.472656 125.28125 306.703125] [121.195313 320.695313 119.296875 337.007813 119.296875 354.9375] [119.195313 373.53125 122.117188 391.238281 127.765625 407.125] [133.164063 422.96875 141.804688 436.75 152.921875 448.34375] [163.726563 459.820313 177.875 468.953125 194.4375 475.390625] [210.851563 481.695313 230.195313 485.046875 252.03125 485.046875] [269.5625 485.03125 284.921875 482.992188 298.078125 478.890625] [311.207031 474.5 322.535156 468.945313 331.984375 461.34375] [341.113281 453.632813 349.335938 444.546875 355.671875 433.734375] [361.78125 422.675781 366.972656 410.882813 370.578125 397.625] [373.988281 384.164063 376.710938 370.046875 378.171875 354.640625] [379.582031 339.03125 380.375 323.171875 380.375 306.421875]] [[304.078125 316.9375] [304.050781 337.476563 302.90625 355.234375 300.5625 369.265625] [298.039063 383.207031 294.722656 394.5 290.046875 402.875] [285.351563 410.96875 279.519531 417.207031 272.5 420.71875] [265.3125 423.988281 257.289063 425.984375 247.9375 425.984375] [238.457031 425.65625 230.875 424.375 224.25 421.15625] [217.539063 417.894531 212.117188 413.414063 207.734375 407.5625] [203.113281 401.53125 200.09375 394.796875 197.9375 386.796875] [195.476563 378.539063 194.71875 370.035156 194.71875 360.484375] [194.476563 350.0 195.644531 341.050781 197.5 333.15625] [199.1875 325.21875 202.273438 318.742188 206.265625 313.578125] [210.175781 308.21875 215.476563 304.5625 221.90625 302.03125] [228.039063 299.488281 236.144531 298.234375 245.3125 298.234375] [256.5 298.15625 267.269531 299.9375 277.3125 303.34375] [287.25 306.632813 296.273438 311.28125 304.078125 316.9375]] [[404.101563 100.0]]]

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Snipping the ears luser droog <luser.droog@gmail.com> - 2019-07-20 13:18 -0700
  Re: Snipping the ears luser droog <luser.droog@gmail.com> - 2019-07-20 16:51 -0700
    Re: Snipping the ears luser droog <luser.droog@gmail.com> - 2019-07-22 00:47 -0700
      Re: Snipping the ears luser droog <luser.droog@gmail.com> - 2019-07-24 00:38 -0700
        Re: Snipping the ears Mark Carroll <mtbc@bcs.org> - 2019-07-24 08:50 +0100
          Re: Snipping the ears luser droog <luser.droog@gmail.com> - 2019-07-29 23:18 -0700
            Re: Snipping the ears luser droog <luser.droog@gmail.com> - 2019-08-06 22:05 -0700
              Re: Snipping the ears luser droog <luser.droog@gmail.com> - 2019-08-08 00:22 -0700
                Re: Snipping the ears luser droog <luser.droog@gmail.com> - 2019-08-11 13:33 -0700
                Re: Snipping the ears luser droog <luser.droog@gmail.com> - 2019-08-13 16:03 -0700
                Re: Snipping the ears luser droog <luser.droog@gmail.com> - 2019-08-19 22:46 -0700
                Re: Snipping the ears luser droog <luser.droog@gmail.com> - 2019-08-21 23:44 -0700
  Re: Snipping the ears jdaw1 <jdawiseman@gmail.com> - 2019-10-10 15:07 -0700
    Re: Snipping the ears jdaw1 <jdawiseman@gmail.com> - 2019-10-10 15:09 -0700
    Re: Snipping the ears luser droog <luser.droog@gmail.com> - 2019-10-13 01:39 -0700
      Re: Snipping the ears luser droog <luser.droog@gmail.com> - 2019-10-13 01:51 -0700
        Re: Snipping the ears jdaw1 <jdawiseman@gmail.com> - 2020-06-04 03:15 -0700
          Re: Snipping the ears luser droog <luser.droog@gmail.com> - 2020-07-09 10:31 -0700
          Re: Snipping the ears jdaw1 <jdawiseman@gmail.com> - 2021-02-13 09:51 -0800

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