I hope that someone can help me understand how to perform the following algorithm in Mathematica, I am taking as reference the next page reference page in your section planar version algorithm desire, the problem is that I still have no idea how to start, I hope someone is So kind to help me. I have tried several hours to implement something but without success. thank you very much for your help

  • $\begingroup$ Show us what you have tried so far; it may be a good starting point for a solution. $\endgroup$
    – MarcoB
    Jan 29, 2017 at 5:12
  • $\begingroup$ Raise or lowered by how much? $\endgroup$
    – Michael E2
    Jan 30, 2017 at 0:01

1 Answer 1


We can use this answer on math.SE to determine on which side of a line a point lies. Based on this formula, we have that the new gray level is given by

f[{{x1_, y1_}, {x2_, y2_}}][gl_, {x_, y_}] := gl + 0.1 Sign[(x - x1) (y2 - y1) - (y - y1) (x2 - x1)]

We can apply this to all pixels recursively in the following manner:

iterate[img_] := Module[{dimx, dimy, pts},
  {dimx, dimy} = ImageDimensions[img];
  pts = Transpose[{RandomInteger[dimx, 2], RandomInteger[dimy, 2]}];
  ImageApplyIndexed[f[pts], img]

img = ConstantImage[0.5, {300, 300}];
Nest[iterate, img, 50]

Mathematica graphics

Below is another test run with more iterations, and I also changed the constant 0.1 in front of Sign to 0.02. This constant determines how much each side is raised or lowered, and it has a big influence on the visual effect.

Nest[iterate, img, 100]

Mathematica graphics

I'm not sure how to prove correctness for this algorithm, so if anyone spots an error please tell me.

  • $\begingroup$ Your pts array is {{x,x},{y,y}} rather than {{x,y},{x,y}} like f is expecting. Maybe throw a Transpose in there so it will work when the image isn't square. $\endgroup$
    – wxffles
    Jan 30, 2017 at 0:52
  • $\begingroup$ @wxffles Good catch, thank you. $\endgroup$
    – C. E.
    Jan 30, 2017 at 1:21

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