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I want to get the right part of the following images from the left part:(Note:the left images generated from Wolfram Mathematica 11.3)

enter image description here

enter image description here

Note that I do not want to create images like on the left.

The left paths are made from circles without center point likes this:

enter image description here

The file’s format is PDF or SVG. I can use the Adobe illustrator or Inkscape.

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Seriously: No automatic tracing can extract the one and only right path under your dot chain. That's because the tracing should know the mathematical criteria for the right path. You may know it but I can only make a guess. Especially ambiquous for automatic methods are the crossings. There's zero information of should it be X or ><. Another difficulty is a gap - there's a wide one in the bottom.

I suggest manual drawing with the pen in Inkscape:

enter image description here

In the left the original pattern is locked to keep it intact. The pen is used by clicking only. There's clicks in the starting point, in the midpoint of every straight dot subchain and in the endpoint.

In the right the generated polyline is selected and Path > Simplify (=Ctrl+L) is applied a few times until the result seemed to be smooth enough.

  • Thank you. The right path in the question was got through clicking some key points of vector image in Illustrator. Because, in practice, there exists a lot of vector image similar to the example to be dealt with, I only want to find an easy method. – likelee Aug 10 at 2:57
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I think this would be easier to draw manually with the Pen tool in Illustrator, or the Bézier tool in Inkscape. At least that way you can get a nice smooth curve. There's nothing automated that will beat the human eye, and a little skill.

All you need is a some practice. If you have a lot of these to do, then you'll get better each time.

enter image description here

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That's a tricky one. I'd know more how to align objects on a path in After Effect then Illustrator. The only thing I can think of would be to create a pattern. Window > Pattern Options.

I'd then select the pathern I'd wish to make, such as a red circle and select Make Pattern in the top right hamburger menu:

enter image description here

You could play with the settings on the Pattern Options and perhaps there are some that'll make it align the path. When your satisfied with the settings, save the pattern and it'll go to your Swatches.

Make an illustration and asign the new patter to your illustration:

enter image description here

I don't have too much time to test out and recreate exactly what you wish to achieve, but I wish this gives you a good path!

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    Thanks, However, I only want to get the path curve that through almost objects, not the patterned image. Can you show how to get the special path curve? – likelee Aug 9 at 13:43
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In Inkscape I would try this:

Edit: I blurred, sharpened, enlarged contrast, then turned it to black and white in Gimp. Then I scaled it down a lot.

In the end, I got:

enter image description here

  • Thank you, After several times trying, I find it generated too many disorder curves along the path that should be only one spline. Can you show how to get only one center-line trace? – likelee Aug 10 at 2:50
  • I've updated my post. Doesn't look so bad. – Moini Aug 11 at 14:38

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