After seeing Petros Vrellis ( ) video I planned to implement it in Houdini.
This was my first project in which I tried to implement a specific idea, and also solve real problems with vex.
In this project, I have made portraits with a continuous string, which means that I can replicate those images with real cotton thread, over a circle canvas with pins on the edges.
The algorithm computes the optimal pin over which the thread draws the referenced image most accurately.
In the above video, the dark thread passes through places that in the reference image are white. So on the right, I have made a layer with the light area correction.
I have adjusted this algorithm to work on three-dimensional objects.
The right side has a white thread above the initial black thread, computed to fix the artifacts that are produced when the black thread slices the image from one end to another, from pin to pin. 
Building it from scratch allowed me to play with different values and get slightly different looks.

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