How to generate G-codes with C axis tangent to XY

Hello everyone,

I have a picture like this:

In the middle of the picture, gray area is a fur, and there are cutting lines on it as you can see.
I want to generate G-codes for the cutting lines. ( either directly from the coordinates of the cutting lines, or "directly" from this picture) with C axis tangent to the cutting lines .

but I don't know how to do it.

I received some suggestions by using gcodetools and inkscape and I did experiments with the picture using inkscape, but I get crashes and errors.

could someone teach me how to do it, or teach me another solution?