Inkscape: Bend a vector along a circular arc

The following screenshot shows a vector with guides forming its horizontal and vertical limits:

How is it possible to bend the vector (along with a line – marked green in the image – which will serve as a reference) along a circular arc (of arbitrary radius)? Assuming the line is drawn along the mean of both the horizontal guides from edge to edge of the vector (i.e. with 145.07mm length in the screenshot).

The arc has the same length as the line, and after the transformation, every point in the reference line will lie along its corresponding point on the circular arc.

I understand this is a simple rectangular to polar transformation, but can't find a way to do it in Inkscape. I can get close results with "Bend path" effect, but close is not enough.

I am okay with using some other software (as long as it is FOSS and can do it without much effort).

Answer

Inkscape has path effect "Pattern Along Path" which can produce something resembling. It's not limited to circular arcs, the bending route can be arbitary. See an example:

1. 
   

   The original shape, must be a vector path, copied to clipboard for step 3

   
   


2. 
   

   The wanted bending route, must be a path, circles, rectangles etc. preset shapes must be converted to paths before use (Path/Object to Path)

   
   



3. 
   

   The curve in (2) has got path effect "Pattern Along Path" The pattern was taken from the clipboard

   
   


4. 
   

   The color was lost, but normal coloring works. A red fill was selected.