Yes I can but when you have 20 sections it's not the same ;)
And I don't know where is the middle of the path ;)

So maybe a possible way
The only thing is exist a very very little glitch

In one word: centers of the rectangle & Polygon are not
the extremity of the path after the automatic sweep!

Perfect except the very little problem at the extemities!
(visible as bold lines on end "rectangle' & "polygon")