Thank you guys for your words.
@Coder - of course it's possible, but that tiny gap is a troublemaker.
Inside this gap can be one, multiple, or no vertex. Or you can pick exactly the start/end of a closed polyline.
Each of these, and maybe more, need to be solved separately and I don't have time right now.
Sorry.
P.S. In case I'd find the time, can you please clarify the multiple polylines thing?
Do you want to pick each point on each polyline?
Or do you want these circles at a specific distance between them?
Or maybe the number of circles etc.