< If so then you don't need to do that - just draw a polyline and use "End" object snap to snap each polyline point to the end of those segments, if you already have things split into parts you can use end snap for that rather than creating any points.

It's a very hard work when you have many points! (conceptual of course)
It's because I had make the trimming above (ellipse trimmed by vertical lines) ;)

It's not a polyline but some separated arc lines
But "end" and "start" points of these arcs can't be visible separated from the control points !

PS These points can be used for drawing something and must be separated from control points