Draw lines and detect the collisions

Hey there
I am looking to create a drawing component on a site. that should be straight forward.
the issue lies with the fact that I would want to detect any collisions say (4) and then attach MC’s to the collision points.

in a nut shell.

can I get a trace of the drawn path on the stage???

from there I guess I can detect any positional similarities?

not sure if anyone will understand this??

cheers