I struggled for awhile to get an elegant solution, saw the data tree conflict and finally gave up.
This is slow (7 secs.) but effective. There is a Data Dam (red group) with a two second delay to allow adjustments (blue group) to the length and angle of the white line which is perpendicular to the strips.
Those strips are organized to match the ‘Input Regions’ data tree.
issue_2020Dec19b.gh (45.4 KB)
P.S. Playing with the ‘Pitch’ and ‘Width’ sliders, I see this fails miserably in some cases.
P.P.S. I see on the DUPLICATE THREAD that you are considering “around 100,000 lines inside dozens of closed curves of various shapes”. This method is probably too slow for that.