Algorithm 4.

Loop Detection Algorithm

	thread:{l(0,1), l(1, 2), … l(N − 1, N)} ▷ N num projected line segments
	t:	▷ tool projection
1:	procedure loopDetection(thread, t)
2:	for i = 0 to N − 1 do
3:	for j = i+2 to N do
4:	e ← line-line-intersection(l(i, i + 1), l(j, j + 1))
5:	if (e ≠ null) then
6:	loopp ← e, i + 1, … j, e
7:	intersection pair ← l(i, i + 1), l(j, j + 1)
8:	if (point-polygon-Inclusion(t, loopp)) then
9:	record loopp, intersection pair
10:	i ← j+ 1
11:	break
12:	end if
13:	end if
14:	end for
15:	end for
16:	end procedure