In the terms of my original post, the functions of lines B & D are different.
- Line B moves radially, to get the cutter clear of the threads. The thread in my example happened to consist of an integral number of full 360° turns, and the threading started & stopped at a 0° bearing from the center, so the B move was just a positive move in X. If the thread had ended with a fractional turn, the B move would have been less simple.
- Line D moves to get back to a common clear position (X0, Y0), away from the thread at 0°.
- If the thread didn't consist of an integral number of full turns, then before Line B the cutter could have been on the other side of the threads, so moving directly to (X0, Y0) couldn't be done safely.