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A cut-off always runs away from its fixed edge: the origin side, the only edge guaranteed to be a real sheet edge. The part order is proposed as a traveling-salesman path over one point per placement, and a cut-off's point was the middle of its line. The route did not know the tool must arrive at the line's start and leaves at its far end, so the parts before a sheet-splitting line finished level with its middle, and the rapid down to its start crossed parts already cut. Each placement now has an entry and an exit point; they differ only for cut-offs (start and departure). Nearest neighbor and Or-opt go on from each part's exit, and 2-opt costs a reversed run along its own directed legs; with no cut-off on the plate the exits are not passed and the symmetric route is unchanged. The part cut before a cut-off faces its start. Cut-off direction is not chosen here: the order reads each cut-off's start and end from its program as given, and the joint search may still reverse a head-locked far-edge segment.