straight line cuts the second layer is going to be a subdivision of those cuts we colored them gray here subdivision but now the important thing is that the cuts are going to be bent right they're going to be bent at the gray bond arees which are the boundaries defined by the first layer cuts and these by these bends you can actually compute bounds for example on the dihedral angles and and these bends are precisely two main continent to maintain continuity of the mapping from the input to the output of this operator if you didn't have these