By the way, I'd expect that with the grid screening in place, the speed of the comparison process would depend significantly on the threshold parameter. To my shame, I have to confess that I haven't tested this, but the number of vertices considered for distance calculation should be roughly proportional to the square of the threshold value. In other words, doubling the threshold should increase the time used for distance calculations by a factor of four. So one would try to  use the smallest threshold that seems safe.

-- I'm not mad at you, just Westphalian.