The proof of the Knight distance formula by Das & Chatterji [Pattern Recog Lett 7,4 (1988) 215-226] is not as simple as certain math-funners seem to think it can be. But it is probably correct. They first established formula gave a "metric." This forces: formula gives a lower bound on true knight distance. Albeit they did not actually say that -- when it came time to actually prove this lower bound claim, then they just said "we can easily show" it, without saying how, then claiming details may be found on p.127 of A.Rosenfeld: Digital geometry, chapter 2 of "pictorial languages" Academic Pr 1979. Annoying, but I do not need Rosenfeld to tell me metricness plus validity at small distances forces lower bounding. So then we also need: formula really is metric, and gives upper bound. This they claim to establish by case arguments depending mod 2 and other stuff. They omit about 70% of the cases from the paper, hence do not actually fully prove it. I guess they expect the reader to fill in the missing cases.
participants (1)
-
Warren D Smith