To my mind, it becomes useful when the distances are much larger,
when thresholded with an exclusive odd-number upper limit it
generates dodecagons,
which pleasingly approximate circles.
Arthur
On Jun 18, 2010, at 12:53 PM, Petr Baudis wrote:
On Fri, Jun 18, 2010 at 08:45:14PM +0900, Darren Cook wrote:
distance=C.(dx+dy+max(dx,dy))
I'm calling this "the gridcular metric", ...
...
Most programs relying on gamma-pattern combinations are probably
using
this; at least Pachi is for sure, CrazyStone and others
apparently too.
Why is it good in those algorithms?
Simple manhatten distance:
X 1 2 3 4
1 2 3 4
2 3 4
3 4
4
Adding in the max(dx,dy):
X 2 4 6 8
2 3 5 7
4 5 6
6 7
8
I.e. it makes the diagonal directions more important, compared to
moves
in a straight line.
I try to make that apparent in the presentation, and maybe also in the
name I use - it creates circle-like structures on the square grid. In
other words, increments in gridcular metric approximate increments in
the classical Euclidean metric. At the same time, the increments
provide
quite fine granularity in the area covered, which is also useful in
the
usual application - matching of variable-sized patterns.
--
Petr "Pasky" Baudis
The true meaning of life is to plant a tree under whose shade
you will never sit.
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