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measuring distance in grids
From: |
address@hidden |
Subject: |
measuring distance in grids |
Date: |
Fri, 11 Jan 2002 15:20:48 -0500 |
Paul,
Perhaps the grid position that includes the agent is not being used in the
calculations?
Consider a grid with an agent having a vision range of r. The diameter of the
circle of the agent's vision range might be 2r+1, since the agent can see in r
grid-units on all sides of the position in which it is located.
2r+1 = r units on the left, r units on the right, plus 1 unit for the agent's
current position.
Regards,
--Dave
----------
Dave Koelle
Founder, The BaseAgent Project
"Interactive software and robots for constructive learning and discovery"
http://www.baseagent.com
(In need of a Principle Investigator!)
-------- Original Message --------
Subject: measuring distance in grids
Date: Fri, 11 Jan 2002 13:44:52 -0600
From: Paul E Johnson <address@hidden>
Reply-To: address@hidden
To: address@hidden
I have a project where agents are in a grid and it is important to
measure distance. The authors of the original article I'm replicating
do not define a distance metric, but I originally assumed the distance
was Euclidean. That is, I guessed the distance between x=(x1,x2) and
y=(y1,y2) would be measured
dist = sqrt[ (x1-y1)*(x1-y1)+(x2-y2)*(x2-y2) ]
but I get some funny results using that, and I'm starting to wonder what
other metrics people might think are standard on a rectangular grid.
One I'm considering is "radial square" distance, where distance is the
radius of the square centered on a point that touches another point.
That means the distance from a cell to all immediate Moore neighbors is
1, and for the next larger neighborhood, the distance would be 2. See
what I mean? Here, the distance from the center point 0 to a neighbor
is:
3333333
3222223
3211123
3210123
3211123
3222223
3333333
Does anybody have an opinion?
--
Paul E. Johnson email: address@hidden
Dept. of Political Science http://lark.cc.ukans.edu/~pauljohn
University of Kansas Office: (785) 864-9086
Lawrence, Kansas 66045 FAX: (785) 864-5700
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