Rob Speer on 30 Jan 2002 21:08:21 -0000

```On Wed, Jan 30, 2002 at 12:46:54PM -0500, Eric Gerlach wrote:
> If a player is playing Football, instead of moving as specified in rule
> 301, e may move to any location within a circle of three units

In a non-continuous space like the Grid, you have to specify what you
mean by that, as "circles" don't actually exist.

. . . x . . .    @ = player's location
. o x x x o .    . = valid move only by chessboard metric
. x x x x x .    o = valid move by chessboard or Cartesian metric
x x x @ x x x    x = valid move by chessboard, Cartesian, or
. x x x x x .        Manhattan metric
. o x x x o .
. . . x . . .

You have to specify a "metric" for measuring distance.

The chessboard metric measures the number of moves a king would have to
make on a chessboard.

The Manhattan metric measures the number of moves one would have to make
if a move consists of going up, down, left, or right one square.

The Cartesian metric is where you pretend there is in fact a diagonal
line from the source to the destination, and measure it with the
Pythagorean formula.

So, you have to decide whether this 'circle' is a diamond, a lumpy
thing, or a square.

--
Rob Speer

```