User:Simplifier69/Chebyshev distance

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The Chebyshev distance is equal to the minimum number of moves a king needs to move from one place to another. Note that the king moves in all directions by just one tile.

Definition

The Chebyshev distance between two points both with (x, y) coordinates, is equal to the maximum distance in one axis.

$D_{\rm {Chebyshev}}:=\max(|x_{\rm {target}}-x_{\rm {position}}|,|y_{\rm {target}}-y_{\rm {position}}|)$

Comparison of Chebyshev, Euclidean and Manhattan distances for the hypotenuse of a 3-4-5 triangle on a chessboard