octileDistanceTo

Octile (king-move with √2 diagonals) distance: the exact minimum cost from this cell to other on a uniform-cost Moore-movement grid with orthogonal cost 1 and diagonal cost √2. The natural admissible heuristic for A* on such a grid.

For a path with maxAxis - minAxis orthogonal steps and minAxis diagonal steps:

octile = (maxAxis - minAxis) * 1 + minAxis * √2