[hfuwqlxj] Selecting checkerboard squares by grain

Consider the task of selecting a square on a checkerboard, on a touchscreen interface using one's fat fingers.  (E.g., chess UI on a smartphone)  To select a black square, swipe horizontally between the two white squares to the left and right of the black square.  To select a white square, swipe vertically between the two black squares above and below the white square.

The UI can accurately distinguish between a horizontal and vertical swipe, which reduces the uncertainty by one half of which square was attempted to be selected, and a checkerboard pattern keeps the squares corresponding to different swipe directions far apart.

This could be extended to 4 different square types, with 4 different swipe directions and a 4 color "checkerboard" pattern.  Need some design that provides a visual aid about which direction to swipe.

Can it be extended to 8 different swipe directions (diagonals)?  Diagonals could be used just for the corners. Can it be extended to a hexagonal grid?  I think yes, though the patterns of which square (or hex) is which direction is less elegant.

It cannot be straightforwardly extended to higher dimensions.  In 3 dimensions, there are 6 different orthogonal swipe directions, but natural checkerboard-like unit cell contains 8 cubes.