The square can be a place to move in. Take note, the Cartesian coordinate system won't be used here. Video game developers and cartographers will likely use that, but not this. Usually, there are eight basic movement directions in a 2 dimensional plane: up, down, left, right, up-left, up-right, down-right, and down-left.
Before moving, one must know one's current position. All is discrete so "nothing in between" two cells.
A position is within a confine of a cell. A position index is a non-zero positive integer and limited by the square size.
1 <= p <= S
where p is the position and S is the square size
To move horizontally is move along a row just as vertical movements to a column.
To move to the left.
np_l(s) = p + s
where p is the current position and s is the number is steps to the left. np means new position.
To move to the right.
np_r(s) = p - s
where p is the current position and s is the number is steps to the right. np means new position.
np_u(s) = p + s*b
where p is the current position, is the base, and s is the number is steps to the top. np means new position.
np_d(s) = p - s*b
where p is the current position, is the base, and s is the number is steps to the bottom. np means new position.
These are special movements that do not go along neither rows or columns.
To move up-left
np_ul(s) = p - s*(b+1)
where p is the current position, is the base, and s is the number is steps to the top-left. np means new position.
To move up-right
np_ur(s) = p - s*(b-1)
where p is the current position, is the base, and s is the number is steps to the top-right. np means new position.
To move down-left
np_dl(s) = p + s*(b-1)
where p is the current position, is the base, and s is the number is steps to the bottom-left. np means new position.
To move down-right
np_dr(s) = p + s*(b+1)
where p is the current position, is the base, and s is the number is steps to the bottom-right. np means new position.
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