Surface

S_x

S_y

$i,j-1/2$

$y_{i+1,j}-y_{i,j}$

$x_{i,j}-x_{i+1,j}$

$i+1/2,j$

$y_{i+1,j+1}-y_{i+1,j}$

$x_{i+1,j}-x_{i+1,j+1}$

$i,j+1/2$

$y_{i,j+1}-y_{i+1,j+1}$

$x_{i+1,j+1}-x_{i,j+1}$

$i-1/2,j$

$y_{i,j}-y_{i,j+1}$

$x_{i,j+1}-x_{i,j}$