It seems like you should be able to calculate it purely from the surrounding four points B,D,F,H. I am doing this right now, but it is not very smooth.
Calculate the x component of the normal:
nx#=0
nx#<0
nx#>0
Calculate the x component of the normal:
nx#=0
D
x
B F
x x
nx#<0
D
x F
B x
x
nx#>0
D
B x
x F
x