gistfile1.txt

to find the linearly interpolated value of (x + 0.4, y + 0.7) 
given the values at (x, y), (x, y+1), (x+1, y), and (x+1, y+1)

let x1 = val(x, y) * 0.4 + (val(x, y+1) * 0.6)
let x2 = val(x+1, y) * 0.4 + (val(x+1, y+1) * 0.6)

the final value is (x1 * 0.7 + (x2 * 0.3))


generalized:

to find the linearly interpolated value of (x + dX, y + dY) 
given the values at (x, y), (x, y+1), (x+1, y), and (x+1, y+1)

let x1 = val(x, y) * dX + (val(x, y+1) * (1-dX))
let x2 = val(x+1, y) * dX + (val(x+1, y+1) * (1-dX))

the final value is (x1 * dY + (x2 * (1-dY)))