Top part (a) illustrates the three second derivatives of a function at the filled red point (i, j). The numbers in orange represent the components of the gradient, for the point (i, j). Bottom part shows the influence of the second derivative (using our four-term scheme) in the interpolation result: (b) with and (c) without, both interpolations using the same initial data (value of +1/−1 at the black crosses). We see on (b) a very smooth result by the edge, whereas the corners are very far from the data in (c). The ruled surface displayed in (c) is a hyperboloïd.