Bicubic interpolation

Summary

Bicubic interpolation builds a smooth surface over a rectangular grid from values and derivatives at the grid points. On each cell it uses a polynomial $\sum_{i,j=0}^{3} a_{ij} x^i y^j$, fixed by the values, the two first partial derivatives and the mixed derivative at the four corners. The patches join with continuous first derivatives, giving smoother results than bilinear interpolation, which is why it is common in image resampling.