interpolation schemes

[kunyuan]

We may want to support three levels of interpolation:

1. Nearest interpolation
2. Bilinear/trilinear interpolation (based on the neighbors)
3. Bicubic/tricubic interpolation ( See Numerical Recipes in C, section 3.6, page 125). It guarantees smoothness. It requires the derivatives: d/dx, d/dy and d^2/dx/dy. (The derivatives don't need to be exact to get a smooth interpolation!).

See https://en.wikipedia.org/wiki/Bicubic_interpolation
and https://en.wikipedia.org/wiki/Tricubic_interpolation