#interpolating polynomial

Earlier I talked about using interpolation to modify images.

Mathematica requires a nice rectangular grid to sample from.

  Here is the result:

   It's a gross blob and you can see weird rectangles. After some searching I found a package that allows non-grid interpolation. Also I think I got some indicies switched because the contour plot looks like it's been rotated or flipped or something.

  Let's say you have a function that looks something like this:

You can create what's called an interpolating polynomial by picking some points along the curve and make a new curve that has to go through each of the points.

Sometimes the interpolating polynomial is a good approximation and sometimes it's not. Interpolating polynomials aren't limited to two dimensions.

   Sometimes the interpolating polynomial is a good approximation and sometimes it's not. 

What happens when you try this with images? I don't know yet but this contour plot is pretty cool!