2nd order interpolation

You start with a collection of heights or intensities that you want to find an equation for:

You find an interpolation for each row:

Notice the 3 equations are of a similar form but they differ in the coefficients. My idea is to interpolate the 3 related coefficients in the y direction. Like the *x^2 coefficents are -3/2, 1/2, -7/2 so we can find the equation in y that produces those 3 values where we want them to occur on the y axis...

Then for the other 2 coefficents...

Then make one big equation substituting the equations in y for the coefficients of the basic formula:

That's the same equation I got doing it the other way in yesterday's post! 

This goes smoothly through the specified grid of z values.