I hadn't really thought about it until Richard's thread on creating a surface fit for random points and Xaviers comments on holes popped up, but the rationalfitnp function might be even better if it allowed specifying there will be no poles over the range x0..x1 rather than xmin..xmax.
I was thinking of this in the context of creating a surface for a 2D plot (an example of multivariate regression). A rational function of the form f(x,y) = (c0 + c1*x + c2*y + c3*x^2 +...)/(1 + d1*x + d2*y +...) with no poles over the grid range might be a useful mesh building routine. I may not even care that it doesn't interpolate the data since small fit errors will still show the trends.
Robert
