Is it possible to create custom boundaries in a contour plot and extrapolate the responses to the edge?

[#1]

I am attempting to plot responses in X/Y coordinate field. The real field should be a perfect circle, but I only measure the responses at a 28 points at random locations in the field. Is there a way to set the boundaries of the field as the circle (even though no responses are actually measured on the very edge) and to extrapolate the contours to this defined boundary? I know origin can do it. I have also seen excel do this with a macro.

[#2]

Contour Plot uses a triangulation of the points to perform interpolation on the data, and it currently does not have an extrapolation capability.  One approach that comes to mind is that you could model the data from your measured responses, and augment the data with estimated values evaluated from the model.

[#3]

I've been thinking about the augmentation process, and I think that I have a plan to be able to compute the extrapolation myself. I can write out X, Y coordinates for several edge points on my circular field. But at this point, I would need to assign a response to each of those new values. What I would like to do is search for the nearest X, Y coordinate that has a response and copy that value to the edge coordinate that I have generated. Is there a formula or script that I can use that would be of use here?

[#4]

Check out KDTable()/K nearest rows in the scripting index. 

It can give you closest point in euclidian space.