I am working on a project where I have a set of known measurements (x,y,z,a) and an input (z,a). I need to be able to interpolate the (x,y,z) so that I can get a list of possible (x,y) coordinates from a given z.
I was looking at bicubic interpolation, but I can only find examples pertaining to regular grids, and my (x,y) pairs are most certainly not regular.
Basically I am looking for some guidance on algorithms/models to achieve this goal. I am considering a triangulated irregular network, which is attractive because it breaks down into planes which are easy to determine the (x,y) from a given Z. But I would like a little more finesse.
I know it sounds like homework, its not.
Efficiency is not a concern.
Thanks!
I actually ended up using Delauney Triangulation to break down the fields into 3 dimensional X,Y,Z surfaces with an Identifier. Then given a set of (Identity,Z) pairs I form a field line from each surface, and from these lines compute the polygon formed from the shortest edges between lines. This gives me an area of potential x,y coordinates.