I have a dataset of scattered 3-D points (non-regular) that carry some variable and am trying to interpolate that variable to a new point. I have currently implemented a couple of methods, but don't like the behavior of inverse distance and am getting overshoot issues with the polyharmonic spline RBF. Is there a method that would simply provide me with a linear interpolation? If possible, a detailed explanation/example of a matrix setup would be greatly appreciated.
For example (and for those familiar), the software Tecplot has an option for linear interpolation, but I can't find any documentation on its method.