I am trying to solve an optimization problem where I need to take as few data points as possible to recreate a field. I know the field will have a shape similar to a 2-d Gaussian with a known center point. However, there may be some directional imperfections in the field (one side might have a steeper slope than the other).Therefore, I've come to the conclusion that an xy scan would provide adequate information to recreate the 2d shape, however I'm having trouble determining how to do this.
I'm working in python and using a linear interpolation function which will not construct the field properly given only x and y axes. One idea I am considering is converting to a polar coordinate system to do the interpolation then converting back. Converting to this coordinate system would force the xy points to be plotted on a grid which might help the interpolation function.
It feels like this will work, but I don't know enough about the math behind different kinds of interpolation methods (or the conversion for that matter) to prove to myself that it will work. Is this the appropriate way to do the interpolation or is there another method I'm not aware of?