How do we deal with possible interpolation error? And how to minimize it?
What do you mean by interpolation error? Interpolation is itself an approximation of surface/curve, so it has "error" built into it in some sense already.
@andrewdotwang: Just as @andrewyli said, when you're trying to approximate a curve using interpolation, you will almost certainly get some sort of error, due to the fact that the interpolation is only an approximation. You can minimize this by using more advanced interpolation schemes, or by using more control points.