In engineering applications, data collected from the field are usually discrete and the physical meanings of the data are not always well known. To estimate the outcomes and, eventually, to have a better understanding of the physical phenomenon, a more analytically controllable function that fits the field data is desirable. The process of finding the coefficients for the fitting function is called curve fitting; the process of estimating the outcomes in between sampled data points is called interpolation; whereas the process of estimating the outcomes beyond the range covered by the existing data is called extrapolation.
The scope of this section is limited to discussing some common interpolation methods including:
Rational Function Interpolation
Cubic Spline Interpolation
The bottom line is, no matter how smooth the interpolation is and how close it is to the raw data, the problem is not completely solved unless the physical meaning behind the theme has been captured.